Radiation effects in materials: учебно-методическое пособие 9786010401594

Table of contents :
The first two criteria limit the number of possible fuels to fewer than 30 atomic isotopes within the entire table of nuclides. Plutonium-238, curium-244 and strontium-90 are the most often cited candidate isotopes, but other isotopes such as polonium...
1.1. The surface photoelectric effect
3) Pair production
Langmuir-McLean theory for surface and grain boundary segregation in binary systems
More complex systems
Kinetics of Segregation
Circular or cyclic accelerators
Cyclotrons
Advantages of the cyclotron
2.3. Linear combinations of atomic orbitals (LCAO) (Линейные комбинации атомных орбиталей ЛКАО)
2.3.1. Sigma and Pi Labels for MOs
a) σ-symmetry
b) π -symmetry
Fig.11.3. For π- and π * – orbitals rotation about the interatomic axis changes the phase of wave function

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КАЗАХСКИЙ НАЦИОНАЛЬНЫЙ УНИВЕРСИТЕТ ИМ. АЛЬ-ФАРАБИ

А. М. Ильин

РАДИАЦИОННЫЕ ЭФФЕКТЫ В МАТЕРИАЛАХ RADIATION EFFECTS IN MATERIALS Учебно-методическое пособие (на английском языке)

Алматы «Қазақ университеті» 2013 1

УДК 614.876 ББК 22. 383 И 460 Рекомендовано к изданию Ученым советом физико-технического факультета и РИСО КазНУ им. аль-Фараби

Рецензенты: доктор физико-математических наук, профессор А.В. Юшков кандидат технических наук А.Г. Нестеренков

Ильин А.М. И 460 Радиационные эффекты в материалах. Radiation effects in materials: учебно-методическое пособие (на английском языке). – Алматы: Қазақ университеті, 2013. – 118 с. ISBN Пособие, написанное на английском языке, рассчитано на студентов магистрантов и PhD студентов, обучающихся по программе «Радиационное материаловедение» или интересующихся радиационной физикой, проблемами и перспективами ядерной энергетики. Все разделы снабжены контрольными вопросами и задачами, позволяющими читателю постоянно проверять и совершенствовать свой уровень восприятия материала. УДК 614. 876 ББК 22.383 © Ильин А.М., 2013 © КазНУ им. аль-Фараби, 2013

ISBN 978-601-04-0159-4

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FOREWORD ПРЕДИСЛОВИЕ Пособие, написанное на английском языке, рассчитано на студентов магистрантов и PhD студентов, обучающихся по программе «Радиационное материаловедение» или интересующихся радиационной физикой, проблемами и перспективами ядерной энергетики. Все разделы снабжены контрольными вопросами и задачами, позволяющими читателю постоянно проверять и совершенствовать свой уровень восприятия материала. Многие из читателей пособия, возможно, в ближайшем будущем будут принимать участие в международных проектах по дальнейшему развитию и внедрению ядерной энергетики в Казахстане и в других странах. В связи с этим, написанное на английском языке пособие поможет достаточно быстро освоить необходимый минимальный уровень профессионального общения с зарубежными специалистами по тематике радиационной физики и радиационного материаловедения. Автор снабдил практически все разделы вкрапленным русским переводом, особенно там, где много профессиональной терминологии и нестандартных оборотов, поэтому студентам практически не придется тратить время на поиски терминов в профессиональных словарях и иметь дело с сомнительными компьютерными переводчиками. Это сделает работу с пособием достаточно приятным занятием. Кроме того, пособие снабжено подробным глоссарием. Некоторые разделы дают учащемуся возможность самостоятельно поработать над текстом, не имея перед глазами «мешающего» готового перевода. Автор надеется, что студент, добросовестно трудившийся над английским языком на первых курсах бакалавриата и хорошо проработавший предлагаемое пособие, сможет вполне удовлетворительно общаться на профессиональные темы, связанные с ядерными 3

технологиями и материаловедением, с зарубежными англоговорящими физииками. При работе над пособием автор использовал материалы, представленные в Интернете и печатных изданиях, в том числе и результаты своих исследований. Например, лекция 12 основывается на главе, написанной автором для монографии «Graphene Simulation», изданной в европейском издательстве «InTech». Часть материала пособия была опробована в виде лекций курса, читаемого автором для PhD-студентов и дала положительный эффект.

LECTURE 1 1. Radioactivity and units of measuring Definition: radioactivity – spontaneous decay of the nucleus of an atom by emission of particles, usually accompanied by electromagnetic radiation. Определение: радиоактивность – спонтанный распад атомного ядра с эмиссией частиц, обычно сопровождающийся электромагнитным излучением. a) Natural radioactivity is exhibited by several heavy elements, including radium, uranium and other elements of the actinide series, and by some isotopes of light elements, for example C14 . (Естественная радиоактивность проявляется несколькими тяжелыми элементами, включающими радий, уран, и другие элементы ряда актинидов и некоторыми изотопами легких элементов, например, С14 ). b) Radioactivity may also be induced or created artificially by irradiation the nuclei of stable elements -artificial radioactivity. (Радиоактивность может также быть индуцирована искусственно путем облучения ядер стабильных элементов – искусственная радиоактивность). In 1899 Ernest Rutherford studied the phenomenon of the rays discovered by Becquerel. During the experiment Rutherford discovered that there were two kinds of such radiation: the first one called the alpha rays was easily absorbed by paper; the second one called the beta rays could penetrate through thick metal brasses like for example 0.25 c m of aluminium. (В 1899 году Э.Резерфорд изучал излучения открытые А.Беккерелем. В ходе эксперимента Резерфорд обнаружил существование двух типов излучения: одно из них, которое получило название альфа лучей, легко задерживалось тонким листом бумаги; второе, названное беталучами, могло проникать через металлические фольги, например слой алюминия толщиной 0.25 см). Soon the third kind of radiation was discovered, which had very high penetrating power it could go through a couple of centimeters thick layer of lead. This third kind of radiation was called the gamma rays. (Вскоре был 5

открыт третий вид излучения, имевший очень высокую проникающую способность – способный проходить через сантиметровые слои свинца. Этот вид излучения был назван гамма лучами). A few next years scientists spent explaining the nature and properties of those three kinds of radiation. Alpha rays have the low penetrating power, move at a slower velocity than the other types and are reflected slightly by a magnetic field and electric field in a direction that indicates a positive charge. It turned out that the ratio q/m (charge to mass) of the alpha particles is two times smaller than of hydrogen nuclei. Scientists concluded that alpha particles are helium nuclei whose mass equals 4*(hydrogen mass) and whose positive charge is equal to 2*e. As you know the helium nucleus consists of two protons and two neutrons. The alpha decay reduces the atomic number of the nucleus by two and the mass number by 4. (Альфа лучи имели самую слабую проникающую способность, а в магнитном и электрическом полях отклонялись таким образом, что им следовало приписать наличие положительного заряда. Оказалось, что отношение e/m для альфа-частиц в два раза меньше, чем для ядер водорода. Ученые сделали вывод, что альфа частицы являются ядрами гелия, имеющими положительный заряд 2*e и массовое число 4). The beta particles are more penetrating than alpha rays , move at a very high speed and are deflected by magnetic field in a direction that indicates a negative charge. In the further study it turned out that they are simply high-speed electrons. (Бета частицы являлись более проникающими, чем альфа частицы, двигались с большим скоростями и их отклонение в магнитном поле указывало на наличие у них отрицательного заряда). In beta decay a n eutron within the nucleus changes to a proton in the process emitting an electron and antineutrino . The electron is immediately ejected from the nucleus, and the result is an increase of 1 in the atomic number of the nucleus but no change in the mass number. (При бета распаде нейтрон в ядре превращается в протон, при этом испускаются электрон и антинейтрино, в результате чего атомный номер ядра увеличивается на единицу без изменения массового числа). 6

The third kind of radiation – the gamma radiation – turned out to be the electromagnetic radiation , having the wave length about 10-2 nm. For comparison, the green part of the visible light radiation has the wave length 550 nm. (Третий вид радиации- гамма лучиоказался электромагнитным излучением, имеющим длины волн примерно 0.01 нм. Для сравнения , центральная зеленая часть видимого спектра имеет длину волны 550 нм).Gamma rays have very high penetrating power and are not affected at all by a magnetic field. (Гамма лучи имеют очень высокую проникающую способность и не отклоняются магнитным полем).Gamma rays result from the transition of nuclei from exited states to ground state and their production is analogous to the emission of ordinary light caused by transitions of electrons within the atom. Gamma decay often accompanies alpha or beta decay and affects neither the atomic number nor the mass number of the nucleus. Later, other, less common types of radioactivity were discovered – electron capture (capture of one of orbiting atomic electrons by the unstable nucleus ) and positron emission – both forms of beta decay and both resulting in the change of a proton to a neutron within the nucleus. Historical note: Natural radioactivity was first observed by A.Becquerel in 1896, who discovered that when salts of uranium are brought into the vicinity of an unexposed photographic plate carefully protected from light, the plate becomes exposed.(Естественная радиоактивность впервые наблюдалась в 1896 А.Беккерелем, который открыл, что когда соли урана располагались близко к защищенной от света незасвеченной фотопластинке, то в результате она оказывалась потемневшей, как если бы подвергалась действию света). Artificial (induced) radioactivity occurs when a previously stable material has been made radioactive by exposure to specific radiation. In 1932 J ames Chadwick identified neutrons with the very penetrating radiation that appeared after beryllium was bombarded with alpha particles. (Искусственная радиоактивность возникает если изначально нерадиоактивный материал подвергался воздействию определенного типа излучения. В 1932 Д.Чадвик обнаружил нейтроны – сильно проникающее излучение, возникавшее при в результате бомбардировки бериллия альфа7

частицами). Using neutrons Frederic and Irene Joliot-Curie created new radioactive isotopes not found in nature, and then measured their decay back to stable isotopes. (Используя нейтроны, Фредерик и Ирен Жолио-Кюри создавали новые изотопы, которые не обнаруживались в природе, а затем наблюдали их распад до стабильных элементов). The first example of artificial radioactivity was produced in 1934 by Frederic and Irene JoliotCurie by bombarding nonradioactive elements with alpha-particles. (Первый пример искусственной радиоактивности был продемонстрирован супругами Ж-Кюри в 1934 г. , в результате облучения нерадиоактивных элементов альфа-частицами). Neutron activation is the main form of induced radioactivity, which happens when free neutrons are captured by nuclei. This new heavier isotope can be stable or unstable depending on the chemical element involved. Because free neutrons disintegrate within minutes outside of an atomic nucleus, neutron radiation can be obtained only from nuclear disintegration nuclear reactions and high-energy reactions (in particle accelerator collisions). Neutrons that have been slowed down through a neutron moderator (thermal neutrons) are more likely to be captured by nuclei than fast neutrons. (Нейтронная активация является основной формой наведенной радиоактивности которая происходит, когда свободные нейтроны захватываются ядрами. Этот новый более тяжелый изотоп может быть стабильным или нестабильным, в зависимости от химического элемента. Поскольку свободные нейтроны распадаются в течение непродолжительного времени, нейтронное излучение может быть получено только в результате распада ядер, ядерных реакций и в ходе реакций при высоких энергиях (в ускорителях). A less common form involves removing a neutron via photodisintegration. In this reaction a high energy photon of gamma radiation strikes a nucleus releasing a neutron. This reaction demands about 10 Mev for most heavy nuclei. (Менее распространенная форма связана с фоторасщеплением ядра. В такой реакции гамма фотон высокой энергии взаимодействуя с ядром выбивает нейтрон. Такая реакция требует около 10 МэВ для большинства тяжелых ядер). 8

It should be noticed, that the isotopes used in food irradiation (Co-60,Cs-137) both have energy peaks below this cutoff and thus cannot induce radioactivity in the food!. Some induced radioactivity is produced by background radiation which is mostly natural. However, since natural radiation is not intense in most places on Earth , the amount of induced radioactivity in a single location is usually very small. The conditions inside certain types of nuclear reactors with high neutron flux can cause induced radioactivity. The components in these reactors may become highly radioactive from the radiation. Induced radioactivity increases the amount of nuclear waste that must be disposed. (Наведенная радиоактивность может создаваться внутри ядерных реакторов с высокими плотностями нейтронных потоков. Конструкционные и другие материалы в таких реакторах могут становиться сильно радиоактивными и наведенная радиоактивность увеличивает количество ядерных отходов, которые должны быть удалены). 2. Activity. Definition: The rate of radioactive transformation or the activity of a so urce equals the number N of identical radioactive nuclei present in the source multiplied by their characteristic radioactive decay constant λ Activity = λ ⋅ N

(1)

(Определение: скорость радиоактивного превращения или активность источника, содержащего N одинаковых радиоактивных ядер равна Активность = λ ⋅ N где λ – постоянная радиоактивного распада, характеристическая для данного типа ядер). The numerical value of λ expresses the statistical probability of decay of each radioactive nucleus per unit time. It should be noticed that (1) is correct only when the number N is very large. For 9

example, if λ = 0.001 s -1 , for a particular radioactive species then each nucleus has a chance of 0.001 of decaying in 1 s econd. The constant λ is one of the most important characteristics of each radioactive nuclide: λ is essentially independent of all physical conditions such as temperature, pressure, concentration etc. (Численное значение λ выражает собой статистическую вероятность распада ядра в единицу времени. Нужно отметить, что выражение (1) справедливо, только если число ядер достаточно велико. Например, если λ = 0.001 сек-1, для определенного типа ядер, то любое одно ядро из 1000 имеет шанс распасться за 1 сек). The original unit for measuring the activity was the curie (Ci) first defined to correspond to one gram of radium-226 and more recently defined as 1 Ci = 3.7 ⋅ 1010 decays per second (three point seven times ten to power 10th) In the SI the curie has been replaced by the becquerel (Bq) , where

1Bq = 2.703 ⋅ 10 −11 Ci = 1 decay per second (two point seven zero three times ten to power minus 11th) It should be noticed that existences one more non-system unit for measuring the activity – Rutherford: 1 Rutherford = 106 decays per second Exercise 1. Change «103 decays per second» to the Ruthefords The main law of radioactive decay can be written in the view:

N (t ) = N 0 ⋅ exp[− λ ⋅ t ]

(2)

Here N0 – the number of radioactive nuclei at an initial moment t = 0. It should be noticed that the law (2) is correct only for large 10

numbers of nuclei. The time interval over which the chance of survival of a particular radioactive atom is exactly one-half is called half-period T (also called the half-life, written T1/2) . The half period T is related to the total radioactive decay constant λ and to the mean life time τ ( τ = 1 / λ ) is given by Eq. (2):

T = ln 2 / λ = 0.693 ⋅ τ

(3)

Usually the half-period T is much more frequently employed than the total decay constant λ or the mean life τ . Exercise2. Prove that T = ln 2 / λ = 0.693 ⋅ τ 3. Radiation Units. The terminology and units used to describe radiation exposure depend strongly on t he type of interaction responsible for property degradation in the irradiated material. If displacement damage is the principal effect, then exposure rate is expressed in terms of a particle current density (i.e., particles *cm-2 s-1). When exposure rate is integrated over time, the result is expressed as particle fluence (i.e., total particles/cm2). (Терминология и единицы измерения, используемые для описания радиационной дозы зависят от типа взаимодействий, ответственных за изменение свойств облучаемого материала. Если основным измеряемым эффектом является повреждаемость из-за смещений, то степень экспозиции может определяться просто плотностью потока: j = частиц *см-2 сек-1). Если интерес представляет интегральная доза, то эффект облучения определяется через флюенс = частиц / см2 ). The magnitude of radiation exposure is specified in terms of the radiation dose. 1. The absorbed dose, sometimes also known as t he physical dose, defined by the amount of energy, deposited in a unit mass in human tissue or other media. The original unit is the rad [ 100 erg / g]; it is now being widely replaced by the SI unit, the gray (Gy) [1 J/kg], where 1 gray = 100 rad. The gray (symbol: Gy) is the SI unit 11

of absorbed radiation dose of ionizing radiation (for example, Xrays), and is defined as the absorption of one joule of ionizing radiation by one kilogram of matter (usually human tissue). (Поглощенная доза, иногда называемая физической дозой, определяется количеством энергии, поглощенной на единицу массы человека или другой среды. Первоначально основной единицей измерения является рад ( 100 эрг / грамм); в настоящее время часто используется также единица системы СИ – грэй (1 Дж кг). 1 грэй = 100 рад). Attention (!): When an SI unit is spelled out in English, it should always begin with a lower case letter (gray), except where any word would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase. –Based on The International System of Units, section 5.2. Since the various kinds of radiation exposure need to be evaluated for biological impact and not just for the amount of energy absorbed by the tissue, the term rem, roentgen equivalent men (or woman), was introduced. In the SI system –it changes to sievert (Sv). 1 sievert = 100 rem The rem dose is the rad dose times a q uality factor Q . For external radiation Q is usually taken as 1, and rads and rems are used interchangeably. However, to reflect the greater biological damage done by alpha particles when inside the body, the rad dose may be multiplied by 20 to give the rem dose. This is another way of saying that the alpha particles do damage of an order of magnitude (20 times) greater when lodged within a tissue, bone or organ. For example, alpha particles giving a 2 rem (or rad) dose to skin would give a 40 rem dose to sensitive lung tissue when inhaled. The biological dose, sometimes also known as the dose equivalent expressed in units of rem (roentgen equivalent men) or, in the SI system sievert (Sv). This dose reflects the fact that biological damage caused by a particle depends not only on t he total energy deposited but also on t he rate of energy loss per unit distance 12

traversed by the particle. (Биологическая доза, иногда обозначаемая как эквивалентная доза, измеряется в единицах Рэм, а в системе СИ это сиверт (Sv). For X-rays and gamma-rays and electrons, 1 rad = 1 rem For neutrons , 1 rad = 5 to 20 rem (depending on energy level) For alpha- radiation , 1 rad = 20 rem. For comparison: 1 rem is roughly the average dose received in 3 years of exposure to natural radiation. (1 рэм это примерно средняя доза, получаемая за три года от естественной (природной) радиации). For comparison: In physics, the erg is a very small unit of energy (of work done). Lifting 1 g of radium 1 centimeter requires 980 ergs of work. (Для сравнения: в физике 1 эрг соответствует очень небольшому количеству энергии. Подъем 1 г радия на 1 см потребует затраты энергии примерно 980 эрг). Абзац для самостоятельного перевода. Sometimes radioactivity is measured in counts per minute on a Geiger counter. But most Geiger counters cannot detect alpha particles emitters like plutonium but produce only noise because of very high intensity of radiation. The radioactivity of elements which experience nuclear decay is measured relative to the radium. For example, it would take more than 1 m illion grams of uranium to be equivalent to in radioactivity, i.e., to have tha same number of nuclear events per second as 1 g of radium has per second. Both 10 6 grams of uranium and 1 gram of radium would be measured as 1 C i. When uranium decays, it passes through 12 radioactive forms, called «daughter products» before reaching a stable chemical form of lead. Exercises: 1) Name the main three kinds of radiation 2) What are alpha rays? 3) What are beta rays? 4) What are gamma rays? 5) Which of above rays have the greatest power of penetrating through materials?

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LECTURE 2 Radiation defects in materials 1. Types of radiation defects Radiation induced changes in material properties are the result of radiation structural defects. An energetic particle (for example neutron or nucleus fragment) collides with an atom in a material transferring to it some energy and knocking it o ut of its lattice position. This atom, knocked out of its position is called primary knocked atom (PKA). (Радиационно индуцированные изменения свойств материала являются результатом действия структурных дефектов. Частица с достаточной энергией (например нейтрон или фрагмент ядра, соударяется с атомом материала, передавая ему часть энергии и выбивая из узла решетки. Этот атом, выбитый частицей из своего узла называется первично выбитый атом –ПВА). It is the first step to create a pair of vacancy and of self interstitial atom. This primary knocked atom and the recoiling particle cause additional collisions with other atoms , generating a cascad e of displaced atoms. (Это является первым этапом создания пары вакансия – собственный межузельный атом. ПВА и рассеянная после соударения частица, двигаясь в решетке способны создавать новые дефекты, генерируя каскады смещенных атомов).

a

b

Fig.2.1. a) Typical radiation defects; b) The computational scheme picture of a cascade of displacements

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Point defects occur as the result of displacements of single atoms from their normal lattice sites. (Точечные дефекты появляются в результате смещений отдельных атомов из их нормальных положений в решетке). As you know, the empty lattice site is called a «vacancy». (Как вы знаете, пустое место в решетке называется вакансией). The displaced atoms usually occupy sites that are not in the lattice framework. They are called «interstitials». (Смещенные атомы обычно занимают места, которые не являются позициями решетки. Они называются «межузельные атомы»). A crowdion – is a special low temperature configuration of interstitials, usually in FCC metals. For making a crowdion, image the row of atoms along a some direction, for example, along a densely packed direction in FCC metal. Now take a number of atoms, say 3 or four – and «crowd in» one more. A kind of elongated interstitial along a some direction is obtained – a crowdion. For the sake of clarity the crowdion in Fig.2 is arranged along an direction in FCC cube lattice.

b

a

Fig.2.2. Typical radiation defects in FCC: a) V + I = Frenkel pair and crowdion; b) typical dumbbell configurations

(Краудион – особая конфигурация междоузельных атомов, возникающая чаще в плотноупакованных ГЦК решетках. Для создания краудиона представьте себе ряд атомов вдоль некоторого направления например, вдоль в ГЦК структуре металла. Теперь берем отрезок, содержащий 3-4 атома и вставляем в него еще один между атомами. Затем можем продолжить эту операцию. Возникает краудион. Этот термин произошел от 15

английского «crowd» – толпа, скопление. Краудионы устойчивы только при низких температурах). If the atom knocked is transferred to an interstitial position , without returning to the vacancy, the defect, which involves a vacancy and interstitial atom is known as Frenkel pair defect (see Fig.2, a). In Fig.2, b one can see typical interstitial configurations which are called dumbbells or split interstitials. The mark of a dumbbell links direction of its axes with crystallographic direction in the lattice. (Если атом был выбит и перешел в междоузельное положение, не имея возможности вернуться в вакансию, то возникает устойчивый дефект, содержащий вакансию и межузельный атом. Это очень важный тип радиационного дефекта, который называется термином пара Френкеля). Interstitial atoms can be of two types: self-interstitial atoms and interstitial impurity atoms. (Междоузельные атомы могут быть двух типов: собственный межузельный атом и примесный межузельный атом). A self-interstitial atom is an extra atom that was introduced into an interstitial void in its own crystal lattice. Interstitial impurity atoms are much smaller in size than the atoms of the bulk matrix. (Собственный межузельный атом внедряется в решетку из таких же атомов, а примесный межузельный атом, обычно меньшего размера, чем атом матрицы). Interstitial impurity atoms fit into the open space between the bulk atoms of the lattice. A good example is the carbon atoms that are added to iron to make steel. Carbon atoms with a radius of 0.07 nm fit nicely in the open spaces between the iron atoms (its radius equals 0.124 nm).(Неплохим примером для сталей является междоузельный атом углерода (всегда присутствующий в сталях), который имеет радиус 0.07 нм и внедряется в решетку матрицы железа, атомы которого имеют радиус 0.124 нм). A substitutional impurity atom is an atom of a d ifferent type than the bulk atoms which has replaced one of the bulk atoms in the lattice. Substitutional impurity atoms are usually close in size to the bulk atoms. Defects, especially vacancies , in general, are unavoidable. Even if you can prepare the sample with the purest materials, vacancy defects will occur because disorder will increase the entropy of the system. (Атом примеси замещения – атом 16

другого элемента, замещающий атом матрицы в решетке. Обычно размеры атомов замещения близки к размерам атомов матрицы). When an atom of material irradiated gets an energy transferring from a fast particle there is a energetic threshold for the atom to be constantly displaced from its position. The threshold displacement energy Td is the minimum kinetic energy that an atom in a solid needs to be a p ermanent displaced from its lattice site to a d efect position. It is also known as «displacement threshold energy» or just «displacement energy». (Когда атом облучаемого материала получает энергию от быстрой частицы, то ему нужно преодолеть определенный энергетический порог для того, чтобы покинуть свой узел необратимым образом. Пороговая энергия смещения Td это минимальная кинетическая энергия которая должна быть передана атому в твердом теле, чтобы он был смещен из узла решетки в дефектное положение без возможности вернуться в вакансию. Эта энергия известна также как пороговая энергия смещения или просто энергия смещения). In a cr ystal a separate threshold displacement energy exists for each crystallographic direction. (В кристалле существуют различные пороговые энергии смещения для различных кристаллографиических направлений). Then one should distinguish between the minimum Td ,min and average Td,ave over all lattice directions threshold displacement energy to describe some other average quantity of interest. Threshold displacement energies in typical solids are of the order 10-50 eV. The energy T that an irradiating particle (for example, a neutron) can transfer in a binary collision (non-relativistic approximation) to an atom in a material is given by

T=

4 ⋅ M1 ⋅ M 2 θ ⋅ E ⋅ sin 2 2 2 (M 1 + M 2 )

(2.1)

where E is the kinetic energy and M1 is the mass of the incoming irradiating particle and M2 the mass of the material atom, θ- the angle of scattering. Obviously, the maximum energy transferring to the atom of material is equal to 17

Tmax =

4 ⋅ M1 ⋅ M 2 ⋅E (M 1 + M 2 ) 2

(2.2)

when we take θ = 180o , it is the approximation of so called centerhead collision. (Энергия, которая может быть передана налетающей частицей (например, нейтроном) атому материала в парном столкновении в нерелятивистском приближении дается выражением (2.1) , где Е – кинетическая энергия и М1 – масса налетающей частицы, М2 – масса атома материала, θ – угол рассеяния. Очевидно, что максимальная энергия передаваемая атому материала определится из (2.2) при θ = 180o , что соответствует приближению так называемого центрального лобового столкновения). For example, by neutron – atom collision, by E = 1.5 M eV in austenitic stainless steel ( M2=60-56) (Ni-Fe) we can obtain a l arge number of PKA with energies near 30-50 keV. High-energy PKA generate a large number of point defects and large-sized volumes of lattice with a high-density of defects – so called cascades of displacements. Cascade involves Frenkel’s pairs, dumbbells, dislocation loops, crowdions . (Например, для столкновения нейтрон – атом, при Е = 1.5 МэВ в аустенитной нержавеющей стали, содержащей в качестве основных компонентов железо и никель (M2=60-56) можно получить большое количество ПВА с энергиями около 30-50 кэВ. Высокоэнергетичный ПВА генерирует большое количество точечных дефектов и большие объемы в решетке с высокой плотностью дефектов – так называемые каскады смещений. Каскады включают в себя пары Френкеля, гантели, дислокационные петли, краудионы). Problem 3. Given M1 =1, M2 = 60 (atomic units), E = 1.5 MeV. For this collision determine Tmax In this case we consider collision between a neutron and a nucleus of the isotope of Ni60 . Problem 4. Given M1 = 1, M2 = 12 , E = 1.5 MeV. For this collision determine Tmax 18

In this case w e consider collision between a neutron and a nucleus of the isotope of ? . In order for a permanent defect to be produced from initially perfect crystal lattice, the kinetic energy that it receives Tmax must obviously be larger than the formation energy of a Frenkel pair. Each crystal direction has in principle its own threshold displacement energy, so for a full description one should know the full threshold displacement surface Td (θ , ϕ ) = Td ([h, k , l ]) for all non-equivalent crystallographic directions [h,k,l]. Then Td ,min = min(Td (θ , ϕ ) and Td,ave = ave ( Td (θ , ϕ ) ) where the minimum and average is with respect to all angles in three dimensions. (Для того, чтобы создать постоянный дефект в первоначально идеальной кристаллической решетке кинетическая энергия, которую он должен получить должна, очевидно, быть больше, чем энергия образования пары Френкеля. Каждое кристаллическое направление имеет в принципе свою собственную энергию смещения, так что для полного описания нужно знать полную пороговую поверхность включающую все неэквивалентные кристаллографические направления в решетке [ h,k,l]). An additional complication is that the threshold displacement energy for a given direction is not necessarily a step function but there can be an intermediate energy region where a defect may or may not be formed depending on t he random atom displacement. The one can define a lower threshold where a defect may be formed and an upper one where it is certainly formed. The difference between these two may be surprisingly large and whether or not this effect is taken into may have a large effect on the average threshold displacement energy. It is not possible to write down a single analytical equation that would relate e.g. elastic material properties or defect formation energies to the threshold displacement energies. 2. Experimental studies of Ed Electron irradiation as a tool of investigations (Электронное облучение как инструмент исследований)

19

The threshold displacement energies have been studied extensively with electron irradiation experiments. Electrons with kinetic energies of the order of hundreds of keV or a few MeV can to a very good approximation be considered to collide with a single lattice atom at a time. Since the initial energy for electrons coming from a particle acceleration is known with a good accuracy, one can thus at least in principle determine the lower minimum threshold displacement energy by irradiation a crystal with electrons of increasing energy until defect formation is observed. (Пороговые энергии смещения обычно изучались в экспериментах использующих электронное облучение. Электроны с кинетической энергий порядка от сотен кэВ до нескольких МэВ могут с достаточной точностью рассматриваться как частицы, испытывающие не более одного соударения с атомом решетки. Поскольку начальная энергия электронов, выходящих из электронного ускорителя известна с большой точностью, можно, по крайней мере, в принципе определить нижний уровень пороговой энергии смещения путем увеличения энергии пучка до обнаружения появления дефектов). Using the equations for energy, transferred by pair collision, one can determine threshold energy Td. (Используя соотношение для энергии, передаваемой в парном столкновении, можно определить пороговую энергию Td). If the irradiation is carried out on a single crystal in a known crystallographic direction one can determine direction – specific thresholds. (Если облучение проводится с использованием монокристалла с пучком вдоль определенного кристаллографиического направления, то возможно определение порога для этого направления). Temperature dependence Particular care has to be taken when interpreting threshold displacement energies at high temperatures, when defects are mobile and can recombine. Usually one should consider two distinct processes: the creation of the defect by the high energy particle (stage A) and thermal recombination (stage B). (Особая тщательность нужна при определении пороговых энергий смещения при высоких температурах, когда дефекты подвижны и могут рекомбинировать). 20

Problem 1. Determine the velocity of the alpha-particle which has the energy of 1 keV. Hint: to estimate the mass of the alpha-particle we must multiply the atom mass of the particle (~ 4.0 a.u.) by the atom unit of mass (1.66 10-27 kg). Problem 2. An alpha-particle with the energy 1 MeV has experienced the central head-on collision with a carbon atom. Determine the kinetic energy of the C atom. Relativistic corrections are negligible. Hint: Maximum energy, transferred in elastic collision of two particles can be estimated by the expression (2.2)

LECTURE 3 Nuclear fission reactors 1. Typical design and principle of operation Definition. A nuclear fission reactor is a device, to initiate and control a sustained nuclear chain reaction of fission. About a physical ground of the nuclear energetic: when a relatively large fissile atomic nucleus (U235, U233, Pu239,Pu241) absorbs a neutron it is likely to undergo nuclear fission. The original heavy nucleus splits into two (or more) lighter nuclei (fragments) releasing kinetic energy, gamma-radiation, and several free fast neutrons (fast neutrons having energy about 1-2 MeV). (О физической основе ядерной энергетики: когда относительно тяжелое ядро изотопов U235, U233, Pu239,Pu241 поглощает нейтрон, то оно с большой вероятностью разделится. Исходное тяжелое ядро делится на два (или больше) фрагментов, выделяя кинетическую энергию, гамма – излучение и несколько свободных быстрых нейтронов с энергий 1-2 МэВ). A part of these neutrons may be later absorbed by other fissile atoms and trigger further fission events, with releasing more energy and neutrons and so on. The total energy released by one act of a nucleus fission equals about 200 MeV. Practically all this energy finally released in the form of heat. (Полная энергия, выделяющаяся в акте деления ядра составляет примерно 200 МэВ. Практически вся эта энергия в конечном счете перейдет в тепловую).A kilogram of uranium 235 c onverted via nuclear fission releases approximately three million times more energy than a kilogram of coal burned by conventional way ( 7.2 ⋅ 1013 J / kg of U235 versus 2.4 ⋅ 10 7 J/kg of coal). That is why nuclear energetic after the World War Second became a subject of great attention for electricity production in many developed countries. Nuclear reactors usually used uranium and plutonium as nuclear fuel. Nuclear reactors can be classified by several methods but commonly they are divided roughly into two classes depending on the energy of the neutrons that sustain the fission chain reaction: 22

thermal and fast reactors. (Ядерные реакторы обычно используют в качестве ядерного топлива изотопы урана и плутония. Хотя ядерные реакторы могут классифицироваться различными способами, но чаще всего они делятся на два основных класса зависящих от энергии нейтронов, использующихся для цепной реакции деления: тепловые и быстрые реакторы). Thermal reactors use slowed or thermal neutrons. Almost all current reactors are of this type. (Тепловые реакторы используют замедленные или тепловые нейтроны. Почти все современные реакторы относятся к этому типу). You must know, that the nuclear cross section of fission reaction for U235 for slow thermal neutrons is about 1000 barns, and for fast neutrons it is in the order of 1 barn. (Вы должны знать, что сечение реакции деления изотопа U235 для тепловых нейтронов составляет примерно 1000 барн, в то время как для быстрых нейтронов оно всего около 1 барн). Therefore these type of reactors use a neutron moderator to slow neutrons until they approach the average kinetic energy of the surrounding particles, that is, to reduce the energy of the neutrons from 1.5 MeV (the average energy of neutrons originated in fission reaction) to low level of thermal energy (~ 0.05 eV). These reactors contain moderator materials that slow neutrons until their kinetic energy approaches the average kinetic energy of surrounding particles. Thermal neutrons have a far higher cross section of fissioning the fissile nuclei U235, Pu239, Pu 241 and a relatively lower probability of neutron capture by U238 compared to the faster neutrons that originally result from fission. It allows use of lowenriched uranium. The moderator is often also the coolant , usually water under high pressure to increase the boiling point. These are surrounded by a reactor vessel, instrumentation to monitor and control, radiation shielding and a containment building. Fast reactors use fast neutrons and needn’t moderator. They use less-moderating coolant, usually liquid metals like sodium (Na). In order to provide chain reaction such reactors requires the fuel to be more highly enriched in fissile material (about 20% or more) due to the relatively low probability of fission versus capture by U238. It should be noticed, that fast reactors have the potential to produce less transuranic waste because all actinides are fissionable with fast neutrons. But fast reactors are more difficult and more expensive to 23

build and operate. Today fast reactors are less common than thermal reactors in all applications.

Fig.3.1. A typical schematic design of a nuclear reactor (thermal reactor) 1 – rods with nuclear fuel, 2 – active zone with moderator, 3 – reflector, 4 – biological shield, 5 – control rods. (типичная схема конструкции теплового реактора. 1 – стержни с ядерным топливом, 2 – активная зона с замедлителем, 3 – отражатель, 4 – биологическая защита, 5 – управляющие стержни).

It should be noticed, that by thermal reactors exists a classification by moderator material. • Graphite moderated reactors • Water moderated reactors o Heavy water reactors o Light water reactors (LWR). LWR use ordinary water as moderator and as coolant. When at operating temperature, if the temperature of the water increases, its density drops, and fewer neutrons passing through it slowed enough to thigger further reaction. That negative feedback stabilizes the reaction rate. • Graphite and heavy water tend to be more effective moderators than light water. Due to the extra thermalization, these types can use natural uranium / unenriched fuel. • Light elements moderated reactors (Li or Be) (Реакторы с замедлителями из легких элементов: Li , Be)

24

• Organically moderated reactors use biphenyl and terphenil as moderator and coolant (Реакторы с замедлителями из бифенила и терфенила). One more type of classification: by coolant. (Еще один способ классификации: по охладителю). Water cooled reactor. For example, there are more than 100 operating reactors in USA, using water cooling. They are divided into two groups: pressurized water reactors (PWR) and boiling water reactors (BWR). (Реакторы с водяным охлаждением. Например, в США работают около 100 реакторов с водяным охлаждением. Они делятся на две группы: реакторы под давлением и «кипящие» реакторы). Most commercial reactors and naval reactors are PWR. BWR are characterized by boiling water around the fuel rods in the lower portion of a primary reactor pressure vessel . A boiling water reactor uses U235, enriched as uranium dioxide as its fuel. The fuel is assembled into rods that are submerged in water and housed in a steel vessel. The nuclear fission generates heat and causes the water to boil, generating steam. This steam flows through pipes into turbines. Liquid metal cooled reactor. Since water is a m oderator it cannot be used as a coolant in fast reactors. Fast reactors usually use for cooling liquid metals: sodium (Na), NaK alloy, lead-bismuth alloy. (Поскольку вода является замедлителем нейтронов она не может использоваться в качестве охладителя в быстрых реакторах. Быстрые реакторы обычно охлаждаются жидко металическими охладителями: натрием, сплавами Na-K, свинецвисмут). Gas cooled reactors . These reactors use as a co olant inert gas, for example, CO2, and often helium (He) in high-temperature designs. (Реакторы этого типа используют в качестве охладителя химически инертные газы, например СО2, а в высокотемпературных реакторах часто используется гелий). A breeder reactor is a nuclear reactor that generates more fissile material in fuel than it consumes. (Бридерный реактор – ядерный 25

реактор, который воспроизводит больше ядерного топлива, чем потребляет). These reactors were initially (1940s and 1960s) considered appealing due to their superior fuel economy: a normal reactor consumes less than 1% of the natural uranium that begins the fuel cycle, while a breeder can burn almost all of it (minus reprocessing losses), also generating less waste for equal amounts of energy. Breeders can be designed to use uranium and thorium, which is more abundant than uranium. (Бридеры могут быть использовать как уран, так и торий, который более распространен в природе, чем уран). Currently, there is renewed interest in both designs of breeders because of the increased price of natural uranium. (В настоящее время вновь проявляется интерес к обоим типам бридеров, т.к. природный уран дорожает). Fissile material is produced by neutron irradiation of fertile material, particularly uranium-238 and thorium-232. (Делящийся материал производится при нейтронном облучении исходных элементов, преимущественно U238 и Th232 ). This happens to some extent in most reactors. (В определенной степени этот процесс идет во всех реакторах). Towards the end of its life, a uranium (not a mixed oxide fuel or MOX, just uranium) pressurized water reactor fuel element is producing more power from bred plutonium than from the remaining uranium-235. In a b reeder reactor, fertile materials are deliberately provided, in the fuel and/or a breeder blanket surrounding the core. Historically, a machine specifically designed to create more fuel than it consumes is called a breeder. Two types of traditional breeder reactor have been proposed: • fast breeder reactor or FBR – The superior neutron economy of a fast neutron reactor makes it possible to build a reactor that, after its initial fuel charge of plutonium, requires only natural (or even depleted) uranium feedstock as input to its fuel cycle. This fuel cycle has been termed the plutonium economy. • thermal breeder reactor – The excellent neutron capture characteristics of fissile uranium-233 make it possible to build a moderated reactor that, after its initial fuel charge of enriched uranium, plutonium or MOX, requires only thorium as input to its fuel cycle. Thorium-232 produces uranium-233 after neutron capture and beta decay. 26

FBRs have been built and operated in the USA, the UK, France, the former USSR, India and Japan. (Быстрые бридерные реакторы были построены и работали в США, Великобритании, Франции, бывшем СССР, Японии). There are very few breeder reactors actually used for power generation, there are a few planned, and quite a few are being used for research related to the Generation IV reactor initiative. (Очень немногие из них действительно работают на производство энергии, несколько в стадии планирования, некоторые используются для исследований относящихся к созданию реакторов 4-го поколения). Two main chains of reproduction of nuclear fuel are:

n + 92 U 238 → 92 U 239 → β − → 93 Np 239 → β − → 94 Pu 239 n + 90Th 232 → 90Th 233 → β − → 91 Pa 233 → β − → 91 Pu 233 2. The first nuclear reactor Этот раздел предназначен для самостоятельного перевода. In 1942 E.Fermi, a USA scientist, with his team, built a new kind of engine at Chicago University in the United States. Fermi’s heat engine was what is now called a nuclear reactor but he called it a pile.

a

b

Fig.3.2. a) Dr.E.Fermi (Nobel Prize, 1938); b) The first nuclear reactor

27

E. Fermi used in his reactor natural uranium which contains about 0.7 % of 92U235 . It is known well that the nucleus of 92U235 splits easily enough by low energy neutrons. The nucleus of U238 is much more stable and it is comparatively difficult to split it. E. Fermi wanted to generate chain reaction by the fission (breaking) of uranium nucleus and he wanted a chain reaction to start. Then the fission of one nucleus would emit neutrons which would hit and break other nuclei, which would set free more neutrons and so on. But Fermi had many problems before him. Neutrons which are shot out of a nucleus by fission have the average energy equal to 2 MeV. They travel very fast, about 5 000 to 10000 kilometers per second. Neutrons moving as fast as this do not usually produce any further fission.

Fig. 3.3. The scheme of nuclear chain reaction

Any substance, which is used for slowing down the neutrons in a reactor is called a moderator. You know that graphite is a good moderator and so are heavy water, Be. Graphite is common, but heavy water is hard to get and more expensive. Therefore Fermi used graphite as moderator. Fermi built his pile slowly, and watched with instruments how many neutrons were flying about inside it. The number increased as the size of the reactor increased, but we can be sure that Fermi was careful. He did not want the whole thing to explode. One way of making a bomb is therefore to have two pieces of U235 which are small and therefore do not explode, but which are big enough to explode when they are together. (Keep them apart!) Place the two pieces a good distance from each other, and then at the right moment, 28

shoot one at the other. When they hit each other, the piece of uranium is above the critical size and it will explode in a f ew millionths of a second. Fermi wanted to control his reactor. If the neutrons got out of control, the heat would be so great that the whole thing would be destroyed, and the radiation effects would be very dangerous. How could he control the number of neutrons which were set free? In order to solve this problem, Fermi used cadmium rods. Cadmium has very large cross section for absorbing neutrons, and he arranged the rods in such a way that they could be lowered into the reactor when he liked. As soon as it began to get too hot, he lowered the rods. Then they absorbed millions of free neutrons flying about inside, so that fewer remained to his other nuclei. The chain reaction was controlled and so the heat produced was limited to the proper amount. E.Fermi with his team has finished building the first nuclear reactor in a racquets court below the bleachers of Stagg Field at the University of Chicago on December 2, 1942. Fermi’s experiments at the University of Chicago were part of the secret Manhattan Project, aimed to create nuclear weapon. It should be noticed, that in 1956 Paul Kuroda of the University of Arkansas postulated that a natural fission reactor may have once existed. Since nuclear chain reaction only requires natural materials (such as water and uranium) it is possible to have this chain reactions occur where there is the right combination of materials within the Earth’s crust. This prediction was verified with the discovery of evidence of natural self-sustaining nuclear chain reactions in the past at Oklo in Gabon (Africa) in September 1972. Notion about a critical mass: If U235 is separated out from natural uranium (a very difficult process indeed) and gathered together, nothing will happen at first. If we suppose that some method is being used to slow down the neutrons, they will break the nuclei, but they will not break a sufficient number of them. But as the piece of U235 gets bigger and bigger, the neutrons have less chance to escape before they hit a nucleus. A time will come, as the piece is added to, when the number of neutrons being produced is greater than the number being used up: the total is increasing. It increases in a fraction of a second at this critical size, and the uranium explodes. 29

But as long as it remains below this size, it is safe. Thermal neutrons will be more likely to cause U235 to fission when it is struck by the neutrons, in this case thermal neutrons, and fewer neutrons will be captured by U238. If at least one neutron from the U-235 fission strikes another nucleus and causes it to fission, then the chain reaction will continue. If the reaction will sustain itself, it is said to be critical, and the mass of U-235 required to produce the critical condition is said to be a critical mass.

Fig. 3.4. The bigger the piece of nuclear fuel, the more chances has a neutron next nucleus to split before escape from the piece

3. Fission and nuclear chain reaction: when an atomic nucleus of U235 or Pu239 absorbs a neutron, it may undergo nuclear fission. The heavy nucleus splits into two or more lighter nuclei, releasing kinetic energy, gamma-radiation and free neutrons with energies about 1.5 – 2 MeV. A portion of these neutrons may later be absorbed by other fissile atoms and trigger further fission events, which release more neutrons, and so on. This is known as a nuclear chain reaction. 3.1.Effective neutron multiplication factor The effective neutron multiplication factor , k , is the average number of neutrons from one fission that cause another fission. (Эффективный коэффициент размножения нейтронов k представляет собой среднее число нейтронов после одного деления, участвующих в последующих реакциях деления). The remaining neutrons (остальные нейтроны) either are adsorbed in non-fission reactions or leave the active zone without being absorbed (или поглощаются в реакциях без деления или покидают 30

активную зону не вызвав деления). The value of k determines how a nuclear chain reaction proceeds: • k< 1 (subcriticality): the system cannot sustain a chain reaction, and any beginning of a chain reaction dies out over time. For every fission that is induced in the system an average total of 1 / (1-k) fissions occur. ( k < 1: подкритичность; в системе не поддерживается цепная реакция и любой начавшийся цепной процесс быстро прекратится. • k= 1 (criticality): every fission causes an average of one more fission, leading to a fission and power level, that is constant. Nuclear power plants operate with k= 1 unless the power level is being increased or decreased. ( k = 1: критичность; каждое деление в среднем вызывает еще одно деление, что создает постоянный уровень выделения энергии). • k> 1 (supercriticality): for every fission in the material it is likely that there will be k fissions after the next mean generation time. Nuclear weapon is designed to operate under this state. ( k > 1: сверхкритичность; каждое деление в среднем приводит к k делениям ). Режим характерный для ядерного взрыва. When describing kinetics and dynamics of nuclear reactors and also in the practice of reactor operation is used the concept of reactivity , which characterizes the deflection of reactor from the critical state:

ρ=

k −1 k

In a n uclear reactor , k will actually oscillate from slightly less than 1 to slightly more than 1. I t will be due primarily to thermal effects (for example, as more power is produced, the fuel rods warm and thus expand , lowering their capture ratio, and thus driving k lower) . This leaves the average value of k at exactly 1. (Для описания кинетики и динамики ядерных реакторов и в практике управления реакторами используется понятие реактивности , которое характеризует отклонение реактора от критического состояния).

31

3.2. Reactivity control It should be noticed, that not all neutrons are emitted as a direct product of fission; some are instead due to the radioactive decay of some of the fission fragments. (Нужно заметить, что не все нейтроны являются прямыми продуктами деления, часть их возникает при распаде фрагментов распавшихся ядер). That occur directly from fission are called «prompt neutrons» and the ones that are result of radioactive decay of fission fragments are called «delayed neutrons» . (нейтроны, появившиеся непосредственно в цепной реакции - мгновенные нейтроны, а возникающие при распаде ядер фрагментов – запаздывающие нейтроны). The fraction of neutrons that are delayed is called β and this fraction is typically less than 1% of all the neutrons in chain reactions. The delayed neutrons allow a nuclear reactor to respond several orders more slowly than just prompt neutrons would alone. (запаздывающие нейтроны создают временную задержку на несколько порядков в реакции системы). In other words, without delayed neutrons changes in reaction rates in nuclear reactors would occur at speeds that are too fast for human to control. (Другими словами, без запаздывающих нейтронов изменения в режиме работы реактора были бы столь быстрыми, что реакция человека не позволила бы управлять им ). Problem. Estimate the number of collisions of a neutron to decrease its energy from E0 to Efin in a material with atomic mass M >>1. Hints: 1) Use the Eq.2.2 from the Lecture 2. 2) Prove, that after the first collision the neutron keeps the energy

2 ) and after the Nth collision the energy of the M 2 N neutron will be equal to E N = E 0 ⋅ (1 − ) M E1 = E 0 ⋅ (1 −

Take А2 = 238 (U238). Then after one collision Т max ≈ 0.016 Е0 and if we average the value of Tmax by a simple way:

Tmax = 1 Tmax , Tmax = 0.008 E 0. 2 32

3.3.Uncontrolled chain reaction and explosions in nuclear power plants It is impossible for a nuclear power plant to undergo a nuclear chain reaction that results in an explosion of power comparable with a nuclear weapon, but even low-powered explosions due to uncontrolled chain reactions that would be considered «fizzles» in a bomb, may still cause considerable damage and meltdown in a reactor. For example, the Chernobyl disaster involved a ran away chain reaction but the result was a low-powered steam explosion from the relatively small release of heat as compared with a b omb. However, the reactor complex was destroyed by the heat, as well as by ordinary burning of the graphite exposed to air. Such steam explosions would be typical of typical of the very diffuse assembly of materials in a nuclear reactor even under the worst conditions. In addition other steps can be taken for safety. For example, power plants licensed in US require a negative void coefficiens of reactivity (this means, that that if water is removed from the reactor core, the nuclear reaction will tend to shut down, but not increase). This eliminates the possibility of the type of accident that occured at Chernobyl (which was due to a positive void coefficient).

Fig.3.5. The contribution of nuclear energy plants into total production of electricity in different countries

33

3.4. Pressurized water reactors – one of mainly used type of nuclear reactors Pressurized water reactors (PWR) constitute a majority of all western nuclear reactors of power plants and one of two types of light water reactors (LWR) , t he other type are being boiling water reactors (BWR). (Водные реакторы под давлением составляют большинство западных ядерных реакторов энергетики и один из двух типов легководных реакторов, другим типом являются водные кипящие реакторы). In a PWR the primary coolant (water) is pumped under high pressure to the reactor core where it is heated by the energy generated by the fission of atoms. The heated water then flows to a steam generator where it transfers its thermal energy to a secondary system where steam is generated and flows to turbines which in turn, spins an electric generator. (В PWR вода подается в активную зону реактора под высоким давлением и нагревается тепловой энергией, выделяющейся при делении. Нагретая вода затем проходит в паровой генератор где вырабатывается пар, которым вращается турбина с электрогенератором). (In contrast to a boiling water reactor pressure in the primary coolant loop prevents the water from boiling within the reactor. All PWR use ordinary light water as both coolant and neutron moderator. PWR were originally designed to serve as nuclear propulsion for nuclear submarines. Several hundred of PWRs are used for marine propulsion in air craft carriers , nuclear submarines and ice breakers. Russia’s VVER reactors are similar to U.S. PWRs. France uses many PWR to generate the bulk of their electricity. 3.5. Negative temperature coefficient of reactivity PWR like all thermal reactors require the fast fission neutrons to be slowed down in order to interact with the nuclear fuel and sustain the chain reaction. In PWRs the coolant water is used as a moderator by letting the neutrons undergo multiple collisions with light hydrogen atoms in the water, losing speed in the process. This «moderating» of neutrons will happen more often when the water is denser. The use of water as a m oderator is an important safety feature of PWR, as an increase of temperature may cause the water to turn to steam – thereby reducing the reactivity of the reactor. 34

Therefore, if reactivity increases beyond normal, the reduced moderation of neutrons will cause the chain reaction to slow down, producing less heat. This property known as negative temperature coefficient of reactivity, makes PWR very stable. 3.6.Usage of nuclear energy in space Since 1961 nuclear power sources have been an important source of energy in space. The main part of them were radioisotope sources. Radioisotope power source uses heat, which is generated by spontaneous decay of radioactive nuclei. This heat is used for operation of thermoelectric generator. Definition: thermoelectric generators (also called thermogenerators) are devices which convert heat (temperature differences) directly into electrical energy, using a phenomenon called the «Seebeck effect» (or «thermoelectric effect»). Their typical efficiencies are around 5-10%. Modern devices often use bismuth telluride (Bi2Te3) semiconductor p-n junctions and can have thicknesses in the millimeter range. These are solid state devices and unlike dynamos have no moving parts, with the occasional exception of a fan. A radioisotope thermoelectric generator (RTG, RITEG) is an electrical generator that obtains its power from radioactive decay. RTGs can be considered as a type of battery and have been used as power sources in satellites, space probes and unmanned remote facilities, such as a series of lighthouses built by the former Soviet Union inside the Arctic Circle. RTGs are usually the most desirable power source for robotic or unmaintained situations needing a few hundred watts (or less) of power for durations too long for fuel cells, batteries, or generators to provide economically, and in places where solar cells are not practical. Safe use of RTGs requires containment of the radioisotopes long after the productive life of the unit. A common application of RTGs is as power sources on spacecraft. Systems for Nuclear Auxiliary Power (SNAP) units were used especially for probes that travel far enough from the Sun that solar panels are no longer viable. As such they were used with Pioneer 10, Pioneer 11, Voyager 1, Voyager 2, Galileo, Ulysses, Cassini and New Horizons. In addition, RTGs were used to power the two Viking landers and for the scientific experiments left on the Moon by the crews of Apollo 12 through 17. By comparison, only a 35

few space vehicles have been launched using full-fledged nuclear reactors: the Soviet RORSAT series and the American SNAP-10A. Although not strictly RTGs, similar units called radioisotope heater units are also used by various spacecraft including the Russian Lunokhod moon rover (using a Polonium 210 he at generator), and the Mars Exploration Rovers, Galileo and Cassini. These devices use small samples of radioactive material to produce heat directly, instead of electricity. 3.7. Criteria of materials choice The radioactive material used in RTGs must have several characteristics: • It should produce high energy radiation. Energy release per decay is proportional to power production per mole. Alpha decays in general release about 10 times as much energy as the beta decay of strontium-90 or cesium-137. • Radiation must be of a type easily absorbed and transferred into thermal radiation, preferably alpha radiation. Beta radiation can give off considerable amounts of gamma/X-ray radiation through bremsstrahlung secondary radiation production, thus requiring heavy shielding. Isotopes must not produce significant amounts of gamma, neutron radiation or penetrating radiation in general through other decay modes or decay chain products. • The half-life must be long enough that it will release energy at a relatively continuous rate for a reasonable amount of time. The amount of energy released per time (power) of a given quantity is inversely proportional to half-life. An isotope with twice the half-life and the same energy per decay will release power at half the rate, per mole. Typical half-lives for radioisotopes used in RTGs are therefore several decades, although isotopes with shorter half-lives could be used for specialized applications. • For spaceflight use, the fuel must produce a large amount of power per mass and volume (density). Density and weight are not as important for terrestrial use, unless there are size restrictions. The decay energy can be calculated if the energy of radioactive radiation or the mass loss before and after radioactive decay is known. 36

The first two criteria limit the number of possible fuels to fewer than 30 a tomic isotopes within the entire table of nuclides. Plutonium-238, curium-244 and strontium-90 are the most often cited candidate isotopes, but other isotopes such as polonium-210, promethium-147, caesium-137, cerium-144, ruthenium-106, cobalt60, curium-242 and thulium isotopes have also been studied. Plutonium-238 has the lowest shielding requirements and longest half-life. Only three candidate isotopes meet the last criterion (not all are listed above) and need less than 25 mm of lead shielding to keep radiation. 238Pu (the best of these three) needs less than 2.5 mm, and in many cases no shielding is needed in a 238Pu RTG, as the casing itself is adequate. 238Pu has become the most widely used fuel for RTGs, in the form of plutonium(IV) oxide (PuO2). 238Pu has a halflife of 87.7 y ears, reasonable power density and exceptionally low gamma and neutron radiation levels. Thus, with a starting capacity of 470 W, after 23 y ears it would have a capacity of 392 W . The plutonium 238 used in RTGs has a half-life of 87.74 years, in contrast to the 24,110 year half-life of plutonium 239 used in nuclear weapons and reactors. A consequence of the shorter half-life is that plutonium 238 i s about 275 times more radioactive than plutonium 239 (i.e. 17.3 Ci/g compared to 0.063 Ci/g). For instance, 3.6 kg of plutonium 238 undergoes the same number of radioactive decays per second as 1 tonne of plutonium 239. Since the morbidity of the two isotopes in terms of absorbed radioactivity is almost exactly the same, plutonium 238 is around 275 times more toxic by weight than plutonium 239. Some prototype RTGs, first built in 1958 by USA Atomic Energy Commission, have used polonium-210 (210Po). This isotope provides phenomenal power density because of its high radioactive activity, but has limited use because of its very short half-life of 138 days, again because of its high activity. A kilogram of pure polonium-210 in the form of a cube would be about 48 mm (about 2 inches) on a side and emit about 140 kW. The heat of melting is about 60 kJ/kg, the heat of evaporation about 10 times larger. If there is no efficient cooling, the self heating power is sufficient for melting then partly vaporizing itself. Americium-241 is a potential candidate isotope with a longer half-life than 238Pu: 241Am has a half-life of 432 years and could hypothetically power a device for centuries. 37

However, the power density of 241Am is only 1/4 that of 238Pu, and 241 Am produces more penetrating radiation through decay chain products than 238Pu and needs about 18 mm worth of lead shielding. Even so, its shielding requirements in an RTG are the second lowest of all possible isotopes: only 238Pu requires less. With a current global shortage of 238Pu, a closer look is being given to 241Am. RTGs use thermoelectric couples or "thermocouples" to convert heat from the radioactive material into electricity. Thermocouples, though very reliable and long-lasting, are very inefficient; efficiencies above 10% have never been achieved and most RTGs have efficiencies between 3–7%. Thermoelectric materials in space missions to date have included silicon germanium alloys, lead telluride and tellurides of antimony, germanium and silver. Studies have been done on improving efficiency by using other technologies to generate electricity from heat. Achieving higher efficiency would mean less radioactive fuel is needed to produce the same amount of power, and therefore a lighter overall weight for the generator. This is a critically important factor in spaceflight launch cost considerations. A thermionic converter – an energy conversion device which relies on the principle of thermionic emission–can achieve efficiencies between 10–20%, but requires higher temperatures than those at which standard RTGs run. Some prototype 210Po RTGs have used thermionics, and potentially other extremely radioactive isotopes could also provide power by this means, but short half-lives make these infeasible. Several space-bound nuclear reactors have used thermionics, but nuclear reactors are usually too heavy to use on most space probes. Thermophotovoltaic cells work by the same principles as a photovoltaic cell, except that they convert infrared light emitted by a hot surface rather than visible light into electricity. Thermophotovoltaic cells have an efficiency slightly higher than thermocouples and can be overlaid on top of thermocouples, potentially doubling efficiency. Systems with radioisotope generators simulated by electric heaters have demonstrated efficiencies of 20%, but have not been tested with actual radioisotopes. Some theoretical thermophotovoltaic cell designs have efficiencies up to 30%, but these have yet to be built or confirmed. Thermophotovoltaic cells 38

and silicon thermocouples degrade faster than thermocouples, especially in the presence of ionizing radiation. It should be noticed, that RTGs may pose a r isk of radioactive contamination: if the container holding the fuel leaks, the radioactive material may contaminate the environment. For spacecraft, the main concern is that if an accident were to occur during launch or a subsequent passage of a spacecraft close to Earth, harmful material could be released into the atmosphere; and their use in spacecraft and elsewhere has attracted controversy. The alpha radiation emitted by either isotope will not penetrate the skin, but it can irradiate internal organs if plutonium is inhaled or ingested. Particularly at risk is the skeleton, the surface of which is likely to absorb the isotope, and the liver, where the isotope will collect and become concentrated. To minimize the risk of the radioactive material being released, the fuel is stored in individual modular units with their own heat shielding. They are surrounded by a layer of iridium metal and encased in high-strength graphite blocks. These two materials are corrosion- and heat-resistant. Surrounding the graphite blocks is an aeroshell, designed to protect the entire assembly against the heat of reentering the Earth's atmosphere. The plutonium fuel is also stored in a ceramic form that is heat-resistant, Chain reactions do not occur in RTGs, so heat is produced at a fully predictable and steadily decreasing rate that depends only on the amount of fuel isotope and its half-life. An accidental power excursion is impossible. On the other hand, heat generation cannot be varied with demand or shut off when not needed. Auxiliary power supplies (such as rechargeable batteries) may be needed to meet peak demand, and adequate cooling must be provided at all times including the prelaunch and early flight phases of a space mission.

LECTURE 4 Structural materials of nuclear fission reactors, waste materials 1. What is Stainless Steel (SS) and why is it stainless? In 1913 English metallurgist Harry Brearly, working on a project to improve rifle barrels , discovered that adding chromium to low carbon steel gives it stain resistance. (В 1913 британский инженер-металлург Гари Бриэл, работавший над совершенствованием винтовочных затворов, открыл, что добавление хрома к низкоуглеродистой стали придает ей стойкость против ржавления). In addition to iron, carbon and chromium, modern stainless steel may also contain other elements, for example nickel, titan, molybdenum, niobium. Ni, Mo, Nb and Cr enhance the corrosion resistance of stainless steels. It is the addition of a minimum 12% Cr to the steel that makes it resist rust, or stain less than other types of steels. (Кроме железа, углерода и хрома современные нержавеющие стали могут также содержать другие элементы, например никель, титан, молибден, ниобий. Минимальная добавка хрома, которая делает сталь устойчивой против ржавления или уменьшает степень коррозии сравнительно с другими сталями, составляет 12%). The chromium in the steel combines with oxygen in the atmosphere to form a thin, invisible layer of chrome- containing oxide, called the passive film. The sizes of chromium atom and their oxides are similar so they pack neatly together on the surface of the metal, forming a stable layer only a few atoms thick. (Хром в стали соединяясь с кислородом атмосферы образует тонкую невидимую пленку, называемую пассивной пленкой. Размеры атомной структуры хрома и окислов близки, поэтому моноатомная пленка хорошо контактирует с поверхностью металла). If the metal is cut or scratched and the passive film is disrupted more oxide will quickly form and recover the exposed surface , protecting it from corrosion.

40

Stainless steels are steels with high corrosion resistance. Modern stainless steels usually are made on the base of Fe-Ni-Cr with different additions like Ti, Nb, Mo, W, V, Zr. The three main types of stainless steels are austenitic, ferritic and martensitic. These three types of steels are identified by their microstructure and crystal phase. (Три основных типа нержавеющих сталей это аустенитные, ферритные и мартенситные. Они отличаются микроструктурой и кристаллическими фазами). 1.1 Austenitic stainless steels: Austenitic SS make up over 70% of total SS production. Steels of this type have austenite as their primary phase (FCC structure) and are not hardenable by heat treatment. For example: a typical composition of 18% chromium and 10% Ni, commonly known as 18-10 stainless steel, is often used in flatware (Например, распространенная сталь, содержащая 18% хрома и 10% никеля, широко известная как сталь 18-10, часто используется при изготовлении столовых приборов). Low-carbon SS , for example 316L or 304L are used to avoid corrosion problems caused by welding (низкоуглеродистые нержавеющие стали, например 316L или 304L используются когда нужно избежать проблем с коррозией при сварке). When Ni is added the austenite structure of iron is stabilized. This crystal structure makes such steels non-magnetic and less brittle at low temperatures. Significant quantities of Mn (manganese) have been used in many SS compositions. Mn preserves an austenitic structure in the steel as does nickel, but at lower cost. (Аустенитная структура железа стабилизируется путем добавления никеля. Эта кристаллическая структура делает стали немагнитными и менее хрупкими при низких температурах). Stainless steels have been videly used as s tructural and core component materials of light water and fast reactors. In fusion reactors stainless steels are also candidate materials. (Нержавеющие стали широко использовались как конструкционные материалы и элементы узлов активной зоны легководных и быстрых реакторов).

41

Table 1. Chemical composition of some widely used austenitic SS (wt.%) type

C

Cr

Ni

Mn

Si

S

P

SS302

0.15

17-19

8-10

2.0

1.0

0.03

0.04

SS304

0.08

18-20

8-12

2.0

1.0

0.03

0.04

SS304L SS316 SS316L

0.03 0.08 0.03

18-20 16-18 16-18

8-12 10-14 10-14

2.0 2.0 2.0

1.0 1.0 1.0

0.03 0.03 0.03

0.04 0.04 0.04

Mo

2.0-3.0 2.0-3.0

1.2. Ferritic stainless steels: Ferritic steels have ferrite (BCC structure) as their main phase and generally have better engineering properties than austenitic steels, but have reduced corrosion resistance, due to lower Cr and Ni content and are usually less expensive. They contain between 10% and 27 % of Cr and very little Ni, if any, some types contain lead (Pb). Most compositions include Mo (molybdenum); some, Al (aluminium) or Ti (titanium). Common ferritic grades include 18Cr2Mo, 26Cr-1Mo, 29Cr – 4Mo and 29Cr-4Mo-2Ni. A typical modern ferritic stainless steel is SS 430 (analog of Cr17 steel). Table 2. Chemical composition of some widely used ferritic SS (wt.%) type

C

Cr

Ni

Mn

Si

S

P

Mo

SS430

0.08

16-18

-

1.0

1.0

0.015

0.04

-

1.3. Martensitic stainless steels: Martensitic steels are not as corrosion –resistant as the other two classes but these steels may be tempered and hardened. Martensite gives steel great hardness, but it reduces its toughness and makes it brittle. Martensitic SS contains 12-14Cr, Mo (0.2-1%), Ni (usually less than 2%), carbon (about 0.1-1%) giving it more hardness, but

42

making it more brittle. A typical modern martensitic stainless steel is SS 410. Table 3. type SS410

C 0.08-0.15

Cr 11-13

Ni 0.7

Mn 1.5

Si 1.0

S 0.015

P 0.04

Mo -

Precipitation-hardening martensitic SS have corrosion resistance comparable to austenitic, but can be precipitation hardened to even higher strength than the other martensitic steels. The most common 17-4PH, uses about 17% Cr -4%Ni . This SS is used in modern aircraft designs. Table 4. The main mechanical characteristics of the typical stainless steel 18Cr-10Ni type

σY, MPa

σB, MPa

Δ, %

SS316

270

660

50

Control question: What is stainless steel and why is it stainless? Control question: What do you think about possible applications of stainless steels? 2. Alloys 2.1. Zr-alloys Table 5. Physical properties of Zr Atomic number Cross-section of absorption for thermal neutrons Temperature of melting, K Crystal phase Atomic mass (at.units)

43

40 0.18 barn 2118 α –Zr, HCP up to 1135 91

Zirconium is a co mmercially available refractory metal with excellent corrosion resistance , good mechanical propreties, very low thermal neutron cross section, and can be manufactured using standard fabrication techniques. (Zr является коммерчески доступным тугоплавким металлом с отличной стойкостью против коррозии, хорошими механическими свойствами, очень низким сечением поглощения тепловых нейтронов и может производиться стандартными промышленными методами). Zr resists corrosive attack in most organic and mineral acids, strong alkalis and some molten salts. A tightly adherent and protective oxide film protects the metal oxide interface to provide corrosion resistance. The initial commercial nuclear power reactors used SS to clad the uranium fuel , but by mid-1960 Zr alloys were the principle cladding materials due to the superior neutron economy and corrosion resistance. These same Zr-alloys are available to designers of high level nuclear waste disposal containers as internal components or external cladding. Additional advantages of Zr-alloys for long term nuclear waste disposal include excellent radiation stability and 100% compatibility with existing Zircaloy fuel cladding to alleviate any concerns of galvanic corrosion. Zirconium alloys are solid solutions of zirconium or other metals a common subgroups having the trade mark Zircaloy. (Циркониевые сплавы, имеющие торговую марку Циркалой являются твердыми растворами с другими металлами подгруппы). Zirconium has very low absorption cross –section of thermal neutrons, high hardness, ductility, and corrosion resistance. Therefore, one of the main uses of zirconium alloys is in nuclear technology, as cladding of fuel rods in nuclear reactors, especially water reactors. A typical composition of nuclear-grade zirconium alloys is more than 95% (wt%) zirconium and less than 2% of tin, Nb (niobium), iron, Cr(chromium), Ni (nickel) and other metals which are added to improve mechanical properties and corrosion resistance. See also Table 7 where typical compositions of some Zr-alloys are given. (Типичный состав циркониевых сплавов для ядерной техники: Zr95%, Sn2% или меньше, ниобий, хром, никель и другие металлы, которые добавляются для улучшения механических свойств и коррозионной стойкости. См. также таблицу 7, 44

где даются типичные композиции некоторых циркониевых сплавов). Table 6. Thermal neutron cross sections (barn) Carbon (graphite)

0.005

Berillium

0.01

Magnesium

0.06

Lead Zirconium Zircaloy-4

0.17 0.18 0.22

Aluminium

0.23

Iron Austenitic SS Ni

2.56 3.1 4.5

Ti

6.1

Table 6 presents thermal neutron cross sections of different materials, which are in common use in nuclear technologies. Table 7. Composition of Zr-alloys alloy

Sn

Fe

Cr

Ni

Zircaloy-2

1.5%

0.15%

0.1%

0.05%

Zircaloy-4 R60804 Zircaloy-4 R60904 ZIRLO

1.5%

0.2%

0.1%

-

Nb

2.5 1.0%

0.1%

1.0%

45

Table 8. Mechanical properties of Zr-alloys at 293 K alloy Zircaloy2

σB MPa 480

σ0.2 MPa 310

δ, % 45

Zircaloy4

Zr-2.5Nb is a binary alloy with niobium to increase the strength. 2.2. Be, Al, Mg- alloys 2.2.1. Be is commercially available a rare metal possessing a good combination of physical and mechanical characteristics specifically suited to a w ide range of applications. The typical strength value of Be is about 300 MPa. Table 9. Physical properties of Be Atomic number Cross-section of absorption for thermal neutrons Temperature of melting, K Crystal phase

4 0.01 barn

density

1.85 g / cm3

Atomic mass (at.units)

9

1556 α –Be, HCP up to 1513

Be metal is extremely stiff and light weight with a modulus of elasticity almost 50% greater than that of steel with only one-fourth the weight. Be has excellent thermal characteristics, is nonmagnetic and is transparent to X-rays. Be is widely used in reactors and other nuclear applications as a reflector or moderator because it has a low thermal neutron absorption cross section. The price of pure Be is generally in the range of $500 per kg. About 50% of the planets beryllium deposits are located in Brazil, Uganda and Russia. A new emerging supplier of Be is 46

Kazakhstan (nuclear national company Kazatomprom). [http://ibcadvancedalloys.com/investors/about-berillium/]. 2.2.2. Al-alloys Aluminum Table 10. Physical properties of Al Atomic number Cross-section of absorption for thermal neutrons Temperature of melting, K Crystal phase

13 0.23 barn

density

2.7 g / cm3

Atomic mass (at.units)

27

953 FСС

Aluminium itself has very low strength (50 MPa) and cannot be used as structural material but a base for making light alloys. Aluminum alloys are materials in which aluminium (Al) is the predominant metal. Aluminium alloys with wide range of properties are used in engineering structures. Attention! Alloy systems are classified by a number system (ANSI) or by names, indicating their main alloy constituents. For example: Al – alloy: 6061 (ANSI) or Al-1%Mg-Cu-Cr . The typical alloying elements are Cu (copper), Mg (magnesium), Mn (manganese), Si (silicon) and Zn (zinc). There are two principal classifications , namely casting alloys and wrought alloys. The most important cast aluminium alloy system is Al – Si, where the high level of silicon (4-13%) contribute to give good casting characteristics. Al alloys are widely used in engineering structures and components where light weight and corrosion resistance is required. Aluminium alloys have very high strength –toweight ratio. 47

For example: Al – alloy 6061 (a typical alloy) has strength about 150 MPa (compare with 50 MPa for pure Al! and compare with 660 MPa for the stainless steel 18-10). Al alloys can be used for making composite materials. Metal matrix composites (MMC) on Al base are emerging as advanced engineering materials for application in space, defence, automotive industries. In MMC a metallic base material is reinforced with ceramic fiber, whiskers or particulate in order to achieve a combination of properties not attainable by either constituents individually. Aluminium or its alloys is favoured as metallic matrix material bcause of its low density, easy fabricability and good engineering properties. In general, the benefits of aluminium metal matrix composites over unreinforced aluminium alloy are increased specific stiffness, improved wear resistance and decreased coefficient of thermal expansion. The conventional reinforcement materials for Al-alloys are SiC , Al2O3 . There are known results of recent investigations where B4C particles were used as reinforced elements. This way of reinforcement is very promising because of very high hardness of B4C (close to diamond) while the conventional reinforcenet like SiC, Al2O3 close to that of Al-alloys matrix. Moreover, due to high neutron capture cross-section of B10 Isotope, composites containing B4C particles have the potential for use in nuclear reactors as n eutron shielding and control rod materials. An example of a composite: Al-5%Mg alloy (matrix) + B4C (reinforced particles) [http://en.wikipedia.org/wiki/Aluminium_ alloy]. 2.3. Refractory alloys Refractory metals are a cl ass of metals that are extraordinarily resistant to heat and wear. The expression is mostly used in the context of materials science, metallurgy and engineering. The definition of which elements belong to this group differs. The most common definition includes five elements: two of the fifth period (niobium and molybdenum) and three of the sixth period (tantalum, tungsten, and rhenium). They all share some properties, including a 48

Zirconium is a co mmercially available refractory metal with excellent corrosion resistance , good mechanical propreties, very low thermal neutron cross section, and can be manufactured using standard fabrication techniques. (Zr является коммерчески доступным тугоплавким металлом с отличной стойкостью против коррозии, хорошими механическими свойствами, очень низким сечением поглощения тепловых нейтронов и может производиться стандартными промышленными методами). Zr resists corrosive attack in most organic and mineral acids, strong alkalis and some molten salts. A tightly adherent and protective oxide film protects the metal oxide interface to provide corrosion resistance. The initial commercial nuclear power reactors used SS to clad the uranium fuel , but by mid-1960 Zr alloys were the principle cladding materials due to the superior neutron economy and corrosion resistance. These same Zr-alloys are available to designers of high level nuclear waste disposal containers as internal components or external cladding. Additional advantages of Zr-alloys for long term nuclear waste disposal include excellent radiation stability and 100% compatibility with existing Zircaloy fuel cladding to alleviate any concerns of galvanic corrosion. Zirconium alloys are solid solutions of zirconium or other metals a common subgroups having the trade mark Zircaloy. (Циркониевые сплавы, имеющие торговую марку Циркалой являются твердыми растворами с другими металлами подгруппы). Zirconium has very low absorption cross –section of thermal neutrons, high hardness, ductility, and corrosion resistance. Therefore, one of the main uses of zirconium alloys is in nuclear technology, as cladding of fuel rods in nuclear reactors, especially water reactors. A typical composition of nuclear-grade zirconium alloys is more than 95% (wt%) zirconium and less than 2% of tin, Nb (niobium), iron, Cr(chromium), Ni (nickel) and other metals which are added to improve mechanical properties and corrosion resistance. See also Table 7 where typical compositions of some Zr-alloys are given. (Типичный состав циркониевых сплавов для ядерной техники: Zr95%, Sn2% или меньше, ниобий, хром, никель и другие металлы, которые добавляются для улучшения механических свойств и коррозионной стойкости. См. также таблицу 7, 44

The melting point of the refractory metals are the highest for all elements except carbon, osmium and iridium. This high melting point defines most of their applications. All the metals are bodycentered cubic except rhenium which is hexagonal close-packed. Most physical properties of the elements in this group vary significantly because they are members of different groups. Creep resistance is a key property of the refractory metals. In metals, the starting of creep correlates with the melting point of the material; the creep in aluminium alloys starts at 200°C, while for refractory metals temperatures above 1500°C are necessary. This resistance against deformation at high temperatures makes the refractory metals suitable against strong forces at high temperature, for example in jet engines, or tools used during forging. Refractory metals are used in lighting, tools, nuclear reaction control rods. Because of their high melting point, refractory metal components are never fabricated by casting. The process of powder metallurgy is used. Powders of the pure metal are compacted, heated using electric current, and further fabricated by cold working with annealing steps. Rhenium is used in tungsten alloys up t o 22% it improves the high temperature strength and corrosion resistance. Tungsten and its alloys are often used in applications where high temperatures are present but still a high strength is necessary and the high density is not troublesome. The high density and strength is also a key property for the use of tungsten in weapon projectiles. (Вольфрам и его сплавы применяются там, где высокая температура сочетается с необходимостью высокой прочности материала. Высокая плотность и прочность также являются ключевыми свойствами для использования вольфрама в военных целях). Molybdenum based alloys are widely used, because they are cheaper than superior tungsten alloys. The most widely used alloy of molybdenum is the Titanium-Zirconium-Molybdenum alloy TZM , composed of 0.5% titanium and 0.08% of zirconium (with molybdenum being the rest). The alloy exhibits a higher creep resistance and strength at high temperatures, making service 50

temperatures of above 1060°C possible for the material. Molybdenum is the most commonly used of the refractory metals. Its most important use is as a strengthening alloy of steel. Structural tubing and piping often contains molybdenum, as do many stainless steels. Its strength at high temperatures, resistance to wear and low coefficient of friction are all properties which make it invaluable as an alloying compound. Its excellent anti-friction properties lead to its incorporation in greases and oils where reliability and performance are critical. Niobium has many uses, some of which it shares with other refractory metals. It is unique in that it can be worked through annealing to achieve a wide range of strength and elasticity, and is the least dense of the refractory metals. It can also be found in electrolytic capacitors and in the most practical superconducting alloys. Niobium can be found in aircraft gas turbines, vacuum tubes and nuclear reactors. 3. Graphite Table 11. Physical properties of graphite Atomic number Cross-section of absorption for thermal neutrons Temperature of melting, K Crystal phase density

6 0.005 barn

Atomic mass (at.units)

12

Sublimation at 3920 Hexagonal 1.65 – 1.75 g / cm3

Nuclear graphite is any grade of graphite , usually electrographite , specifically manufactured for use as a moderator or reflector within nuclear reactors. Graphite is an important material for the construction of both historical and modern nuclear reactors as it is one the purest materials manufactured at industrial scale and it retains its properties at high temperatures. You know (see Lecture3) that the design of the first nuclear reactor, which was created by E.Fermi, involved graphite as a moderator. The first attempt to create a self sustaining chain reaction 51

was not successful as t he graphite was not sufficiently pure. A second attempt was made by graphite of higher purity and it was successful one. Later similar work had been undertaken in the USSR leading to findings similar to those in the USA. So that, purity of reactor-grade graphite is very important factor by using it in nuclear reactor. Special care must by taken that graphite is free of neutron absorbing elements such as B (boron). Usually not more than 4 10 -5 % believe as acceptable level of B in reactor graphite.[ [ http://en.wikipedia.org/wiki/nuclear_graphite]

LECTURE 5 Waste materials (Радиоактивные отходы) Radioactive wastes are usually by-products of nuclear power generation and other applications of nuclear fission or nuclear technology, such as research and medicine. Radioactive wastes are wastes that contain radioactive materials. (Радиоактивные отходы обычно являются побочными продуктами ядерной энергетики и других применений ядерных технологий, например в исследованиях или медицине). Radioactive wastes are hazardous to human health and the environment, and are regulated by government agencies in order to protect human health and the environment. (Радиоактивные отходы являются опасными для здоровья человека и окружающей среды и контролируются правительственными агентствами с целью обеспечения безопасности). Radioactivity diminishes over time, so waste is typically isolated and stored for a period of time until it no longer poses a hazard. The period of time waste must be stored depends on the type of waste. (Радиоактивность снижается с течением времени поэтому отходы обычно изолируются и хранятся в течение времени после которого они не будут представлять опасность. Период времени, в течение которого отходы должны храниться, зависит от их типа). Low-level waste with low levels of radioactivity per mass or volume (such as some common medical or industrial radioactive wastes) may need to be stored for only hours, days, or months, while high-level wastes (such as spent nuclear fuel or by-products of nuclear reprocessing) must be stored for thousands of years. Current major approaches to managing radioactive waste have been segregation and storage for short-lived wastes, nearsurface disposal for low and some intermediate level wastes, and deep burial or transmutation for the long-lived, high-level wastes. A summary of the amounts of radioactive wastes and management approaches for most developed countries are presented and reviewed periodically as part of the International Atomic Energy Agency (IAEA) Joint Convention on the Safety of Spent Fuel Management and on the Safety of Radioactive Waste Management. 53

All radioisotopes contained in the waste have a half-life–the time it takes for any radionuclide to lose half of its radioactivity–and eventually all radioactive waste decays into non-radioactive elements (i.e., stable isotopes). Certain radioactive elements (such as plutonium-239) in «spent» fuel will remain hazardous to humans and other creatures for hundreds of thousands of years. Other radioisotopes remain hazardous for millions of years. Thus, these wastes must be shielded for centuries and isolated from the living environment for millennia. Some elements, such as iodine-131, have a short half-life (around 8 days in this case) and thus they will cease to be a problem much more quickly than other, longer-lived, decay products, but their activity is therefore much greater initially. The two tables show some of the major radioisotopes, their half-lives, and their radiation yield as a proportion of the yield of fission of uranium-235. The faster a radioisotope decays, the more radioactive it will be. The opposite also applies; for instance, 96% of the element Indium in nature is the In-115 radioisotope, but it is considered non-toxic in pure metal form and mainly like a stable element because its multitrillion-year half-life means that a relatively minuscule portion of its atoms decay per unit of time.[3] The energy and the type of the ionizing radiation emitted by a p ure radioactive substance are also important factors in determining its danger. The chemical properties of the radioactive element will determine how mobile the substance is and how likely it is to spread into the environment and contaminate humans. This is further complicated by the fact that many radioisotopes do not decay immediately to a stable state but rather to a radioactive decay product leading to decay chains. Radioactive waste comes from a n umber of sources. The majority of waste originates from the nuclear fuel cycle and nuclear weapons reprocessing. However, other sources include medical and industrial wastes, as well as naturally occurring radioactive materials (NORM) that can be concentrated as a result of the processing or consumption of coal, oil and gas, and some minerals, as discussed below. High-level waste is full of highly radioactive fission products, most of which are relatively short-lived. This is a concern since if the waste is stored, perhaps in deep geological storage, over many years the fission products decay, decreasing the radioactivity of the waste 54

and making the plutonium easier to access. The undesirable contaminant Pu-240 decays faster than the Pu-239, and thus the quality of the bomb material increases with time (although its quantity decreases during that time as well). Thus, some have argued, as time passes, these deep storage areas have the potential to become "plutonium mines", from which material for nuclear weapons can be acquired with relatively little difficulty. moderately enriched with U-235 relative to U-238, so the U-238 continues to serve as a denaturation agent for any U-235 produced by plutonium decay. Vitrification of waste Long-term storage of radioactive waste requires the stabilization of the waste into a form which will neither react nor degrade for extended periods of time. One way to do this is through vitrification. The 'calcine' generated is fed continuously into an induction heated furnace with fragmented glass. The resulting glass is a n ew substance in which the waste products are bonded into the glass matrix when it solidifies. This product, as a melt, is poured into stainless steel cylindrical containers ("cylinders") in a batch process. When cooled, the fluid solidifies ("vitrifies") into the glass. Such glass, after being formed, is highly resistant to water. After filling a cylinder, a seal is welded onto the cylinder. The cylinder is then washed. After being inspected for external contamination, the steel cylinder is stored, usually in an underground repository. In this form, the waste products are expected to be immobilized for a long period of time (many thousands of years). The preparation of radioactive materials The preparation of radioactive materials takes place in so-called hot cells, which are special enclosures, where radioactive specimens are handled with manipulators. Since the radioactivity in the cells will eventually attack plastics and electric parts, their use should be cut down to a minimum. Cleaning and decontaminating the whole system should be easy, and minimal waste should be generated during use. Also, it must be possible to repair the equipment in the cell using the manipulators only. Considering that all parts in the cell will be radioactively contaminated, the equipment should be dependable in operation, because if not repairable in the cell, it will 55

have to be discarded as radioactive waste. The amount of waste for final disposal must be kept at a minimum.

Fig.1. A typical view of a hot laboratory

A hot laboratory is used for studying the chemical and physicomechanical properties of irradiated structural materials, nuclear fuels and waste materials. In a hot laboratory all work with irradiated materials is carried out only from a distance, the laboratory is equipped for this through a process chain of hot chambers and cells interconnected by by a system for transporting preparations and samples both between the various compartments and with the storage area for the radioactive materials. Hot cells are hermetic chambers with strong biological shielding. They are made of high density materials: barytoconcrete, cast iron or lead. Work with high-activity preparations demands that complex biological measures be taken to protect staff and surrounding population against ionizing radiation and contamination by radioactive substances. A hot laboratory is equipped by powerful suction-and exhaust ventilation that provides for an exchange of air from ten to 30 times per hour dust removal and air conditioning in the forced-ventilation system and filtration of the air removed. One can see in Fig.1 a g eneral view of a hot laboratory which is equipped with hot cells for working with radioactive 56

materials. Operators work with radioactive materials from distance , using manipulators and observing through special viewing windows. But these windows are made of special glass: lead glass. The most common glass for production viewing windows has density about 5 g / cm3. A rough calculation for lead equivalence would be to multiply the Pb thickness by 2.5 (e.g. 10 mm Pb would require a 25 mm thick lead glass window). Telemanipulators are used for the remote handling of equipment inside hot cells. Lead loaded gloves are often used in low radiation environment (such as hot cells used in hospital nuclear medicine labs).

LECTURE 6 Passage of electromagnetic radiation through matter Three the main types of interaction of EM photons with matter: 1) Atomic photoeffect, 2) Compton effect, 3) Pair-production From the standpoint of radiation protection, radiation is often separated into two categories, ionizing and non-ionizing, to denote the level of danger posed to humans. Ionization is the process of removing electrons from atoms, leaving two electrically charged particles (an electron and a positively charged ion) behind. The negatively charged electrons and positively charged ions created by ionizing radiation may cause damage in living tissue. Basically, a particle is ionizing if its energy is higher than the ionization energy of a typical substance, i.e., a f ew eV, and interacts with electrons significantly. Definition: According to the International Commission on NonIonizing Radiation Protection (see: http://www.icnirp.de/), electromagnetic radiations from ultraviolet to infrared, to radiofrequency (including microwave) radiation, static and time-varying electric and magnetic fields, and ultrasound belong to the non-ionizing radiations. • Sometimes one photon gives all of its energy to a single atomic electron, ionizing the atom in a single interaction. This way that electromagnetic radiation can interact with matter is known as the atomic photoelectric effect. • Sometimes a p hoton collides elastically with an atomic electron, transferring both momentum and energy to the target electron. This type of interaction is known as Compton scattering. • Sometimes, if the photon has enough energy, the kinetic energy of the photon is converted to a combination of mass of two new particles (a particle and its anti-particle, such as an electron and a positron) and their kinetic energy. (If they aren't given some kinetic energy, they will annihilate each other right away.) An electron or nucleus of the target material will recoil, absorbing the "left-over" momentum and some kinetic energy. This type of interaction is called pair production. 58

1. Photoelectric effect 1.1. The surface photoelectric effect A.Einstein won the Nobel Prize for Physics not for his work on relativity, but for explaining the photoelectric effect! He proposed that light is made up of packets of energy called photons. Photons have no mass, but they have momentum and they have an energy given by: Energy of a photon: E =  ⋅ ω (1) The photoelectric effect works like this. If you shine light of high enough energy on t o a metal, electrons will be emitted from the metal. Light below a certain threshold frequency, no m atter how intense, will not cause any electrons to be emitted. Light above the threshold frequency, even if it's not very intense, will always cause electrons to be emitted. The explanation for the photoelectric effect goes like this: it takes a certain energy to eject an electron from a m etal surface. This energy is known as the work function (W), which depends on the metal. Electrons can gain energy by i nteracting with photons. If a photon has an energy at least as big as the work function, the photon energy can be transferred to the electron and the electron will have enough energy to escape from the metal. A photon with an energy less than the work function will never be able to eject electrons. Before Einstein's explanation, the photoelectric effect was a real mystery. Scientists couldn't really understand why low-frequency high-intensity light would not cause electrons to be emitted, while higher-frequency low-intensity light would. Knowing that light is made up of photons, it's easy to explain now. It's not the total amount of energy (i.e., the intensity) that's important, but the energy per photon. Note that this is the maximum possible kinetic energy because W is the minimum energy necessary to liberate an electron. The threshold frequency, the minimum frequency the photons can have to produce the emission of electrons, is when the photon energy is just equal to the work function:

59

1.2. Atomic photoelectric effect One of the ways electromagnetic radiation interacts with matter is known as the photoelectric effect, which is characterized by a photon giving all of its energy to an atomic electron, ionizing the atom in a single interaction. The photoelectric effect is therefore observed only for photon energies greater than the binding energy of at least some of the atomic electrons. The photoelectric effect is the dominant interaction of photons with matter, for those photons whose energy falls approximately in the range 1 keV < Eγ < 0.5 MeV. This includes virtually all dental and medical diagnostic X-rays, airport baggage inspection X-rays, and X-rays emitted during relaxation of the atomic electrons following radioactive nuclear decay. 2. The Compton effect by:

Although photons have no mass, they do have momentum, given

p=

E c

(2)

Convincing evidence for the fact that photons have momentum can be seen when a photon collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved in such a collision.

Applying the principles of conservation of energy and momentum to this collision, one can show that the wavelength of the 60

outgoing photon is related to the wavelength of the incident photon by the equation:

∆λ = λc ⋅ (1 − cos θ ) Here λc is the compton’s wave length, λc =

(3)

h =2.4 10-12 m me c

One can see that Δλ has very small value of the order about 10-10 cm, independently of the initial wave length of the photon. Exercises: 1) determine the maximum value for Δλ by the Compton effect. 2) write down expression for Δλ by the Compton effect on proton. 3) Pair production At photon energies above roughly 1 M eV another possibility becomes available when matter is struck by the photon: the creation of particle-anti-particle pairs. The lightest mass material particle (excluding neutrinos) is the electron; to make an electron and its antiparticle, a positron, requires twice the rest energy of an electron, since the positron is identical in mass to an electron. Thus the lowest energy at which pair production is observed is

Ethr = 2me c 2 = 1.02 MeV (При энергиях фотона примерно 1 MeV и несколько выше, начинает проявляться еще один эффект: образование пар частица – античастица. Частица с наименьшей массой покоя электрон; минимальная энергия, которая требуется чтобы образовать электрон и его античастицу – позитрон равна удвоенной энергии массы покоя электрона. Поэтому минимальная энергия, при которой наблюдается образование пар составляет 1.02 MeV). Conservation of energy asserts that pair production will never be observed at lesser photon energy than given above. In fact, the probability is very small for photon energies appreciably less than about double the threshold, but it rises rapidly as the photon energy increases and becomes the dominant interaction 61

for > 10 MeV. ( Из закона сохранения энергии следует, что образование пар не будет наблюдаться при энергиях фотона меньших, чем указанная выше. Фактически вероятность процесса очень мала для энергий фотона меньших чем удвоенная пороговая энергия, но резко возрастает при увеличении энергии фотонов и процесс становится доминирующим при энергиях больше 10 MeV). Observe that the fate of the electron created is identical to that of beta radiation of the same initial kinetic energy. (Дальнейшая судьба возникших электронов аналогична обычным бета электронам с близкими кинетическими энергиями. Позитрон ожидает такая же судьба, как и все другие анти – частицы: после постепенной потери кинетической энергии (так же как это происходит с электроном) он провзаимодействует с одним из электронов в веществе (один из атомных электронов) и аннигилирует образуя два кванта с общей энергией соответствующей энергии удвоенной массы покоя электрона). The positron has the same fate as any other anti-particle: after gradually losing its kinetic energy (just as the electron does) it finds a natural particle (one of the atomic electrons in the target) and annihilates with it, producing two photons of energy equal to the electron rest energy, roughly 0.511 M eV. (As mentioned above, photons of this energy typically interact with matter by the photoelectric or Compton effects, and are fairly penetrating.)

LECTURE 7 Materials of nuclear reactor and corrosion Corrosion is the disintegration of a material into its constituents atoms due to chemical reactions with its surroundings. (Коррозия это распад материала на составляющие его атомы вследствие химических реакций с окружающей средой). In the most common use of the word this means electrochemical oxidation of metals in reactions with an oxidant such as oxygen. (В самом общепринятом употреблении этого слова это означает электрохимическое окисление металлов окислителями типа кислорода). Formation of an oxide of iron due to oxidation of the iron atoms in solid solution is a well-known example of electrochemical corrosion, usually known as rusting. (Образование окисла на железе является хорошо известным примером коррозии, обычно называемым ржавлением). Many structural alloys corrode merely from exposure to moisture in the air, but the process can be strongly affected by exposure to certain substances. Corrosion can be concentrated locally to form a pit or crack or it can extend across a w ide area more or less uniformly corroding the surface. Nuclear power plants are designed for many years of operation. One of the challenges in maintaining nuclear power plants is how to predict some types of problems related to corrosion. (Ядерные энергетические установки создаются с расчетом на длительный срок работы. Поэтому прогнозирование и предупреждение проблем, связанных с коррозией, является одной из важнейших задач ядерной энергетики). Stress corrosion cracking (SCC) Stress corrosion cracking is the growth of cracks in metallic materials, enhanced by both stress and corrosion. In this phenomenon too, it is the properties of the oxidized layer that affect the pace at which the degradation proceeds. Stress corrosion cracking is a significant issue for nuclear power plants. (Коррозионное растрескивание под напряжением представляет собой рост трещин в металлических материалах, который усиливается из-за совместного действия напряженного состояния и коррозии). 63

Intergranular (Intercrystalline) corrosion (IGC, ICC) You know that Cr is added to steels to make them «stainless». The Cr-rich oxide film (based on Cr2O3) is thin, adherent and very protective. (Вы знаете, что Cr добавляется в стали, чтобы сделать их «нержавеющими». Богатая хромом окисная пленка (на основе Cr2O3) является тонкой, хорошо связана с поверхностью и имеет хорошие защитные свойства). But if heated into range 500-800oC the steels «sensitize» and become prone to IGC (ICC). Sensitization involves the precipitation of Cr carbide (Cr23C6) at the grain boundaries ; at the high temperatures its solubility is virtually zero. The C diffuses readily and the disorder in the boundaries provides nucleation sites. This depletes the boundaries of Cr. "Intergranular" or 'intercrystalline" means between grains or crystals. As the name suggests, this is a form of corrosive attack that progresses preferentially along the grain bourdaries. Positive identification of this type of corrosion usually requires microstructure examination under a microscopy although sometimes it is visually recognizable as in the case of weld decay. (Однако при нагреве в интервале температур 500-800 оС сталь «сенсибилизируется» и становится склонной к межкристаллитной коррозии (МКК). Сенсибилизация включает в себя выделение частиц карбида хрома (Cr23C6) по границам зерен; При высоких температурах углерод быстро диффундирует на границы, которые представляют собой дефектные зоны, являющиеся местами зарождения выделений. Таким образом, граница обедняется хромом. Как следует из названия, это одна из форм коррозионного воздействия, которая сосредоточена в основном на границах зерен. Обнаружение этого типа коррозии обычно требует исследования микроструктуры под микроскопом, но в некоторых случаях она может обнаруживаться визуально, как например, в случае сварных швов). Interranular stress corrosion cracking (IGSCC) This type of corrosion cracking may occur along grain boundaries in the presence of tensile stress. Control question: What is intergranular corrosion? What is the difference between intergranular corrosion and IGSCC? 64

Fig.7.1. The schematic picture of double electric layer on the metal surface in water

a

b

Fig.7.2. a) A typical profile of Cr concentration across a grain boundary after sensitization of an austenitic SS ; b) a typical microstructure of austenitic stainless steel after sensitizing to ICC. Bold

The figure on the right shows a typical composition profile of Cr across grain boundary after sensitizing and forming carbide particles Cr23C6 between grains in a typical austenitic stainless steel. One can see, that in this state boundaries are depleted of chromium. The picture on the right presents the "sensitized" microstructure which is 65

susceptible to intergranular corrosion or intergranular stress corrosion cracking.

Fig.7.3. a) A typical distribution of Cr near a grain boundary after sensitization of an austenitic SS

Тема для самостоятельного перевода. An electrical double layer (EDL) An electrical double layer is a st ructure that appears on the surface of a material when it is placed into a liquid. The EDL refers to two layers of charge, surrounding the object. The first layer the surface charge (either positive or negative) comprises ions adsorbed directly onto the material due to a host of chemical interaction. The second layer is composed of ions attracted to the surface charge via coulomb force, electrically screening the first layer. This second layer is loosely associated with the material because it is made of free ions which move in the fluid under the influence of electrical attraction and thermal motion . The EDL plays a very important role in many real systems involving materials interacting with a medium. Fig.7.1 presents a schematic picture of EDL in the case of metal – water system. In the case a) the surface charge layer is formed by ions of metal lattice and in the case b) it is formed by free electrons of metal. 66

Control questions. 1) What is the difference between structures of the double electric layer in Fig. 7.1,a,b? ; 2) This scheme is correct for metal surface. Why? Corrosion in nonmetals Most ceramic materials are almost entirely immune to corrosion. The strong ionic and /or covalent bonds that holds them together make these materials like as already corroded. Polymers also have very high resistivity to corrosion. A more common and related problem is swelling, where small molecules infiltrate the structure reducing strength and stiffness and causing a volume change. (Большая часть керамических материалов является практически инертной по отношению к коррозии. Это объясняется тем, что сильные ионные и /или ковалентные связи в таких материалах делают их близкими по свойствам к окисленным веществам. Полимеры также очень устойчивы против коррозии. Более распространенной для них проблемой является распухание, при котором небольшие по размеру молекулы проникают в структуру и снижают прочность и жесткость, а также вызывают изменение объема ). Passivation Given the right conditions, a thin film of corrosion products can form on metal’s surface spontaneously, acting as a b arrier to further oxidation. When this layer stops growing at less than a micrometer thick under the conditions that a material will be used in, the phenomenon is known as passivation. Rust on iron sutface, for example, usually grows to be much thicker and so it is not considered passivation because this mixed oxidized layer is not protective). While this effect is in some sense a property of the material, it serves as an indirect kinetic barrier: the reaction is often very rapid unless and until an impermeable layer forms. Passivation in air and water at moderate pH is seen in such materials as aluminium, stainless steels, titanium.

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Pitting corrosion In some cases almost all of the material’s surface remain protected by the passivating film , but tiny local point sites remain without protection. Corrosion in these points will be greatly amplified and can cause corrosion pits of several types, depending on conditions. In extreme cases the sharp tips of extremely long and narrow corrosion pits can cause stress concentration to the point that otherwise tough alloys can shatter. These problems are especially dangerous because they are difficult to detect before a part of structure fails. (В некоторых случаях почти вся поверхность материала может остаться защищенной пассивированной пленкой, но небольшие точечные участки оказываются открытыми, лишенными защиты. В этих точках коррозия существенно усилена и может стать причиной появления подвергнувшихся коррозии ямок – «точечной» коррозии различного типа, в зависимости от условий. В особых случаях вершины особенно длинных и узких ямок коррозии могут стать причиной концентрации напряжений, результатом чего является охрупчивание изначально вязких сплавов. Эти проблемы представляют собой особую опасность поскольку такие дефекты обычно трудно обнаружить до появления разрушения материала). High temperature corrosion High temperature corrosion is chemical deterioration of a material (typically a metal) under very high temperature conditions. This form of corrosion can occur when metal is subject to a high temperature atmosphere containing oxygen, sulphur or other compounds capable of oxidizing the material concerned. For example, materials, used in power generation, airspace have to resist periods of high temperature in which they may be exposed to atmosphere containing highly corrosive products. (Высокотемпературная коррозия связана с химическим воздействием на материал (обычно металл), при высокой температуре, вызывающим ухудшение его характеристик.Эта форма коррозии может проявляться если металл находится в высокотемпературной среде, содержащей кислород, серу или другие вещества, способные вызывать окисление. Например, 68

материалы, работающие в энергетических установках, аэрокосмической технике должны выдерживать периоды одновременного воздействия высоких температур и газовой атмосферы, содержащей вещества с высокой коррозионной способностью). What is pH factor? It is well known that in chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at 25 °C. Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline. pH measurements are important in medicine, biology, chemistry, agriculture, forestry, food science, environmental science, oceanography, civil engineering and many other applications. In a solution pH approximates but is not equal to p[H], the negative logarithm (base 10) of the molar concentration of dissolved hydronium ions (H3O+); a low pH indicates a high concentration of hydronium ions, while a high pH indicates a low concentration. This negative of the logarithm matches the number of places behind the decimal point, so, for example, 0.1 molar hydrochloric acid should be near pH 1 and 0.0001 molar HCl should be near pH 4 (the base 10 logarithms of 0.1 and 0.0001 being −1, and −4, respectively). Control question: How to prevent intergranular corrosion? Possible answer: Intergranular corrosion can be prevented through: • Use low carbon (e.g. 304L, 316L) grade of stainless steels • Use stabilized grades alloyed with titanium (for example type 321) or niobium (for example type 347). Titanium and niobium are strong carbide- formers. They react with the carbon to form the corresponding carbides thereby preventing chromium depletion. • Use post-weld heat treatment.

LECTURE 8 Radiation embrittlement and swelling in structural materials Definition: 1) Embrittlement is a loss of ductility of a material, making it brittle. In general, embrittlement is a reduction in the toughness of the steel due to a microstructural change and chemical effects. 2) Swelling is one of a class of phenomena collected under the term «dimensional instability» • Other examples of dimensional instability – radiation creep (all materials) – radiation growth (anisotropic materials) – swelling by gas bubbles, cracks, … (nuclear fuels) – growth of and changes in type of pores and cracks (graphite) – shrinkage due to mass loss (polymers) • Primary concern--swelling may cause substantial changes in dimensions of engineering components Swelling can also result from gases produced in materials, such as helium formed by (n,α) reactions and other gaseous impurities present in the metals. These traces of gas increase the concentration of voids formed upon e xposure to radiation. For example, the (n,α) and (n,2n) reactions between fast neutrons and beryllium form helium and tritium gases that create swelling. Under certain conditions, embrittlement can be enhanced by the presence of the helium bubbles (helium embrittlement). The accepted view is that this embrittlement is the result of stress- induced growth of helium gas bubbles at the grain boundaries. The bubbles eventually link up and cause intergranular failure. Fissionable metals suffer from radiation damage in a manner similar to that encountered in structural alloys (see fig.8.1). Figure 1 shows the growth in a uranium rod upon irradiation. The gas formation produces eventual swelling of the fuel and may place the cladding under considerable pressure as well. [(http://www.tpub.com/content/doe/h1017v2/css/h1017v2_103.htm).

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Fig.8.1. A – after irradiation, B – before irradiation

Additional problems are introduced by the high energy fission fragments and the heavy gases xenon and krypton, which appear among the fission products. Two fragments that share 167 M eV of kinetic energy, in inverse proportion to their atomic masses, are produced from each fission. Each fragment will have a r ange of several hundred angstroms as it produces a displacement spike. A core of vacancies is surrounded by a shell of interstitials, producing growth and distortion. One of the major challenges in alloying metallic uranium is the attainment of better stability under irradiation. Small additions of zirconium have shown marked improvement in reducing growth and distortion. The physical effects of ionizing radiation in metals is a uniform heating of the metal. Ions are produced by the passage of gamma rays or charged particles through the metal, causing sufficient electrical interaction to remove an external (or orbital) electron from the atom. Metals with shared electrons, which are relatively free to wander through the crystal lattice, are effected very little by ionization. Various materials have different mechanisms of embrittlement • Hydrogen embrittlement is the effect of hydrogen absorption on grain boundaries in some metals and alloys • Neutron radiation causes embrittlement of some materials, due some different mechanisms. The main of them are: o direct structure damages which result in creation of radiation defects o He accumulation on grain boundaries (He embrittlement) 71

o Radiation-induced grain boundary segregation • These processes are especially important for neutron moderators, nuclear reactor vessels and other structural materials. • Neutron radiation -induced swelling Radiation induced changes in microstructure and composition of materials can cause degradation of materials. But in many cases degradation can be made because of changes in distribution of chemical components through material’s bulk. It is known, that radiation effects in different materials under the same conditions of irradiation strongly depend on chemical composition. To begin, let’s consider the notion of embrittlement in general, without referring to irradiation. In general, grain boundary embrittlement is a phenomenon , characterized by tendency of a material, subjected to stress, to failure by brittle mode along grain boundaries. Hydrogen grain boundary embrittlement. Hydrogen embrittlement (HE) is the process by which metals and very often high-strength steels become brittle and fracture following the exposure to hydrogen. (Водородное охрупчивание это процесс, при котором металлы и широко распространенные высокопрочные стали становятся хрупкими и разрушение является результатом экспозиции в атмосфере водорода). The mechanism starts with lone hydrogen atoms diffusing into metal. At high temperatures the elevated solubility of hydrogen allows hydrogen to diffuse into the metal. At a low temperature hydrogen can also diffuse into metal due concentration gradient. In some cases h ydrogen atoms can combine inside metal matrix (especially at defects and microvoids) to form molecules. After that they create pressure inside matrix. The pressure can increase to levels where metal looses its ductility and tensile strength up to the point where it cracks open. High-strength and low-alloy steels, nickel and titanium alloys are most susceptible. Hydrogen embrittlement can occur during many various manufacturing operations or operational use – anywhere that metal 72

comes into contact with atomic or molecular hydrogen. Hydrogen may also be added to nuclear reactor coolant to remove oxygen from reactor coolant systems. Examples of hydrogen embrittlement are cracking of weldments or hardened steels when exposed to conditions which inject hydrogen into the component. Presently the phenomenon of HE is not completely understood and hydrogen embrittlement detection, in particular, seems to be one of the most difficult aspects of the problem. Hydrogen embrittlement does not affect all metallic materials equally. The most vulnerable are highstrength steels, titanium alloys and aluminum alloys. ( Водородное охрупчивание имеет причинами много факторов практического воздействия на материалы, по крайней мере везде, где материал находится в контакте с атмосферой атомарного или молекулярного водорода. Водород может также быть введен в охладитель реактора с целью удаления кислорода из системы. Примерами водородного охрупчивания являются эффекты, проявляющиеся на сварных швах упрочняющихся сталей, подвергавшихся воздействию водорода. В настоящее время явление НЕ еще не понятно в достаточной мере и определение НЕ, в частности, выглядит одним из сложных аспектов проблемы в целом. НЕ не влияет на все металлические материалы в одинаковой степени. Наиболее подверженными являются высоко-прочными стали, титановые сплавы и алюминиевые сплавы). Some features of hydrogen embrittlement of stainless steels are as follow: hydrogen diffuses along the grain boundaries and combines with the carbon, which is alloyed with the iron, to form methane gas. The methane gas is not mobile and collects in small voids along the grain boundaries where it builds up enormous pressures that initiate cracks. Hydrogen embrittlement is a primary reason that the reactor coolant is maintained at a neutral or basic pH in plants . (Некоторые особенности водородного охрупчивания в нержавеющих сталях следующие: If the metal is under a high tensile stress, brittle failure can occur. At normal room temperatures, the hydrogen atoms are absorbed into the metal lattice and diffused through the grains, tending to gather at inclusions or other lattice defects. If stress induces cracking under these conditions, the path is transgranular. At high temperatures, the absorbed hydrogen tends to gather in the grain boundaries and 73

stress-induced cracking is then intergranular. The cracking of martensitic and precipitation hardened steel alloys is believed to be a form of hydrogen stress corrosion cracking that results from the entry into the metal of a portion of the atomic hydrogen that is produced in the following corrosion reaction. Hydrogen embrittlement is not a permanent condition. If cracking does not occur and the environmental conditions are changed so that no hydrogen is generated on the surface of the metal, the hydrogen can rediffuse from the steel, so that ductility is restored. To address the problem of hydrogen embrittlement, emphasis is placed on controlling the amount of residual hydrogen in steel, controlling the amount of hydrogen It is known, that proposed application of a m aterial dictates its heat treatment. For example, you know that quenching is a rapid cooling of a steel from high temperature, in order to fix homogenous microstructure of solid solution state of material. But for many steels this state is far from equilibrium. Moreover, many steels are very hard and too brittle, because of internal stresses. In order to improve their mechanical properties, technologists use tempering. Essentially, tempering is the modification of this newly formed microstructure toward equilibrium. A temper is a heat treatment that alters the microstructure and properties. In general, tempering lowers strength and hardness, while improving ductility and toughness. Essentially it is very important for martensite steels. Let’s learn more. Temper embrittlement is a phenomenon inherent in many steels, characterized by reduced impact toughness. It occurs in certain quenched and tempered steels and even in irons with susceptible composition. This form of embrittlement does not affect room-temperature properties, but causes significant reduction in impact toughness and fatigue performance. Although normally associated tempered martensite , temper embrittlement can also occur if the matrix is tempered to the fully ferritic conditions. Temper embrittlement is a good example of intergranular embrittlement. A common factor in such effects is the presence of elements that segregate to the grain boundaries. This type of embrittlement partly relates to grain –boundary segregation of impurity elements (e.g. phosphorus, antimony and tin) . This causes decohesion of the 74

boundaries, resulting in tendency for low-energy intergranular fracture under certain loading conditions. Usually indicated by an upward shift in ductile-brittleness transition temperature, this type of embrittlement develops during thermal processing after austenitizing and quenching to martensite. All steels are susceptible so the real question becomes how susceptible and what factors affect that susceptibility. It is important to understand, that the degree of embrittlement is affected by the grain size and hardness. So, if we are dealing with a fine-grained plain-carbon steel of low hardness, it may not experience embrittlement symptoms despite of its phosphorus content whereas a more highly alloyed Cr-Ni steel used at higher hardness is more susceptible to impurity content. Widely used alloying elements like Cr, Ni, Mn tend to promote temper embrittlement with the highest embrittlement effect observed in Cr-Ni and Cr-Mo steels. Small additions of Mo in Cr-Ni steels (0.3% in solution) can diminish temper embrittlement caused by phosphorus. In order to decrease the TE effects technologists must keep the levels of P and Si in such materials as low as p ossible. Susceptibility also depends on impurity control and here is where the steelmaking process is critical. Foe example, in plain carbon and CrMo steel (without Ni) where P is the most important embrittling element, percentage can be controlled by the steelmaking process. Question: How can be TE of a steel correct? Answer: TE can be reversed by re-tempering above the critical temperature of 575 oC, then cooling rapidly, or by re-austenitizing and cooling rapidly. Impact toughness can be restored.

LECTURE 9 Impurity and alloying segregation in materials Segregation in materials refers to the enrichment of a material constituent at a free surface or an internal interface of a material. In a polycrystalline solid, a segregation site can be a dislocation, grain boundary, stacking fault, or an interface with a precipitate or secondary phase within the solid. There are two recognized types of segregation: equilibrium segregation and non-equilibrium segregation. Equilibrium segregation is associated with the lattice disorder at interfaces, where there are sites of energy different from those within the lattice at which the solute atoms can deposit themselves. The equilibrium segregation is so termed because the solute atoms segregate themselves to the interface or surface in accordance of with the statistics of thermodynamics in order to minimize the overall free energy of the system. This sort of partitioning of solute atoms between the grain boundary and the lattice was predicted by McLean in 1957. Non-equilibrium segregation, first theorized by Westbrook in 1964 [2], occurs as a result of solutes coupling to vacancies which are moving to grain boundary sources or sinks during quenching or application of stress. It can also occur as a result of solute pile-up at a moving interface. There are two main features of non-equilibrium segregation, by which it is most easily distinguished from equilibrium segregation. In the non-equilibrium effect, the magnitude of the segregation increases with increasing temperature and the alloy can be homogenized without further quenching because its lowest energy state corresponds to a uniform solute distribution. In contrast, the equilibrium segregated state, by definition, is the lowest energy state in a sy stem that exhibits equilibrium segregation, and the extent of the segregation effect decreases with increasing temperature. But under neutron or other fast particles irradiation, a large number of defects are created per unit of time and flows of defects move to sinks like grain boundaries, dislocations and porous. Impurity atoms forming complexes with defects like interstitials and vacancies move to sinks with a high intensity and form non 76

equilibrium segregation with higher level than that in equilibrium conditions. The non-segregation of a so lute to interfaces and grain boundaries in a solid produces a section of material with a discrete composition and its own set of properties that can have important (and often deleterious effects) on the overall properties of the material. These ‘zones’ with an increased concentration of solute can be thought of as the cement between the bricks of a building. Segregation to grain boundaries, for example, can lead to grain boundary fracture as a result of temper brittleness, creep embrittlement, stress relief cracking of weldments, hydrogen embrittlement, environmentally assisted fatigue, grain boundary corrosion, and some kinds of intergranular stress corrosion cracking. Very interesting and important field of study of impurity segregation processes involves AES of grain boundaries of materials under irradiation. This technique includes tensile fracturing of special specimens directly inside the UHV chamber of the Auger Electron Spectrometer was developed by Ilyin. Langmuir-McLean theory for surface and grain boundary segregation in binary systems This is the earliest theory specifically for grain boundaries, in which McLean uses a model of P solute atoms distributed at random amongst N lattice sites and p solute atoms distributed at random amo ngst n independent grain boundary sites. The total free energy due to the solute atoms is then:

G = p ⋅ e + P ⋅ E − kT ⋅ ln(n! N !) − ln(n − p )! p!( N − P)! P! (1) where E and e are energies of the solute atom in the lattice and in the grain boundary, respectively and the kT*ln term represents the configurational entropy of the arrangement of the solute atoms in the bulk and grain boundary. McLean used basic statistical mechanics to find the fractional monolayer of segregant, Xb, at which the system energy was minimized (at the equilibrium state), differentiating G with respect to p, noting that the sum of p and P is constant.

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Xb Xc ∆G = ⋅ exp(− ) RT X − Xb 1− X c

(2)

0 b

Here, X b0 is the fraction of the grain boundary monolayer available for segregated atoms at saturation, Xb is the actual fraction covered with segregant, Xc is the bulk solute molar fraction, and ΔG is the free energy of segregation per mole of solute. Values of ΔG were estimated by McLean using the elastic strain energy, released by the segregation of solute atoms. More complex systems Other models exist to model more complex binary systems. The above theories operate on the assumption that the segregated atoms are non-interacting. If, in a binary system, adjacent adsorbate atoms are allowed an interaction energy , such that they can attract (when is negative) or repel (when is positive) each other, the solid-state analogue of the Fowler adsorption theory is developed as:

∆G + Zω ( X b X b0 ) Xb Xc = ⋅ exp(− ) RT X b0 − X b 1 − X c

(3)

When ω is zero, this theory reduces to that of Langmuir and McLean. However, as ω becomes more negative, the segregation shows progressively sharper rises as the temperature falls until eventually the rise in segregation is discontinuous at a c ertain temperature. Guttman, in 1975, extended the Fowler theory to allow for interactions between two co-segregating species in multicomponent systems. This modification is vital to explaining the segregation behavior that results in the intergranular failures of engineering materials.

X bi = X bi0

X ci 2

[

]

1 + ∑ X cj ⋅ exp(− ∆G j RT ) − 1 j =1

78

⋅ exp(−

∆G ) (4) RT

Kinetics of Segregation In some situations where segregation is important, the segregant atoms do not have sufficient time to reach their equilibrium level as defined by the above adsorption theories. The kinetics of segregation become a limiting factor and must be analyzed as well. Most existing models of segregation kinetics follow the McLean approach. In the model for equilibrium monolayer segregation, the solute atoms are assumed to segregate to a grain boundary from two infinite halfcrystals or to a surface from one infinite half-crystal. The diffusion in the crystals is described by Fick’s laws. The ratio of the solute concentration in the grain boundary to that in the adjacent atomic layer of the bulk is given by an enrichment ratio, β. Most models assume β to be a constant, but in practice this is only true for dilute systems with low segregation levels. The kinetics of segregation can be described by the following equation:

X b (t ) − X b (0) FDt FDt = 1 − exp( 2 2 ) ⋅ erfc( 2 2 )1 / 2 (5) X ( ∞ ) − X b ( 0) β f β f Where F=4 four grain boundaries and 1 for the free surface, Xb(t) is the boundary content at time t, D is the solute bulk diffusivity, f is related to the atom sizes of the solute and the matrix b and a, respectively, by relation f = a3b − 2. For short times, this equation is approximated by:

X b (t ) − X b (0) 2 b 2 FDt 1 / 2 = ⋅ ( ) X ( ∞ ) − X b ( 0) β a 3 π

(6)

In practice, β is not a constant but generally falls as segregation proceeds due to saturation. If β starts high and falls rapidly as the segregation saturates, the above equation is valid until the point of saturation . Radiation embrittlement of reactor pressure vessel (RPV) steels The factors controlling RE in low alloy steels including steels for PWR are now broadly understood in terms of observed irradiation 79

induced microstructure changes. These effects can be linked to material composition, starting microstructure and irradiation conditions and irradiation induced degradation in impact properties, and associated fracture toughness understood as a function of these parameters. Now the accepted model for the observed hardening and embrittlement phenomena of RPV steels is that these effects are a consequence of at least two irradiation induced microstructural components. 1) a dominant aspect of embrittlement process is the key role of minor elements. For example, As, Sn or Cu present as an impurity in steels are the principal elements of concern. They have very little equilibrium solubility in α-iron (< 0.02%) so that even an alloy with 0.1% such elements are highly supersaturated at operating temperature, but with a diffusivity close to self-diffusivity of α-iron. Evidently, Cu atoms are actually immobile in the absence of irradiation. But the segregation process enhances sufficiently under irradiation, when intense vacancies fluxes exist in material. 2) Clusters formed directly by coalescence of point defects generated during irradiation induce a second component of irradiation strengthening . The clusters are considered to be dislocation loops or microvoids, formed in cascade zones.

LECTURE 10 Application of accelerators in radiation materials science Experiments with accelerators and radiation sources Introduction It is known very well, that a charged particle moving along the electric field E accelerates and get the increment of the energy accordingly to

dE = evE dt

(1)

When the charged particle uniformly moves across magnetic field H it’s trajectory is a circle of the radius R:

R=

M ⋅v⋅c v2 eH 1 − 2 c

=

p⋅c e⋅H

(2)

The period of a circulation can be determined from the expression

T=

2π ⋅ M ⋅ c eH 1 − β

2

(3)

Particle accelerator is a device that uses electric fields to propel electrically-charged particles to high speeds and to contain them. An ordinary television set is a simple form of accelerator. There are two basic types: linear accelerators and circular accelerators. Everyday examples of particle accelerators are cathode ray tubes found in television sets and X-ray generators. These low-energy accelerators generators use a single pair of electrodes with a DC voltage of a few thousand volts between them. In an X-ray generator, the target itself is one of the electrodes. A low-energy particle accelerator called an 81

ion implanter is used in the manufacture of integrated circuits. The main two types of accelerators are: a)accelerators of a direct action and b) accelerators of continuous action. One of the main type of accelerator of a direct action is a Van de Graaf accelerator. It accelerates charge particles by electrostatic field. Typically the energy about 2-5 MeV in a VdG accelerator can be achieved for single charged ions. This device has found widespread use in materials science, radiation physics and industry.

Fig.10.1. A simple scheme of a Van de Graaff accelerator

А typical design of Van de Graaf accelerator, which was invented in 1929, is a type of high –voltage electrostatic generator that serves as a type of particle accelerator. The principle of operation of the VdG accelerator. A high potential difference is built up and maintained on a smooth conducting surface by the continuous transfer of positive static charges from a m oving belt to the surface. When used as a particle accelerator an ion source is located inside the high-voltage terminal . Ions are accelerated from the source to the target by the electric voltage between the high-voltage supply and ground. 82

Linear particle accelerators All linear accelerators are of continuous action. In linear accelerator (linac), particles are accelerated in a st raight line with a target of interest at one end. They are also used to provide an initial low-energy kick to particles before they are injected into circular accelerators. Linear high-energy accelerators use a linear array of plates (or drift tubes) to which an alternating high-energy field is applied. As the particles approach a p late they are accelerated towards it by an opposite polarity charge applied to the plate. As they pass through a hole in the plate, the polarity is switched so that the plate now repels them and they are now accelerated by it towards the next plate. Normally a st ream of "bunches" of particles are accelerated, so a carefully controlled AC voltage is applied to each plate to continuously repeat this process for each bunch. Linear accelerator are very often used in material science as sources of fast electrons in experiments and technological operations. Circular or cyclic accelerators In the circular accelerator, particles move in a circle until they reach sufficient energy. The particle track is typically bent into a circle using electromagnets. The advantage of circular accelerators over linear accelerators (linacs) is that the ring topology allows continuous acceleration, as the particle can transit indefinitely. Another advantage is that a circular accelerator is relatively smaller than a linear accelerator of comparable power (i.e. a linac would have to be extremely long to have the equivalent power of a circular accelerator). Depending on the energy and the particle being accelerated, circular accelerators suffer a d isadvantage in that the particles emit synchrotron radiation. When any charged particle is accelerated, it emits electromagnetic radiation and secondary emissions. As a p article traveling in a c ircle is always accelerating towards the center of the circle, it continuously radiates towards the tangent of the circle. This radiation is called synchrotron light and depends highly on t he mass of the accelerating particle. For this reason, many high energy electron accelerators are linacs. Certain accelerators (synchrotrons) are however built specially for producing synchrotron light (X-rays). Since the special theory of relativity requires that matter always travels slower than the speed of light in a vacuum, in high-energy accelerators, as the energy increases the 83

particle speed approaches the speed of light as a limit, never quite attained. Therefore particle physicists do not generally think in terms of speed, but rather in terms of a p article's energy or momentum, usually measured in electron volts (eV). An important principle for circular accelerators, and particle beams in general, is that the curvature of the particle trajectory is proportional to the particle charge and to the magnetic field, but inversely proportional to the (typically relativistic) momentum. Cyclotrons The earliest circular accelerators were cyclotrons, invented in 1929 by Ernest O. Lawrence at the University of California, Berkeley. Cyclotrons have a single pair of hollow 'D'-shaped plates to accelerate the particles and a si ngle large dipole magnet to bend their path into a circular orbit. It is a characteristic property of charged particles in a u niform and constant magnetic field B that they orbit with a constant period, at a frequency called the cyclotron frequency, so long as their speed is small compared to the speed of light c. This means that the accelerating D's of a cy clotron can be driven at a constant frequency by a radio frequency (RF) accelerating power source, as the beam spirals outwards continuously. The particles are injected in the centre of the magnet and are extracted at the outer edge at their maximum energy. Cyclotrons accelerate charged particles using a high-frequency, alternating voltage (potential difference). A perpendicular magnetic field causes the particles to spiral almost in a ci rcle so that they re-encounter the accelerating voltage many times. Cyclotrons reach an energy limit because of relativistic effects whereby the particles effectively become more massive, so that their cyclotron frequency drops out of synch with the accelerating RF. Therefore simple cyclotrons can accelerate protons only to an energy of around 15 million electron volts (15 MeV, corresponding to a speed of roughly 10% of c), because the protons get out of phase with the driving electric field. If accelerated further, the beam would continue to spiral outward to a larger radius but the particles would no longer gain enough speed to complete the larger circle in step with the accelerating RF. Cyclotrons are nevertheless still useful for lower energy applications.

84

Fig.10.2. A cyclotron’s scheme. 1 – duants, 2 – a source of charged paricles, 3 – trajectory of a particle.

The electrodes must be placed into a vacuum chamber, which is flat and placed in a narrow gap between the two poles of a large magnet. In the cyclotron, a high-frequency alternating voltage applied across the "D" electrodes (also called "dees") alternately attracts and repels charged particles. The particles, injected near the center of the magnetic field, increase in speed (and therefore energy) only when passing through the gap between the electrodes. The perpendicular magnetic field (passing vertically through the "D" electrodes), combined with the increasing energy of the particles forces the particles to travel in a spiral path. With no c hange in energy the charged particles in a magnetic field will follow a circular path. In the cyclotron, energy is applied to the particles as they cross the gap between the dees and so they are accelerated (at the typical sub-relativistic speeds used) and will increase in mass as they approach the speed of light. Either of these effects (increased velocity or increased mass) will increase the radius of the circle and so the path will be a spiral. (The particles move in a spiral, because a current of electrons or ions, flowing perpendicular to a magnetic field, experiences a force perpendicular to its direction of motion. The charged particles move freely in a vacuum, so the particles follow a spiral path.) 85

The radius will increase until the particles hit a target at the perimeter of the vacuum chamber. Various materials may be used for the target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis. The results will enable the calculation of various properties, such as the mean spacing between atoms and the creation of various collision products. Subsequent chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target. Uses of the cyclotron For several decades, cyclotrons were the best source of highenergy beams for radiation materials science and nuclear physics experiments; several cyclotrons are still in use for this type of research. Advantages of the cyclotron • Cyclotrons have a single electrical driver, which saves both money and power, since more expense may be allocated to increasing efficiency. • Cyclotrons produce a continuous stream of particles at the target, so the average power is relatively high. • The compactness of the device reduces other costs, such as its foundations, radiation shielding, and the enclosing building.

Fig.10.3. Tracks of heavy ions in condensed matter.

When high-energy heavy ions impinge on m atter they travel a certain distance and slow down by transferring their energy (mostly) to the electrons. For example, the range of 8 MeV/ nucl Xe ion in a polymer is about 0.1 mm. As a result, a v ery small volume (like a 86

tube with a length of 0.1 mm and a radius of 7 nm) has to dissipate this energy. When the matter has a crystalline structure, the thermal shock leaves amorphous track behind, which is shown in figure. In the case of a plastic all long polymer strings will be broken and lighter molecules will be left along the tracks. These smaller molecules are easy to flush out in alcohol or can be etched by alcohol solutions. This is usually used in radiation etching technologies. When well controlled 3 dimensional structures are required one has to use masks. One can use masks during etching or during the irradiation. The easiest of the two ways is to first irradiate the complete structure. After this a lithographic mask can be mounted on the surface. It is then impossible for the etchant to reach the pores under this mask, allowing only the required structure to be etched out. The main disadvantage of this technique is that the complete structure contains latent tracks, diminishing material properties. Using a m ask during the irradiation does solve this problem. These masks need an aspect ratio comparable with the stuctures that are going to be produced, making them rather expensive. The ion track technique actually introduces an anisotropy that can be determined by the user, while normally this is determined by the crystal structure.

Fig.10.4. Radiation etching operations

87

accelerator propel Electric field

ускоритель Приводить в движение Электрическое поле

contain

удерживать

linear

линейный

circular

круговой

strip

обдирать

Drift tube

Пролетная трубка

bunch

сгусток

cyclotron

циклотрон

spiral

спираль

Light particles

Легкие частицы

Heavy particles

Тяжелые частицы

LECTURE 11 Computer simulation and quantum mechanical calculations 1. Introduction (раздел для самостоятельного перевода) Carbon nanostructures especially graphene and carbon nanotubes attract great attention of scientists because of their unique mechanical and physical properties. As you know, graphene is a single layer of carbon atoms arranged in a chicken-wire-like hexagonal lattice and in spite of its recent availability for experimental investigations it is an object of intensive investigations, because of amazingly wide field of its potential applicability: electronics, sensors, materials science, biology etc. In particular, graphene and few layer graphene fragments as well as carbon nanotubes can be used in production of composites, based on metal, ceramic, polymer matrices, filled with graphene’s or few layer graphene fragments as el ements of reinforcement. Obviously, the main goal of using graphene or nanotubes in making composites is using their extremely high mechanical characteristics in combination with low weight. It should be noticed, that many difficulties concerning graphene’s applications originate from its surface chemical inertness. In other words, the sp2 electron structure of ideal graphene often results in very low binding energy between graphene’s surface and atoms of many elements. It is one of the obstacles for modifying and applications of graphene in production of electronic devices, when controllable electronic properties are needed. Besides, it results in poor interfacial bonding of the graphene fragments with matrices in composite materials and with sliding between few layer graphene sheets under stressed state. Moreover, today’s technologies especially in the field of materials science need much more wide area of possible compositions and special materials. It was reasonable to suppose, that radiation defects may essentially improve binding ability of graphene with atoms of other elements due to production of additional chemical bonds. It is especially important for application of graphene species in R&D of composites. Moreover defects in such structures may improve mechanical 89

properties by linking reinforcing carbon nanoelements to each other and by increasing the strength and stiffness of the composite. Unfortunately, it is not yet well understood which kinds of stable radiation defects and their complexes can exist in graphene and its derivatives. Obviously, it is not easy to create definite types of radiation defects and perform direct studies of them in nanoobjects in direct laboratory experiments. In this situation computer simulation of radiation defects in graphene- and relative nanostructures becomes of great importance. This chapter presents some introduction into known techniques of computer simulation and some examples of calculations of some possible kinds of stable radiation defects in graphene, and more complex configurations, involving atoms of light metals: Be and Al, which are linking with radiation defects. 2. Computer simulation techniques 2.1. Molecular dynamics (highly simplified description of the molecular dynamics). Molecular dynamics (MD) is a computer simulation of physical movements of atoms and molecules, so that MD allows to calculate dynamical processes in many-atomic systems. The atoms and molecules are allowed to interact for a period of time giving a view of the motion of the atoms. In the most common version the trajectories of molecules and atoms are determined by numerically solving the Newton’s equations of motion for a system of interacting particles, where forces between particles and potential energy are defined by computational calculations. The MD method is based on a knowledge of a potential energy U(rij) of an atom i in the potential field created by others atoms (j) of the system . (Молекулярная динамика (МД) это метод компьютерного моделирования движения и расчета динамических процессов в многоатомных системах. Атомам и молекулам предоставляется возможность взаимодействовать в течение периода времени, дающего возможность увидеть их движение. В наиболее распространенной простой версии МД траектории атомов и молекул определяются путем численного решения уравнений движения Ньютона для системы взаимодействующих частиц, при этом силы между частицами и потенциальная энергия определяются компьютерным расчетом. МД основывается на знании потенциальной 90

энергии U(rij) атома i в потенциальном поле созданном другими атомами (j) системы).

 ∂U ij Fi = −∑  ∂ri j  ∂U ij d 2 ri − ∑  = mi ⋅ 2 dt j ≠ i ∂ri

(1)

(2)

Molecular dynamics is a simulation of the time-dependent behavior of a molecular system, such as v ibration of atoms or Brownian motion. It requires a way to compute and monitor the energy of the system. In general, the steps in a molecular dynamics techniques of an atomic system are as follows: 1. Choosing set of initial positions for the atoms. (Выбор массива начальных положений атомов) 2. Choosing set of atom velocities ( for example, may be chosen Boltzmann distribution). (Выбор массива скоростей атомов, например это может быть распределение Больцмана - Максвелла) 3. The program compute the forces on each atom, accelerations, velocities. (Программа рассчитывает силы, действующие на каждый атом, ускорения, скорости). 4. Compute new positions for the atoms after a short time: time step. It is a feature of a numerical integration of Newton's equations of motion. (Рассчитываются новые положения атомов через короткое время: временной шаг. Это характерный параметр численного интегрирования уравнений движения). 6. Massive of new positions treated as the initial one. Repeat steps 3-4. (Массив новых координат подставляется в качестве исходного. Повторяются шаги 3-4,). 7. Repeat this iteration long enough for the system. (Такие итерации для системы повторяются достаточно долго). 8. After reaching the equilibrium, the program begins saving the atomic coordinates every few iterations. (После достижения равновесия программа начинает сохранять атомные координаты через несколько итераций). 91

9. Continue iterating and saving data until enough data have been collected to give results with the desired accuracy. (Итерации выполняются, пока не набирается достаточное количество данных чтобы получить результат с нужной точностью). 10. Analyze the trajectories and coordinates to obtain all information needed about the system. It should be noticed, that the a value of a time step is very important parameter of calculation. If a time step is chosen too large, it cause atoms to move too far along a given trajectory, thus poorly simulating the motion. If a time step is too short it will increase time of calculation without positive result. One general rule of is that the time step should be one order of magnitude less than the timescale of the shortest motion (vibrational period or time between collisions). In this case a time step usually is on the order of units of femtoseconds with acceptable accuracy of calculations. The algorithm described above is for a system with a co nstant volume, number of particles, and temperature. It is also possible to set up a calculation in which the velocities are rescaled slightly at each step to simulate a changing temperature. Raising the temperature very slowly fixes possible problem but can lead to extremely long simulation times. In this chapter well known commonly used Monte Carlo calculations are not considered.  For equations above, the trajectory ri (t ) can be obtained by integration of (2). Because a sy stem of interest in many cases consists of a vast number of atoms (103 – 106) it is impossible to find the properties of such complex system analytically. However, long MD simulations generate errors in numerical integrations. That’s why numerical integration methods always require special algorithms. There are several algorithms available for performing the numerical integration of the equations of motion. The well known Verlet algorithm is widely used because it requires a minimum amount of computer memory and time. One can see that all equations of MD involve Uij as a m ain function. Uij - a potential energy of pair interaction between atoms in the system of interest. For example, one of the first known pair potentials is the Lennard –Jones potential, which originates from 92

well known van der Waals interactions. (Видно, что все уравнения для метода МД включают U как основную функцию для расчета. U – потенциальная энергия атома с индексом i в поле, создаваемом другими атомами системы. Например, один из первых известных парных потенциалов – потенциал ЛеннардаДжонса, ведущий историю от описания сил Ван дер Вальса). LJ potential usually is written as

U (rij ) =

A B − 6 12 rij rij

(3)

In (3) A,B >0 and rij - the distance between atoms i and j. Now there are many other types of potentials for MD usage and some of them are much more complicated than LJ potential. For example, well known the Tersoff potential, which is widely used by MD simulation and calculations of carbon materials and structures. And moreover, some potentials (like Tersoff) are multi-particle potentials. (В (3) параметры А,В > 0, rij - расстояние между атомами i,j системы. Сейчас имеется множество других типов потенциалов для использования в МД и некоторые из них существенно сложнее, чем ЛД. Например, хорошо известен потенциал Терсоффа, который широко используется для МД расчетов углеродных структур. Кроме того, этот потенциал является многочастичным). Today many MD programs use actually different forms of quantum mechanical approaches in order to reach more adequate description of multiatomic systems. (В настоящее время многие МД программы используют различные формы квантово механические подходов, что улучшает адекватность описания многоатомных систем). 2.2. Molecular orbitals theory In many important problems of materials science physicists must calculate energy and structural characteristics of atomic and molecular systems with taking into account possible chemical interactions between atoms. But these problems are being much more complicated than common MD simulation. Such problems demand 93

using quantum mechanical approaches. One must take into account that calculations of molecular properties even for simplest systems are being much more complicated that for atoms. (Во многих важных задачах материаловедения физики должны вычислять энергию и структурные характеристики атомных и молекулярных систем, принимая во внимание возможные химические взаимодействия между атомами. Такие задачи требуют использования квантово-механических подходов. Нужно учесть, что при переходе к расчету свойств даже самой простой молекулы расчет резко усложняется по сравнению с атомными расчетами). In chemistry, a molecular orbital (or MO) is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first used in English by Robert S. Mulliken as the English translation of Schrödinger's 'Eigenfunktion'. It has since been equated with the "region" generated with the function. Molecular orbitals are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory. Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. 2.3. Linear combinations of atomic orbitals (LCAO) (Линейные комбинации атомных орбиталей ЛКАО) Molecular orbitals were first introduced by Friedrich Hund and Robert S. Mulliken in 1927 and 1928. The linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones. They are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory. Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the 94

same orbital, the Pauli principle demands that they have opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do n ot have orbitals (see configuration interaction). Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule’s constituent atoms. Similar to an atomic orbital, a Schrodinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the molecular Schrodinger equations. For simple diatomic molecules, the obtained wavefunctions are represented mathematically by the equations and

Ψ = caψa + cbψb Ψ* = caψa - cbψb

where Ψ and Ψ* are the molecular wavefunctions for the bonding and antibonding molecular orbitals, respectively, ψa and ψb are the atomic wavefunctions from atoms a and b, respectively, and ca and cb are adjustable coefficients. These coefficients can be positive or negative, depending on the energies and symmetries of the individual atomic orbitals. As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and as a co nsequence, molecular orbitals are formed between the two atoms. The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals. (Молекулярные орбитали были впервые введены Ф.Хандом и Милликеном в 1927 и 1928 годах. Линейная комбинация атомных орбиталей ( приближение ЛКАО) была введена в 1929 г. Леннардом Джонсом. Эта концепция МО неоценима для получения простого представления и для приближенного построения молекулярных электронных состояний, которые формируются при образовании связей между атомами, составляющими молекулу. Линейные комбинации (суммы или разности) атомных волновых функций дают приближенное решение уравнения 95

Шредингера для молекулы.Для простых двухатомных молекул такие комбинации имеют вид и

Ψ = caψa + cbψb Ψ* = caψa - cbψb

где Ψ и Ψ* представляют собой волновые функции связывающих и антисвязывающих электронных орбиталей в молекуле, ψa и ψb - соответственно атомные волновые функции атомов a и b , и ca и cb - варьируемые коэффициенты. Эти коэффициенты могут быть положительными или отрицательными в зависимости от энергий и симметрий отдельных атомных орбиталей. Когда два атома сближаются их электронные атомные орбитали перекрываются, образуя область с повышенной электронной плотностью и, как следствие, между атомами формируются молекулярные орбитали. Можно использовать представление, что атомы связываются вместе электростатическими силами притяжения между положительно заряженными ядрами и отрицательно заряженными электронами связывающих молекулярных орбиталей между атомами). 2.3.1. Sigma and Pi Labels for MOs The type of interaction between atomic orbitals can be further categorized by the symmetry labels: σ (sigma) and π (pi). (Характер взаимодействия между атомными орбиталями может быть в дальнейшем классифицирован двумя типами: σ (sigma) и π (pi)). a) σ-symmetry A MO with σ-symmetry results from the interaction of either two atomic s-orbitals or two atomic pz-orbitals. A MO will have σsymmetry if the orbital is symmetrical with respect to the axis joining the two nuclear centers, the internuclear axis. This means that rotation of the MO about the internuclear axis does not result in a phase change. (МО с σ-симметрией возникает при взаимодействии двух атомных s – орбиталей или двух атомных pz – орбиталей. МО имеет σ – симметрию, если она симметрична относительно оси, соединяющей центры атомов. Это означает, что вращение МО относительно межатомной оси не меняет фазу 96

волновой функции). A σ*-orbital, sigma antibonding orbital, also maintains the same phase when rotated about the internuclear axis. The σ*-orbital has a n odal plane that is between the nuclei and perpendicular to the internuclear axis. (A σ*-orbital, sigma антисвязывающая орбиталь, также сохраняет фазу при вращении вокруг межатомной оси. При этом σ*-orbital имеет узловую плоскость, расположенную между ядрами атомов, перпендикулярно оси связи).

Fig.11.1. For σ – and σ * - orbitals rotation about the interatomic axis doesn’t change the phase of wave function

Example: In the hydrogen atom, the 1s atomic orbital has the lowest energy, while the remainder (2s, 2px, 2py and 2pz) are of equal energy (ie.degenerate), but for all other atoms, the 2s atomic orbital is of lower energy than the 2px, 2py and 2pz orbitals, which are degenerate. In atoms, electrons occupy atomic orbitals, but in molecules they occupy similar molecular orbitals which surround the molecule. The simplest molecule is hydrogen, which can be considered to be made up of two seperate protons and electrons. There are two molecular orbitals for hydrogen, the lower energy orbital has its greater electron density between the two nuclei. This is the bonding molecular orbital - and is of lower energy than the two 1s atomic orbitals of hydrogen atoms making this orbital more stable than two seperated atomic hydrogen orbitals. The upper molecular orbital has 97

a node in the electronic wave function and the electron density is low between the two positively charged nuclei. The energy of the upper orbital is greater than that of the 1s atomic orbital, and such an orbital is called an antibonding molecular orbital. Normally, the two electrons in hydrogen occupy the bonding molecular orbital, with anti-parallel spins. If molecular hydrogen is irradiated by ultra-violet (UV) light, the molecule may absorb the energy, and promote one electron into its antibonding orbital (σ*), and the atoms will seperate. The energy levels in a hydrogen molecule can be represented in a diagram - showing how the two 1s atomic orbitals combine to form two molecular orbitals, one bonding (σ) and one antibonding (σ*). This is shown below - by clicking upon either the σ or σ* molecular orbital in the diagram - it will show graphically in a window to the right:

Fig.11.2. A representation of the energy levels of the bonding and antibonding orbitals formed in the hydrogen molecule

The diagram in the fig. 11.2 i s a representation of the energy levels of the bonding and antibonding orbitals formed in the hydrogen molecule. Two molecular orbitals were formed, one antibonding (σ*) and one bonding (σ).The two electrons in the hydrogen molecule have antiparallel spins. Notice that the σ* orbital is empty and has a higher energy than the σ orbital. 98

b) π -symmetry A MO with π –symmetry results from the interaction of either two atomic px-orbitals or py-orbitals. A MO will have π-symmetry if the orbital is asymmetrical with respect to rotation about the internuclear axis. This means that rotation of the MO about the internuclear axis will result in a phase change. A π*-orbital, pi antibonding orbital, will also produce a phase change when rotated about the internuclear axis. The π *-orbital also has a nodal plane between the nuclei.

Fig.11.3. For π- and π * – orbitals rotation about the interatomic axis changes the phase of wave function

Раздел для самостоятельного перевода. When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding. Bonding MOs: • Bonding interactions between atomic orbitals are constructive (in-phase) interactions. 99

• Bonding MOs are lower in energy than the atomic orbitals that combine to produce them. Antibonding MOs: • Antibonding interactions between atomic orbitals are destructive (out-of-phase) interactions. • Antibonding MOs are higher in energy than the atomic orbitals that combine to produce them. Nonbonding MOs: • Nonbonding MOs are the result of no interaction between atomic orbitals because of lack of compatible symmetries. • Nonbonding MOs will have the same energy as t he atomic orbitals of one of the atoms in the molecule.

LECTURE 12 Computer Simulation of Radiation Defects in Carbon Nanostructures The first model which is considered in this chapter is a si mple configuration, which consists of a graphene sheet and a carbon atom adsorbed with it. In this case no chemical bond between graphene and C atom exists. This kind of interaction refers to well known van der Waals forces, which were considered above. These interactions are weak and insignificant in our common life, but their role increases dramatically among the nano-scaled objects. One of the important features of them - the additivity i.e. every particle of the system makes its contribution into the total interaction energy. Therefore, they can be relatively large for nanosystems, involving 102 – 103 atoms or molecules. But van der Waals interactions are not accounted by the use widespread computer techniques like molecular orbital linear combination of atomic orbitals by self consistent field (MO LCAO SCF) or density functional theory (DFT). Therefore, in this problem the method of molecular dynamics (MD), which is recognized as the effective tool for similar systems, was chosen. A graphene sheet for MD simulation of single- and diatomic defects on the undamaged structure was built of 78 atoms. Van der Waals interaction between adsorbed atoms and graphene was described by well known Lennard-Johns potential in the usual general form (3).

Fig. 12.1. Configuration of a single adsorbed atom on a graphene structure

Presented in Figure 12.1 is one of investigated defect configurations which is actually a single carbon atom, adsorbed on 101

the surface of the undamaged graphene sheet . The maximum value of the binding energy for the single adsorbed atom E = – 0.18 eV at a distance Z = 0.25 n m from the graphene plane. One of important characteristic is also the energy of carbon atom in the center point of graphene’s hexagon (Z = 0). This position was found to be very unstable with the positive energy equals to E0 = 11.4 eV. It means also, that the graphene sheet is impermeable for displaced carbon atoms with energies lower than E0.

Fig 12.2. Configuration of a dumbbell defect on a graphene (N=78) structure

Fig.12.2 presents a configuration of a m ore complicated, twoatom defect which is like a d umbbell with a symmetrical configuration of the atoms d1 and d2 normal to the graphene sheet. Calculations of this defect were performed by MD, using the LJ potential. To begin, in all cases the minimum energy lateral position of the atoms adsorbed, had been found out at the normal axis of symmetry of hexagon (Z-axis). Further we performed calculations with movement of atoms along the Z-axis. Results of calculations of the binding energies for these defects as a function of a distance Z over the center of hexagon are presented in Figure 3. It can be seen, that there is an interval between approximately 2 a nd 3 angstroms that exhibits a trough with a negative energies, which is evidence of the existence of stable binding states. Low values of bonding energies testify of the vdW nature of the interaction. The black marks – the single atom configuration (see Figure 12.1) , the light marks – the dumbbell configuration (see Figure 12.2) 102

Fig. 12.3. The binding energy for the single atom and the dumbbell defect as a function of a distance Z over the center of hexagon.

a

b

Fig. 12.4. The electron charge distribution for the dumbbell presented in Fig.2. Density of electron charge equals: a) 0.02 el / Ǻ3 , b) 0.5 el / Ǻ3 .

Figure 12.4 illustrates the results of calculations of electron charge distribution for the dumbbell presented in Figure 12.2, performed by MO LCAO method. These calculations were performed in order to check our assumption about vdW interaction between atoms adsorbed and graphene. One can see some overlapping of electron charge only by very low level of electron density (Figure 4,a). And, obviously, there are no s igns of overlapping of electron charge at high level of electron density, which could be responsible for some kind of bonding between graphene and atoms adsorbed. One can see w ell distinguished electron charge clouds, obviously closed on graphene and d1 and d2 atoms with a gap between them. At the same time graphene’s 103

structure is linked with dense electron clouds, which provided strong bonding. It proves that weak bonding interaction for the defects presented above is controlled by vdW forces. It is unlikely, that such defects can be useful for essential modifying of mechanical properties of composite materials. 2.1.Vacancies in graphene It is known very well, that irradiation of graphene-based electronic devices by fast electrons or ions will be always accompanied by creation of atom vacancies. Therefore, it is very important to know about changes in electronic properties of graphene fragments which should be expected under irradiation and about how they depend on de fect concentration. For such estimation large enough graphene’s fragment (N=208) has been used.

Fig. 12.5. Graphene for calculations with edge-bonds shut by H-atoms

In order to avoid end-effects by such calculations, free end-bonds of carbon atoms must be shut with hydrogen atoms. Afterwards, in order to take into account the possible effect of a larger size of a real graphene sheet, which can restrict the atoms neighboring to the vacancy, all edge atoms of graphene must be fixed at their initial positions. After that simulated and calculated one-, two- and three – vacancy configurations with using in all cases a procedure of energy minimization. It was revealed, that in all cases, after energy optimization the vacancy zone increased so that all the three twocoordinated atoms, neighboring the vacancy, were shifted nearly symmetrically: all three distances between surrounding atoms 1-2, 2-3, 3-1 (Figure 12.6) become as l arge as 2 .76 Ǻ instead of usual value 2.46 Ǻ in the initial state. 104

Fig. 12.6. Vacancy zone in graphene after the relaxation

Figure12.7 presents a configuration of a graphene with 3 single vacancies displayed by the electron charge distribution.

Fig. 12.7. Graphene with 3 single separated vacancies in the structure

2.2. Radiation defects with strong bonding As the next step one can see energetic and structural characteristics of 3D defect configuration presented in Figure 12.8. This type of radiation defect, which involves two carbon atoms arranged symmetrically over a v acancy can be named «dumbbell», like to configuration presented in Figure 2.

Fig. 12.8. The complex radiation defect, involving a vacancy and a dumbbell configuration.

105

But in this case the two carbon atoms (d1,d2) of the dumbbell are chemically bonded with free bonds of atoms, neighboring at the vacancy. One can see from the graph in Figure 12.9 , that there is a strong bonding.

Fig. 12.9. The binding energy for the dumbbell placed over a vacancy as a function of the distance Z over the graphene sheet

Obviously, the elastic properties of composite materials and their uniformity are of great importance in using composite materials. The Eb - Z curve in Figure 12.9 can be used for estimation of elastic characteristics of the C-C dumbbell defect along the graphene sheet (under shear stress). One can see, that the maximum slope of the curve is near the point Z = 1.3 Ǻ. The numerical estimation by using ∆E ∆Z at this point with small segments gives the value 0.5 TPa. The maximum binding energy of the dumbbell over the relaxed vacancy was obtained as large as -10.0 eV and the corresponding distance between the graphene’s plate and atoms equals 0.7 A. Figure 12.10 presents a typical configuration of the bridge-like linking radiation induced defect that can be produced under ion-, fast electrons or neutron irradiation. 106

Fig. 12.10. A bridge-like bonding defect linking two single-walled carbon nanotubes

Fig.12.10 presents a typical the couple-cluster configuration from two carbon nanotubes (6,6) with single vacancies in structures. The nanotubes are oriented in such a way that vacancies are arranged to be opposed to each other. This situation is typical for irradiation of nanotubes clusters with fast particles. The configuration was constructed and calculated using energy minimization. ( Рис.12.10 представляет конфигурацию кластера из двух нанотрубок (6,6) с одиночными вакансиями в структуре. Нанотрубки ориентированы таким образом, что вакансии находятся друг против друга. Это типичная ситуация, которая возникает при облучении быстрыми частицами кластеров нанотрубок. Конфигурация была сконструирована и рассчитана с использованием процедуры минимизации полной энергии системы). After minimization procedure the binding energy of the configuration was obtained and yielded values as large as 3 .9 eV for every bond of bridge-like configuration. It is a large value, when considering, that in the sp2 structure every bond equals about 5.4 eV. Figure 12.11 presents a bridge-like defect in the case of a twowalled carbon nanotube with the inner tube (5,0) and the outer tube (14,0), which were chosen for the inside between –distance close to graphite interlayer distance reasons. Diameters of CNT’s (5,0) and (14,0) are equal to 3.9 A and 10.96 A accordingly. Vacancies were created in both inner (5,0) and outer (14,0) nanotubes to be close to 107

each other, for we supposed this configuration as a result of irradiation. An interstitial atom i was placed between vacancies. The configuration of defect after relaxation is shown in Figure 12.11. (Рисунок 11 представляет мостиковый дефект для случая двухслойной нанотрубки с внутренней трубкой типа (5,0) и внешней типа (14,0). Вакансии в обеих трубках создавались опять таки исходя из вероятного результата предполагаемого облучения быстрыми частицами: напротив друг друга. Выбитый атом размещался в пространстве между трубками, непосредственно между вакансиями. Конфигурация дефекта после релаксации показана на рис.12.11). One can see that some atoms, closest to vacancies after relaxation have moved slightly into the gap between the nanotubes. This movement is necessitated to facilitate the creation of the bonding bridge between the inner and outer nanotubes. (можно видеть, что часть атомов слегка вошла в пространство между трубками, что необходимо для формирования мостиковых связей между внутренней и внешней трубками).For example, the distance between atoms 1-2 equals 2.49 A, between i - 1: 1.56 A, i - 2: 1.49 A. In this case the angle between bonds is very near to 180o. The total binding energy of the i atom equals -4.7 eV.

Fig. 12.11. The electron charge distributions by the density equals 0.5 el / A3 (b).

Bridge-like bond between fullerens. Figure 12.12 presents possible bridge-like defect linking two fullerenes together. This configuration of defect, involving three bonds, when atoms 1 and 2 are being from the structure of one 108

fullerene. It should be noticed, that the angles between the bonds with the i in the top in this case are close to 120o. The total binding energy is equal to -10.5 eV while the binding energy for the i -3 pair equals 3.3 eV.

Fig. 12.12. Electron charge distribution at the electron density equals to 1.4 el/A3.

It should be noticed that the electron charge distribution presented in Fig.12.12 proves formation of fast bonds between fullerenes. for a bridge-like defect with three bonds at the electron density equals to 1.4 el/A3. No doubt, graphene fragments also can be used as reinforcement elements in different matrices. But this technology demands strong bonds between few layer graphene sheets and possible bonds of metal atoms with defect sites. An example of configurations which can be used to perform these new types of composites are given in Fig.12,13 and 12.14. So that it was interesting to simulate at least small graphene cluster for performing the similar calculations. Therefore a cluster with the configuration presented in Figure 12.13 was simulated. Two graphene sheets were arranged in the usual bilayer graphite-like configuration. The interstitial atom i was placed between them. One can see from figures 12.13 and 12.14 that after relaxation the center parts of graphenes near the defect significantly entered into the gap. Distances between atoms 1-2 and 3-4 turned out equal nearly 1.43 A, i.e. usual bond length for graphitic structure. It means, that in the vacancy area instead of one (primary) bridge-like defect, three defects appeared, which link graphene plains together by fast covalent bonds. 109

Fig. 12.13. The bonding radiation defects in a two-layer grapheme

The total binding energy for this defect configuration was calculated as large as -11.3 eV.

Fig. 12.14. Bridge-like radiation defect in two- layer graphene with Al atoms attached

a

b

c

Fig. 12.15. Configurations of Be atoms bonded with a vacancy. a) a stable position of the single Be atom in the graphene sheet. The binding energy Eb equals 2.6 eV; b) configuration of an initially flat Be-cluster over vacancy after optimization. The binding energy of the cluster with graphene was obtained as large as 7.2 eV; c) the electron charge distribution in the area of the metal cluster – vacancy with a density of charge 0.2 el / Ǻ 3 .

110

GLOSSARY alloy Alpha-, beta-, gamma radiation Artificial (induced) radioactivity Austenitic (ferritic, martensitic) stainless steel Asymmetry (fission)

сплав α,β,γ - излучение Искусственная (наведенная) радиоактивность Аустенитная нержавеющая сталь

Atom at rest

Покоящийся атом

backscattering band

обратное рассеяние Зона, полоса, диапазон

bar

Бар (105 Н/м2 )

Bridge-like defect

Мостиковый дефект

cave, cell (hot cave)

Coolant

полость, камера, (горячая камера для радиоактивных материалов) цепь Камера, вакуумная камера заряд Канал, упругий канал (ядерной реакции) Охладитель

creep Curie (Ci) , unit of activity 1Ci=3.7 1010 decay / s Dumbbell

ползучесть Кюри, единица активности: 1К = 3.7 расп сек-1 Гантель – конфигурация дефекта

Decay constant λ Dislocation loop doping

Постоянная распада

ductility dumbbell

Пластичность (реже вязкость) Гантель (также и тип структурного дефекта) Энергия смещения Эрг – единица энергии в системе СГС Множитель, коэффициент Усталость металлов

chain Chamber, vacuum chamber charge Сhannel , elastic channel

Energy of displacement, Ed Erg – unit of energy in cgs factor Fatigue of metals

Асимметрия (деления ядра)

Дислокационная петля легирование

111

feature Frenkel pair grain boundary segregation Geiger counter Hydrogen embrittlement Impact toughness Interstitial atom Ionizing radiation irradiation

Особенность, характерное свойство Пара Френкеля Зернограничная сегрегация Счетчик Гейгера Водородное охрупчивание Ударная вязкость межузельный атом Ионизирующее излучение облучение

Life span

Продолжительность жизни

Lead glass

Свинцовое стекло, которое используется в горячих камерах, содержит свинец для защиты от излучений Манипулятор («искусственная рука») - устройство для дистанционной работы с радиоактивными материалами в горячих камерах. Многоатомная система

manipulator

Many-atomic system Moderator Neutron radiation

Замедлитель – материал, использующийся для замедления нейтронов в тепловых реакторах Нейтронное излучение

Point defect

Точечный дефект

Premier knocked atom (PKA) Radioactive wastes Radioisotope thermoelectric generator Reflector Refractory metals

Первично выбитый атом (ПВА) Радиоактивные отходы Радиоизотопный термоэлектрический генератор отражатель Тугоплавкие металлы

Segregation of impurity (RIS segregation) Semiempirical method

Сегрегация примеси (радиационно-индуцированная сегрегация) Полуэмпирический метод

Set of data

Набор данных 112

Structural materials

Конструкционные материалы

strike

Ударять, попадать

Thermal neutrons cross section Threshold energy

Поперечное сечение поглощения тепловых нейтронов Пороговая энергия

trial

Испытание, проба

Two-particle Vacancy zone vitrification

двухчастичный Зона вакансии Остекловывание (при герметизации радиоактивных отходов) Радиоактивные отходы

Waste materials

LITERATURE 1.V.V.Gerasimov, A.S.Monakhov. Materials for nuclear engineering. 2nd Ed.M., 1982. 2. Ю.М.Широков и Н.П. Юдин. Ядерная физика, Уч. пос., 1972, 688 с. 3. В.Ф.Зеленский и др. Радиационные дефекты и распухание материалов. – Киев: Наукова Думка, 1998.-296с. 4. http://en.wikipedia.org/wiki/Gray_%28unit%29 5. David C. Young. Computational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems. Copyright ( 2001 J ohn Wiley & Sons, Inc.ISBNs: 0-471-33368-9 6. Practical surface analysis by Auger and X-ray electron spectroscopy. Ed. D.Briggs and M.P.Seach, 1983. 7. http://en.wikipedia.org/wiki/Radioisotope_thermoelectric_generator 8. "Voyager Mission Operations Status Reports". Voyager.jpl.nasa.gov web. Retrieved 24 July 2011. 9. An Overview and Status of NASA's Radioisotope Power Conversion Technology NRA, NASA, November 2005 10. http://www.totse.com/en/technology/space_astronomy_nasa/spacnuk e.html 11. Novoselov, K.; Geim A.; Morozov, S.; Jiang, D; Zhang, Y.; Dubonos, S.; Grigorieva, I.& Firsov,A.(2004). Electric field effect in atomically thin carbon films. Science, Vol. 306, pp.666-669, ISSN 00368075. 12. Elias,D.; Nair,R; Mohiuddin,T; Morozov, S.; Blake,P.; Halsall,M.; Ferrari,A.; Boukhvalov,D.; Katsnelson, M.; Geim,A. & Novoselov,K. (2009) . Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for Graphane. Science , Vol.323, pp.610–613. 13. Sofo,J.; Chaudhari A. & Barber,G. (2007). Graphane: a twodimensional hydrocarbon. Phys.Rev.,B75, pp.153401-153404, ISSN 09740546 . 14. Luo,Zh.; Yu,T.;Kim,K.; Ni,Zh.;You,Y.; Lim,S.; Shen,Z.;Wang ,S.& Lin,J. (2009). Thickness-Dependent Reversible Hydrogenation of Graphene Layers. ACS NANO, Vol.3, No 7, pp.1781-1788. 15. L. K. Mansur, "Void Swelling in Metals and Alloys under Irradiation: An Assessment of the Theory," Nucl. Technol. 40 (1978) 5-34 16. L. K. Mansur, "Mechanisms and Kinetics of Radiation Effects in Metals and Alloys," A chapter in the book, Kinetics of Non-Homogeneous Processes, edited by G. R. Freeman, Wiley-Interscience, New York 1987, pp. 377-463. 114

17. L. K. Mansur, "Theory and Experimental Background on Dimensional Changes in Irradiated Alloys," International Summer School on the Fundamentals of Radiation Damage, Urbana, Illinois, August 1993, J. Nucl. Mater. 216 (1994) 97-123. 18. Teweldebrhan D & Balandin A. (2009). Modification of graphene properties due to electron- beam irradiation. Appl.Phys.Lett., Vol. 94, 013101 19. Ilyin,A.; Daineko,E.& Beall,G. (2009). Computer simulation and study of radiation defects in graphene. Physica E, Vol.42, No pp. 67-69, ISSN 1386-9477. 20. Ilyin,A.; Guseinov,N.;.Nikitin, A & Tsyganov,I. (2010). Characterization of thin graphite layers and graphene with energy dispersive X-ray analysis. Physica E, Vol.42, No 8 , pp. 2078-2080. 21. Ilyin,A. (2010). Simulation of end-bridge-like radiation defects in carbon multi-wall nanotubes. Book of Abstracts of 10th International Conference on Computer Simulations of Radiation Effects in Solids, p.123, ISBN, Poland, Krakov, July 19-23, 2010. 22. Ilyin,A &.Beall,G. (2010). Computer simulation and study of bridge-like radiation defects in the carbon nano-structures in composite materials. Proceedings of NanoTech Conference, pp.312-315, ISBN 978-14398-3401-5, Annaheim, California, USA, June, 21-25, 2010. 23. Ilyin,A; Beall, G & Tsyganov,I. (2010). Simulation and Study of Bridge-Like Radiation Defects in the Carbon Nano-Structures. Journal of Computational and Theoretical Nanoscience , Vol. 7, No. 10 (Oct.,2010) ,pp. 2004-2007, ISSN 1546-1955. 24. P.J.F.Harris. Carbon nanotube composites. Intern. Mater. Reviews, V.49, N1, 2004, 31. 24. K.T.Kashyar and R.G.Patil. On Young’s modulus of multi-walled carbon nanotubes Bulletin of Materials Science, V.31, N 2, 2008, 185-187 25. H.Yanagi, Y.Kawai, T.Kita, S. Fujii, Y. Hayashi, A.Marario and T.Noguchi. Carbon nanotube/ aluminium composites as a novel field electron emitter. Jpn. J. Appl. Phys.45, 2006, L650-L653. 26. T.Laha, Y.Liu and A.Agarwal. Carbon nanotube reinforced aluminum nanocomposite via plasma and high velocity oxy-fuel spray forming. Journal of Nanoscience and Nanotechnology, V.7, 2007, 1-10. 27. V.M.K.Bagci, O.Gulseren, T.Yildirim, Z.Gedik, and S.Ciraci. Metal nanoring and tube formation on carbon nanotubes//Phys.Rev. B66, 2002, P.045409 . 28. M.G.Futa and P.C.Kelires . Simulations of composite carbon films with nanotube inclusions. Appl.Phys.Lett. 86, 2005, 191916

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29. A.Hashimoto, K.Suenaga, A.Gloter, K.Urita & S.Iijima, Direct evidence for atomic defects in graphene layers, Nature 430, 2004, 870-873. 30. A V Krasheninnikov, K.Nordland, M.Sirvio, E.Salonen, and J.Keinonen. Formation of ion –irradiation –induced atomic scale defects on walls of carbon nanotubes. Phys.Rev. B.63, 2001, P.245405 31. http://en.wikipedia.org/wiki/Breeder_reactor 32. http://www.nuc.berkeley.edu/designs/ifr/ 33. A.M.Ilyin, V.N.Golovanov. Investigation of the Grain Boundary Elemental Composition of the Low-Alloy Steel // Phys. Stat. Sol. 1996. V.153. 93. P.93-100. 34. A.M.Ilyin, V.N.Golovanov. Auger Spectroscopy Study of the Stress Enhanced Impurity Segregation in a Cr-Mo-V Steel// J. Nucl.Mater. 1996. 233-237. 233-235. 35. A.M.Ilyin.Some features of grain boundary segregation in sensitized austenitic steel. Journ.Nucl. Mater. 252 (1998) 168 36. A.M.Ilyin. Computer Simulation of Radiation Defects in Graphene and Relative Structures. In: «Graphene Simulation», «InTech», Ed. J. R. Gong, 2011, P. 39-52, ISBN 978-953-307-556-3. 37. A.M.Ilyin. Computer Simulation of Carbon- and Graphene-Metal Nanostructures. In: «Computer Simulation: Technology and Industrial Applications» «Nova_Publishers», Ed. B.Nemanjik, 2012, NY, USA.

Contents FOREWORD ..........................................................................................3 LECTURE 1. Radioactivity and units of measuring ..............................5 LECTURE 2. Radiation defects in materials ..........................................14 LECTURE 3. Nuclear fission reactors....................................................22 LECTURE 4. Structural materials of nuclear fission reactors ................40 LECTURE 5. Waste materials ...............................................................53 LECTURE 6. Passage of electromagnetic radiation through matter ......58 LECTURE 7. Materials of nuclear reactor and corrosion ......................63 LECTURE 8. Radiation embrittlement and swelling in structural materials .............................................................................70 LECTURE 9. Impurity and alloying segregation in materials ................76 LECTURE 10. Application of accelerators in radiation materials science .....................................................................................81 LECTURE 11. Computer simulation and quantum mechanical calculations ..........................................................................89 LECTURE 12. Computer simulation of radiation defects in carbon nanostructures .........................................................................101 GLOSSARY ...........................................................................................111 LITERATURE........................................................................................114

Учебное издание

Ильин Аркадий Михайлович РАДИАЦИОННЫЕ ЭФФЕКТЫ В МАТЕРИАЛАХ RADIATION EFFECTS IN MATERIALS Учебно-методическое пособие (на английском языке) Выпускающий редактор Г. Бекбердиева Компьютерная верстка С. Сарпековой Дизайнер обложки Р. Шангараев ИБ №6696

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