Physica status solidi / A.: Volume 85, Number 1 September 16, 1984 [Reprint 2021 ed.] 9783112501368, 9783112501351

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plxysica status solidi (a)

ISSN 0031-8965» -X- VOL. 85 • NO. 1 . SEPTEMBER 1984

Classification Scheme 1. Structure of Crystalline Solids 1.1 Perfectly Periodic Structure 1.2 Solid-State Phase Transformations 1.3 AlloysrMetallurgy 1.4 Microstructure (Magnetic Domains See 18; Ferroelectric Domains See 14.4.1) 1.5 Films 1.6 Surfaces 2. Non-Crystalline State 3. Crystal Growth 4. Bonding Properties 5. Mössbauer Spectroscopy 6. Lattice Dynamics. Phonons 7. Acoustic Properties 8. Thermal Properties 9. Diffusion 10. Defect Properties (Irradiation Defects See 11) 10.1 Metals 10.2 Non-Metals 11. Irradiation Effects (X-Ray Diffraction Investigations See 1 and 10) 12. Mechanical Properties (Plastic Deformations See 10) 12.1 Metals 12.2 Non-Metals 13. Electron States 13.1 Band Structure 13.2 Fermi Surfaces 13.3 Surface and Interface States 13.4 I m p u r i t y and Defect States 13.5 Elementary Excitations (Phonons See 6) 13.5.1 Excitons 13.5.2 Plasmons 13.5.3 Polarons 13.5.4 Magnons 14. Eleetrical Properties. Transport Phenomena 14.1 Metals. Semi-Metals 14.2 Superconductivity. Superconducting Materials and Devices 14.3 Semiconductors 14.3.1 Films 14.3.2 Surfaces and Interfaces 14.3.3 Devices. Junctions (Contact Problems See 14.3.4) 14.3.4 High-Field Phenomena, Space-Charge Effects, Inhomogeneities, Injected Carriers (Electroluminescence See 20.3; Junctions See 14.3.3) 14.4 Dielectrics 14.4.1 Ferroelectrics 15. Thermoelectric and Thermomagnetic Properties 16. Photoconductivity. Photovoltaic Effects 17. Emission of Electrons and Ions 17.1 Field Emission Microscope Investigations 18. Magnetic Properties 18.1 Paramagnetic Properties 18.2 Ferromagnetic Properties 18.2.1 Ferromagnetic Films 18.3 Ferrimagnetic Properties 18.4 Antiferromagnetic Properties (Continued on cover three)

phys. stat. sol. (a) 85 (1984)

Author Index G . A . ADEGBOYEGA M . ADOLF S. C. AGABWAL J . M . ALAMEDA J . A . ALONSO S. A . ALTEROVITZ V . M . ALYABIEV S . AMELINCKX K . P . AREFIEV D . A . ARONOV A . K . ARORA V . G . ARTYUSHENKO H . ATMANI Y . ATZRODT M . AUBIN S. A . AZIMOV

215 K81 297 511 423 69 11,315 29 K31 K159 491 167 399 K9 649 KL59

V . HARI BABU I . BAKER D . BALTRTJNAS A . BARBULESCU U . BARKOW A . BARTL J . H . BASSON B . A . BAUM G . BERGER H . BERGER K . - H . BERTHEL P . A . BESIRGANYAN V . A . BESPALOV U . BIRKHOLZ G . BLASEK M . G . BLAZHA R . BLINC H . BOOYENS S . BREHME W . BRUNNER G . H . BU-ABBUD W . BURCKHABDT P . BUSSEMER

265 481 K97 KL29 K77 257 243, 449 497 K9 45 KL75 349 K73 K81 473 553 409 243, 449 627 257 69 97 97

J . CABRERA-CANO J . CASTAING J . CERMÂK A . R . CHELYADINSKII V . CHERNYI V . G . CHUDINOV M . C. CONTRERAS J . W . CORBETT M . COUZI M . R . CZERNIAK

445 445 173 K43 627 105,435 511 K109 359 235

Y U . N . DALUDA M . DAVID

575 375

G . A . DENISENKO I . DIACONU U . DIETRICH R . DIETSCH K . DINI A . DOMÍNGUEZ-RODRÍGUEZ A . F . DUNAEV R . A . DUNLAP J . DURAN A . V . DVURECHENSKII V . P . DYMONT S . A . DZUBA D. A. V. N. C. R.

553 283 97 473 K101 445 591 K101 291 K39 K69 257

D. ELEY A . EL-SHARKAWY V . EMTSEV P . ESINA ESNOUF ETHIRAJ

283 429 575 655 463 K27

G . FANTOZZI G . M . FILARETOVA H . - J . FITTING Z . FRAIT J . FRÖHNER Y.FUKUDA

463 655 195 179 257 K141

M . GABER R . T S . GABRIELYAN V . I . GATALSKAYA P . GAWORZEWSKI R . GEVERS M . H . GHONIEM S . GHOSH H . GLAEFEKE H . - C H R . GOLINSKY E . M . GOLOLOBOV E . S . R . GOPAL I . K . GOPALAKRISHNAN B . N . GOSHCHITSKII G.GÖT Z I . N . GRINCHESHEN R . GROETZSCHEL J . GRONKOWSKI A . K . GROVER V . I . GUBSKAYA A . I . GUSEV V . S . GUSIICHIN P . HARGRAVES F . HASHIMOTO H . HASHIMOTO W . HERGERT B . HEKMONEIT

195 349 K51 133,575 375 429 535 KL49 569 K51 KL65 K89 435 KL K85 K35 389 K89 585 159 497

.

K101 227 . 335 641 553

Author Index

662 W . HERREMANS

375

R . HERRMANN

K183

F . C. L O V E Y

29

P . L . LOYZANCE

359

H . HESS

543

P . F . LUGAKOV

441

E . HILD

133

T . A . LUKASHEYICH

441

D . HILDEBRANDT

K35

G . HÖLZER

K43

K . HOSHINO

K5

K . IKEZAKI

615

T . JSHII

615

M . IWATA

K105

K.JACOBS

627

Z. JANÁCEK

77

K . N . JOG

417

T.JUNG

K15

K . JÜRGENS

K77

S . KACIULIS

K179

A . A . KAMINSKII Y . KAMIURA S. B. P. S. E.

A . KARANDASHEV P . KASHNIKOV R . KESSLER KHAN KIBICKAS

F . - G . KIRSCHT Y . P . KISELEV J . KLIKORKA N . M . L . KÖCHE H . - J . KÖHLER 0 . KOHMOTO Y . G . KOHN M . KOIZUMI L . S . KORNIENKO E . KOTAI W . KRAAK A . R . KRASNAYA H . KRAUSE W . KRECH P . V . KUCHINSKII YTJ. A . K U L Y U P I N A . KUMAR G. N. L. M.

553 227 655 K39 K77 535 K179 273,

133 K73 K123 K65 K175 K155 349 523 167 K35 K183 K145 569 K175 585 45 297

S . KUMAR KURAMOCHI A . KUROCHKIN F . KUZNETSOV

K27 121 K51 K31

J . LAUZIER H . M. LEDBETTER H . LEMKE M . L . LEVITAN P . LILLE Y J . L . LINDSTRÖM

463 89 K133, K137 51 235 K109

1. S . L I S I T S K J I D . C. LTU V . M . LOMAKO V . A . LOMONOV J . M . LÓPEZ

585,

167 69 K57 553 423

C. W . LUNG

K113

G . I . MAKOVETSKII

K69

S . A . MAKSIMENKO J . MÁLEK

K23 KL 23

C. MALGRANGE V . I . MALTSEV

389 529

R . MÁRQUEZ SH. R . MASTOV

445 K31

B . A . MEN

51

M . MESSAOUDI H.-G. MEYER P . MICHEL P . MICHON G. C. D. T. E. H. K. P. N.

291 K175 K1 399

MICOCCI MINIER S . MISRA MIURA MIZERA MIZUBAYASHI MOCHIZUKI C. MORÁIS V . MOSEEV

609 463 297 615 83 121 249 K65 435

V . G . KRISHNA M U B T H Y

K27

E . NEBAUER

K169

S. A. NEPIJKO S. NESPUREK M . NEVRIVA J . E . NICHOLLS D . 0 . NORTHWOOD P . NOVÁK R . NOVAK G. G. H. K. T. S. C. L.

45 619 173 235 149 173 173

S . OEHRLEIN OELGART OESTERREICHER OESTERREICHER OHKAWA OKUDA K . ONG N . OSTER

K109 205 K61 K61 335 121 199 K145

J . PABSELIÜNAS

K179

G . PARTHASARATHY

K165

L . PASEMANN P . PASZTI

641 K35

V.A.PAVLOV A. PAWELEK

11,315 K117

R.PÉREZ Y U . E . PERLIN R . PICKENHAIN G . S . PLOTNIKOV A . D . POGREBNYAK

113 553 273,

627 K73 K31

Author Index G . P . POKHII V . P . POPOV N . S. POPOVICH E . D . POZHIDAEV V . I. PROTASOV J . PULTORAK L . PÜST S . V . RAKITIN I . H . RASHED B . RAUSCHENBACH P . REICHE M. RIEDEL A . RIZZO J . ROSENZWEIG L . ROTH V . M. RUBINOV H . RUBIO G . RUDLOF V . V . RYABCHENKOV A . 0 . RYBALTOVSKII V . S. SAENKO A . M. SALETSKII B . SANDOW S . P . SANYAL S . E . SARKISOV A . SASAKI T . SATOW U . SCHALLER F . SCHAUER M. SCHELL K . SCHMALZ M . SCHMIDT F . SCHNEIDER E . M. SCHULSON D . SCHULTZE N . N . SEDOV P . SEIDEL W . SEIFERT K . SEN V . I . SHALAEV R . V . SHARMA M. SHIMADA A . A . SHTANOV L . A . SHUVALOV V . E . SIDOROV E . H . SIN L . SINCAN R . K . SINGH P . SIRCAR K . SKEFF NETO I . O. SMITH K . SOMAIAH P . Y A . STAROSTIN H . STRUSNY S . SUDHAKAR

663 K39 K39 K85 591 105, 435 K93 179 K31 429 473 553 K175 609 K81 K15 K159 511 KL49 553 167 591 K73 K169 417 553 K105 K5 KL83 619 569 575 K19 455 481 553 45 K175 627 603 11, 315 39 523 K85 409 497 199 K129 417 649 K65 149 265 K57 K35 K27

M. A. K. M. K. B.

SUEZAWA SUKIENNICKI SUMINO SUNDBERG SUZUKI G. SVENSSON

H . TAGUCHI N . TAKEUCHI H . S. TAN G. VAN TENDELOO A . TEFORE N . T . THUC HIEN L . TICHY V . D . TKACHEV R . TOGNATO A . TOMITA A . H . TONEYAN B . TOPIC M. TUICHIEV A . V . TULINOV A . A . TURINGE B . P . TYAGI A . P . TYUTNEV

469 189 469 83 249 K109 523 K141 199 29 609 219 K123 K43 K47 K141 349 409 KL59 K39 K39 603 591

0 . UEMURA K . UHLMANN S. UNTERRICKER

K5 K19 455

D. A. C. L.

61 591 399 133

M. VANDERWALKER V . VANNIKOV VAUTIER VECSERNYES

S. V . VLNTSENTS

273

Y . V . VOITSEKHOVSKII

167

G. VÖLKEL

257

V . G . VOLOGIN S. A . VOROBIEV

529 K31

F . WALZ T . WATANABE B . WEBER P . WERNER U . WERNER W . WESCH M. R . WILLIS J . A . WOOLLAM

503 K5 KL 83 205 K169. 283 69

J . V . YAKHMI V . Y A . YASKOLKO

K89 K145

M. S. ZAGHLOUL K . ZDANSKY J . J . 2EBROWSKI O. ZMESKAL N . V . ZOTOVA

429 219 189 619 655

phys. stat. sol. (a) 84 (1984)

Author Index A . M . AFANASEV S . ALEXANDROVA A . R . ALI G . B . ALTSHULLER S . AMELINCKX C. ANTONIONE V . V . ARISTOV V . I . ARKHIPOV D . A . ARONOV A . H . ASHOTJR A . ASHRY I . M . ASKEROV M . ASLAM G . K . ASLANOV C. AUST V . M . BABICH G . BABOMAS R . BACEWICZ M . BACMANN K . V . S . BADARINATH J . S . BAIJAL G . E . BAJARS P . BALK T . K . BANDYOPADHYAY N . P . BARAN A . S . BARRIERE R . BASU J . BASZYNSKI L . BATTEZZATI H . BEIGE H . BERNDT A . L . BHATTACHARYYA M . BOHM YTR. B . BOLKHOVITYANOV I . E . BONDARENKO V . L . BORBLIK A . BORCHARDT V . V . BORIMSKII T . E . BORISENKO 0 . YCR. BORKOVSKAYA 1. BRATU G . BRAUER W . BRODKORB E . BTJGIEL K . H . J . BUSCHOW M . Z . BUTT E. S. P. B. C. G.

I . CHAIKINA R . CHAUDHURI CHAUDOUET CHENEVIER CHIANG V . CHIKVAIDZE

73 561 K67 555 185 371 K43 327 301 337 451 K59 659 K59 K75

607,

263 113 K89 199 K93 535 K197 659 651 263 273 K35 K129 371 433 K149 493 291 K13 K43 263 143 237 K193 285 K17 451 379 143 207 K125 541 651 199 199 K189 K101

Z. P. G. P. E.

CHOBOLA E . CLARK COCCO CUI CTJLEA

693 31 371 157, 4 6 5 K17

R . L . DAVIDOVICH J . L . DEMENET V . M . DERKACHENKO V . N . DERKACHENKO V . V . DESHPANDE J . C . DESOYER P . DEUS V . V . DIKAREVA R . DIMMICH S . S . DIMOV N . L . DMITRUK Y U . P . DOTSENKO N . N . DRYOMOVA P . I . DUBENSKOV R . DURAJ J . DURAN A . Y . DVURECHENSKII

387 481 K63 215 K105 481 87 K173 K85 555 285 263 K43 585 229 411 171

S . S H . EGEMBERDIEVA Y A . A . EIDUSS S . ENZO 0 . ERB

541 K101 371 291

R . FASTOW V . E . FEDOROV V . V . FEDOTOVA 1. FELLEGVÀRI P . FELTHAM S . D . FERRIS A . S . FILIPCHENKO J . FILIPOWICZ I . FÒLDVÀRI W . FRENTRUP D . FRUCHART S. A . FYSH

49 K165 K63 547 K125 363 541 K89 547 269 199 31

H . GAREM A. P . GES G . GEYERS A . A . GHANI V . GHIORDÀNESCU P . GILLE K . D . GLINCHUK R . GONZALEZ P . S . GORDIENKO L . GOSZTONYI M . GRIEPENTROG J . GRIGAS

481 K63 273 337 K139 K121 237, 567 179 387 547 269 387

698

Author I n d e x

L . S. GRIGORYAN P . GROCHULSKI V . GRÖGER P . GROSBRAS R . GRÖTZSCHEL S . L . GRUVERMAN P . GÜNTER A . I . GUSEV

597 K5 475 481 171 423 103 527

S . EL-HALAWANY I . HEVESI C. A. HEWETT B . HINTZE D . HINZ J . HOBÄK W . HOYEB Q. HUANG H . - J . HUNGER

K89 639 49 87 KL 33 K143 11, K 9 7 465 K149

G. I . IBAEV N . M. IGONINA Y . IKEDA R . M. IMAMOV T . IMUEA A . 0 . ISMAILOV A . V . IVANOV V . M. IVASTCHENKO K . IWAUCHI

K185 171 55 73 501 K51 417 669 55

A. L. D. D.

39 KL 3 3 311 363

JABLONSKI JAHN P . JOSHI C. J O Y

B . K H . KADIROV A . M. KADOMTSEVA T . A . KAIDALOVA ZS. KAJCSOS M. KALITZOVA M. S . KAMARA A . A . KAMINSKII L . N. KAMYSHEVA L . KASSAMAKOVA G. KÄSTNER V . V. KAZMIRUK A . V . KAZUSHCHIK T. S. KI: H. V. KEER F . KEEBE R . KHANNA H . E . KHODENKOV I . 1 . RHODOS L . C. KIMERLING PRAN KISHAN L. B . KISS M. KITTLEB H . KLOSE

K71 215 387 451 K23 613 K81 K115 561 K23 K43 K173 157^ 4 6 5 K105 451 95 K135 79 363 535 639 143 269

P . I . KNIGIN Y . KOBAYASHI É . KOCSÂRDY K . KOLEV R . V . KONAKOVA V. I . KONONENKO N. N . KOREN L . KOUDELKA B . A . KOVAL V . B . KOVALCHUK N. M. KOVTUN G.KOWALSKI G. KREYSCH P . KRISHNA P . KRISPIN N . N . KUDELKIN A . KUHN G. KÜHN A . KÜHNEL G. KÜHNEL S . I . KULIEVA I . N . KUROPYATNIK V . V . KVEDER C. Y . KWOK

301 K29 165 K23 669 423 K173 K143 171 263 215 119 269 401 573 K135 411 87 433 251 KL85 KL 6 5 149 KL

R . LAB TJSCH J . L . LAGZDONS 0 . L . DE LANGE K . K . LAROIA S . S . LAU N . I . LEBEDEYA E . I . LEONOV V . I . LEVCHENKO 1. T . LIDDELL C. H . LING N. M. LITOVCHENKO V . G . LITOVCHENKO B . V . LOKSHIN V . A . LOMONOV P . LOSTÄK A . LUBOMIRSKA-WITTLIN

149 K197 517 535 49 171 113 KL 73 K75 KL 237 285 K101 K81 K143 K181

T . LUCIRISKI

607

P . F . LUGAKOV M. G. LUKASHEVICH S . N . LUKIN M. M. LUKINA V . V . LUKYANITSA L . LUNDGREN A . R . LÜSIS

457 613 223 215 457 199 K197

T . MAEDA J . MAEGE O. I . MAEVA T . G. MAGERRAMOV S . A . MAHMOUD H . S . MAITI S . K . MAKSIMOV

55 573 285 K185 K67 631 79

Author Index

699

B . R . MAMATKULOV A . V . MASLOV E . E . MATYAS W.MATZ J . W . MAYER S . A . MÄZEN A . I . MELKER M . MENYHÄRD M . MESSAOUDI M . MIKHAILOV S. D . MILOVIDOVA S. K H . MILSHTEIN G . S . MINGALEEV V . P . MIROSHKIN E . B . MIRZA A . V . MISHCHENKO V . V . MITIN X . CH. MITRA L . MOERNER D . B . DE MOOIJ Y U . N . MOSKVICH P . MROZEK A . MUELLER A . A . MUKHIN A.MÜLLER U . MÜLLER-JAHREIS I . MUMINOV S . RAMANA MURTHY V . MUSILOVÄ J . MUTO

301 73 K193 11 49 337 417 39, 65 411 K23 K L 15 363 327 645 KL05 K165 669 493 509 207 K109 39 K97 215 11 269 113 655 693 K29

L . NÄNAI E . NEBATTER H . NEUMANN NGUY HTJTJ CHI NGUYEN D A I HUNG NGUYEN MANH SON G . NICOARÄ A L . NICULA G . M . NIFTIEV V . I . NIKITENKO A . NOHARA D . 0 . NORTHWOOD

639 K39 87 KL 59 K159 K159 K139 K17 K59 443 501 509

B . OLEJNIKOVA B . Z . OLSHANETSKII V . M . ORLOV Y U . A . OSSIPYAN

621 K13 113 149

J . PAITZ T . PALEWSKI Y A . I . PANOVA M . PARDAVT-HORVÄTTT R . PAREJA A . V . PARYGIN L . PASEMANN E . M . PASHAEV

547 K47 645 547 179 K101 133 73

N . PASHOV L . I . PAVLOV M . A . PEDROSA A . E . PLAUDIS W . POSSART CHANDRA PRAKASH K . PRASAD A . V . PROKHOROVIOH

K23 555 179 K153 319 535 KL 567

S. I . RADAUTSAN S . RAJENDRAN F . S . RAKHMENKULOV V . V . RANDOSHKIN B. RAY S . M . RAZA T . M . RAZYKOV S . A . REBROV A . A . REMPEL F . REYNAUD H . RICHTER G . RIONTINO A . RÖDER H . ROEMER A . I . ROMANENKO M . ROTHBAUER O . V . ROZANOV A . I . RUDENKO

KL 69 631 K165 KL 35 K75 K125 K71 K169 527 393 143 371 319 KL 77 KL 65 693 KL09 327

R . Z . SADYKHOV V . S. SAENKO G . SAID A . V . SALKER J . SALM Z . A . »ALNIC R . SANCTUARY S. E . SARKISOV R.SATYANARAYANA A . SCHARMANN M.SCHENK D . SCHWARZ M . T . SEBASTIAN S . SEKIMOTO G . K . SEMIN J . P . SENATEUR D . SENULIENE A . K . SHARMA E . G . SHAROYAN V . A . SHERSHEL M . SH. SHIKHSAIDOV Y . SHIMADA M . SHIOJIRI S. D . SHUTOV A . S . SLDORKIN

W . SIEGEL J . SIKULA A . A . SIMASHKEVICH M . V . SIMONYAN

K51 327, 585 K67 K105 379 237 103 K81 655 291 K121 K177 401 55 K101 199 113 439 597 263 79 K55 55 343 K115

251 693 343 597

700 S. SiMOv R . SINGH V . SITAKARA RAO

Author Index K23 659 631

L . N . SKTJJA

K153

L . SMARDZ I . O . SMITH 1 . 1 . SNIGHIRYOVA R . S . SRIVASTAVA K . V . STAMENOV F . STANGLER E . STEINBEISS V . F . STELMAKH S . I . STENIN J . D . STEPHENSON F . STOBIECKI C. M . SU

K129 509 79 311 555 475 379 613 KL3 19 K129 157

A. SUBRAHMANYAM T. T. A. A. G. M. A.

SUGIURA SUKEGAWA L . SUKHMAN A . STJKHOVSKII D . SULTANOV A . S. SWEET J . SZADKOWSKI

K93 K9 K9 423 K109 K59 K75 KL 8 1

A. SzEKEEES

561

E . SZONTAGH A . SZYTULA

165 229

B . G . TAGIEV A . TANAKA V . T . TELEPA G . VAN TENDELOO D . P . TEWARI S. A . TEYS E . THOMAS F . THUSELT R . D . TOMLINSON M . I . TÖBÖK V . V . TOROKIN J.TOULOUSE TRAN K I M A N H

K59 K9 223 185 439 K13 .* K 9 7 677 87 639 423 411 K159

M. A. R. A. A.

TRAPP N . TRUKHIN TRYKOZKO E . TSURKAN P . TYUTNEV

K39 K153 K89 K169 327, 585

W . ULRICI K . UNGER H . - G . UNRUH L . URAY V . URBONAVICIUS

243 677 K177 65 387

L . M . VALIEV A . V . VANNIKOV R . S . VARDANIAN P . VASINA V . N . VASYUKOV Y U . D . VAULIN

K51 327, 585 K7 693 223 K13

F . WARKUSZ A . WATTERICH Z . WAWRZAK J . WERNISOH W . WINKLER M . WOBST

11,

E . B . YAKIMOV N . A . YARYKIN C. J . YOUNG

443, K 4 3 443 517

R . ZACH N . S . ZAYATS L . A . ZEMNUKHOVA B . S . ZHANG L . D . ZHANG Z . I . ZHMUROVA M . ZIEGLER R . ZURCHER A . K . ZVEZDIN I . 1 . ZYATKOV

K85 165 K5 39 193 K97

229 567 387 465 465 K81 79 475 215 645

physica status solidi (a) applied research

B o a r d of E d i t o r s

S. A M E L I N C K X , Mol-Donk, J. AUTH, Berlin, H. B E T H G E , Halle, K. W. BÖER, Newark, P. GÖRLICH, Jena, G. M. HATOYAMA, Tokyo, C. H I L S U M , Malvern, B. T. K O L O M I E T S , Leningrad, W. J. MERZ, Zürich, A. SEEGER, Stuttgart, C. M. VAN Y L I E T , Montréal Editor-in-Chief

P . GÖRLICH

Advisory Board

L. N. A L E K S A N D R O V , Novosibirsk, W. ANDRÄ, Jena, E. B A U E R , Clausthal-Zellerfeld, G. C H I A R O T T I , Rom, H. CURIEN, Paris, R. GRIGOROVICI, Bucharest, F. B. H U M P H R E Y , Pasadena, E. K L I E R , Praha, Z. M A L E K f , Praha, G. O. M Ü L L E R , Berlin, Y. N A K A M U R A , Kyoto, T. N. R H OD IN, Ithaca, New York, R. SIZMANN, München, J . STUKE, Marburg, J . T. W A L L M A R K , Göteborg, E. P. W O H L F A R T H , London Yolume 85 • Number 1 • Pages 1 to 304, K 1 to K 9 6 , and A l to A 8 September 1 6 , 1 9 8 4 P S S A 85(1) 1 - 3 0 4 , K l — K 9 6 , A 1 - A 8 (1984) ISSN 0031-8965

AKADEMIE-VERLAG • BERLIN

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P o s t f a c h 1233 b z w . D D R - 6 9 0 0

Jena,

Verlag: Akademie-Verlag, D D R - 1 0 8 6 Berlin, Leipziger Str. 3 —4; F e r n r u f : B a n k : Staatsbank der D D R , Berlin, Kto.-Nr.: 6836-26-20712. Chefredakteur: Dr. H.-J. Hänsch. Redaktionskollegium: Prof. Dr. E. Gutsche,

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Telex-Nr.: 114420;

D r . H . - J . H ä n s c h , D r . H . L a n g e , D r . S. O b e r l ä n d e r .

Anschrift der R e d a k t i o n : D D R - 1 0 8 6 B e r l i n , L e i p z i g e r S t r a ß e 3 — 4 , P o s t f a c h 1 2 3 3 ; F e r n r u f : 2 2 3 6 2 79. V e r ö f f e n t l i c h t u n t e r d e r L i z e n z n u m m e r 1620 d e s P r e s s e a m t e s b e i m V o r s i t z e n d e n d e s M i n i s t e r r a t e s d e r D e u t s c h e n Demokratischen Republik. Gesamtherstellung: V E B Druckerei „Thomas Müntzer", DDR-5820 Bad Langensalza. Erscheinungsweise: D i e Z e i t s c h r i f t „ p h y s i c a s t a t u s s o l i d i ( a ) " e r s c h e i n t j e w e i l s a m 16. e i n e s j e d e n M o n a t s . J ä h r l i c h e r s c h e i n e n 6 B ä n d e zu j e 2 H e f t e n . Bezugspreis: J e B a n d 200,— M z u z ü g l i c h V e r s a n d s p e s e n ( P r e i s f ü r d i e D D R : 130,— M). B e s t e l l n u m m e r dieses B a n d e s : 1 0 8 5 / 8 5 . © 1984 b y A k a d e m i e - V e r l a g B e r l i n . Printed in the German Democratic Republic. AN

EDV

20735

Contents Review Article

V . A . PAVLOV, V . I . SHALAEV, a n d V . M . A L Y A B I E V

Effect of Dislocation Structure on Creep and Fracture of Metals and Alloys (I)

11

Original Papers and Short Notes

Structure

F . C . L O V E Y , G . VAN T E N D E L O O , a n d S . A M E L I N C K X

R. V.

SHARMA

The Nature of Some Planar Defects in 2 H Martensite of Cu-Al Alloys as Determined b y H R E M

29

Partial Higher-Order Structure Factors in the Long-Wavelength Limit for Molten Cuprous Chloride

39

H . B E R G E R , Y U . A . K U L Y U P I N , S . A . N E P I J K O , a n d N . N . SEDOV

Quantitative Interference Electron Microscopy for Spherical Objects . . .

45

B . A . M E N a n d M . L . LEVITAN

Analysis of the Ground State of a Solid Solution with Interactions up to k-th Coordination Spheres of the Crystal Lattice. Selection of the Subdivision of the Lattice into Sublattices

51

D . M . VANDERWALKER

A Dark-Field TEM Method for Crystal Structure Determination of Cu-Rich Phases on Twins in Silicon

61

S . A . ALTEROVITZ, G . H . B U - A B B U D , J . A . WOOLLAM, a n d D . C . L i u

Z.

JANACEK

Structural and Chemical Analysis of a Silicon Nitride Film on GaAs by Null Ellipsometry

69

Coherence Properties of Radiation Diffracted by an Elastically Bent Crystal

77

E . MIZERA, M . SUNDBERG, a n d P . W E R N E R

Defect Structure of ZnSe Crystals Investigated by Electron Microscopy

83

P . M I C H E L , B . W E B E R , a n d G . GOTZ

Formation of P t Silicides by a Millisecond Laser Pulse

K1

T . SATOW, 0 . U E M U R A , K . HOSHINO, a n d T . W A T A N A B E

The Neutron Diffraction of Molten T1C1, TlBr, and T i l l*

K5

4

Contents

G . B E R G E R a n d V . ATZRODT

I n Vitro Characterization of Bioactivity of Glassy or Glass-Crystalline Implant Materials Using Auger Electron Spectroscopy

K9

T . JUNG a n d L . ROTH

DC Plasma Nitridation of Thin Aluminium Films

K15

K . UHLMANN a n d M . SCHMIDT

Influence of Work Function Change Due to Oxygen Chemisorption on the Secondary-Ion Emission Probability K19 S . A . MAKSIMENKO

On X-Ray Surface Diffraction

Lattice

K23

properties

H . M . LEDBETTER

Monocrystal-Polycrystal Elastic Constants of a Stainless Steel

89

W . BURCKHABDT, P . BUSSEMER, a n d U . DIETRICH

Structure and Molar Refraction and I t s Wavelength Dependence a t Different Alkali and Ammonium Halides

97

G . S . K U M A R , S . STTDHAKAR, R . E T H I R A J , a n d V . G . K R I S H N A M U R T H Y

Strain-Optical Constant (pu) of Mixed Crystals of K C l - K B r of Equimolar Concentration K27

Defects,

atomistic

aspects

V . G . C H U D I N O V a n d V . I . PROTASOV

R . PEREZ

Kinetics of Vacancy Mechanism of the Solid-Liquid Transition in F.C.C. Metals

105

On the Identification of the Nature of Stacking Faults in H.C.P. Materials

113

N . KURAMOCHI, H . MIZUBAYASHI, a n d S. OKUDA

Dislocation Pinning at Low Temperature in Nb

121

P . GAWORZEWSKI, E . H I L D , F . - G . K I B S C H T , a n d L . V E C S E R N Y E S

Infrared Spectroscopical and TEM Investigations of Oxygen Precipitation in Silicon Crystals with Medium and High Oxygen Concentrations . . .

133

D . 0 . NORTHWOOD a n d I . O . SMITH

A. I .

GUSEV

Steady-State Creep and Strain Transients for Stress-Dip Tests in Polycrystalline Magnesium a t 300 °C

149

Structural Vacancies in Nonstoichiometric Compounds a t High Pressure. Thermodynamic Model

159

5

Contents V . G . ARTYUSHESTKO, Y . V . VOITSEKHOVSKII, L . S . K O R N I E K K O , I . S . L I S I T S K I I ,

and

A . O . RYBALTOVSKII

Effect of Ionizing Radiation on Optical Properties of Thallium Halides in t h e 0.36 to 15 [xm Range A . D . P O G R E B N Y A K , S H . R . MASTÖV, M . F . K U Z N E T S O V , K . P . A R E F I E V , S . V . R A K I T I K , S . A . VOROBIEV

Observation of

R F

167

and

Pulses from Solids during Laser Irradiation

K31

D . H I L D E B R A K D T , H . STRTTSNY, R . G R O E T Z S C H E L , E . K O T A I , a n d F . P A S Z T I

Damage and Trapping Behaviour of Crystalline Silicon a t Low Energy Deuterium I m p l a n t a t i o n K35 A. V. A. A.

DvuRECHEirsKii, TURINGE

B. P . K A S H N I K O V , G . P . P O K H I L , V. P . P O P O V , A. V. T U L I N O V , and Defect Structure Study with P l a n a r Channeling in Pulse-Annealed IonI m p l a n t e d Silicon K39

V . D . TKACHEV, G . HÖLZER, a n d A . R . CHELYADINSKII

Damage Profiles in Ion I m p l a n t e d Silicon R.

TOGNATO

K43

Influence of Dislocation Core Density on Overheating Absence

. . . .

K47

V . I . G A T A L S K A Y A , E . M . GOLOLOBOV, a n d L . A . K U R O C H K T N

Relaxation Time and Electron Scattering Cross Section in I r r a d i a t e d p-Silicon a t Temperatures of Liquid Helium from Cyclotron Resonance D a t a K51

V . M . L O M A K O a n d P . Y A . STAROSTTTC

Temperature Dependence of t h e Charge-Carrier Removal R a t e in n-GaAs Containing Defect Clusters K57

Magnetism

J . CERMAK, R . NOVAK, P . NOVAK, a n d M . NEVRIVA

Y t t r i u m Iron Garnet Films Substituted b y Gd and Mn

173

L. PUST a n d Z. FRAIT

Method for Measurement of Magnetostriction Constants in (001) Thin Films Using F M R

179

J . J . ZEBROWSKI a n d A . SUKIENNICKI

On t h e Inhibition of Dynamic Conversion in Bubble Garnet Domains b y a Thin Midplane Layer

189

K . OESTERREICHER a n d H . OESTERREICHER

Structure and Magnetic Properties of Nd 2 Fe 1 4 BH 2

7

K61

N . M . L . K O C H E , P . C . MORAIS, a n d K . S K E F F N E T O

The Usefulness of the Photoacoustic Cell for Magnetic Measurements

. . K65

G . I . MAKOVETSKII a n d V . P . DYMONT

Crystallographic, Magnetic, and Electrical Properties of Nickel-Substituted Chromium Telluride K69

6 Extended

Contents electronic

states

and

transitions

M . GABER a n d H . - J . FITTING

E . H . SIN,

C.

E n e r g y - D e p t h Relation of Electrons in Bulk Targets b y Monte-Carlo Calculations

195

and H . S . T A N Temperature Dependence of I n t e r b a n d Optical Absorption of Silicon a t 1152, 1064, 750, and 694 n m

199

K . ONG,

G . OELGAET a n d U . W E R N E R

Kilovolt Electron Energy Loss Distribution in GaAsP

Localized

electronic

states

and

205

transitions

G . A . ADEGBOYEGA

Electrical Measurements on Silver-Diffused GaAs

215

K . ZDANSKY a n d N . T . THUC H I E N

Analysis of D L T S Curves of Aggregated Deep Level Impurities

219

Y . KAMIURA a n d P . HASHIMOTO

Origin of a Shallow Acceptor in Quenched Germanium

227

P . L I L L E Y , M . R . CZERNIAK, a n d J . E . NICHOLLS

Photoluminescence a n d Electrical Properties of Vapour Phase Epitaxial ZnSe Grown on GaAs

235

H . BOOYENS a n d J . H . BASSON

Piezoelectrically Induced Charge Distributions around Dislocations in CdTe and HgCdTe

243

K . MOCHIZUKI a n d K . SUZUKI

Effect of t h e Stoichiometry Control on the Photoelectrical Properties of ZnSjSei-s

249

G . V O L K E L , S . A . D Z U B A , A . BAJRTL, W . B R U N N E R , a n d J . F R O H N E R

Time-Resolved E P R on Polyacetylene

257

K . SOMAIAH a n d V . H A R I B A B U

Two Types of F-Centres and Thermoluminescence in BaFCl Crystals . . .

265

S . V . VINTSENTS, V . F . K I S E L E V , a n d G . S. PLOTNIKOV

Energy Transfer between Excited Adsorbed Dye Molecules and Charged Defects in Insulator-Semiconductor Structures

273

V . A . BESPALOV, V . F . K I S E L E V , G . S . PLOTNIKOV, a n d A . M . SALETSKII

Fluorescence Decay of Adsorbed Dye Molecules on Solid Surfaces . . . .

K73

F . R . K E S S L E R , U . BARKOV, a n d K . J U R G E N S

Cathodoluminescence of I n G a A s P

K77

7

Contents

Electric

transport

I . DIACOHU, D . D . E L E Y , a n d M . R . WILLIS

AC Conductivity in Single Crystals and Compactions of TCNQ Complex Salts

283

M . MESSAOUDI a n d J . D U R A N

Conductivity in One-Dimensional Disordered Cs 2 TCNQ 3 Salts

291

D . S . M I S R A , A . K U M A R , a n d S . C . AGARWAL

Intensity and Temperature Dependence of Steady-State Photoconductivity Down to 8 K and DOS Distribution Obtained from These Measurements in a-Si:H

297

M . A D O L F , J . ROSESTZWEIG, a n d U . B I R K H O L Z

Bipolar Photoconductivity and Hall Effect of the Acoustoelectric Current in CdTe K81 I . N . G R I N C H E S H E N , N . S . P O P O V I C H , a n d A . A . SHTANOV

Relaxation Peculiarities in TlSbSe 2 Crystals

K85

J . V . Y A K H M I , I . K . G O P A L A K R I S H X A N , a n d A . K . GROVER

Electrical Resistivity Studies on the Heusler Alloys Co 2 Ti_a;Ali+ x (T = Ti orZr) K89

Device-related

J.

PUI/TORAK

phenomena

Current-Voltage Characteristic of the p - n Junction with an Exponential I m p u r i t y Distribution a t Its Base Contact K93

Pre-Printed Titles of papers to be published in the next issues of physics status solidi (a) and physics status solidi (b)

A1

Contents

9

Systematic List

Subject classification:

1 1.1 1.2 1.3 1.4 1.5 1.6 2 4 7 8 9 10.1 10.2 11 12.1 12.2 13 13.3 13.4 14.1 14.3 14.3.1 14.3.3 16 17 18 18.2 18.2.1 19 20 20.1 20.3 21 21.1 21.1.1 21.3 21.7

Corresponding papers begin on the following pages (pages given in italics refer to the principle subject classification):

K5 77 105 69 29, 51, 61, 83, 113, 133 45,69, K19 Kl, K9, K15, K23 39, 297, K5, K9 97 K81 159 11, K15 11, 29, 105, 113, 121, 149, 159, K47 83, 133, 167, 227, 243, 265, K35, K39, K43, K61 167, 195, 205, Kl, K15, K35, K39, K43, K51, K57 89, 121, 149, 159 K27 205 45, K19, K73 215, 219, 227, 235, 243, 273, K57 K69, K89 215, 227, 243, 283, 291, K81, K85 235 219, K93 249, 297, K81, K85 195, K9, K15, K19 K65 K69 173, 179, 189 179, 257, 273, K o l , K65 K27 97, 133, 167, 199, 265 235, 249, 265, 273, K73, K77 11, 29, 121, 195, K l , K47, K89 29, 105, 159, K61 89, K19 149 45

10 22 22.1.1 22.1.2 22.2. 1 22.2.4 22.4.2 22.4.3 22.4.4 22.5 22.5.2 22.5.4 22.6 22.8 22.8. 1 22.8.2 22.9 23

Contents 69, K15, K93 227, 273, K73 61, 77, 133, 199, 273, 297, K27, K35, K39, K43, K51 215, K27, K57 205, K77 83, 235 219, 243, K81 243, 249 39, 97, 167 97, K 5 265 K73 K69, K85 K9 173, 179, 189, K65 283, 291 257

Contents of Volume 85 Continued on Page 307

Review

Article

phys. stat. sol. (a) 85, 11 (1984) Subject classification: 10.1; 9 ; 21 Institute of Metal Physics, Academy of Sciences of the USSR,

Ural Scientific

Centre,

Sverdlovsk1)

Effect of Dislocation Structure on Creep and Fracture of Metals and Alloys I. Normal Deformation Conditions2) By V . A . PAVLOV, V . I . SHALAEV, a n d V . M . A L Y A B I E V

Contents 1.

Introduction

2. Dislocation 3. Dislocation

structure and grain

boundary

diffusion

4. Effect

of stacking

fault energy

on creep

5. Effect

of stacking

fault energy

on

6. Effect

of relative

7.

density

of screw

rate

fracture dislocations

on creep

of metals

and

alloys

Conclusions

References

1. Introduction With the rapid advance of nuclear engineering in the past few years need has arisen for materials capable of satisfactory performance under irradiation. The major features peculiar to the behaviour of materials under load when irradiated by highenergy particles are: 1. high acceleration of creep in the 0.4 to 0.5T m e it temperature range (Tmeit is the melting point) as compared to normal deformation conditions, 2. considerable increase in volume swelling, 3. embrittlement, 4. heterogenization of solid solutions and the emergence of segregations on point defect sink surfaces. In the final analysis, these phenomena stem from the fact that during irradiation a considerable point defect (vacancy and interstitial atom) concentration is produced which is largely in excess over the equilibrium concentration determined by the temperature conditions of deformation. Point defects promote diffusion processes and, by interacting with dislocations, affect the development of plastic deformation, void formation, and embrittlement. The interaction of point defects with atoms of solid solution elements may lead to the development of a fast diffusion of point defect complexes " d e f e c t - a t o m " , which largely affect the rate of void formation, the rate creep, etc. !) GSP-170, 620219 Sverdlovsk, U S S R . 2 ) Part I I see phys. stat. sol. (a) 86, No. 2 (1984).

12

V . A . PAVLOV, V . I . SHALAEV, a n d V . M . A L Y A B I E V

To approach correctly the problem of selecting reactor engineering materials, consideration should be given to the peculiarities of the mechanism of plastic deformation and fracture under irradiation. It would be expeditious to draw a thorough comparison of the behaviour of materials when subject to load under normal deformation conditions and when exposed to irradiation. Investigations should probably be carried out in the temperature range between 0.4 and 0.67'meit where the acceleration of creep and the swelling of reactor materials are most pronounced and the creep under normal deformation conditions is controlled by the climb of edge dislocations due to point defects migrating to them. 2. Dislocation Structure Let us examine the structure of dislocations, since the character of the interaction of point defects with them depends on the structural peculiarities of their nuclei. Dislocations are subdivided into edge and screw dislocations. In the nucleus of an edge dislocation there is an edge of an incomplete plane of atoms, and the motion of that dislocation is associated with a particular crystallographic slip plane. Screw dislocations contain no extra plane and can, as they move, pass from one slip plane to another by way of cross slip. During plastic deformation, dislocation pile-ups are produced near obstacles, the elastic stress field of the pile-ups hindering plastic deformation. The deformation can develop further only provided the dislocations are capable of surmounting these obstacles in some way or another. The motion of edge dislocations becomes possible only when the deformation temperature is so high as to allow point defects to migrate with sufficient velocity to dislocations. By the action of an external force and due to the diffusion process of the "growth" or "dissolution" of the incomplete plane, the leading pile-up dislocation will then climb over to a higher-lying (or lower-lying) slip plane. The dislocation that has become free will move over the new plane up to the next obstacle, and the dislocation source will be able to come into play again. These features of the motion of an edge dislocation are responsible for the shearing mechanism of the deformation which, however, is governed by the dislocation climb diffusion process. I t stands to reason that the deformation in this case may develop only at sufficiently high temperatures capable of assuring the requisite rate of migration of point defects to dislocations and an adequate point defect concentration. Screw dislocations surmount obstacles by cross slip. Under the effect of an external force and thermal energy, part of the dislocations present in the pile-up head pass over to another slip plane and from the latter, again by cross slip, to a higher-lying or lower-lying slip plane parallel to the first, and move further over a new plane. Thus, an obstacle in the way of screw dislocations is surmounted by double cross slip. In this case the shearing mechanism of plastic deformation is governed by a thermally activated, but diffusionless cross slip process. Point defects do not interact with a screw dislocation. Plastic deformation can easily develop at low temperatures if, of course, the mobility of screw dislocations does not lower with decrease in temperature, as is the case with b.c.c. metals [1]. The motion of dislocations becomes more complicated in the case of their splitting (Fig. lb). A dislocation splits up into two partial dislocations with a stacking fault between them. The degree of splitting, i.e. the width of an extended (splitting) dislocation is determined by the stacking fault energy y. The dislocation width is h m » Gb2ly, where G is the shear modulus and b the Burgers vector. In order that an edge dislocation may climb several vacancies (or interstitial atoms) at a time should approach one and the same dislocation site. The climbing event in this case assumes cooperative character. The cross slip of extended dislocations becomes difficult because

Effect of Dislocation Structure on Creep and Fracture in Metals (I)

13

Fig. 1. Diagram of motion of edge and screw dislocations: a) no splitting, b) splitting

a

jii.HL JILJILilLi ooo ooo

b

preliminarily, additional energy is required to convert an extended dislocation to a contraction of stacking faults. In the place where cross slip will occur the dislocation is compressed by external stresses and then the dislocation splits up in a new plane. 3. Dislocation and Grain Boundary Diffusion Studying the parameters of dislocation and grain boundary diffusion is of great importance in many aspects. Primarily, these studies have general scientific significance in terms of establishing regularities of diffusion for the most frequently occurring crystal lattice defects. The evidence obtained permits judgement as to the state of the lattice in these defets. Secondly, the dislocation diffusion plays an important part in the behaviour of metals during creep, when plastic deformation is controlled by the climb of edge dislocations. Thirdly, dislocations and grain boundaries are good point defect sinks. Dislocation and grain boundary diffusion ensures the sinking of excessive vacancies. Therefore, the diffusing power of the dislocation structure of a material predetermines, in the final analysis, the swelling and embrittlement of materials during irradiation. The most trustworthy evidence for the effect of defects being formed during plastic deformation on the diffusion characteristics was probably first obtained in [2], The investigations were carried out on zinc single crystals with mercury serving as a diffusing element. Three crystals of different orientation were subjected to plastie deformation by extension and cut into portions along the basal plane, on whose thoroughly cleaned surface a mercury drop was placed. The diffusion was studied in the temperature range between 287 and 363 K . Fig. 2 presents curves, where x is the

-1.5, J 275 •

3.00

3.25

3.50

Fig. 2. In x vs. 1 ¡T curves for diffusion of mercury in zinc; non-deformed crystal (•), crystal deformed by 11 (O), 23 (A), and 4 6 % ( + ) [2]

14

V . A . PAVLOV, V . I . SHALAEV, a n d V . M . A L Y A B I E V

p e n e t r a t i o n d e p t h of m e r c u r y , for a n o n - d i s t o r t e d crystal a n d t h r e e specimens of different degrees of p r e l i m i n a r y d e f o r m a t i o n : 11, 23, a n d 4 6 % c h a n g e in l e n g t h . I n t h e r a n g e of low t e m p e r a t u r e s , below 314 K , t h e d i f f u s i o n in d e f o r m e d specimens proceeds p r e f e r e n t i a l l y along dislocations p r o d u c e d b y plastic d e f o r m a t i o n , a n d t h e a c t i v a t i o n e n e r g y is v e r y low, a b o u t 1.5 x 10~ 20 J . A t h i g h e r t e m p e r a t u r e s , d u e t o p a r t i a l lattice d e f e c t r e l a x a t i o n a n d t h e v o l u m e diffusion coming i n t o p l a y , t h e a c t i v a t i o n energy rises u p t o a b o u t 5.0 x 10" 2 0 J , which coincides a p p r o x i m a t e l y w i t h t h e q u a n t i t y Q of 5.5 x 10 - 2 C J for a n o n - d i s t o r t e d crystal. T h e r a t i o of t h e dislocation diffusion a c t i v a t i o n energy Q d to t h e mercury-in-zinc d i f f u s i o n a c t i v a t i o n energy t h u s a m o u n t s t o Qv ^ 0.3. Besides, d i s t o r t e d crystals exhibit high p r e - e x p o n e n t i a l D0 values. R e c e n t l y , c o m p r e h e n s i v e investigations of b o t h t h e i n d i v i d u a l isolated dislocation directional self-diffusion a n d t h e small-angle crystal b o u n d a r y directional self-diffusion h a v e been p e r f o r m e d f o r d i f f e r e n t m e t a l s using r a d i a t i v e isotopes [3 t o 15], local X - r a y analysis [16], i n t e r n a l friction [17], a n d c o m p u t e r simulation [18] m e t h o d s . F o r small-angle b o u n d a r y self-diffusion e x p e r i m e n t s specimens w i t h small-angle boundaries were p r e p a r e d (Fig. 3). T h e self-diffusion coefficient d e p e n d s o n : 1. t h e Burgers vector, 2. t h e direction of diffusion, 3. t h e t y p e of dislocation (edge or screw dislocation), 4. t h e degree of dislocation splitting, which is d e t e r m i n e d b y t h e magnit u d e of t h e stacking f a u l t energy y. To suit t h e p u r p o s e , crystals w i t h a small-angle slope b o u n d a r y f o r m e d b y a series of edge dislocations (Fig. 3 a) or e x t e n d e d dislocations (Fig. 3 b) were p r e p a r e d . I n t h a t case, p a r t i a l dislocations w i t h a s t a c k i n g f a u l t r i b b o n b e t w e e n t h e m lay along t h e small-angle b o u n d a r y . To s t u d y screw dislocations small-angle torsion b o u n d a r i e s were used. B y changing t h e crystallographic planes t h a t f o r m small-angle boundaries, dislocations with d i f f e r e n t B u r g e r s vectors could be p r o d u c e d . T h e results of t h o s e investigations h a v e been analysed in d e t a i l in a review [11]. Table 1 f u r n i s h e s dislocation diffusion d a t a for m e t a l s w i t h a f.c.c. lattice. T h e d i f f u sion p a r a m e t e r s were o b t a i n e d s t r a i g h t f o r w a r d l y f r o m e x p e r i m e n t a l d a t a , w i t h o u t resorting t o a n a s s u m p t i o n concerning t h e effective values of t h e cross-section of a dislocation pipe. F o r m a t e r i a l volume d i f f u s i o n t h e s t a n d a r d expression Dv = D0v e x p

(-QJkT)

(1)

was employed. Similarly, for dislocation d i f f u s i o n Dd = Dod exp [0011

(-QJkT).

(2)

[211]

Fig. 3. Diagram of small-angle boundaries; a) boundary formed by a series of non-dissociated edge dislocations aligned in > C o c3 eg a 3 o CC | X 'S m © c o (3 O 60 c T3 o cS 0J 60 _ o T3 c; -3

a

«

T3 C o

o c o

ti cS "O' 0 3 o

OJ "60 a C C3 "60 -g ^ C 3 cS X O

ft £

SO 35

t

Jt « 60 C

"3 O o '. S

o

o

>c

>o

*

i ap

(N

2 CO § • —

g S t -

CO

O £

0Q "

2

60-C g c d

CD t-;

o

h d O O

u

- j a C8

00

>> «X> l

"c3 — G tu M ® ^ ea 'TP — c3 ,o2

.2

g

o

i-H N/

(5 . S ft S

a

£ H

ca o g - s6dI S •a ts ° O v the volume self-diffusion coefficient, a the stress, E the elasticity modulus. Fig. 4 presents the stacking fault energy dependence of referred steady-state creep rate sjDy. The behaviour of the curve is qualitatively similar to that established in [43, 44], However, the creep tests here have been carried out using two values of the diffusion coefficient and referred stress. This allows the influence of the variation of the quantities Dv and a on the creep rate to be considered separately. Comparison of the data obtained shows that an increase of Z>v or (alE) s by a factor of ten leads to an increase of e by one order of magnitude. In addition, other conditions being equal, the referred rate of creep (¿/Z>v) of different metals increases systematically with the magnitude of their stacking fault energy. However, some discrepancies from the results of [44] have been noticed. In experiments [46, 47] the stacking fault energy dependence of the creep rate is iless sharp q = 2.4 0.2 at n = 4.7 than that established in [43, 44] where q = 3.5 has been obtained with n = 5. A similar conclusion may be drawn from [48 to 50] where, from measurements on pure metals with f.c.c. lattice, values from 2.4 to 3.5 are indicated for the quantity q. Nonetheless, investigations of the creep in a number of copper-based solid solutions [45] may be mentioned where it is asserted that the dependence of ¿/Z)v on y is exponential in character. The above discrepancy of experimental data apparently may not be attributed to only random errors in experiment or errors in the choice of the initial elasticity modulus values and in allowance for their actual variation with temperature [46, 47], Thus, as a fact, the occurrence of a sharp stacking fault energy dependence of steady-state creep rate is confirmed by many investigations and evokes no doubts. The variation of the stacking fault energy y by a factor of ten results in t h a t the steady-state creeep rate e varies by more than two orders of magnitude in metals with f.c.c. lattice. For b.c.c. metals the e = f(y) dependence behaves similarly. In some papers, the adopted value of the stacking fault energy for metals with b.c.c. lattice is, in our view, too high [54], In this case the s = f(y) dependence in the region of high creep rates decviates from the linear dependence towards high y values. The decrease of the creep rate e with decrease in stacking fault energy y can probably be explained, as already indicated above, by the fact that the dislocation diffusion velocity decreases and the formation of jogs is difficult.

Fig. 4. Dependence of steady-state creep rate of pure metals (e/Dv) on magnitude of stacking fault energy y [47, 52 to 55]; (1) a/E = 8.1 X 10"5, (2) a/E = 5 X 10" 5 : f.c.c. metals (empty symbols D V = 10"11 cm 2 /s, full symbols 10"12 cm 2 /s: A1 (O, • ) , Pt ( • , •),'Pd (A, A), Ni (O, • ) , Ag (V, • ) ; b.c.c. metals a/E = =

2*

8.1 x

10"5: W H , M O

x , N b © , T a I, V +

20

V . A . P a v l o v , V . I . S h a l a e v , and V. M. A l y a b i e v

Mention should be made of the peculiarities in the behaviour of nickel which displays a creep rate corresponding to metals with low stacking fault energy (y = = 40 mJ/m2). In their work Barret and Sherbi [43] set y equal to 225 mJ/m2 which is apparently too high. It has been shown in [56, 57] that when passing through the Curie point (above 633 K ) nickel has low stacking fault energy. 5. Effect of Stacking Fault Energy on Fracture Investigations of the creep under the deformatioon conditions mentioned above have also permitted detection of another important regularity. I t has turned out that the time to fracture r as a function of stacking fault value y may be described by the empirical equation [46, 50] r = By~P ,

(4)

where B and p are constants at the a/E and Dv values selected. The regularity is graphically represented in Fig. 5. It is worth noting that B depends on the quantity 1.5, and when D = 10 12 cm2 s a/E, and p on Dv. When Dw = 10~ n cm2 s 1 p

p « 1.0.

In creep tests of metals and alloys, the well-known relationship between the time to fracture r and the steady-state creep rate s has been established [59, 60], T¿m = e0 ,

(5)

where e0 is a constant. The exponent m is close to unity in most of the f.c.c. metals and m a y take on values between 0.8 and 1.2 for different groups of metals [61]. The quantity c0, known as the "plasticity margin", determines the plasticity of materials and has, for each material, a characteristic value which depends weakly on test conditions. The product re coincides in most cases with the magnitude of deformation accumulated by a specimen on the equilibrium creep area. Clearly, ascertaining the nature of the constant e0 is an important problem. However, all the expressions proposed earlier, on the basis of which it could be calculated, involve parameters not always capable of direct measurement and explain only the constant e0 for a given material [63, 64], From this point of view, [46, 58] are of interest. In virtue of (4) and (5) it is possible to write e0 = r£ = A'yi-v

.

(6)

I t should be noted that (6) with q — p = 1 satisfies a large body of experimental evidence obtained by different authors. Davis and Wilshire [64] have gathered numerical values of the quantity s0 for f.c.c. metals in which the exponent m is equal to unity. These data are presented in Table 5 (second column) in which the mean values of the product measured in [46] and the known values of stacking fault energies of metals are also given.

Fig. 5. Dependence of time to fracture T of metals on the magnitude of stacking fault energy y [47]; (1) ajE = 8.1 X 10"5, (2) a/E = 5 X 10-5, Dv = 10"11 cm2 a"1; • Pt, A Pd, O Ni, V Ag, O A1

Effect of Dislocation Structure on Creep and Fracture in Metals (I)

21

Table 5 Comparison of quantity £0 and stacking fault energy y metal silver nickel copper palladium platinum aluminium

10 2 e„

io2™

2 4.5 6

4.5

2 16.5 16.0 33

32

y (mJ/m 2 ) 25 40 70 90 120 250

The values cited in columns 2 and 3 coincide, and the parameter e0 increases with increase in the stacking fault energy of the metals. The data given in the table permit to plot e0 versus stacking fault energy y (Fig. 6). The plot shows a linear relation between plasticity at equilibrium creep stage and stacking fault energy. Comparison of a sufficiently large body of experimental creep test data for materials with f.c.c. lattice leads to the important conclusion that the plasticity of metals at the equilibrium creep stage is proportional to the magnitude of the stacking fault energy in them. This relation between the magnitude of plasticity at equilibrium creep stage and stacking fault energy explains not only the constancy of the product er for a particular material but also the experimentally observed differences in the plasticity of the pure f.c.c. metals studied. It is highly essential that all these metals possess an approximately equal and sufficiently high plasticity under active extension conditions both at room temperature and in the region of high temperatures. This allows one to speak of the existence of the phenomenon of embrittlement of materials under creep, when plastic deformation is controlled by the climb of edge dislocations. It is a simple matter to see t h a t the degree of embrittlement increases with decreasing stacking fault energy y. A decrease of the stacking fault energy from 250 to 25 mJ/m 2 , by approximately a factor of 10, leads to a decrease in plasticity from 33 to 2 units, i.e. by about an order of magnitude. Under these deformation conditions the fracture occurs due to void formation processes, as a result of vacancy coagulation [64 to 66]. At present there exist a great deal of investigations concerned with the void formation under creep conditions at temperatures of materials of about 0.5T me i t . We mention here only some of them [67 to 75]. All of them confirm the earlier concepts about the mechanism of fracture under creep as resulting from the diffusion growth of voids due to excess vacancies that arise by the action of thermal energy and plastic deformation. It should, however,

AL

0

50

100

150

ZOO 250 r(mJ/m2i-—

Fig. 6. Dependence of rè on y [58]

22

1

V . A . PAVLOV, V . I . SHALAEV, a n d V . M . A L Y A B I E V

Fig. 7. Creep duration dependence of void density for silver (1) tested at 773 K and for copper (2) tested at 848 K [76]

300

s •§200

%100

0

50

100

750 z(h)—

be noted that the void nucleation mechanism has not yet been ascertained. Some authors propose that nucleation centres in a non-distorted material exist in advance. Quite naturally, it appears necessary to study the void formation in metals with different stacking fault energy. Relevant investigations have been carried out in [76], The materials investigated were silver, copper, and aluminium, with stacking fault energies of 25, 70, and 250 mJ/m 2 , respectively. All the metals had a purity as high as 99.99%. The experiments were carried out at the same homoglogous temperatures TjTme\t = 0.6 and at 10"7 s"1 strain rate at equilibrium creep stage. Fig. 7 presents void density versus creep duration curves for silver and copper. It is seen that the void nucleation rate for silver is much higher than that for copper. The technique employed for silver and copper did not permit the authors to detect the void formation in aluminium. Therefore, the density of the material was measured after different creep test durations. Fig. 8 presents curves depicting the variation of the density of aluminium and copper with increase in test duration. Throughout the experiment, no density variations were found to occur in aluminium, whereas the density in copper decreased appreciably, by about 4%, due to void formation. Consequently, it may be said that the phenomenon of swelling of materials exists also under normal creep conditions, similar to the phenomenon of increase in volume which occurs in metals irradiated by high-energy particles. The data obtained thus evidence that the void nucleation during creep is largely affected by the stacking fault energy. These results are plotted in Fig. 9. The plot illustrates the void formation process during plastic deformation as a function of stacking fault energy under creep conditions at temperatures of about 0.6T me it, when the flow of material is governed by the climb of dislocations due to the dislocation diffusion of point defects such as vacancies or interstitial atoms.

.A?

10'

200 250 zih)—-

10'

70"

10 70' numberofvoids (mm~ I •

w

Fig. 8 Fig. 9 Fig. 8. Density variation in creep tests for copper (1) at 848 K and for aluminium (2) at 583 K [76] Fig. 9. Stacking fault energy y dependence of density of voids arising during creep

Effect of Dislocation Structure on Creep and Fracture in Metals (I)

23

The most typical case, under normal test conditions, is the formation of voids at grain boundaries. However, when the density of defects becomes very high for some or another reason, the void formation occurs not only a t grain boundaries but also within them. This situation takes place, for example, in the case of evaporating zinc from brass or irradiating metals and alloys by high-energy particles, when t h e density of point defects becomes high. This may be illustrated with reference to the example of irradiation of nickel by Ni + ions at 877 K to doses of the order of 25 dpa or irradiation of niobium by 8 x 1019 neutrons/cm 2 a t 533 K [77, 78], For normal creep conditions, just as in the case of radiative irradiation, the strain r a t e thus consists of two parts: s = ce0 + ps , where e 0 is the rate of creep and s the rate of swelling. B u t the quantity s is much smaller compared to t h a t in the case of radiation-initiated creep. 6. Effect of Relative Density of Screw Dislocations on Creep of Metals and Alloys I t has been noted in the foregoing that in their nuclear structure screw dislocations differ significantly from edge dislocations. A pure screw dislocation is not capable of climbing. A splitting screw dislocation can climb, but the rate of screw dislocation diffusion is a factor of five lower than t h a t of edge dislocation diffusion (see Table 1), and therefore the climbing power of an extended dislocation is extremely low. I t is of interest to study the effect of screw dislocations on the behaviour of materials subject to load in the temperature range where the deformation is controlled by the climb of edge segments. In [79, 80] the effect of the relative length of screw dislocations on the mechanical properties of armco iron at room temperature and at higher temperatures was studied. The dislocation structure was characterized by the ratio L^ijL, where Lhkl is the length of all the dislocations aligned with the projection in {hkl) direction, and L is the length of all the dislocations measured. B y hot and cold rolling and subsequent annealing a t 953 K (680 °C), specimens of armco iron with different ratios of dislocations oriented along » t *'Vti * A«-*-— s * * * % • - . » * * ». » * « * » » n j d t i j * ? v« • • • < 6 - » - ' • *• •'•'>»••»•*• * •» *»-»• * ** * * » tA '•_%"»• * • '« •*•* * * * * * ». > * * A » * > * * » »• * v * « ». * ' * j».-« a, V» ! »ft> *•"» « * * if j m , *••>• «• * * * Vfi •»'* .*,*'.•». ». A * ft * » k *A • ) •'•*'» » V » » » » > « • ## r S * ¡» » * * 0 f %'•* •«

« »'»

« * * *-' v * flirti*

» * " • « » . » • * • < « • ' . • »

» >' t t. »•»

* *J*.

»

» * »

» »^r*'»-» « », * *

"I *

•

•«

if

»

*

>

W

»'

* * * * m » » j p l is * * *

* +

»

0

«

* * * * » « *

>.

» * 4 «

* 4

•«•**»»•#'» 1 * '*

'

* » *> * i * *

» « » * * # # « . » • # # * « • 41

' '« * < » * - * « .4 * * » * V V » « * « • » , V » •• - - -u -) -1 ' Fig. 4. E n l a r g e d image of t h e u p p e r p l a n a r defect observed in Pig. 3. T h e inserted c o m p u t e r simulated image corresponds t o a thickness of 30 n m a n d a defocus value of —142.5 n m

¡m'it'.mww-P*«-»on. • ! ' » . , , • !ivi

» i W t w ' M i ' t V ' fttftrt

»

tru^rvf

.' i t t i M t.i>»lt>t*> i;vi',>>:1 , n | i'ii i-| i | r f l n ' ' ' ' i | i 'litfjfj&f.left < I'rn^V^iS'cv»'« »"•'ìV«-»'"^» f > » - 'rI'fV» » ? i> f V'«" >'»V» «V 1 » . ' I . . 11 • 1 « i jffpyfth: t jp»*»» 1« >M'n • • • o » - . •.>y,i'iDr , .-«'e,,',-.V., a t ^ g i " » B M * » ' ' ' • « ' • • ' • >A >

* f ' ' QiiiZZZ '

f à ' "-T I'" i ' J ' I ! 1 ' 1 i '

Mi'

iVll'Ti^^l'fl'i 11 n'virt^t'i'? ('iifi-fri'» • A I M ' S I I I K I ' I K i ft» ! fi I .«•»,«• • u !' I1 • « l ' I '•« ! ••.••»'»< • • • !'| • ¡1 ft

y «

t»»'>>ji J

i

!

>

»

/

»

•••imi • ti < t ^ ^ i i > t ' i >it m i • i n - • 1 » »>» • f> i »• > » o ' r t Vi « j . M I M h •.»> n'l'i 1 . . i* . . ' ' 1 ».-• n ! • • ""'

2fir

« < ' •[• • ' i . i r . 1.1'. . i

r

f^t • kf t>

II

>111 i t . v f . -. • - . v - . •'¡¿ììj >;'••'ftftéAuiààtékiiùàé» f.™ • • » - • f.ita •' i. ' '» «; w ì m ì w « - • f

•

'

V-v

11. i •, • • • - •••:•'« -'• • / • '••»'> •>: >••»»••• i• ^nW^wrt ji 1 '•»••v 1 • »'-*»'- m r A ? .•

Fig. 5. H i g h resolution image along t h e [210] direction showing t w o defects in basal planes linked by a p l a n a r defect parallel to t h e (121) plane. See arrows 3 physica (a) 85/1

34

P . C . L O V E Y , G . VAN T E N D E L O O , a n d S . A M E L I X C K X

Ï HI

—

• •

i i

• •

•

Fig. 6. Orthorhombic superstructure. Atomic arrangements of the different (001) planes. Full circles correspond to copper atoms and open circles to aluminum atoms

u

0 l i m

0

^ k )

\

[ S

n

= lim o

S

( k )

S

+

(5)

2

{ k )

a

( k ) ]

=

l i m

i-i- o

S

n

{ k )

.

(6)

Fluctuations in density are described in ¿-space by the structure factor $(&), given by S ( k )

=

S ^ k )

+

S

2

.

( k )

(7)

The long-wavelength limits are determined by l i m

S ( k )

=

l i m

i-s-0

[ S ^ k )

+

S

{ k ) ]

k-*0 =

n k

B

T

X

r

•

(8)

Now from (5), (6), and (8) we get S(0) + 4!>(0) = n k T and B

^ i l H O )

2

=

-§- n k

B

T %

T

X

(9)

T

.

( 1 0 )

The superscript (2) simply corresponds to the order of the correlation function. S ( k ) , S ( k ) , and S ( k ) are the structure factors corresponding to g { r ) , g [ r ) , and g (r) and £(0), £g>(0), and £(0) are the values of S ( k ) , S { k ) , and S { k ) in the long-wavelength limits, respectively. In order to evaluate $^>(0), S$>(0), and(S'^O) we have adopted a simple procedure. In a recent publication Sharma and Sharma [10] have derived an expression for the structure factor in the square well system, in which the square well (SW) potential has been treated as a perturbation on the hard-sphere potential for liquid metals. Further the calculation of the partial static structure factors of molten cuprous chloride has been reported [11] in which the expression given by Powles [12] for a molecular liquid has been utilized. According to his argument the cuprous chloride could be treated as a molecular liquid with the chlorine atom as the molecular centre. The object of this paper is to calculate the partial higher-order structure factors of n

1 2

2 2

1 2

n

n

2 2

2 2

1 2

Partial Higher-Order Structure Factors for Molten Cuprous Chloride

41

molten cuprous chloride using SW potential. The potential parameters of SW X and s which represent breadth and depth, respectively, are taken from the earlier calculations [13] where these parameters were determined from the chlorine-chlorine structure factor [$ci-ci(fc)] by comparing its first peak with the experimental data. The expression of Sci~ci{k) is given by

The C(k) in the SW potential is given by C(k) =

-

24rj \oc(ko)3 [sin ka — ka cos ha] + {kaf

+ ß(ka)2 [2ka sin ka — (k2a2 - 2) cos ka — 2] + + y[(4F( 0) ^r V T ' (I -,,)* 1 + 4 jj +

— 4rf + (1 - V)*

8rjs(X3 - 1) knT

(17)

42

R . V . SHARMA

T h e expression [1] which is used to evaluate the third-order and higher-order partial structure factors in the long-wavelength limit is S « ( f c 1 ; ... , kn_lt

0) = nkBT A

g ( » - i ) ( f c 1 ; ...f

fen_l}

+

+ ^ 2 ) ( 0 ) i S ( « - 1 ) ( f e 1 . . . /£„_!)• The derivatives «

M

of/S' (2) (0) -

®

-

and$(3,(0, ^

(18)

0, 0) with respect to pressure are governed b y [1]

0 ) « .

(19)

3. Results and Discussion T h e calculated values of S Rt °f the set R are sublattices if R,T = R } (where T is any translation of the lattice) and UR 4 = R. The enumeration of the sublattices (or of the lattice divisions) is an independent problem. G is the group of transformations of the sublattices under the action of the translations. |G| = t for s.c., b.c.c., f.c.c. lattices. If 2 also, the volume of calculations even for the case of a high dimension is comparatively small. 4. The Diagram Lemma The most difficult moment of the procedure is the choice of the extreme points of the set N forming the vertices of the polyhedron M " . The choice is easily done on the plane visually (v = 2); at v = 3 the visual choice is difficult, and at v = 4 is impossible. The bounds of visuality are extended by the using of point-number diagrams. The selection rule is formulated in terms of point-number diagrams. The element of the (p + 1)-dimensional diagram {yv y2, ..., yp) Y is the ^-dimensional point (ylt y2, ..., yv) in which the number Y is located. The convex combination of several elements is determined as usual: «í?/^- Hoiiy^, ..., X ^iV^) 2 ( £ Xi = 1, Si 0). _ Now let us determine the rule of the element crossing-out on the diagram. L e t N be a set of point-numbers forming the A-diagram.

55

Ground State of a Solid Solution with Interactions up to fc-th Coordination Spheres

The rule: The element (ylt y2, ..., yP) Y must be crossed out if the element (yv y2, ... ..., yv) Y can be obtained by the convex combination of other elements, where YfS Y. The retained elements of the diagram after crossing-out are basic ones. Let the set of points N = {x^, . . . , x m e e t the requirements: 1. a f ^ 0 ; 2. (0, 0, ..., 0) e N (let us suppose t h a t this is the first point of the set, i.e. i — 1); 3. xf > 0 for i =f= 1. Then we form the A-diagram, the element ( x ^ j x f , x ^ / x f , ..., x ^ / x f ) l / ^ i ' corresponding to every point, except the first one. It is obvious t h a t the correspondence between the points N/(0, 0, ..., 0) and the elements of the diagram is reciprocally unambiguous. The lemma: There is one and only one basic element of the ¿-diagram for a n y extremal point of the set N (except (0, 0, ..., 0)) and vice versa. 4.1

Proof

Let us prove t h a t the crossed-out elements correspond to the internal points of the set N and vice versa. Let { x f , x f , ..., x^} be an internal point of N, then it is a convex combination of the other points, oci = 0 ,

oij ^ 0 ,

£ a ? = 1.

(4)

But then a£>\ (0 ' X\(0 '

i

~~W) x\'/ ~0 x\'

=

x

Ji)

xf

x f ) xf A

z

% &

xf

(5)

where the factors OCjxf Pi =

S

(6)

«.¡xf

satisfy all conditions of a convex combination, being equal to zero. According to the rule the element {xf ¡xf, x f j x f , ..., x^jxf) 1/xf is crossed out. On the other hand, if the element {xf ¡xf, x f / x f , ..., x f j x f ) 1/xf is crossed out, then for some X sS (»)

(0 »3

(») Xy) (i)

x\

Ji) xf

' xf

' "'

Ji)

Pc = Xi

0,

Z ft =

l.

(?)

Now 4° '

x

xfx,

f X

=£

(8)

where the factors Mti

tXj =

2

U) .0)

(9)

ft/*"

satisfy to the all conditions of the convex combination. So, the point C( 1/X, x f / x f X ,

56

B. A. Men and M. L. L e v i t a n

... x ^ j x i ' X ) is an internal point of the set N. In its turn, the point /1 (¿) ( P^IPA) 1 IPA elements and determine the basic elements of this diagram. The point-number diagram for the s.c. lattice with these elements is represented in Fig. 4. When the point-number diagram is formed we have 33 elements. 2 ) After further crossing-out only three basic elements are retained. Along with point (0, 0, 0) we get four extremal points of the set N: 1. "pure" ferromagnetic A| (Table 1; 2); 2. "pure" metal B (Table 1; 2); 3. "pure" antiferromagnetic AfAj, (Table 1; 1); 4. alloy AB (Table 1; 1). b.c.c. lattice: There are two different ways of divisions into two sublattices; 2 - 3 ; 7 - 4 ; 5 - 5 ; 10-6; 7 - 7 ; 20-8 (it is interesting that we have for the f.c.c. lattice as many divisions as for the b.c.c. lattice). If t 4, then there are 13 divisions, 669 coordinated structures, 29 elements on the diagram, three basic elements and four extremal points of the set N: 1. "pure" ferromagnetic Af (Table 1; 4); 2. "pure" metal B (Table 1; 4); 3. "pure" antiferromagnetic AfAj. (Table 1; 3); 4. alloy AB (Table 1; 3). f.c.c. lattice: In this case we have seven basic elements on the diagram, eight extremal points of the set N: 1. "pure" ferromagnetic Aj (Table 1; 7); 2. "pure" metal B (Table 1; 7); 2 ) If several numbers correspond to the same point of the diagram, then the minimal number should be retained according to the rule of crossing-out.

60

B. A. MEN and M. L. LEVITAN : Ground State of a Solid Solution

3. "pure" antiferromagnetic AjA|: a) superstructure with two sublattices (Table 1; 7), b) superstructure with four sublattices (Table 1; 5), the sublattices e, a are filled by atoms Af, and a 2 , a 3 by A J,; 4. alloy A B : a) superstructure with two sublattices (Table 1; 6), b) superstructure with four sublattices (Table 1; 5), the sublattices e, a are filled by atoms B , and a 2 , a 3 by A (only Af or only Aj); 5. alloy AB 3 : superstructure with four sublattices (Table 1; 5, 5), one of which is filled by atoms of sort A, and three other ones by B . 6. alloy A 3 B : superstructure with four sublattices (Table 1; 5, 5), one of which is filled by atoms of sort B , and three other ones by A; 7. magnetic superstructure A|AJ,B2 (Table 1; 5, 5), two sublattices are filled by atoms of sort B , one by A|, the other by A|; 8. magnetic superstructure (A|)2A|B (Table 1; 5, 5), two sublattices are filled by atoms Aj, one by AJ, the other by B . I t should be noted that the microstructures 1 - 4 in case of the s.c. lattice correspond to the optimal divisions 1 and 4 (Table 2). Analogous statements are correct for b.c.c. and f.c.c. lattices also. I t is the numerical confirmation of the selection rule. The calculations show that the selection rule for the case oil = 1, m = 1, k0 = 1 is correct. The difficulties occurring in more complicated cases are connected with the high dimension of the diagrams. Let us notice that if the rule is correct a priori, the volume of the necessary calculations decreases considerably. References [1]

D . VAN D Y C K , R . DE R I D D E R ,

and S.

AMELINCKX,

phys. stat. sol. (a)

59,

513 (1980).

[ 2 ] R . DE R I D D E R , D . VAN D Y C K , a n d S . AMELINCKX, p h y s . s t a t . s o l . ( a ) 6 1 , 2 3 1 [ 3 ] D . VAN D Y C K [ 4 ] J . KANAMORI,

and R . DE R I D D E R , phys. stat. sol. (a) 6 7 , 6 0 3 Progr. theor. Phys. (Kyoto) 3 5 , 1 6 ( 1 9 6 6 ) .

(1980).

(1981).

[5] L . N. LARIKOV, V . V. GEITCHENKO, and V . M. FALTCHENKO, Diffuzionny protsessy v uporya-

dotchenny splavach, Izd. Naukova dumka, Kiev 1975. [6] L . D. LANDAU and E . M. LIFSHITS, Statisticheskaya Pizika, Vol. 1, Izd. Nauka, Moskva 1976. [7] E . M. LIFSHITS, Zh. eksper. theor. Fiz. 11, 255 (1941). [8] E. M. LIFSHITS, Zh. eksper. theor. Fiz. 11, 269 (1941). [9] F. I. KABNELEVICH and L. E . SADOVSKII, Elementy lineinoi algebry i lineinogo programmirovaniya, Izd. Nauka, Moskva 1967. [10] B. A. MEN, Izvestiya vuzov, Fizika 1, 50 (1983). (Received January 10, 1984)

D . M.

V A N DERWALKER

: D a r k - F i e l d T E M Method for Crystal S t r u c t u r e D e t e r m i n a t i o n

61

p h y s . s t a t . sol. (a) 85, 61 (1984) S u b j e c t classification: 1.4; 22.1.2 Department

of Materials

Science, State University

of New

York1)

A Dark-Field TEM Method for Crystal Structure Determination of Cu-Rich Phases on Twins in Silicon By D. M.

VANDERWALKEB

A d a r k - f i e l d T E M m e t h o d is developed to i d e n t i f y t h e crystal s t r u c t u r e s of second phases which is b a s e d on t h e f a c t t h a t t h e difference in s t r u c t u r e f a c t o r b e t w e e n m a t r i x a n d precipitate is proport i o n a l t o t h e i n t e n s i t y difference. I t can distinguish b e t w e e n phases whose s t r u c t u r e factors a r e e q u a l in m a g n i t u d e b u t opposite in sign. The m e t h o d is applied t o Cu silicide phases on twin b o u n d aries in Si. T h r e e phases a r e observed, a cloud-like phase, a small spherical phase e m b e d d e d in t h e cloud, a n d a layer which f o r m s on t h e t o p a n d b o t t o m edges of t h e t w i n . T h e cloud a n d t h e layer a r e f o u n d t o be CuSi a n d t h e small spherical phase a t r a n s i t i o n phase of t h e Si lattice w i t h Cu on o c t a h e d r a l sites. W e a k - b e a m l a t t i c e images show t h e cloud-like a n d spherical phases are coherent a n d t h a t vein-like voids can e m a n a t e f r o m t h e precipitate interface. U m die K r i s t a l l s t r u k t u r e n der zweiten P h a s e zu identifizieren, wird eine T E M - D u n k e l f e l d m e t h o d e e n t w i c k e l t , die d a r a u f b e r u h t , d a ß die Differenz der S t r u k t u r f a k t o r e n zwischen Matrix u n d Präzip i t a t p r o p o r t i o n a l zur I n t e n s i t ä t s d i f f e r e n z ist. E s k a n n zwischen P h a s e n unterschieden werden, deren S t r u k t u r f a k t o r e n in d e r Größe gleich, jedoch im Vorzeichen unterschiedlich sind. Die M e t h o d e wird a u f Cu-Silizidphasen a u f Zwillingsgrenzen in Si a n g e w e n d e t . Drei P h a s e n werden b e o b a c h t e t , eine wolkenähnliche P h a s e , eine kleine kugelförmige P h a s e , die in der Wolke eingebettet ist, u n d eine Schicht, die sich an d e n oberen u n d u n t e r e n K a n t e n des Zwillings ausbildet. E s wird g e f u n d e n , d a ß die W o l k e u n d die Schicht CuSi ist u n d die kleine kugelförmige P h a s e eine Ü b e r g a n g s p h a s e des Si-Gitters m i t Cu auf O k t a e d e r p l ä t z e n darstellt. S c h w a c h s t r a h l g i t t e r d i a g r a m m e zeigen, d a ß die wolkenähnliche u n d die kugelförmige P h a s e k o h ä r e n t sind u n d d a ß aderförmige H o h l r ä u m e v o n d e r P r ä z i p i t a t g r e n z f l ä c h e ausgehen k ö n n e n .

1. Introduction

The crystal structures of second phases in a solid can in most cases be determined from X-ray diffraction experiments [1]. However, only the magnitude of the structure factor be found, and phases whose structure factors are equal in magnitude but opposite in sign are indistinguishable. In the study of transformations involving metal silicides, it is important to differentiate between the structures having structure factors of opposite sign. The transition phase of the Si sublattice with metal atoms on octahedral sites has a structure factor which is opposite in sign to the phase of the Si sublattice with metal atoms on tetrahedral sites. The crystal structures of the phases in the Cu-Si system identified using X-ray diffraction are listed in Pearson [2, 3]. In 1955, Dash examined the decoration of hexagonal dislocation loops in Si with Cu precipitates using an infrared image tube [4], It is not possible to use X-ray diffraction methods to identify the crystal structure of the particles on the dislocations. Thus, this paper introduces a new method to identify crystal structures using dark-field transmission electron microscopy and applies it to study the formation of Cu-rich phases on twin boundaries in Si. S t o n y Brook, New Y o r k 11794, USA.

62

D. M. Vanderwalker

2. Experimental Procedure A layer of Cu was evaporated on a cast Si specimen before annealing for six hours at 500 °C in a He furnace and quenching in air. The specimens were thinned for transmission electron microscopy (TEM) in two steps, first mechanically then chemically with a 6/7 nitric acid, 1/7 hydrofluoric acid solution. All of the transmission electron microscopy (TEM) was performed on the J E M 200CX at Stony Brook except the high resolution lattice images which where taken on t h e Phillips 400 a ST a t IBM. The high resolution lattice images were taken using "weak-beam" diffracting conditions. Weakbeam conditions [5] are set by tilting the beam such t h a t g is on the optic axis and w = s£g 5, where s is the deviation parameter and the extinction distance. In the weak-beam lattice images g was placed on the optic axis and a large aperture positioned to include a portion of the 2g and 0 spots. 3. Results and Discussion 3.1 The use of dark-field precipitate reflection the crystal structure of second phases

images

to

identify

A method has been developed to identify the crystal structure of small precipitates which involves comparing intensity ratios to structure factor ratios. I t is the only method available to distinguish between two structures whose structure factors are equal in magnitude but opposite in sign. When precipitates are coherent, the main contribution to the image is structure factor contrast [6]. The change in intensity due to the presence of a particle is thought of as an effective change in thickness. The intensity change is proportional to the difference in the structure factor. The following relations from Hirsch et al. [6] are used in this analysis : nV Q cos 6 ~W 0 AJ = * A J — - — I s i n ^ ,

AF = F

R

(2)

- F„ ,

(4)

where is the extinction distance in the precipitate, is the extinction distance in the matrix, Ai is the particle thickness, X the electron wavelength, FG the structure factor, and F c is the volume of the unit cell. Dark-field precipitate reflection images are taken with a known hkl, and the intensity of each phase present measured relative to the background. Since the change in intensity is proportional to AF = FV — FU, AF values can be calculated and the ratio of the AF'B for two phases compared to the measured intensity ratios. 3.2 Application

of the method

to the Cu-Si

system

The method developed to identify the crystal structures of small second phases was applied to the precipitation of Cu rich phases on twin boundaries in Si. There are three phases present, a cloud-like phase (Fig. 1 a n d 2), a small phase which is surrounded by the cloud (Fig. 1 and 2), and a layer of second phase which forms along the top

Dark-Field TEM Method for Crystal Structure Determination in Silicon

63

Fig. 1. Weak-beam lattice image of precipitation on a crack. Both phases are coherent

m

1

- •• v : m

mm5nm

mm

1

1

a n d b o t t o m edges of the twin boundary (Fig. 3). I n Fig. 4-, the small phase is periodically spaced within the layer on the edge of t h e boundary. The dark-field precipitate reflection image in Fig. 5 a shows the layer of second phase to be in strong contrast and the region of twin b o u n d a r y in the center to produce no contrast. Fig. 5 b is a dark-field precipitate reflection image of the same b o u n d a r y tilted to a different orientation. The cloud appears grey and the small phase white. I n this experiment, the intensities of the phases were measured with respect to background b y taking profiles across the phases in Fig. 5 with a microdensitometer. The ratio of the intensities of the white phase to t h e layer in Fig. 5 a and the ratio of the intensities of t h e white phase to t h e grey phase in Fig. 5 b were both found t o be a b o u t 2.6. The phases can be identified b y finding the two whose ratio of structure factor differences is 2.6. The assumption t h a t At is the same for each phase was used in this analysis because there do not a p p e a r to be any intensity variations within the precipitate when its thickness changes. The structure factors were calculated from the positions of the a t o m s in a unit cell (.x, y, z) and the atomic scattering factor / 4 [1],

Fhki = £ ft

e^Cz+^+k».

i

a

b

Fig. 2. Bright field and weak-beam images of precipitates on twin boundary (B2). Two phases are visible, a cloud-like phase and a smaller phase which is within the cloud

64

D . M . VANDERWALKER

Fig. 3. A strip on each side of the twin (B2) has been replaced by a layer of second phase

Table 1 lists the structure factor values for the crystal structures of Cu-Si phases listed in Pearson [2, 3] when hkl = 020. The reflection hkl = 020 was chosen because it is a forbidden reflection in Si. The phases considered are CuSi (A2), CuSi (B3) [7], CuSi (A3), Cu15Si4 (D8S), Cu5Si (A13), Cu3Si (A2), and two CuSi2 transition phases. The transition phases are the Si sublattice with Cu atoms on either the tetrahedral or octahedral sites. Their structure factors are equal in magnitude but opposite in sign. The ratio of the change in structure factor can be taken from this chart. The closest value to 2.6 is attained when the cloud-like phase and the layer are both CuSi and the small spherical phase is the transition phase of the Si sublattice with Cu on octahedral sites.

Pig. 4. Twin boundary (B2) shows that most of the precipitates are periodically spaced within the layer region on the side of the boundary

65

Dark-Field TEM Method for Crystal Structure Determination in Silicon Wnm

a

b

Pig. 5. Dark field precipitate reflection images of the same twin boundary (B2) taken at two different orientations, g = 020. a) The layers on each side of the twin are in contrast while the middle section is out of contrast, b) The cloud-like phase appears grey and the small phase white Table 1 A list of Cu-Si second phases and their structure factors for the hkl = 020 reflection

CuSi (A3) disordered CuSi (A2) CuSi (B 3 , dc) Cu 15 Si 4 (D8.) Cu5Si (A13) CuSi, (Si sublattice with Cu on tetrahedral sites) CuSi2 (Si sublattice with Cu on octahedral sites) Cu3Si (Aj) disordered

3.3 The structure

of the twin

- 6.25 + 12.5 + 2 0 0 -26

0 0 0 0 0 0

-

6.25 12.5 2 0 0 -26

+26

0

+26

+ 12.75

0

+ 12.75

boundary

The twin boundary was characterized by finding the boundary plane, angle and axis of rotation. B y tilting the crystal so the boundary plane is parallel to the electron beam, the boundary plane was found to be (120). The misorientation angle was measured by taking diffraction patterns one each side of the boundary and measuring the magnitude of the shift in Kikuchi lines. The angle corresponding to the shift is 3.7°. This method is similar to that used by Young et al. [8] to measure misorientation angles in low-angle grain boundaries. The rotation axis, found by taking the cross product between the beam direction and the shift vector, is a 2 = (12l). A second boundary ( B l ) which contains the Cu rich phases has a misorientation angle of 2.5° and an axis of rotation a ± = (611). Dislocations appear in the twin boundary shown in Fig. 6. Since the second phases are only observed on the top and bottom edges of the twin boundary, the stress fields of the defect must promote the transformation by either reducing the strain 6

physica (a) 85/1

66

D. M. VAN'I)ERWALKER

Fig. 6. Dislocation array in twin boundary (B2). Precipitation occurs at the top and bottom edges of the twin

energy or acting as a fast diffusion path enabling a critical concentration of solute to be accumulated [9], The dislocations terminate at the edges of the twin plate. Since there are changes in the pressure and stress field near the end of a terminating dislocation [10, 11], the region near the termination point is a preferred nucleation site. The most unusual observation is the lines of contrast which start from the interface of either the small spherical phase or the cloud-like phase and penetrate the crystal in branches (see Fig. 7). The branches cannot be dislocations because dislocations cannot end in the middle of a crystal. The lines may be voids whose formation is associated with the emission of vacancies, which has been suggested to occur in order to relieve strain associated with the transformation [12].

Fig. 7. Weak-beam lattice image which shows vein-like voids emanating from the precipitate interfaces

67

Dark-Field TEM Method for Crystal Structure Determination in Silicon

4. Summary and Conclusions (i) A dark field TEM method was developed to identify the crystal structures of second phases based on the concept that the change in intensity between precipitate and matrix is proportional to the structure factor difference. It can distinguish between phases whose structure factors are equal in magnitude but opposite in sign. (ii) The method was applied to Cu-rich phases on twin boundaries in Si. Three phases were observed, a cloud-like phase, a small phase embedded in the cloud, and a layer at the top and bottom edges of the twin. The cloud and layer were found to be CuSi and the small phase a transition phase of Si sublattice with Cu on octahedral sites. (iii) Dislocations were found to be present in the twin boundary. The region near where the dislocations terminate at the edge of the twin plate is a preferred nucleation site because the gradients in the dislocation's pressure and stress field can assist the transformation. (iv) Weak-beam lattice images show that the cloud and small phases are coherent and that vein-like voids emanate from the precipitate's interface. Acknowledgements

The author would like to thank Dr. K. N. Tu, Dr. D. A. Smith, Dr. C. R. M. Grovenor, and Dr. P. E. Batson of IBM, Dr. J . B. Warren of Brookhaven National Laboratory, and Prof. A. H. King and Prof. R. Reeder of SUNY Stony Brook for their assistance. References [1] B. D. CULLITY, Elements of X - R a y Diffraction, Addison-Wesley Publ. Co., Reading (MA) 1978. [2] W. B. PEARSON, Internat. Ser. Monographs Metal Physics and Physical Metallurgy, Pergamon Press, N e w York 1958. [3] W. B. PEARSON, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Vol. 2, Pergamon Press, New York 1967. [4] W. C. DASH, J. appl. Phys. 27, 1193 (1956). [5] D. J. H. COCKAYNE, J. Microscopie 98, 116 (1973). [ 6 ] P . B . H I R S C H , A . H O W I E , R . B . NICHOLSON, D . W . P A S H L E Y , a n d M . J . W H E L A N ,

Electron

Microscopy of Thin Crystals, Krieger Publ. Co., N e w York 1977. [ 7 ] G . D A S , J. appl. Phys. 4 4 , 4 4 5 9 ( 1 9 7 3 ) . [ 8 ] C. T. Y O U N G , J . H . S T E E L E , JR., and J . L . L Y T T E N , Mctallurg. Trans. 4 , 2 0 8 1 ( 1 9 7 3 ) . [9] D. M. VANDERWALKER, Proc. Ann. Electron Microscopy Soc. Amer., Vol. 42, Ed. G. W. BAILEY, 1984 (p. 346).

[ 1 0 ] S. J . SHAIBANI a n d P . M. HAZZLEDINE, P h i l . Mag. 4 4 , 657 (1981).

[11] D. M. V A N D E R W A L K E R and J. B . V A N D E R S A N D E , Proc. Internat. Conf. Solid-Solid Phase Transformations, New York 1982 (p. 667). [12] R. BULLOUGH and R. C. NEWMAN, Rep. Progr. Phys. 33, 101 (1976). (Received June 19,

1984)

69

S. A. ALTEKOVITZ et al. : Structural and Chemical Analysis of Silicon Nitride phys. stat. sol. (a) 85, 69 (1984) Subject classification: 1.3 and 1.5; 22 Department of Electrical Engineering, University of Nebraska, Lincoln1) and NASA Lewis Research Center, Cleveland2) (b)

(a)

Structural and Chemical Analysis of a Silicon Nitride Film on GraAs by Null Ellipsometry By S. A . ALTEROVITZ3) (a), G . H . BU-ABBUD (a), J . A. WOOLLAM (a),

and D. C. Liu (b) Multiple-wavelength-angle-of-incidence null ellipsometry, together with the effective medium approximation, are used to evaluate both the composition and the geometrical structure of an insulating film made of silicon nitride and silicon oxide on a GaAs substrate. The results are found to be in good agreement with AES measurements on the same film. L'ellipsometric nulle, à ondes et angles d'incidence multiples, avec l'approximation du milieu effectif, sont utilisées pour evaluer la composition et la structure geometrique d'une couche diélectrique mince constituée de nitride du silicon et d'oxyde du silicon sur GaAs. Les résultats cont affirmés par les measurements en AES faits sur le même échantillon.

1. Introduction An accurate, non-destructive testing of thin films on substrates is one of the most important applications of ellipsometry [1, 2], The ultimate goal of the test is the chemical composition of the film as a function of depth. However, this type of result can be obtained in practice only for rather simple structures, and only where the optical properties of the materials included in the film can be estimated ahead of time. This is not a major restriction in one of the most important applications, namely, the study of insulating thin films on top of semiconducting (or metal) substrates. In these cases, the films are deposited or grown in such a way that the major chemical components of the film are known, and only their distribution is being examined. Under these conditions, ellipsometry as a non-destructive method, is superior to AES depth profiling by ion milling, which is destructive and lacks the depth resolution of ellipsometry. The experimental arrangements used in ellipsometry can be divided into two general categories-spectroscopic, and fixed wavelength. In scanning spectroscopic ellipsometry [1, 3 to 6], measurements are made to obtain two ellipsometric parameters tp and A (or a combination of the sin and cos of these parameters) at a large number of wavelengths. Usually, this technique is used at a fixed angle of incidence. However, the spectroscopic ellipsometry technique is not trivial to implement. First, the hardware of a completely working system is not commercially available today. In addition, a sophisticated and hardware dependent on-line computer is essential for driving the system and acquiring and analyzing data. Thus the number of such systems in operation is small. !) W 194 Nebraska Hall, Lincoln, Nebraska 68588, USA. 2 ) Cleveland, Ohio 44135, USA. 3 ) Now at NASA Lewis Research Center, Cleveland, Ohio 44135, USA.

70

S. A . ALTEROVITZ, G. H . BU-ABBTTD, J . A. WOOLLAM, a n d D . C. LIU

The other experimental category includes all the systems where single wavelength measurements are considered to be a distinct aspect of the experiment. The largest example in this category is null ellipsometry [2]. More generally this class includes any ellipsometer that needs one or more manual operations to change the wavelength. Thus, commercial " a u t o m a t i c " ellipsometers are included in this second class. The most common type, the null ellipsometer, is now a standard tool in many research and development laboratories. I t is simple to use, commercially available in various forms, and (in many cases) can be used at multiple angles of incidence. All ellipsometers in this class are limited to a small number of wavelengths, because of the manual operation mentioned above, and (for null ellipsometry) the need for a strong light source, e.g., a laser line or a strong gas emission line. Null ellipsometry has never been used (to our knowledge) to get information on both structure and composition of a thin film. Y e t , many more null or semiautomated ellipsometers are in use than automated systems. In this paper, we show that null or fixed wavelength ellipsometry can be used in a similar way to the scanning automatic technique. The material studied is a silicon nitride film on a GaAs substrate. I t is known that silicon nitride films tend to be nonstoichiometric Si 3 N 4 , i.e., they contain other components, unless special precautions are taken. For this reason, we have tested several films made under typical industrial laboratory conditions. Layers with extra oxide or a-Si were expected. However, we had no a priori knowledge of the existence of these layers, nor their position or chemical composition. Thus, the ellipsometric measurement has been put to a difficult test in order to show the problems encountered in growing these films. The results are given in terms of a model assuming several layers, each with its particular chemical composition. 2. Experimental Method and Results The experimental method is essentially based on the multiple wavelength-angle of incidence ellipsometric technique [7, 8]. However, the data analysis has been changed in order to obtain composition rather than optical constants. The method includes two parts: (i) experimental, and (ii) data analysis. In the first part, the ellipsometric parameters f and A are measured at multiple angles of incidence (MAI) „ to obtain the effective dielectric constant of the layer (sn) using the effective medium approximation (EMA) i.e. [14, 15] Y, i Za Jm, n m

n n

(1)

Structural and Chemical Analysis of a Silicon Nitride Film on GaAs

71

where „ is the volume fraction of the m-th material in the w-th layer. The expected y>' and A' were calculated using an assumed set of thicknesses dt (i = 1, ..., n) of the layers, using standard equations [2]. In step I I I , we use a Marquardt algorithm to minimize the error function F [16, 17], or p, where J - = £ [(y, - y O 2 + ( z J - z T ) 2 ]

(2)

V

and

F

Here y> = if(dit?.j) and A = Zl (