Engineering materials and their applications [4 ed.] 0395296455, 9780395433058

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Engin

and Their Applications

PHYSICAL PROPERTIES OF SELECTED ELEMENTS Atomic Element

Aluminum Argon Barium Beryllium

Boron Bromine

Cadmium

Symbol Number Al

A Ba Be B Br

Calcium Carbon Cerium

Cd Ca C Ce

Cesium

Cs

Chlorine

Chromium Cobalt

Copper

Co Cu

Fluorine

F

Germanium

Ge

Gold Helium Hydrogen

Au He H

1

Iodine

13 18

56

Atomic Weight

901

5

10.82 79.92 112.41

4008

6

1201

58 55

140.13

CI

17

Cr

24 27 29

35.46 52 01

1

Iron

Fe

Lead

Pb

Lithium

Li

Magnesium Manganese

Mg Mn

Mercury

Hg

Molybdenum Neon

9

32 79 2 1

53 26 82

132.91

5894 63 54

3

6.94

2432 20061

Mo

25 80 42

Ne

10

95 95 20.18

Nickel

Ni

28

5871

Niobium

Nb

41

92.91

Nitrogen

N

7

14.01

Oxygen Phosphorus 2

8

16.00

P

15

54 94

Platinum Potassium

Pt

K

19

Scandium

Sc

21

30 98 195 09 39 .10 44 96

Silicon

Si

14

Silver

Sodium

Ag Na

Strontium Sulfur 3 Tin

1.85

Ortho.

3 12

Ortho

1.19

1

321

8.65

1

1.55

HCP FCC

1.50

838 3727 804

1.97

1.06

225

Hex

0.71

S

£

i

t. OS -

in CO

c

oo OS

=

U

S

X

c

In

U.

1

E

The Structure of Engineering Materials

TABLE

1.4

31

Bond Energies

(in

kj/mol)* Single Bonds

H H

432

C N

411

346 305 358 272 485 327 285 213

386 459 363 565 428 362 295

O S F

CI Br I

N

O

167 201

—

142

283 313

190

218

—

201 201

C

—

—

F

S

226 284 255 217

CI

Br

/

240 216 208

190 175

149

155

249 249 278

—

Multiple Bonds

C=C

C=N C=N N= o=o

.i).1

C=C

835 418 942

N=C N=N

"Data are taken from Used by permission.

EXAMPLE

J.

E.

Huheey, Inorganic Chemistry. 2nd

1.4

C = =o c= E=0 s= =o s= =o

615 887 607 494 ed.

|New

York: Harper

XA

XB

=

Xc

—

-

Xf

S0 2 S0 3

& Row,

|

|

1978), pp.

842-850.

is

BE(A

to B)

- l/2[BE(A

to A)

(4.0) as a

+ BE(B

reference

to B)]

96.5 kj

485 kj - 1/2(346 +155) kj 96.5 kj

= Therefore, carbon

in

[ES]

Calculate the electronegativity of carbon, using fluorine and the data of Table 1.4.

Answer

in

799 1072 532 469

1.56

1.56

below

which

fluorine, or 2.44,

is

close to the value

of 2.5 given in Table 1.3.

Mixed Ionic and Covalent Bonding We in

rarely encounter cases of perfect ionic or covalent

which the electrons

bonding

— that

are completely donated or equally shared.

is,

cases

Another

Pauling formula can be used to calculate the percent ionic bonding (the rest of the

bonding

is

covalent).

Fraction ionic

where

XA

and

XB

=

1

-

e

^*s)2

- 1/4(;f

are electronegativities of the

two

species.

(1-5)

32

Fundamentals

CRYSTALLINE AND NONCRYSTALLINE GLASS STRUCTURES 1.12

Comparison

of Crystalline

Noncrystalline Structures

and

— General

Now

that we have studied the electronic structures of the atoms and how they lead to bonding into interatomic groups, we are ready to see how these groups are assembled in engineering materials as larger groups that make up crystals, grains, the noncrystalline structures of glasses, including glassy metals, the mixed glass-ceramics, and the glassy and crystalline polymers.

Before getting into the details of these

two groups,

let

us compare their prin-

cipal features.

atoms occupy regular positions describe by using a space lattice. Metals, for example, are crystalline under normal conditions. We developed a rather striking example by acIn the typical crystalline material, the

we can

that

cident (Figure 1.15). We were attempting to dissolve magnesium in liquid cast iron using a pressure chamber with an argon atmosphere. After cooling we fine, brilliant crystals of magnesium on the inside of the cover. (At these temperatures magnesium vaporized from the melt and condensed on the cover.) The hexagonal faces were quite evident; they are manifestations of the hexagonal arrangement of magnesium atoms within. In the usual case, as

found

magnesium, we would expect to find not crystal faces but a number of grains (Figure 1.16, page 34). However, if we examine the structures of the individual grains, we find the atoms arranged in an independent space latin a bar of

tice in

This

is

each grain, with the same hexagonal structure as in the single crystals. called long-range order.

As an example quartz.

page

We

of a

ceramic crystal, we may consider the structure of network of Si and O atoms (Figure 1.17a,

find a regular, hexagonal

34).

By

is no regular space lattake a crystal of quartz, melt it, and cool the melt in air, we obtain a glassy mass called fused silica (Figure 1.17b). We still find that each silicon atom is surrounded by four oxygen atoms, forming a tetrahedron, but there is no regular repetition of this structure on a space lattice. Another major differ-

tice. If

contrast, in the noncrystalline materials there

we

ence from the original quartz, which exhibits a definite melting point, is that the noncrystalline mass gradually softens upon heating and finally turns to a viscous liquid. In addition to the ceramic glasses, the polymers are entirely or partly glassy*

'Sometimes the word amorphous is used to describe the lack of crystallinity. However, we have no long- or short-range order for it to be called amorphous.

will require that a material

33

The Structure of Engineering Materials

FIGURE

1.15

Magnesium condensed from

the vapor: approximately l,000x

|Stephen Krause, Department of Mechanical Engineering, Arizona State University]

(Figure 1.18, page 35). For example, in the case of the phenol

resin (often called "bakelite") encountered in a bowling ball,

formaldehyde

we have

a single,

three-dimensional network that is essentially a giant molecule but lacks the long-range order of a crystal (Figure 1.18a). In another type of polymer in which the giant molecules are linear, and which is made up of a backbone of a chain of carbon atoms, some crystallization may occur when the chain is bent back and forth regularly (Figures 1.18i>, c). With those distinctions in mind, let us review the crystalline structures

and some ceramics and then consider the noncrystalline structures encountered in other ceramics and polymers. typically encountered in metals

34

Fundamentals

FIGURE

1.16

Grain structure in bar

FIGURE

1.17

Schematic representation of {a) ordered crystalline form and of the same composition

network glassy form

of

magnesium

[b]

random-

35

The Structure of Engineering Materials

Folded-chain theory

Giant noncrystalline molecule of phenol formaldehyde, [b] Crysby the folding back of chains. The growth mechanism involves the folding over of the planar zigzag chain on itself at intervals of about every 100 chain atoms. A single crystal may contain many individual molecules, (c) Spherulites (spherelike areas of crystallinity) in polycarbonate polymer; transmission electron mi-

FIGURE

1.18

{a)

tallinity created

crograph, 66, 000 x. [Parts (a)

and

New York,

University of

1.13

(b)

from

L. E.

Nielsen, Mechanical Properties of Polymers. Litton Educational Publishing, Inc., Van Nostrand Reinhold Company. Part (c) courtesy Jim de Rudder,

1962. Reprinted by permission of

Michigan]

Crystalline Structures We

— Metals

have already agreed that the hallmark of a crystal structure is the regular repeating arrangement of atoms. It will be very useful to us in the next chapter, when we investigate the effects of stress on crystal structure, to have a clear, simple mathematical model of the atoms' positions. To create one, we begin with a space lattice to suit our particular metal. For example, if the crystal is

36

Fundamentals

we choose

cubic,

called a unit cell,

module

By describing

of cubes.

can specify the entire

scribing just one office

1.14

made up

a lattice

we

in a skyscraper

a single cube, analogous to deup of identical modules.

This

lattice.

made

is

The Unit Cell describe the unit cell and later the movement of an atom in the cell, we need a system for specifying (1) atom positions or coordinates, (2) directions in the cell, and (3) planes in the cell.

To

Position position of an atom is described with reference to the axes of the unit and the unit dimensions of the cell. Suppose that a grain or crystal is 1 built of unit cells of dimensions a ' b and c angstroms, as shown in Figure

The cell

,

,

axes are at right angles to each other. To construct the cell, we merely lay out a (the lattice parameter) in the x direction, b in the y direction, and c in the z direction. The figure shows the coordinates of sev1.19. In this case the

eral atoms in the cell. An atom at the center would have coordinates \, \, \, whereas an atom in the center of the face in the xy plane would have coordinates \, \, 0. It is important to note that commas after coordinates in space are a signal that we are referring to points in that space. These coordinates are not enclosed in parentheses; we do not want you to confuse them with

planes,

Up

which we

shall discuss in a later section.

to this point

we have used

a relatively simple cell as an example. In

nature, 14 different types of crystal lattices are found (Figure 1.20). These lat-

and

tices cover the variations in the length of a, b,

tween the

we

Fortunately, in metals

shown

c

and in the angles be-

axes.

find mostly the three simple types of cells

in Figure 1.21 (page 39): body-centered cubic (BCC), face-centered cu-

Some of the other types are encountered occasionally in a few metals, ceramics and polymers.

bic (FCC), and hexagonal close-packed (HCP).

Direction To

specify a direction in the unit

of the direction ray at the origin

cell, we merely place the base of the arrow and follow the shaft until we encounter in-

tegral coordinates (Figure 1.22, page 40). Instead of constructing other cells,

'The subscript ally 68°F (20°C).

'The angstrom meter;

1

A

= 10

specifies that this

When 10

|A)

dimension

is

measured

the unit cell expands with temperature,

=

at a

a, b,

standard temperature, usu-

and c change.

10~ 8 cm. In the SI system of units, the linear unit of measure

meter (m) =

0.1

12

perimenters prefer picometers (10~ sociated with the larger nanometer.

nm

is

the

= 10" m. Both A and nm will should also be noted that some exm) in order to have whole numbers rather than decimals as-

nanometer (nm), where

be used in the following discussion of unit cell dimensions.

1

It

The Structure of Engineering Materials

FIGURE atom

1.19

A shown

37

Coordinates of atoms in the face-centered positions in a unit cell. The would have coordinates T, 0, 1. Note: T is equiva-

in the next unit cell

lent to -1.

we can

use a point that has fractional intercepts in the unit cell and multiply common denominator. Thus direction A is obviously [111], but B has coordinates \,\, at the edge of the cell. These become [210]. Note that in specifying a direction, we put square brackets around the numbers to distinguish direction from the notation for coordinates and parentheses for a plane, described later. Note also that we can have negative-direction indices, as

by the

least

shown by C. We indicate If we wish to find the

we

origin,

these with an overbar. indices of a direction that does not pass through the merely pass a parallel direction through the origin and proceed

as before.

system the dimensions of the unit cell are the same: a = order in a given set of indices, such as [110], depends on which

In the cubic

b = c

The

.

directions

we happened

to choose for x, y,

and z in the crystal, because in the we wish to signify a set of direcand [011]. These are all directions

cubic system the indices are identical. Often

tions that are related, such as [110], [101], across the face diagonal of the cube. To specify these similar directions, we use pointed brackets and the indices of only one direction. Thus