Stacking faults in ceramics Some ceramic oxides may be described in terms of

4.4.3.4 Stacking faults in ceramics Some ceramic oxides may be described in terms of

fcc or cph packing of the oxygen anions with the cations occupying the tetrahedral or octahedral intersti- tial sites, and these are more likely to contain stacking

faults. Sapphire, ˛-Al 2 O 3 , deforms at high tempera- tures on the ⊲0 0 0 1⊳ h1 1 2 0i basal systems and dis-

Figure 4.33 A diamond cubic lattice projected normal to sociated 1 3 h 1 0 1 0i C 1 3 h 0 1 1 0i dislocations have been

⊲1 1 0 ⊳. represents atoms in the plane of the paper and C observed. Stacking faults also occur in spinels. Stoi-

represents atoms in the plane below. ⊲1 1 1 ⊳ is

perpendicular to the plane of the paper and appears as a deforms predominantly on the f1 1 1gh1 1 0i slip system horizontal trace .

chiometric spinel (MgAl 2 O 4 or MgO. nAl 2 O 3 , n D 1)

at high temperature ⊲¾1800 ° C⊳ with dissociated dislo- cations. Non-stoichiometric crystals (n > 1) deform at

faults ¾50 mJ/m 2 . Dislocations could slip between lower temperatures when the f1 1 0gh1 1 0i secondary

the narrowly spaced planes Ba, called the glide set, slip system is also preferred. The stacking fault energy

or between the widely spaced planes bB, called the decreases with deviation from stoichiometry from a

shuffle set, but weak beam microscopy shows dis- value around 0.2 J/m 2 for n D 1 crystals to around

sociation into Shockley partials occurs on the glide

0.02 J/m 2 for n D 3.5. set. A 60 ° dislocation (i.e. 60 ° to its Burgers vec- tor 1 2 ah 1 1 0i) of the glide set is formed by cutting

4.4.3.5 Stacking faults in semiconductors out material bounded by the surface 1564 and then Elemental semiconductors Si, Ge with the diamond

joining the cut together. The extra plane of atoms cubic structure or III-V compounds InSb with the spha-

terminates between a and B leaving a row of dan- lerite (zinc blende) structure have perfect dislocation

gling bonds along its core which leads to the electrical Burgers vectors similar to those in the fcc lattice.

effect of a half-filled band in the band gap; plastic Stacking faults on f1 1 1g planes associated with partial

deformation can make n-type Ge into p-type. The 60 ° dislocations also exist. The f1 1 1g planes are stacked in

dislocation BC and its dissociation into υC and Bυ the sequence AaBbCcAaBb as shown in Figure 4.33

is shown in Figure 4.34. The wurtzite (ZnS) structure and stacking faults are created by the removal (intrin-

has the hexagonal stacking sequence AaBbAaBb . . .. sic) or insertion (extrinsic) of pairs of layers such

Similarly, stacking faults in the wurtzite structure are as Aa or Bb. These faults do not change the four

thin layers of sphalerite BbAaBbCcAA . . . analogous nearest-neighbour covalent bonds and are low-energy

to stacking faults in hexagonal metals.

Figure 4.34 (a) The 60 ° dislocation BC, (b) the dissociation of BC into υC and B υ .

104 Modern Physical Metallurgy and Materials Engineering

4.5 Volume defects

more strongly than vacancies. Interstitial loops are therefore intrinsically stable defects, whereas vacancy

loops are basically unstable defects during irradiation. Defects which occupy a volume within the crystal

4.5.1 Void formation and annealing

Thus interstitials attracted to a vacancy loop, i.e. a may take the form of voids, gas bubbles and cavities.

loop formed by clustering vacancies, will cause it to These defects may form by heat-treatment, irradia-

shrink as the interstitials are annihilated. Increasing the tion or deformation and their energy is derived largely

irradiation temperature results in vacancies aggregating

to form voids. Voids are formed in an intermediate als with low stacking fault energy a special type of

from the surface energy (1–3 J/m 2 ). In some materi-

temperature range ³ 0.3 to 0.6T m , above that for long- three-dimensional defect is formed, namely the defect

range single vacancy migration and below that for tetrahedron. This consists of a tetrahedron made up

thermal vacancy emission from voids. To create the from stacking faults on the four f1 1 1g planes joined

excess vacancy concentration it is also necessary to together by six low-energy stair-rod dislocations. This

build up a critical dislocation density from loop growth defect is discussed more fully in Section 4.6.2.3.

to bias the interstitial flow.

The growth of the original vacancy cluster into There are two important factors contributing to void

a three-dimensional aggregate, i.e. void, a collapsed formation. The first is the degree of bias the disloca- vacancy disc, i.e. dislocation loop, should, in principle,

tion density (developed from the growth of interstitial depend on the relative surface to strain energy values

loops) has for attracting interstitials, which suppresses for the respective defects. The energy of a three-

the interstitial content compared to vacancies. The dimensional void is mainly surface energy, whereas

second factor is the important role played in void that of a Frank loop is mainly strain energy at small

nucleation by gases, both surface-active gases such sizes. However, without a detailed knowledge of the

as oxygen, nitrogen and hydrogen frequently present surface energy of small voids and the core-energy of

as residual impurities, and inert gases such as helium dislocations it is impossible to calculate, with any

which may be generated continuously during irradia- degree of confidence, the relative stability of these

tion due to transmutation reactions. The surface-active clustered vacancy defects.

gases such as oxygen in copper can migrate to embryo The clustering of vacancies to form voids has now

vacancy clusters and reduce the surface energy. The been observed in a number of metals with either

inert gas atoms can acquire vacancies to become gas fcc or cph structure. In as-quenched specimens the

molecules inside voids (when the gas pressure is not in voids are not spherical but bounded by crystallographic

equilibrium with the void surface tension) or gas bub- faces (see Figure 4.58) and usually are about 50 nm

bles when the gas pressure is considerable (P ⱚ 2 s /r ). radius in size. In fcc metals they are octahedral in

Voids and bubbles can give rise to irradiation swelling shape with sides along h1 1 0i, sometimes truncated by

and embrittlement of materials.

f 1 0 0g planes, and in cph metals bounded by prism and pyramidal planes. Void formation is favoured by

4.5.3 Voiding and fracture

slow quenching rates and high ageing temperatures, and the density of voids increases when gas is present

The formation of voids is an important feature in in solid solution (e.g. hydrogen in copper, and either

the ductile failure of materials. The fracture process hydrogen or oxygen in silver). In aluminium and mag-

involves three stages. First, small holes or cavities nesium, void formation is favoured by quenching from

nucleate usually at weak internal interfaces (e.g. par-

a wet atmosphere, probably as a result of hydrogen ticle/matrix interfaces). These cavities then expand by production due to the oxidation reactions. It has been

plastic deformation and finally coalesce by localized postulated that small clustered vacancy groups are sta-

necking of the metal between adjacent cavities to form bilized by the presence of gas atoms and prevented

a fibrous fracture. A scanning electron micrograph from collapsing to a planar disc, so that some critical

showing the characteristics of a typical ductile failure size for collapse can be exceeded. The voids are not

is shown in Figure 4.35. This type of fracture may be conventional gas bubbles, however, since only a few

regarded as taking place by the nucleation of an inter- gas atoms are required to nucleate the void after which

nal plastic cavity, rather than a crack, which grows it grows by vacancy adsorption.

outwards to meet the external neck which is growing inwards. Experimental evidence suggests that nucle-

4.5.2 Irradiation and voiding

ation occurs at foreign particles. For example, OFHC copper necks down to over 90% reduction in area,

Irradiation produces both interstitials and vacancies in whereas tough-pitch copper shows only 70% reduction excess of the equilibrium concentration. Both species

in area; a similar behaviour is noted for super-pure and initially cluster to form dislocation loops, but it is the

commercial purity aluminium. Thus if no inclusions interstitial loops formed from clustering of interstitials

were present, failure should occur by the specimen which eventually develop into a dislocation structure.

pulling apart entirely by the inward growth of the In general, interstitial loops grow during irradiation

external neck, giving nearly 100% reduction in area. because the large elastic misfit associated with an

Dispersion-hardened materials in general fail with a interstitial causes dislocations to attract interstitials

ductile fracture, the fibrous region often consisting

Defects in solids 105 sections these features will be brought out as well as

those which relate to specific structures. In dealing with dislocation interactions and defects in real material it is often convenient to work with

a vector notation rather than use the more conven- tional Miller indices notation. This may be illustrated by reference to the fcc structure and the Thompson tetrahedron.

All the dislocations common to the fcc structure, discussed in the previous sections, can be represented conveniently by means of the Thompson reference tetrahedron (Figure 4.36a), formed by joining the three nearest face-centring atoms to the origin D. Here ABCD is made up of four f1 1 1g planes ⊲1 1 1⊳, ⊲1 1 1⊳, ⊲ 1 1 1⊳ and ⊲1 1 1⊳ as shown by the stereogram given in Figure 4.36b, and the edges AB, BC, CA . . . corre- spond to the h1 1 0i directions in these planes. Then, if the mid-points of the faces are labelled ˛, ˇ, , υ, as shown in Figure 4.37a, all the dislocation Burgers

Figure 4.35 SEM micrograph of a medium-carbon (0.4%) steel with a quenched and tempered martensite structure,

vectors are represented. Thus, the edges ⊲AB, BC . . .⊳ showing large dimples associated with oxide inclusions and

correspond to the normal slip vectors, a/2h1 1 0i. The small dimples associated with small carbide precipitates

half-dislocations, or Shockley partials, into which these (courtesy Dr L. Sidjanin) .

are dissociated have Burgers vectors of the a/6h1 1 2i type and are represented by the Roman–Greek sym- bols A , B , D , Aυ, Bυ, etc, or Greek–Roman sym-

of many dimples arising from the dispersed particles bols A, B, D, υA, υB, etc. The dissociation reaction given in the first reaction in Section 4.4.3.2 is then

nucleating holes and causing local ductile failure. Duc-

simply written

tile failure is discussed further in Chapter 8.

BC ! Bυ C υC and there are six such dissociation reactions in each of

4.6 Defect behaviour in some real

the four f1 1 1g planes (see Figure 4.37). It is conven-

materials

tional to view the slip plane from outside the tetrahe- dron along the positive direction of the unit dislocation

4.6.1 Dislocation vector diagrams and the

BC, and on dissociation to produce an intrinsic stack-

Thompson tetrahedron

ing fault arrangement; the Roman–Greek partial Bυ is on the right and the Greek–Roman partial υC on

The classification of defects into point, line, planar the left. A screw dislocation with Burgers vector BC and volume is somewhat restrictive in presenting an

which is normally dissociated in the υ-plane is capable overview of defect behaviour in materials, since it is

of cross-slipping into the ˛-plane by first constricting clear, even from the discussion so far, that these defects

Bυ C υC ! BC and then redissociating in the ˛-plane are interrelated and interdependent. In the following

BC ! B˛ C ˛C.

Figure 4.36 (a) Construction and (b) orientation of the Thompson tetrahedron ABCD. The slip directions in a given f1 1 1 g plane may be obtained from the trace of that plane as shown for the ⊲1 1 1 ⊳ plane in (b) .

106 Modern Physical Metallurgy and Materials Engineering

Figure 4.37 A Thompson tetrahedron (a) closed and Figure 4.38 Single-faulted, double-faulted (A) and unfaulted (b) opened out. In (b) the notation [1 1 0 i is used in place of

(B) dislocation loops in quenched aluminium (after Edington the usual notation [1 1 0 ] to indicate the sense of the vector

and Smallman, 1965; courtesy of Taylor and Francis) . direction .

observed directly (see Figure 4.39). This reaction is

4.6.2 Dislocations and stacking faults in fcc

more easily followed with the aid of the Thompson

structures

tetrahedron and rewritten as

4.6.2.1 Frank loops

Dυ C υC ! DC

A powerful illustration of the use of the Thompson Physically, this means that the disc of vacancies aggre- tetrahedron can be made if we look at simple Frank

gated on a ⊲1 1 1⊳ plane of a metal with high stack- loops in fcc metals (see Figure 4.32a). The Frank par-

ing fault energy, besides collapsing, also undergoes tial dislocation has a Burgers vector perpendicular to

a shear movement. The dislocation loops shown in the ⊲1 1 1⊳ plane on which it lies and is represented

Figure 4.39b are therefore unit dislocations with their by A˛, Bˇ, C , Dυ, ˛A, etc. Such loops shown in

Burgers vector a/2[1 1 0] inclined at an angle to the the electron micrograph of Figure 4.38 have been pro-

duced in aluminium by quenching from about 600 °

original ⊲1 1 1⊳ plane. A prismatic dislocation loop lies

C. on the surface of a cylinder, the cross-section of which Each loop arises from the clustering of vacancies into

is determined by the dislocation loop, and the axis of

a disc-shaped cavity which then form a dislocation which is parallel to the [1 1 0] direction. Such a dislo- loop. To reduce their energy, the loops take up reg-

cation is not sessile, and under the action of a shear ular crystallographic forms with their edges parallel to

stress it is capable of movement by prismatic slip in the h1 1 0i directions in the loop plane. Along a h1 1 0i

the [1 1 0] direction.

direction it can reduce its energy by dissociating on Many of the large Frank loops in Figure 4.38 an intersecting f1 1 1g plane, forming a stair-rod at the

(for example, marked A) contain additional triangular- junction of the two f1 1 1g planes, e.g. A˛ ! Aυ C υ˛

shaped loop contrast within the outer hexagonal loop. when the Frank dislocation lies along [1 0 1] common

to both ˛- and υ-planes. Some of the loops shown in Figure 4.38 are not Frank sessile dislocations as expected, but prismatic dislocations, since no contrast of the type arising from stacking faults, can be seen within the defects. The fault will be removed by shear if it has a high stacking fault energy thereby changing the sessile Frank loop into a glissile prismatic loop according to the reaction

a/ 3[1 1 1] C a/6[1 1 2] ! a/2[1 1 0] Stressing the foil while it is under observation in

Figure 4.39 Removal of the stacking fault from a Frank the microscope allows the unfaulting process to be

sessile dislocation by stress (after Goodhew and Smallman) .

Defects in solids 107

Figure 4.40 The structure of a double dislocation loop in quenched aluminium (after Edington and Smallman, 1965; courtesy of Taylor and Francis) .

The stacking fault fringes within the triangle are usu- ally displaced relative to those between the triangle and the hexagon by half the fringe spacing, which is the

(a)

contrast expected from overlapping intrinsic stacking faults. The structural arrangement of those double-

faulted loops is shown schematically in Figure 4.40, Figure 4.41 Triple-loop and Frank sessile loop in A1-0.65% from which it can be seen that two intrinsic faults Mg (after Kritzinger, Smallman and Dobson, 1969; courtesy

of Pergamon Press) .

on next neighbouring planes are equivalent to an extrinsic fault. The observation of double-faulted loops in aluminium indicates that it is energetically more

and of higher energy. This vector is written in Thomp- favourable to nucleate a Frank sessile loop on an exist-

son’s notation as υD/A˛ and is a vector equal to twice ing intrinsic fault than randomly in the perfect lattice,

the length joining the midpoints of υA and D˛. and it therefore follows that the energy of a double or extrinsic fault is less than twice that of the intrinsic