Fim contrast from lattice defects in ordered alloys

SURFACE SCIENCE 23 (1970) 160-176 0 North-Holland Publishing Co.

FIM CONTRAST

FROM LATTICE

DEFECTS IN ORDERED ALLOYS

H. N. SOUTHWORTH Department

of Physical Metallurgy and Science of Materials, of Birmingham, Birmingham 1.5, England

University

Lattice defects produce recognisable contrast in field-ion images from ordered alloys. It is shown how this contrast can be understood in terms of the known mechanism of alloy image formation. Examples are presented of lattice defects in the PtCo superlattice, and the amount of metallurgical information that can be extracted is critically discussed.

1. Introduction Superlattice formation is a particularly simple form of phase transformation to study since effects due to the long range transport of atoms along a concentration gradient are avoided. Its mechanism is strongly dependent on the presence and nature of lattice defects, and in particular interfaces. Fieldion microscopy has already been shown to possess a unique ability for the direct observation of such defects in pure metals I). For a full utilisation of this ability in the case of alloys it must be possible to distinguish between the different atomic species. Such a distinction was first achieved by Southworth and Ralph2) for the case of an ordered PtCo alloy, although a complete interpretation of the difference in image contrast exhibited by the two species of atom has only recently been accomplished3), following the development of a unified approach to the entire problem of alloy imaging4p6). In this paper the analysis is extended to explain the contrast shown by defects in the superlattice. Although the discussion is restricted mainly to PtCo, very similar principles would apply to other superlattices and to ordered precipitates in other alloy systems. 2. Image formation from ordered alloys 2.1. SELECTIVE EVAPORATION AND SELECTIVEIONISATION Field-ion image formation must be considered in two separate stages: first, the specimen surface is formed by the process of field evaporation; second, it is imaged via the process of field ionization. 160

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The difference in the field evaporation behaviour of the two species of and it is possible to calculate the atom is termed “selective evaporation”, fields required to evaporate them from specific coordination sites on the alloy surfaces). In general one species will evaporate preferentially from the imaging surface, hence producing a distinctive “vacant site” image contrast. If preferential evaporation happens to be small or absent then it is possible that both species of atom could occupy similar and neighbouring sites within an imaged plane. They are again capable of being distinguished if they give rise to image points of different intensity. This is termed “selective ionisation”. It can only occur when the selective evaporation process permits it, and in the few cases where it has been observed the relative spot brightness can be attributed to a local enhancement in field at the site of one atom relative to the other due to charge transfer between them6). 2.2. THE PtCo IMAGE Diffraction patterns from superlattices contain two quite distinct sets of reflections - fundamental and superlattice. In the Ll, structure (to which PtCo belongs) the superlattice planes are made up of alternate layers, each containing one species only. In the fundamental planes each successive layer contains an equal number of each species of atom. It is convenient to retain this nomenclature here since the two types of plane exhibit quite different contrast in the field-ion image. It was first noticed by the present author that, on the superlattice planes, only one of the alternating layers of cobalt and platinum atoms was imaging 2). This was attributed to the preferential evaporation of the cobalt atom layer until it reached the edge of the overlying platinum layer, thus forming a step of double height on the specimen surface. This is illustrated schematically in fig. 2. Later Tsong and Miiller7) showed that on the fundamental planes the cobalt atom positions exhibited vacant site contrast, although their interpretation of this was that the cobalt atoms were still present within the plane, but being prevented from imaging due to selective ionisation. However their reasons for believing the relative field enhancement to be in this sense have been shown to be invalid, and indeed a simple consideration of the anticipated direction of charge transfer predicts the cobalt atoms to image more brightly if they were presente). In any case it is the selective evaporation behaviour that must be considered first, and, when calculated, the selective evaporation parameter predicts that the cobalt atoms will be preferentially field evaporated at a field at least 24% less than that required to evaporate the platinum atomss). In addition to this there are several fine details of the image contrast that can only be

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interpreted in terms of preferential evaporation of the cobalt atoms, and where the latter can be induced to image under certain conditions it is found that they do indeed image more readily than the platinum.

3. Contrast from point defects There are several possible sources of point defects in ordered alloys. At temperatures above about three-quarters of the critical temperature there is a substantial interchange of atoms between “right” and “wrong” sites. Here this departure from perfect degree of long range order is in dynamic equilibrium, but it may be retained on quenching the alloy down to lower temperatures. A similar misplacement of atoms would be present in an alloy in which the homogeneous ordering process was still incomplete. The presence of such defects in the ordered structure should in principle be readily detectable: in PtCo, misplaced cobalt atoms should give rise to vacant site contrast among the nominally platinum atom sites, while misplaced platinum atoms should give rise to image points in sites not expected to image. However there is clearly no direct method for distinguishing between cobalt atoms, whether misplaced or not, and genuine lattice vacancies, although it may be possible to obtain an independent estimate of the probable concentration of the latter from the known thermal history of the material. A further departure from perfect long range order must occur if the alloy is not perfectly stoichiometric. The excess number of atoms of one component may be accommodated on the sublattice normally reserved for the atoms of the other component; alternatively the excess may be balanced by the presence of vacancies on this other sublattice. It should be possible to separate the contributions made by “thermal” and “compositional” disorder by subtracting the degrees of disorder obtained by counting both misplaced platinum atoms and misplaced cobalt atoms (they should be equal if only the former effect occurs). In practise it is probable that the point defects arising out of nonstoichiometry, and thermal vacancies, will tend to partition strongly to the domain boundariess,s). Structural details of the domain boundary interface are discussed in the following section. In the case of thermal disorder the misplaced atoms could exist either as two isolated wrong atoms, or as a bound pair of wrong atoms, i.e. as nearest neighbour misplacement sites. Studying the p-CuZn superlattice in which they had quenched in about 2 per cent of disorder, Clark and Brown’s) came to the conclusion, based on measured energies of formation, that bound wrong pairs prevailed. An examination of a series of micrographs of the (001) superlattice plane

FIM CONTRAST

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in PtCo suggests that a similar

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effect could be occurring

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here. Fig. 1 shows

a typical example of the (001) plane, on which it has previously been shown that misplaced cobalt atoms give rise to gaps in the platinum rings, while misplaced platinum atoms are left behind as the cobalt layer in which they

Fig. 1. Micrograph of PtCo ordered for 71 hr at 800°C. The area shown is of the (001) superlattice plane, and contrast corresponding to both single misplaced atoms and “bound wrong pairs” can be seen.

lie is evaporated, thus giving rise to additional image points between the rings2). This alloy was ordered at 800°C where the equilibrium long range order parameter is not expected to exceed about 0.8711), and two instances are indicated where there is a bright spot/vacancy pair. This is certainly not true of every bright spot or every vacant site, but at the same time it must be realised that not every lattice site is in an imaging position at the same time. The lifetime of a bright spot remaining behind on the ledge as evaporation proceeds is not the same as that of a vacant site, only evident while the imaged edge of the plane is level with it.

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Nevertheless this constitutes some tentative evidence for at least a limited occurrence of this bound pair phenomenom, and it is intended that further studies will be made. If a quantitative analysis of the degree of long range order is to be attempted then there are several precautions to be observed. There is the obvious one that a statistically significant sample must be taken. Son and Hrenra) have recently developed an analysis for obtaining a significant count of misplaced atoms on the superlattice planes, and have applied it to PtFe. Then it is necessary to perform a bonding calculation for atoms in “wrong” sites in order to check whether their selective evaporation behaviour, and hence their image contrast, remains the same. For example, a species normally undergoing preferential evaporation might become stabilised when occupying a wrong site, giving rise to image point rather than vacant site contrast. Such a calculation is easily performed for a single misplaced atom on a given plane. However if the amount of disorder is at all appreciable, then further neighbouring misplaced atoms, for example in the sub-surface plane, could upset the bonding once more. Thus to be wholly accurate such defect configurations should be noted and their possible effects considered. Although more tedious to determine, a long range order parameter obtained from field-ion data may be more valuable than one obtained using X-ray diffraction, since the latter technique produces what is effectively an average figure, obtained from bulk material over which the degree of order is not necessarily uniform. For example there may be regions of complete long range order coexisting with regions of disorder; there may be local compositional fluctuations; the departure from perfect order may tend to be localised near to domain boundaries, or at other singularities in the microstructure. Field-ion investigation would permit these effects to be distinguished, and hence enable more precise models of the ordering mechanism, or of the mechanical properties, to be formulated. 4. Contrast from antiphase domain boundaries (APDBs) Superlattice formation in PtCo occurs with a change in lattice symmetry, from the disordered fee structure to an ordered face-centred tetragonal structure. The latter consists of alternate layers of platinum and cobalt atoms each on (002) planes. An APDB separates two domains whose c axes are parallel but which are related by a + (101) translation vector. The habit plane of lowest energy would be { 1OO}. 4.1. CONTRAST CONDITIONS The antiphase

translation

vector serves to place cobalt

atoms in platinum

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atom sites, and vice versa. In principle, therefore, it detect where an APDB crossed a fundamental plane the image spot pattern. In practise it would be difficult achieved when the plane was sufficiently small for

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should be possible by careful analysis since it could only all the atoms in

16.5

to of be its

interior to image, and very good image resolution would also be required. However very distinctive contrast is given when the boundary crosses a superlattice plane ls). Ranganathan14) has pointed out that this is analogous to the situation in electron microscopy where APDBs are only visible when g *r is non-integral. Here g is the reciprocal lattice vector of the operating reflection and r the translation vector of the boundary: g *r is non-integral only for the superlattice reflections 15). Fig. 2 shows how contrast is obtained in the field-ion microscope. This figure describes how the surface geometry is altered by the passage of a + [iOl] (010) APDB across the (001) superlattice plane. Fig. 2a represents the first three rings of image points on the plane, while fig. 2b is a radial

(b)

Fig. 2

Diagram showing the formation

cb, of APDB contrast on the (001) plane.

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cross-section through the specimen tip at this point, showing the alternating layers of platinum and cobalt atoms. The cobalt layer is shown evaporated back so as to form a step of double height with the platinum layer (section 2.2) and the platinum atoms imaging are indicated. The translation $[iOl] may be resolved into two stages: (i) + [TOO] + (ii) $ [OOl]. Fig. 2c shows the effect of stage (i). Since the ledge width in practice may be ten to twenty times the magnitude of this displacement it has been greatly exaggerated here. In practice it would be very difficult to detect. However, the translation *[TOO] alone is not one that would be expected to occur. Fig. 2d shows the effect of stage (ii). The displacement is of virtually the same magnitude as before, but this time it is normal to the atomic planes. It corresponds to one planar separation - half of the double step. The terrace structure of a plane must conform to an effectively spherical envelopei6a6). Thus when the planes on the right hand side of the boundary are displaced vertically up the normal to the plane they must then exhibit a decreased radius. Thus a mismatch surface is produced, rings of image points interleaving, rather than joining up, across the boundary. Fig. 2e shows a radial section through the plane containing the APDB. This analysis nicely illustrates the fact that in field-ion micrographs, the effective magnification achieved is very much greater in the direction normal to the specimen surface, than in the plane of the surface. Such APDB contrast is exactly analogous to stacking fault contrast in pure metals 17). 4.2. OBSERVATION OF APDBs Fig. 3 shows an APDB crossing almost exactly through the centre of the (001) plane in ordered PtCo. The contrast corresponds with that predicted in fig. 2. The interleaving of rings of image points can be detected out to about the tenth ring from the centre. The contrast becomes progressively more difficult to detect because the ledge width, and hence the amount of mismatch, decreases the further out from the centre the ring is located, as is shown in fig. 2. Other superlattice planes have smaller step heights, resulting in decreased ledge widths, making APDB contrast less easy to detect. Fig. 4 is an example of an APDB crossing the (112) superlattice plane; examples have also been seen on the (110) and (021) superlattice planes. If the APDB intersects the plane some distance out from its centre the contrast becomes much more difficult to detect, since the displacement becomes more tangential to the rings of image points. Nevertheless several examples of these have been observed and analysed in a similar way to fig. 22.9. The main limitation is that, although the APDB may give rise to

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@a)

(3b) Fig:. 3.

(a) APDB in ordered PtCo seen crossing the central (001) area. The habit I)lane is close to (100). (b) crystallographic map of (a).

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Fig. 4.

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APDB in ordered PtCo seen crossing the (112) superlattice plane. The habit plane cannot be {loo}.

extremely clear contrast when crossing a particular superlattice plane, it is very difficult to trace its path over the entire field of view. APDBs have been shown to exhibit analogous contrast in Pt,Co18) and Ni,Molg). A particularly interesting achievement has been the direct resolution of the periodic antiphase domain boundary structure in CuAu 1120~13). 4.3. THE STRUCTUREOF THE BOUNDARY Since disordering is a cooperative phenomenon, and since some alteration in binding is present at a domain boundary, a certain amount of additional disorder is expected to exist heres). Brownzl) has calculated the width of a domain boundary to be about one atomic plane, rising to about four or five planes at temperatures approaching the critical temperature. This width is the distance over which the degree of long range orders differs from that within the bulk domain. In a non-stoichiometric alloy excess solute atoms may also become segregated to the domain boundary, as already described.

FIM CONTRAST

Okamura

FROM LATTICE

et a1.2s) have obtained

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experimental

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on the degree of

disorder at a domain boundary using Fourier synthesis of electron diffraction patterns of CuAu II. They found that the probability of finding a gold atom (for example) followed the sequence 0.97, 0.87, 0.63 : 0.32, 0.08 in successive average atomic positions across the boundary. For a perfect degree of order it would of course be 1.0, 1.0, l.O:O.O, 0.0. Examination of the boundary shown in fig. 3 reveals that the mismatch at the interface is not quite as clear cut as expected from fig. 2, and that within about one to two atomic distances from the interface there is a certain departure from perfect order (c.f. section 3). In particular, where the boundary crosses the central ring of the plane there is a string of spaced out image points completing that first half-ring. Similar structures have been observed in other such boundaries, and these isolated image points are interpreted as platinum atoms misplaced onto nominally cobalt atom sites across the boundaryls). The composition of this alloy was very close to the stoichiometric. The fraction of sites wrongly occupied is about a quarter to a third, which is comparable with the values quoted above. However the notable thing is that these misplaced platinum atoms appear to be regularly spaced out along the boundary. Thus even the disorder appears to be ordered. The habit plane of the boundary shown in fig. 3 is (100) i.e. corresponding to that of lowest energy. All that can be deduced from the boundary shown in fig. 4 is that the pole of its habit plane lies in the [ilO] zone, which is not consistent with a { lOO} habit. Analysis of other such boundaries shows that a variety of habit planes occur with no overwhelming predominance of {loo}. Thus there is no evidence that the boundaries have any strong tendency to take up their minimum energy habit plane, even after long annealing times. Furthermore it can be seen from the smoothness of the boundary trace on the micrograph that the interface is distinctly planar. In other words, although the interface could be considered to be stepped on the atomic scale, due to the misplacement of atoms at the interface, there is no tendency for it to be stepped on any larger scale. These observations have been mainly qualitative. With improved image resolution, and more rigorous application of the alloy image contrast theory, a considerable amount of structural information could be extracted from such studies. 5. Contrast from rotational domain boundaries and twins During formation of the PtCo superlattice the ordered tetragonal cell forms in an approximately similar orientation to the disordered cubic cell. If the orientation relationship ‘between the two phases is to be (1 lo} dis-

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II(lOl}

orderedss)

[lOO],,

then

the following

relationships

must

hold:

(1lO)n II (lOl)o, P1OlLl II c01010~ [OOl], at about 3” from [ 1001, and [OOl],.

Two ordered particles nucleating in proximity may, on contacting, exhibit one of several axis misorientation/interface habit plane relationships4). The tetragonal c axes may be parallel, there then being a 50 per cent chance of an APDB being formed. Alternatively the c axes may turn out to be approximately 90” to each other, the precise angle being one of several possibilities within about 2” of 90”. The interface between the two ordered domains is then termed a rotational domain boundary. Under some conditions of ordering a lamellar twinned microstructure results which has been attributed to some form of stress relief 24). The crystallography of this microtwinning is such that the c axes are rotated through a specific angle of about 883”, the twin plane being accurately { lOl}. This relationship is identical to one of those which can come about by the random nucleation of c-orientated domains, above. 5.1. ROTATIONALDOMAINBOUNDARYCONTRAST The misorientation between the two domains can be expressed as a rotation of about 90” about the [OlO] axis. Because the rotation is not necessarily exactly 90”, and because the [OlO] axis is only a diad axis of

Fig. 5. Diagram showing the formation of rotational domain boundary contrast, for the situation where low index superlattice and fundamental planes are brought into near-coincidence.

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symmetry in the tetragonal structure, there emerge two factors which lead to distinctive boundary contrast. One is that there will usually be a small angular misorientation between the poles of planes brought into (near) conjunction across the boundary. The other is that the poles meeting across the boundary in this way will not necessarily be equivalent - superlattice planes will meet fundamental planes whose indices would only be equivalent if the symmetry was cubic. For example the (021) superlattice plane might meet up with the (OTT) fundamental plane. Fig. 5 shows the contrast to be expected when a superlattice plane meets a fundamental plane across the boundary. Here the boundary plane is shown at right angles to the angle of misorientation of the two poles. In addition to this angular misorientation, there will be a 1: 2 correspondence in the number of rings of image points from the side of the superlattice plane (A) to the fundamental plane (B). In practice the precise mismatch at the interface will depend on differences in the radius of curvature of the specimen over each plane. The ring structure of a superlattice plane always develops much more prominently than that of the analogous fundamental plane. Thus the above form of contrast might not be shown with the higher index planes, if the fundamental plane failed to develop a recognisable structure. If two fundamental planes meet each other across the boundary then there should be a 1: 1 correspondence in the number of rings meeting. While there will generally be some angular misorientation, there are certain combinations that occur for the c-domain relationship identical to that of the twin, where the poles would coincide instead. These can be found by constructing the appropriate stereogram and performing the twinning operation. Fig. 6 is a micrograph showing a small ordered particle situated within the (001) plane region of the ordered matrix in a PtCo alloy ordered for 2 hr at 660°C. The pole seen in the particle is (loo), and it coincides with the (001) pole of the matrix. Hence the particle is in a c-domain relationship to the matrix, and contrast similar to that depicted in fig. 5 may be seen at its top interface. The particle as a whole is easily picked out due to the inherent different in image point brightness between a (100) region and an (001) region. By successive small field evaporations through the specimen it was found that the particle was lenticular in shape, with its interface close to (101). A large number of rotational domain boundaries have been examined as part of a general investigation into the mechanism of ordering in this alloyep4). Examples have been found of many of the slightly differing types of rotational domain boundary relationships that are possible, and it is believed that this is the first time that such a fine distinction between such boundaries has been made.

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Fig. 6.

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Small ordered particle set in an ordered matrix, but at an approximately misorientation to it. The interfaces between particle and matrix are rotational domain boundaries.

90”

5.2. MICROTWIN CONTRAST Fig. 7 is a micrograph from PtCo ordered for 5 hr at 500°C. It reveals a number of parallel twin boundaries, each lying on { 101 } planes, and running approximately from top to bottom of the micrograph. The characteristic small angular disparity between adjacent poles across the boundary can be seen quite clearly. However in almost every case the two poles so related are of an identical type. This would not be true for a single twin boundary where a superlattice plane was involved. By examining the changing features of these planes during field evaporation, and by measurement of the angular disparities involved, it is possible to determine that most of these planar contrast features is in fact a very thin region of twinned crystal, rather than a single boundary. Thus this lamellar structure consists of twinned regions about lo-15 A wide and separated by a region of the matrix about ten times wider. It is

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(7a)

(7b) Fig. 7.

(a) Ordered PtCo showing a lamellar microtwinned map of (a).

structure. (b) crystallographic

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difficult to investigate the actual structure of the interface since the superlattice and fundamental planes develop with differing degrees of regularity. However when these twin boundaries pass through the broad regions of the matrix (001) plane some observations can be made, and the interface appears to be fully coherent. This is to be expected since the (101) habit plane is common to both twin and matrix. 6. Contrast at the order/di~rder interface A combined X-ray diffraction and field-ion microscopy investigatione) has revealed that the mechanism of ordering in PtCo is not as simple as had been thought 24). Even where straightforward nucleation and growth of ordered regions does occur there is a strong contribution present from a homogeneous ordering mechanism as well. This is illustrated by fig. 8, which shows the order/disorder interface in an alloy ordered for 6 hr at 500°C. The disordered area to the right of the micrograph exhibits very little image regularity. This is because here the preferentially evaporated cobalt atoms are randomly distributed. Within the ordered region the image regularity is not perfect; the rings of image points are considerably ragged, indicating a certain departure from perfect degree of long range order. Thus as the ordering reaction continues, and the ordered regions increase in volume, they must also undergo a homogeneous increase in the degree of order within them. The details of the interface region itself are interesting. Although the transition from fairly well ordered to disordered is fairly abrupt on a local scale, the actual position of the interface is extremely diffuse spatially. Small salients of ordered material can be seen extending irregularly into the disordered matrix. The diffraction line broadening that is observed on ordering at this temperature cannot be due to coherency strains at the interface, as previously suggested 24), but must instead be due to there being a range over which the degree of order varies 25>. 7. Conclusions The field-ion microscope can be used to produce detailed information on the state of long range order in an alloy. Characteristic vaIues of the long range order parameter may be obtained by direct counting of the misplaced atoms. Structural and crystallographic information about antiphase domain boundaries, rotational domain boundaries and twins may be obtained, and details of the order/disorder interface examined. The methods of analysing defect contrast described in this paper could readily be extended to other ordered structures.

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@b) Fig. 8.

(a) Interface region between a partially ordered domain and the disordered matrix. (b) crystallographic map of (a).

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Acknowledgements The experimental results described in this paper were obtained while the author was in the Department of Metallurgy at the University of Cambridge, in association with Dr. B. Ralph. Thanks are due to Professor R. W. K. Honeycombe for the provision of laboratory facilities, and to the United Kingdom Atomic Energy Authority, Harwell, and the Science Research Council, for financial support. The platinum-cobalt alloys were kindly supplied by International Nickel. References 1) E. W. Mtiller, Advan. Electron. Electron Phys. 13 (1960) 83. 2) H. N. Southworth and B. Ralph, Phil. Mag. 14 (1966) 383. 3) H. N. Southworth and B. Ralph, Phil. Mag. 21 (1970) 23. 4) H. N. Southworth, Scripta Met. 2 (1968) 551. of Field-Ion 5) H. N. Southworth and B. Ralph, in: Applications 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 27.) 23) 24) 25)

Microscopy (Georgia Tech. Press, 1969) p. 291. H. N. Southworth and B. Ralph, J. Microscopy 90 (1969) 167. T. T. Tsong and E. W. Mtiller, J. Appl. Phys. 38 (1967) 545. J. W. Cahn and R. Kikuchi, J. Phys. Chem. Solids 27 (1966) 1305. S. G. Cupschalk and N. Brown, Acta Met. 15 (1967) 847. J. S. Clark and N. Brown, J. Phys. Chem. Solids 19 (1961) 291. P. S. Rudman and B. L. Averbach, Acta Met. 5 (1957) 65. U. T. Son and J. J. Hren, Surface Sci. 23 (1970) 177. H. N. Southworth and B. Ralph, in: Applications of Field-Ion Microscopy (Georgia Tech. Press, 1969) p. 329. S. Ranganathan, H. B. Lyon and G. Thomas, J. Appl. Phys. 38 (1967) 4957. M. J. Marcinkowski, in: Electron Microscopy and Structure of Crystals, Eds. G. Thomas and J. Washburn (Interscience, New York, 1963). A. J. W. Moore, J. Phys. Chem. Solids 23 (1962) 907. D. A. Smith, M. A. Fortes, A. Kelly and B. Ralph, Phil. Mag. 17 (1968) 1065. T. T. Tsong and E. W. Miiller, J. Appl. Phys. 38 (1967) 3531. B. G. LeFevre, H. Grenga and B. Ralph, Phil. Mag. 18 (1968) 1127. P. J. Turner, Thesis, Cambridge University, 1967. N. Brown, Phil. Mag. 4 (1959) 693. K. Okamura, H. Iwasaki and S. Ogawa, J. Phys. Sot. Japan 21 (1966) 1616. J. B. Newkirk, R. Smoluchowski, A. H. Geisler and D. L. Martin, J. Appl. Phys. 22 (1951) 290. J. B. Newkirk, A. H. Geisler, D. L. Martin and R. Smoluchowski, Trans. AIME 188 (1950) 1249. H. N. Southworth and B. Ralph, in: The Mechanism of Phase Transformations in Crystalline Solids (Institute of Metals Monograph No. 33, 1969) p. 224.