OBSERVATION DIRECTE DES JOINTS INTERGRANULAIRES.MICROSCOPY OF STATIC AND DYNAMIC PROPERTIES OF INTERFACES

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OBSERVATION DIRECTE DES JOINTS

INTERGRANULAIRES.MICROSCOPY OF STATIC AND DYNAMIC PROPERTIES OF INTERFACES

D. Smith

To cite this version:

D. Smith. OBSERVATION DIRECTE DES JOINTS INTERGRANULAIRES.MICROSCOPY OF

STATIC AND DYNAMIC PROPERTIES OF INTERFACES. Journal de Physique Colloques, 1975,

36 (C4), pp.C4-1-C4-15. �10.1051/jphyscol:1975401�. �jpa-00216306�

OBSERVATION DIRECT€

DES JOINTS INTERGRANULAIRES.

MICROSCOPY OF STATIC AND DYNAMIC PROPERTIES OF INTERFACES

D. A. SMITH

Department of Metallurgy, University of Oxford, Parks Road, Oxford, England.

RCsum6. - I1 faut dCfinir toutes les constantes cristallographiques qui dbcrivent les joints de grains pour comprendre leur structure. Une technique tr&s utile est la microscopie Clectronique.

Les dislocations interfaciales conservent I'ordre dans les joints et leurs propriCtCs peuvent contrbler les processus qui se produisent aux joints.

Abstract. - The metallographers' problem in the context of interfaces is to relate the crystallographic variables to structure. This can be done at high resolution and magnification using principally transmission electron microscopy. Interfacial dislocations conserve the order at boundaries and their behaviour may be the mechanism underlying the properties governed by grain boundary processes.

1 . Microscopy of static and dynamic properties of interfaces. - INTRODUCTION. - The object of this article is to survey some of the recent contributions made by metallography, especially transmission electron microscopy, to the understanding of the structure and properties of interfaces. In addition an attempt will be made to indicate some potentially significant avenues for future work.

There are eight macroscopic degrees of freedom which must b e assigned in order t o specify the axis and angle of rotation (three), an interface plane (two) and a rigid body translation (three) relating the orientation and position of two lattices. These must all be determined together with the microsco- pic structure in order to characterise the interface.

Most structural models are geometrical and d o not take any account of changes in chemical composi- tion at interfaces although the associated energy

changes can be substantial and thus in turn affect the interface structure. A proper comparison of experimental observations and the predictions of the various hypotheses concerning interface struc- ture requires the precise definition of the interfacial crystallographic parameters and their correlation with details of the microscopic structural features, particularly dislocations. Modern theories of inter- face structure [ I , 2, 3, 41 emphasise the importance of periodicity and have been most thoroughly investigated in the context of grain boundary structure. The essence of the theories is that in equilibrium interfaces can be described in terms of periodic structures in which, depending on the exact angular relationship of the grains and the boundary plane, there are arrays of dislocations, not necessarily with lattice Burgers vectors, but otherwise similar in geometry to low angle grain boundaries. The question of the validity of this,

model for all orientations and all crystal structures is still under investigation a s are the nature and properties of the interfacial dislocations and the structures which they conserve.

Table I summarises the main features of images from interfaces, and their structural origins, in the transmission electron microscope (TEM), scanning electron microscope (SEM) and field-ion micro- scope (FIM).

2 . Determination of interface crystallography.

Grain rotations. - There are remarkably few data concerning the crystallographic relationships of individual grains in a polycrystalline specimen.

Such data would be extremely valuable in clarifying the roles of highly mobile or low energy boundaries in recrystallisation and would permit a correlation between the grain population of an annealed sample and the various hypotheses concerning the rela- tionship of boundary structure, energy and mobi- lity. Techniques have been developed which permit the rotation angle and axis to be found rapidly and with high precision [5, 61. However, correspondin- gly accurate determination of interface planes(s) has not been achieved owing to the difficulties in estimating foil thicknesses or changes, after speci- men tilting, in the projected lengths of particular linear features.

A versatile and labour saving technique for determining the misorientation at grain or phase boundaries is as follows. Diffraction patterns at known stage tilt settings in each grain are recorded for a t least two and preferably more, e. g. five different foil orientations. A typical geometry of Kikuchi lines and diffraction spots is indicated in figures 1 a and 1 b. Figure I b is obtained from a pattern such as by construction and the cons-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975401

C4-2 D. A. SMITH

TABLE I

TEM SEM (not STEM)

-

grains grains in different diffraction condi- different secondary electron misoriented tions, thickness fringes yield, different electron chan-

nelling patterns

grains continuous g, if g.R # integer, surface steps after macrosco- translated interference fringes like stacking pic translations, e.g. during

fault grainlphase boundary sliding

interface invisibilities for g.b = 0, double detection of consequences of dislocations peaks for g. b = 2, different in de- dislocation movement from tail from lattice dislocations be- change in configuration of cause of change in strain fieldlpre- reference grid

sence of second grain, periodic relaxations may act as grating

topography projection of three dimensions into surface changes and section

two through three dimensional

structure

FIM -

two part single crystal patterns misoriented

*n.R # integral num- ber of planar spacings, horse-shoe contrast spiral structures if

'

n.b # 0, small Bur- gers circuit shows dis- locations in boundary

series of sections from which three dimensio- nal structure can be deduced

*n is local unit surface normal

tructed lines are shown dashed. The marked angles calculates the (five) beam directions in the indices and distances are measured o n . each plate and of each grain in turn, Uil? and Ui2), i = 1 , 2, . .. 5.. . , constitute the input for a computer program which which then (over) determines the rotation matrix R

Frc. la. - Is a typical Kikuchi pattern recorded with the electron beam direction not close to a low index direction.

(Courtesy Clark W. A. T.)

Frc. l b . - Is a sketch showing the measurements and constructions made in order to identif-y the electron beam.

direction (plate normal) in figure l a . The beam direction was found to be [863, 315, 3961. (Courtesy Clark W. A. T.)

given by :

. .

up) .= RUI').

The output includes the axis and angle of rotation and an estimate of the effect of any internal inconsistency in the data on the calculated angle of rotation on the arbitrary assumption that the rotation axis is correct. In addition the crystallogra- phically equivalent variants of R corresponding to the various ways of indexing crystal (1) are calculated so that the most convenient form of R may be used in subsequent analysis. The disorienta- tion angle (smallest angle of rotation) and the pbssible existence of a twin description (rotation by 180" about a rational direction) are of particular interest. These facilities have proved especially valuable in situations where the implications concerning structure are much clearer from one variant of an orientation relationships than another, e. g. in a magnesium bi-crystal 28.6" about

[- 0.064, - 0.052, - 0.6151 (near 2 = 13) is equi- valent to 179.2" about [- 0.827, 0.282, 0.0081 (i. e.

allowing for experimental error and deviation from the exact coincidence orientation relationship a rotation of 180" about a rational direction).

An important argument in favour of the measure- ment technique described above is that all the angular measurements on the diffraction pattern which affect the accuracy of the final result are made between diffraction spots and Kikuchi lines and the inherently less accurate information, e. g.

the measured angles between Kikuchi lines is used

MICROSCOPY O F STATIC AND DYNAMIC PROPERTIES O F INTERFACES C4-3

only for preliminary indexing of the Kikuchi poles at the apices of the Kikuchi triangle.

Not only is the measurement of grain orientation important in the comparison of observations of grain boundary structure with theories but where the grains are free to rotate into low energy configurations the frequency, F, of particular orientations can be interpreted in principle to give information concerning the variation of grain boun- dary energy with orientation, the distribution of low energy orientations and the mechanism of grain rotation. Such experiments have been done in several different ways : ( a ) the production of fine crystals of MgO or CdO with an { 001 } habit some of which formed polycrystals [8] ; (b) the vapour growth of F e single and polycrystals, again with an { 001 } habit [9] ; ( c ) the production of overlaid single crystal gold foils with a { 1 1 1 } habit and a

FIG. 2. - IS an electron micrograph with the beam parallel to the common [001] twist axis showing a group of MgO single crystals ( x 150,OO) which have formed coincidence twist boun-

daries. (Courtesy Chaudhari P. and Matthews J. W.)

thickness of - ²⁰⁰ A [lo] ; (d) the equilibration of approximately spherical single crystaI 100 p m dia- meter particles of silver or copper on planar single crystal substrates of the same material [ l l ] . In experiments ( a ) and (b) the orientation measure- ments were made directly by measuring the angle between the readily recognisable < 100 > edges of the crystals whilst in ( c ) and (d) electron diffraction and an X-ray texture goniometer were used. The measurements in experiment (d) differ from those in the other experiments in that individual grain orientations are not determined, the boundary plane can vary and numerically larger samples can be used. In experiment ( a ) with MgO & CdO the results obtained .were consistent with what was conventionally expected from coincidence site latti- ce theory, i. e. F ^{( I )} ( 2 ) a2-I with the modification that in the strongly ionic MgO the 2, = 17 boundary was not observed. The result 'was consistent with

(1)

F ( S ) means the frequency with which a particular 2 value was observed.

FIG. 3a, b and c. - Show respectively ( a ) a scanning electron micrograph of an almost < 001 > tilt boundary between vapour grown iron single crystals (beam direction along the tilt axis) and ( 6 ) and (c) electron channelling patterns from the two large crystals with beam contamination marks, indicating that in addition to the large tilt angle which is deduced from the relative rotation of t h e patterns about their normals there is also a small (precisely measurable) deviation from exact parallel orientation of the two < 001 > directions. (Courtesy Ishida Y., Yamamoto

T. and Kimura S.)

0 (DEGREES)

FIG. 4 Is a histogram showing the frequencies with which high angle twist boundaries were found in MgO as a function of rotation angle. The crystals were grown under conditions f a v ~ u r i n g the production of coincidence boundaries. (Courtesy

Chaudhari P. and Matthews J . W.)

calculations of boundary energy which suggested a

high energy for this particular interface owing to

the unfavourable proximity of like charges. In

experiments (b) and ( c ) the csl interpretati&de-

pended on attaching energetic significance t o higher

values of 2 than are usually considered. The

question of how large a value of 2 is important in

governing interface structure is controversial and is

D. A. SMITH

FIG. 5. - Is a histogram of the frequency N of the rotation angles measured for < 001 > tilt boundaries in vapour grown iron crystals. The preponderance of boundaries near the B = 41 and 25 coincidence orientations, in preference to ,Z = 5, 13 and 17, is striking. (Courtesy Ishida Y . , Yamamoto T. and Ki-

mura S.)

equivalent to the problem of defining a random grain boundary. The practical problem can be stated as one of resolving or detecting periodic structures and the defects conserving them. At present, smallest feasible dislocation spacings are on the limit of the microscopic techniques availa- ble. Coinputer calculations d o not a t present resolve the problem since all calculations involving an acceptably large number of atoms rely on periodic boundary conditions and thus only refer t o csl orientations [ 2 , 131. Recent calculations suggest

FIG. 6. - I S a computer simulation of the relaxed structure for a 8 = 1 1 , 50.5"/< 110 > { 113 symmetrical tilt boundary between two fcc crystals. The triangles and crosses represenj the ABA ... stacking sequence of the { 220 ) planes. Note the remarkably small disturbance to the crystal structure at the boundary which reflects the low calculated internal energy.

(Smith D. A . , Vitek V. and Pond R . C . , unpublished.)

- -

only a factor of. two difference in energy between

the 2 = 5 , (210), [001] and 2 = 41, (910), [001] classical ( 2 ) c o i n c i d e n c e boundaries e x c e p t symmetrical tilt boundaries [13] and the calcula- 2 ⁼ 3 twins in fcc metals the evident high energy tions of Baroux et ai.

[12] attribute relatively low of the .overlapping atoms adjacent t o a coincidence energy to the 2 = 65 boundary. Experiment ( d ) has atom outweighs any favourable contribution from suggested however that whilst the textures pro- the latter.

duced during equilibration can be described in

terms of a set of coincidence boundaries ' ~ ( 2 ) is 3 . Interface planes. - The accurate determina- not proportional t o

and furthermore F ( C ) is tion of interface planes when the boundary is not different for copper and silver thus emphasising the planar on a fine scale is difficult. Methods which importance of factors other than geometry. This rely on knowledge of the foil thickness and the behaviour parallels the known variation of intrinsic counting of thickness fringes can be improved by stacking fault energy from one fee metal t o another working in weak beam conditions where the even though the geometry is thought to be identical. effective extinction distance is decreased and the I n addition since experiments [ l 4 , 151 a n d number of thickness fringes increased [IS]. An computer [12, 13, 161 calculations suggest that in alternative procedure is to note the change in certain low energy interfaces there are no coinci- apparent separation of two readily identifiable dence sites the conclusion must be drawn that atom image points before and after a known rotation of coincidence per se is not a criterion f o r low energy. the specimen [191. Despite these difficulties careful In this context the results from an experiment measurement of boundary planes using transmis- similar to that of Gillet but using sedimentation of sion electron m i c r o s c o ~ ~ and parallel work by mineral flakes such a s kaolinite in which there is an optical and field ion microscopy has given results approximately hexagonal unit may be significant which extend our understanding of grain boundary since peaks in the ~ ( 0 ) vs. 0 curve exist where Structure. Electron microscopy establishes that for there are exact coincidence orientations for a 2 = 3 twins high index orientations of the twin hexagonal lattice even though exact periodicity plane occur in annealed samples; e - g- { 171 1 El51 could only be established with lattice strain [17].

in aluminium and { 334 in austenitic type 316 One almost self-evident possibility supported by stainless steel. These observations appear to chal- computer calculations is that low energy boundaries

are those where the sing1e crystal coordination is

Boundaries where there are atoms which occupy sites of

best conserved for each atom in the boundary. In the CSL.

MICROSCOPY O F STATIC A N D DYNAMIC PROPERTIES O F I N T E R F A C E S C4-5

FIG. 7. - Shows ( a ) the unrelaxed and ( b ) the relaxed structure f o r the 2 = 19, 26S0/< 110 > { 331 } symmetrical tilt boundary.

T h e triangles and crosses represent the - ABA ... stacking sequen- - - c e of t h e { 220 } planes In figure 7 b the atoms separated by less than an atom diameter have relaxed and the calculated energy is reduced from 3 672 ergs cmp2 to 191 ergs cm-?. A lower energy

-

configuration w a s found by removing three ( 331 ) layers parallel to the boundary plane. (Smith D. A . , Vitek V. and Pond,

R. C . , unpublished.)

lenge the view that low energy is associated with small repeating units in the boundary plane ; this last argument rests on the (unproved) hypothesis that the strain being relaxed in all boundaries is of the same magnitude. Recent calculations suggest that grain boundary energy is not monotonically related to 2 or the size of a repeating boundary unit [l2, 131.

Field-ion microscopy [20] and optical micro- scopy 121, 221 both indicate the apparent signifi- cance of non-periodic boundaries even in cubic metals since in situations remote from short period c o i n c i d e n c e o r i e n t a t i o n s , b o u , n d a r i e s i n annealed tungsten and silver are observed to facet into near coincidence orientations establishing some

FIG. Sa, b. - Shows respectively optical micrographs of

type figure In the facetting of th,e boundary plane in well annealed zinc (courtesy

observations of dislocation arrays in non-periodic Bishop G. H . , Hartt W. H . and Bruggeman G. A.), and silver

boundaries in magnesium [I] and in phase boun- (courtesy Wiens M J . and Wiens J . J . ) bicrystals and figure 8 ; daries 1231, emphasise the possible significance of shows a similar phenomenon in a field-ion micrograph of

annealed, polycrystalline tungsten. In all cases the boundary

periodicities other than that of the exact coinci- plane has lacrased its area by facetting into non-periodic

dence type. orientations.

C4-6 D. A. SMITH

direction in grain (1) is parallel to another rational direction in grain ( 2 ) , e. g. the Z = 9, 38.9°/[110]

rotation may be described by the matrix :

8 1

'I9[ 1 8 2)

- 4 4 7

and the direction [hkl] in grain ( 1 ) is rotated into the direction 18 h + k + 4 I , h + 8 k - 4 1,

- ^{4 h} + 4 h + 7 11 in grain ( 2 ) . If the misorienta- tion is a pure rotation and corresponds exactly to coincidence all members of certain families of atom planes in grain ( I ) (hl kl 11) are parallel to and continuous with identically spaced planes in grain ( 2 ) ( p 2 q2 Y * ) ; h? + k f + ^{1: =} p: + qS + Y I . The two beam transmission electron microscope image of such a boundary with g ( l , = h l kl 1 1 ilnd g(2) = p2 q2 1-2 (necessarily) simultaneously satisfied should show no fringe contrast. This prediction is verified for { 11 1 } Z = 3 twins in aluminium and stainless steel but when the interface plane i s in other orientations stacking fault like fringes are observed. The interpretation of this result is that the planes (hl kl I f ) and (p2 q2 r2) are not conti- nuous but offset by R, so that g . R # integer, a s predicted by computer calculations [ 2 5 ] , figure 9 . The fringe profile is sensitive to the deviation

parameter and the fringes extinguish when g . R = integer. Using these properties R can be found. Calculations suggest that the lower limit on

I g . R I modulo 1 for fringes to be visible is - ^0.02.

This implies that values of I ^R I a s low as - ^{0.04 A}

can be detected. There is necessarily a dislocation at the junction between facets with different normals and different rigid translations. The dislo- cation at the { 1 1 1 }I{ 171 ) 2 = 3 facet junction in

FIG. 9. - a and b show electron micrographs of facetted twins in aluminium and stainless steel respectively photographed in a common diffraction condition. Stacking fault like interference fringes appear on the rncoherent feces whilst the { 1 1 1 } faces give no fringes. Figures 9 c and 9d are similar micrographs for 2 = 9 (stainless steel), 2 = 3 (Mo 35% Re, bcc) twins (all in bright field). (Fig. 911 courtesy Pond R. C., Fig. 9 h and c, courtesy Clark W. A . T. and Fig. 9d courtesy Mahajan S . )

4 . Determination of R (rigid body translation a t a grain boundary. - Computer calculations suggest that the lowest internal energy at grain boundaries occurs when grains are rotated into coincidence orientations and then translated rigidly s o that there are no atoms occupying sites common to both grains in the boundary plane. The physical basis of this behaviour is shown in figure 7. A technique has been developed which permits the determination of the magnitude and direction R in coincidence boundarLs L14, 151. The rotation matrices describ-

FIG, - Shows a partial grain boundary dislocation at the

ing coincidence boundaries consist entirely of junction of two facets of a 8 = 3 twin in stainless steel in dark

rational fractions [24]. Consequently any rational field ; note the asymmetry of the fringes.

MICROSCOPY O F STATIC AND DYNAMIC PROPERTIES O F INTERFACES C4-7

aluminium is a partial dislocation of the DSC to the specimen surface. Computer simulation and lattice [ I , 2, 261. Displacement fringes have also image matching are powerful ancillary techniques been observed in 2 = 9 fcc boundaries and X = 3 for analysing the images of twins in both field-ion bcc boundaries ; the technique described above can and electron microscopes since in both cases there be used, in principle, for any coincidence boundary are limitations on the range of experimental varia- although the indices of the continuous planes bles which may be employed.

increase as 2 increases and the number of experi-

mentally available common conditions decreases. 5 . Grain boundary dislocations. - Perfect grain When the orientation deviates from the exact boundary dislocations (gbds) can be defined for coincidence orientation the simple displacement periodic boundaries with the aid of the appro- fringes disappear ; they are particularly sensitive to priate DSC lattice [26]. The DSC lattice is defined any component of misorientation which gives a as the lattice of difference vectors, X(2L) - x ( I L ) , for change in the deviation parameter as the boundary the two lattices in the coincidence orientation and

is crossed. position. The DSC lattice contains lattices (1) and

The detection of rigid body translations is a (2) and the coincidence site lattice as sub-lattices.

problem where the field-ion m i c r o s c o ~ e (FrM) may The DSC lattice vectors for simple cubic lattices be applied since the FIM image is particularly may be deduced from the matrix equation : sensitive t o displacements along the local surface

normal 1251. The maximum apparent ledge displace- DSCLT. CSL = I [26] ( 1 ) ment in the image for a displacement d along the where C S L and DSCLT a r e t h e coincidence local normal is - A- where d is the spacing of and, DSC lattice transposed, matrices respectively, the planes normal to the surface concerned and p i s or equivalently :

the specimen apex radius The quantity is _x(2L) - ^x(IL) = d S C

typically - 10. Consequently, small normal displa- (2)

cements e. g. at stacking faults, antiphase bounda- where X ( 2 ~ ) = A ~ ( I L ) and A is a rank 3 transformation ries or twins can give rise to distinct mismatching of which describes the coincidence orientation. In

addition, the DSC lattice is characteristic of each csl and depends on whether or not the crystal lattice is primitive. The DSC lattice unit cells for each periodic orientation with a particular rotation axis are usually similar. In general two of the three basis vectors decrease a s 2-'I2 whilst the third is essentially independent of 2. Thus, particularly for large values of 2, the primitive DSC vectors can show large variations in magnitude, e. g. for 2 = 5 in f c c b1 = 1/10 [031], bz = 1/10 [ 0 i 3 ] , and b3 = 1/10 [5i?]. Whilst for 2 ⁼ 41 also in fee b l = 1/82 10911, b2 = 1/82 10i91, and b3 = 1/82 141, In the limit of very high 2 (3) two of the three primitive DSC dislocations are infinitesimal and the third approximates in magnitude to a planar spacing in the direction of a low index rotation axis. This situation has been described in terms of plane matching line defects [29, 30, 3 I]. Since experi- ments and calculations suggest that the rigid body translation R is non zero in the majority of cases FIG 11

IS a computer s~mulated micrograph of a fleld

studied it appears that just as atoms do not occupy _{- -}

microscope pattern showing a twin (marked is a faint curved coincidence sites, planes d o not match as a general

line) a t which there has been a rigid body displacement R leading

to stacking fault like horse shoe

contrast (ringed), where rule, although our calculations have never revealed

n . R # an integral number of planar spacings (n

is the local unit any translation along an < 001 ' ^{or < 110 >}

normal). (Courtesy ~handrasekharaiah M . N.) rotation axis.

Since the DSC lattice is continuous and perfect across a periodic boundary it is a convenient originally concentric image ring configurations. The reference lattice for Burgers circuits of grain technique can detect a component of R along the boundary dislocations, figure 12 [32]. DSC disloca- local normal which amounts t o - ^0.2 A but there is tions are perfect in the sense that they conserve the an unresolved problem of how t o separate the

effects of the components of R normal and parallel

For station about low index directions.

C4-8 D. A . SMITH

FIG. 12. - IS a diagram showing a glissile edge dislocation with b

1/10 [I301 in a 2 = 5 , 36.9/< 001 > { 310 } symmetrical tilt boundary. The fine mesh is the DSC lattice and the triangles and circles represent the ABA ... stacking sequence of the { 002 } planes. For simplicity of drawing the rigid body translation has

been set equal zero. (Courtesy Pond R. C.)

(imaginary) periodic pattern of lattice points defined by two interpenetrating lattices in the coincidence orientation and position. An important corollary of this property is that sets of planes continuous across a boundary remain continuous when translated by a DSC vector thus confirming that partial gbds must exist at certain facet junctions. The pattern conserving nature of DSC dislocations is not affected by the presence of a rigid body translation R ; this simply changes the nature of the pattern not its periodicity.

DSC dislocations have an associated step at their cores ; the height of the step depends on the

FIG. 13. - IS a diagram showing a strain free step in a facetted

H = 3 twin. The circles 0 & represent crystal & CSI sites in one { 220 } layer of the ABA ... stacking sequence. The step would only remain strain free in practice if the rigid body translations on the two boundary planes were identical. (Cour-

tesy Clark W. A . T.)

particular dislocation and boundary plane. The origin of the step is in the fact that DSC vectors are difference vectors and thus motion of a DSC dislocation transfers atoms from lattice ( I ) to lat- tice (2). These steps are t o be distinguished from macroscopic changes of boundary plane such as that shown in figure 13 ; such a step can be dislocation free (in the absence of rigid body translations). An experimental discrimination bet- ween a step and a grain boundary dislocation is difficult in practice but can be attempted by (a) tilting the specimen so that the electron beam is parallel t o the facet junction t o optimise the chance of resolving the step directly and ( 6 ) noting the presence or absence of strain contrast ' a t the putative step. It should be noted that displacement of thickness fringes which occurs a t dislocation free steps also occurs at dislocations (even in the total absence of a step) owing t o the change in deviation parameter near the dislocation 1331.

Equation (1) shows that DSC lattices exist for all coincidence orientations. However, for crystals with lower than cubic symmetry csls become increasingly rare, e. g. three dimensional csls exist in hexagonal crystals only for rotations about the c axis (unless there is a rational value of la)^) 171.

6 . Electron microscopy of grain boundary disloca- tions. - The nature and behaviour of grain boundary dislocations are central to the understand- ing of the principles governing grain boundary structure and probably the mechanical properties of grain boundaries. For these

reasons the dislocation structure and the interactions of this structure with lattice dislocations have been the major thrust of electron microscopic investigations. In elastically isotropic media an interface is not an elastic singularity and in this situation the elastic displace- ment field of a dislocation is unchanged by incorporation into an interface ; the displacement field of a DSC dislocation can be deduced simply by substituting the appropriate value of b. Thus providing that only one grain is diffracting strongly it is not surprising that the usual g.b = 0 and g.bxu = 0 extinction rules appear t o apply, figure 14 1341. An additional supplementary source of information concerning the nature of gbds is found by noting (a) the geometry of networks 1351 and ( b ) their interactions with lattice dislocations in the context of conservation of Burgers vector, figure 15. For < 110 > twist boundaries the primi- tive DSC vectors have magnitudes in the ratio l h : 1 and hence a network accommodating a twist deviation from coincidence should be rectangular with sides in the ratio 1 : lh, as is found [36]. On a

4 b; criterion lattice dislocations can often disso- ciate into DSC dislocations with a reduction in

elactic energy. Since the DSC dislocations are

perfect there is no energy term corresponding to

MICROSCOPY OF STATIC AND DYNAMIC PROPERTIES OF INTERFACES C4-9

FIG. 14. - Shows dislocations in a 2: = 9 coincidence boundary of contrast experiments a & c bright field, b & d dark field.

in stainless steel identified as having b = 1/18 [411] on the basis (Courtesy Clark W. A. T.)

stacking fault energy although a proper calculation would include an allowance for the increase in grain boundary area accompanying the production of DSC dislocations.

The systematic transmission electron micro- scopy experiments carried out by Schober and

~ i l l u f f i [34, 371 using bicrystal foils with the boundary plane approximately normal t o the elec- tron beam revealed networks of grain boundary

dislocations geometrically consistent with those required t o accommodate deviations from exact coincidence orientations for < 001 > twist and tilt boundaries and < 110 > twist boundaries. The expected dislocation arrays were observed in t h e following symmetrical tilt boundaries,

2 = 5 , { 210 ) a n d { 310 ), = 13, ( ' 3 2 0 )

and { 510 ), S = 17, { 410 ) and also in 2 = 5, 13

and 17 < 001 > twist boundaries. In the case of the

C4-10 D. A. SMITH

FIG. 15. - Shows t h e dissoc'iation of a lattice dislocation into DSC dislocations in a 2

29 < 100 > coincidence boundary according to the reaction

112 [ l 101 -+ 1/58 [370] (3) + 1/58 [ l o , 4, 01 (2) ; note the latter Burgers vector is not primitive. (Courtesy

Michaut B.)

Z ⁼ 5 < 001 > twist boundary the dislocations were out of contrast when g . b was zero although only one extinction was reported. The grain boun- dary dislocations became-increasingly difficult t o resolve as 2 increased and their Burgers vectors decreased ; for the Z = 25 boundary, where I b [ is 0.58 4, dislocations were not observed. The angular range in which dislocation networks were observed decreased as 2 increased. It was 8" for lattice dislocations in low angle boundaries and - 1.4" for 1/10 < 310 > dislocations in a 2 = 5 twist boun- dary.

Both techniques have made significant contribu- tions to knowledge of grain boundary structure from the point of view of establishing the Burgers vectors of gbds and giving a lower limit to the value of 2 corresponding to a pattern worth preserving energetically. The observations of dissociation in a 2 ⁼ 41 boundary [33] are doubly interesting since ( a ) they imply that the periodic pattern for such a relatively high 2 value is energetically significant and ( b ) it can be deduced that a 12.6" rotation about < 001 > is already an alternative structure t o the low angle regime. There are difficulties in interpreting the dissociation data when some of the product dislocations are out of contrast o r when rival theories would suggest practically indistin- guishable images, e. g.

in the 2 = 27, fcc < 110 > boundary 129, 30, 38, 391. Grain boundary dislocations can be invisible when g. b = 0 and g. bxu = 0. In addition the work p f Schober and Balluffi establishes that the visi- bility of gbds decreases as b 1 or the dislocation spacing decrease, e. g. the lower limit on visibility of lattice dislocations in a low angle grain boun- dary array w,as found to be 20 A whilst for d l 0 < 3 10 > gbds, I b I ^{= 0.32} a, in a 2 = 5 related boundary the lower limit was 50 A. Caution must be used in interpreting the absence of gbd contrast in a grain boundary. The contrast from gbds depends on 1g.b 1 and the volume of strained material ; both decrease a s 2 and A 0

increase and very weak contrast may lead to the misappre- hension that gbds are not present. As a further method for the characterisation of gbds which is a substantially more complex problem than for lattice dislocations since there are s o many possibilities t o be considered, attempts are being made to extend the successful technique of image matching by computer simulation from lattice dislocations to interface dislocations [7, 40, 41, 421. This technique has the advantage of using much more of the information available in a micrograph than extinc- tion rules alone. In addition, owing to its sensiti- vity, the technique offers a chance of distinguishing closely similar Burgers vectors d 4 101 1 J & a/54 [ I , 16, 1 I] and determining the magnitude of b as well as its direction. Apart from these questions there are several anomalous features of gbd contrast.

Three different sets of viewing conditions have been investigated :

a ) a diffracting wedge on an absorbing wedge or vice versa,

b ) two diffracting wedges in different two beam conditions ;

c ) two diffracting wedges in a common two beam condition,

in addition Balluffi et al. [7] have investigated these contrast conditions for two superimposed crystals viewed with the electron beam at normal incidence.

The first condition is the easiest t o investigate theoretically apart from the difficulty of choosing a value for the absorbtion coefficient in the non diffracting crystal. However, conditions (b) and ( c ) combine relative ease of calculation with physical realism. In many respects the contrast from grain boundary dislocations is similar to that of lattice dislocations within a grain. For example Balluffi et al. [37] report that screw gbds viewed in bright field and dark field with either the upper or lower grain diffracting exhibit similar contrast in bright field and complementary contrast in dark field. The

(4)

A 0 is the deviation from the nearest significant coincidence

orientation.

Bright field Dark field

FIG. 16 IS a s e t of computer simulations showing, in a common diffraction condition, the effect in t h e electron microscope image of increasing t h e separation of t h e DSC dislocations produced in t h e following reaction

112 [lie] -+ 113 [ I ~ I I + ^{116 [liZ]}

g

31 1 and the dislocation separation is (from top to bottom) 0.0, 0.08 [ g , 0.20 <g e t 0.41 [g. (Courtesy Clark W. A . T.)

C4- 12 D. A. SMITH

same result is predicted from two beam calculations using the Howie-Whelan equations [43]. Good agreement was found for the contrast modulations observed and predicted for edge dislocations.

Whilst the contrast m,odulations are relatively well understood the practically achieved resolution of finely spaced gbds (18 A in gold, i. e. - ^{0.08 5,)} is consistently higher than expected from the two beam calculations. This is suggested to be a consequence of a combination of factors including :

(i) contributions from weakly excited beams, (ii) lattice imaging owing to the periodic relaxa- tion in the grain boundary.

For low angle boundaries and those near periodic orientations certain diffraction spots from each grain are close together, e. g. 420 and 420 in a

2 ⁼ 5, fcc periodic boundary. When these spots are used for imaging Moir6 fringes perpendicular to A g are produced and if I A g ( = I/( b ( the dislocation and 'fringe spacing are, the same. However even in this case a distinction can be made by changing g in which case the orientation of a dislocation image would not change. In most cases the spacings of the MoirC fringes and the dislocations would not be the same. However at fine dislocation spacings the dislocation image and Moir6 pattern become indistinguishable according t o c o m p u t e r calculations [42].

An anomalous feature of some grain boundary electron microscope images is that lattice disloca- tions which are partly in a boundary and partly in a grain show a broadening of the image from that part of the dislocation in the boundary. Computer simulations suggest that this is a consequence of

dissociation of the lattice dislocation and that initially the image broadens before separate disloca- tions can be resolved (Clark, unpublished research).

7. Microscopy of dynamic properties of interfaces.

- Transmission electron microscopy at 100 kV had a seminal influence on our understanding of dislo- cation behaviour but the difficulties of extrapola- tion to bulk material which although present for dislocations become more serious for interfaces.

Most investigations have therefore been of the kind where structures are studied before and after known thermomechanical treatments e. g. the work of Horton et al. [38, 441 suggests strongly that grain boundary sliding involves the glide and climb motion of grain boundary dislocations. Attempts to study, e. g. recrystallisation in thin foils are ham- pered by boundary migration so as to minimise boundary area and the loss of stored elastic energy by dislocation rearrangement during specimen pre- paration. These problems are less severe with the thicker foils which may be used in 1 MV electron microscopes and dynamic experiments involving interfaces in superplasticity [45] and recrystal- lisation [46] have received a new impetus although new difficulties arise owing ( a ) to radiation damage of all but the highest atomic number metals and (b) the difficulty of optimising diffraction conditions for several grains simultaneously. Table I1 summa- rises some experimental results, relating to the dynamic properties of grain boundaries, which have been deduced from before and after experiments.

The conventional scanning electron microscope (SEM) is a valuable tool in the study of macrosco-

Observation

-

gbds straight in annealed metals and curved in crept metals

Orowan loops around particles in grain bounda- ries

gbd spiral structures

void denuded zone varies from boundary to boundary in irradiated metals

dislocation absorbtion reaction is temperature dependent and varies with boundary misorien- tation

TABLE I1

gbds glissile

Implication

-

Ref.

-

r33, 31,441 boundaries can be precipitation hardened and [481

gbds react with 2nd phases analogously to lattice dislocation

gbds can multiply like lattice dislocations, mo- [33,49]

vement, if climb involved, is mechanism for point defect sink action and boundary migra- tion

sink efficiency of grain boundaries is a function [ ~ O I of structure of boundary (gbds ?)

dissociation into DSC or infinetksimal disloca- [5 11 tion requires diffusion

grain boundary migration accompanies the absorption of point defects produced by in situ 1 MeV electron irradiation

absorption of point defects by a gbd mechanism 1521

MICROSCOPY OF STATIC AND DYNAMIC PROPERTIES OF INTERFACES _{C4- 13} stress.

stress.

c = 0.00

4 e = 0.26

u

10

r' = 3

1 0 , '

7' = 270 " C . ,r - 1 . 7 i k p . ' m ~ n ~ . ,:

^{7 r: 10;} '

^{7' =} 270 "C'. rr 1 .75 kpirlIn,

Fla 17. -Changes in an evaporated gold reference grid during grain boundary offsets irnd grain rotation. (Courtesy Attwood D.

superplastic deformation of Mg 6 76 Zn 0.5 %, Zr :~lloy. Note the G . and Hi~zzledine P. M.)

C4-I4 D. A. SMITH pic behaviour especially with the aid of a recently developed technique for marking a fine fiducial grid on the surface of a specimen [7]. Owing to the SEM's inherent higher resolution than optical microscopy optimum use of the SEM in high resolution studies requires a fiducial grid with edge dimensions of the order - 100 nm. The production of a fiducial grid using an electron resist technique rather than scratches, etc. offers optimum regula- rity, ease of use and potentially improved resolu- tion. The essence of the technique is to coat a metallographically prepared sample with polyme- thy1 methacrylate which is then exposed t o the scanning beam of an SEM. The effect of electron irradiation is to degrade the polymer which-can them- be selectively dissolved. Evaporation of e. g. a 250 A layer of gold onto the grid of exposed metal and dissolution of the remaining polymer completes the preparation. A typical grid would be 100 k m square with 0.3 pm wide lines at 10 p m intervals.

Such grids habe been used t o investigate the processes which occur during in situ superplastic deformation of Mg 6 % Zn 0.5 % Zr alloy. In this way grain rotations amounting to 33S0 at 41 % strain have been measured and study of the change of shape of the fiducial grid indicates which deformation mechanisms are operating, e . g. a change of grid shape suggests dislocation motion. A study of the paths followed by grain during strain suggests that the SEM surface results d o not differ drastically from bulk behaviour.

8. Conclusion. - There is firm evidence that periodicity is important in grain boundaries and it can be either of the coincidence lattice type o r similar to epitaxy. In both instances grain boundary dislocations, not necessarily with lattice vectors a s Burgers vectors, have an important structural role.

Experimental and theoretical techniques have not yet been sufficiently developed to prove or dis- prove the universality of the dislocation models for interfaces. The implicit foundations of the coinci- dence model must be modified t o reflect the observed absence of a simple'~relationship between energy and geometry.

Grain boundary dislocations can move and multi- ply analogously to lattice dislocation within a grain and gbds may be central t o the dynamic properties of boundaries, such as sliding and migration.

Acknowledgements. - The author is grateful to D. G. Attwood, W. A. T. Clark, Dr. P. M.

Hazzledine and Dr. R. C . Pond for stimulating discussions and permission to quote unpublished results. The work reported here was supported by the Royal Society through an Armourers and Brasiers Fellowship and by SRC and expedited by the encouragement and provision of facilities by Professors J. W. Christian, F. R. S . and P. B. Hirsch, F. R. S. The editors of Acta Metallurgica, Philosophycal Magazine, Physica sta- tus solidi & Scripta Metallurgica kindly allowed reproduction of figures 8, 9d and 15.

References

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and CLARK, W. A. T., 1975 EMAG Meeting, Bristol, Inst. of Physics.

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Stat. Sol. (a), 26 (1974) 215.

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206.

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DISCUSSION

D. WARRINGTON : IS it not important to distin- guish clearly in our notation between boundaries between crystals at a CSL rotation and boundaries between crystals merely in a CSL orientation and t o realise that the 0 lattice approach is as capable as any other in dealing with both kinds of boundaries ?

D. SMITH : Absolutely. 1 have attempted t o distinguish CSL orientation from coincidence posi- tion in my paper.

K. LUCKE : D o you mean that there is evidence that there exist several stable boundaries which agree in the five parameter but disagree in the 3 translational parameters ?

D. SMITH : That is exactly what I mean.

R. W. BALLUFFI : I would question the assign- ment of 8 degree of freedom to a general grain boundary. Surely, if the crystal misorientation is specified (3 degrees of freedom) and the boundary plane misorientation is specified (2 degrees of freedom) any other parameter such as the rigid body translational coordinates of the two adjoining crystals would be fixed automatically i. e., they could not be varied independently. Hence, they would not contribute additional degrees of freedom, and the number of true degrees of freedom remains at 5.

D. SMITH : Computer calculations and experi- ments using the displacement fringe technique both indicate that there exists more than one configura- tion for a given rotation and boundary plane with comparable energy but differing by the amount of translation. In other words there appears to be a degeneracy of boundary structure.

G. SAADA : What is the vector characterizing the rigid body translation of which you showed some examples ?

D. SMITH : The translation vector is characteris- tic of the particular rotation axis and angle together with the boundary plane. It is claculated t o be

1

[I l i ] for a 2 = 3 (1 12) twin in abcc metal 12

and for a (155) = 3 twin in aluminium is 0.52 a in a high index direction near [2ii].

C. GOUX : Dans nos calculs de structure les paramktres cr de translation >> Ctaient nkcessaires pour dCterminer la configuration d e moindre Cner- gie mais nous n'avons pas I'impression que des structures rtelles peuvent correspondre B des valeurs difftrentes de ces paramktres.

D. SMITH : In our calculations the starting configuration of the two grains in a symmetrical tilt orientation is varied systematically by removing atom planes parallel t o the grain boundary. The relaxed structures produced in this way sometimes have comparable calculated energies but different translations (not simply differing by a lattice vector). In certain cases we have also found two minima resulting from the same starting conditions.

In addition the experimental results of Pond show

different translation fringe patterns (implying a

different translation) on incoherent faces of a twin

where the faces have the same indices. This implies

that more than one low energy configuration with a

different translation can exist in the same boun-

dary.