An electron diffraction study of graphitisation in evaporated carbon films

An electron diffraction study of graphitisation in evaporated carbon films

Micron, 1970, 2:73-88 with IV plates 73 An electron diffraction study of graphitisation in evaporated carbon films A. E. B. P R E S L A N D * Depart...

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Micron, 1970, 2:73-88 with IV plates


An electron diffraction study of graphitisation in evaporated carbon films A. E. B. P R E S L A N D * Department of Chemical Engineering and Chemical Technology, Imperial College, Prince Consort Road, London, S. W. 7, U.K. and J. R. W H I T E Department of Biophysics, John Hopkins University, Baltimore, Maryland, U.S.A.

Manuscript received J u n e 14, 1970

From electroJz diffraction measurements of layer diameter, a value of approximately 2eV has been found for the activation energyfor the early stages of graphitisation in thin evaporated carbon flms. Specimens heat treated at temperatures of 1640°C and above have beenfound to exhibit contrastfeatures in electron micrographs which have been interpreted as rotation moirg patterns from overlapping crystallites. The orientation of these crystallites relative to the local film direction has been established. En utilisant la diffraction glectronique pour mesurer le diam~tre de couches, on a trouvd une valeur d'environ 2eV comme gnergie d'activation pour les premi#es gtapes de la graphitisation dans de minces pellicules gvaporges de carbone. Des &hantiUons qui ont subi le traitement par la chaleur it une tempgrature de 1640°C et au-dessus montrent des caractgristiquescontrastges dans les micrographes ilectroniques. On a interprgt~ ceci comme dessins moirds rotatifs formgs par des cristallites qui se chevauchent. On a gtabli quelle est l'orientation de ces cristallites par rapport ?z la direction locale de la pellicule. Ein wert yon ungefiihr 2eV wurde fiir die Aktivierungsenergie fiir die ersten Stufen der Graphitierung in diinnen verfliichtigen Kohlenstoffilmen gefunden durch Elektrondiffraktionsmessungen des Schichtdurchmessers. Man fand, dass Proben die bei 1640°C und dariiber hitzebehandelt wurden, Kontrastmerkmale in den Elektromikrographen zeigten, die als Drehungsmoirdmuster durch die iiberlappenden Kristalliten ausgedeutet wurden. Die Richtung dieser Kristalliten relativ ZU der lokalen Filmrichtung wurdefestgestellt.

INTRODUCTION Kinetic studies on the graphitisation of commercial carbons have revealed the presence of more than one process, from which it has not been possible to establish a unique activation energy. (Fischbach, 1963a; Mizushima, 1959; Fair and Collins, 1961). Fischbach (1963b) however, has identified a first-order process in pyrolytic carbon at temperatures above 2500°C, having an activation energy of (11.3eV). It seems possible, therefore, that graphitisation mechanisms to which a single activation energy can be assigned can only be observed in well-characterised, single phase high-purity carbons of this type, and it was believed that vacuum-evaporated carbon would come into this category. Carbon of this type is prepared by the thermal evaporation of graphite in a vacuum, followed by the condensation of the carbon vapour on to a cool substrate. It is difficult to prepare films > 1 0 0 0 A in thickness this way, and characterisation by electron, rather than X-ray diffraction is necessary. *Present address: Potterton International Ltd., De La Rue House, Regent Street, London, W.1, U.K.


P R E S L A N D and W H I T E

Presland and White (1969a) have shown that such films develop a marked preferred orientation on heat treatment, the c-axis lying predominantly normal to the film plane, as evidenced by the absence of 002 reflections. The only graphitisation parameter available for characterisation purposes is thus La, the crystallite diameter measured parallel to the basal plane, and this is obtained from the breadths of the two dimensional 10 or 11 reflections. The need for accurate data for a quantitative kinetic analysis necessitated the elimination of the effect of this preferred orientation on the diffraction patterns (Presland and White, 1969a). This was achieved by the use of undulating films, as described in the next section. EXPERIMENTAL The requirement that the crystallites should have random orientations, given also that they preferentially take up positions with their c-axes perpendicular to the local film surface, is satisfied by an undulating film with a random distribution of surface orientation. The simplest shape with this property is the thin hemispherical shell, and it was decided to prepare films on a substrate consisting of close packed hemispheres of about one micron diameter. This size is sufficiently small to give a large number of periods within the area which is sampled for diffraction (approximately 100 microns diameter), ensuring that random orientations will in fact be displayed. On the other hand, the curvature is unlikely to be great enough to hamper layer plane growth in the early stages of graphitisation, although the production of an effect similar to polygonisation (Akamatu and Kuroda, 1959) in carbon blacks would not have been surprising for films heat-treated at temperatures in excess of 2000°C; no such effect was in fact observed. The problem of producing the required substrate topography was solved by painting a water suspension of polystyrene latex on to a clean glass slide and allowing it to dry. The latex was supplied by the Dow Chemical Company, and had a particle diameter of 0.8 microns. Carbon evaporation was carried out as described by Presland and White (1969a), and the film stripped on hot chloroform or hot benzene, which removed a large fraction of the polystyrene from the film. The final traces were removed by heating for one hour at 500°C at 10 -4 torr pressure. Large batches of specimens were given this preliminary heat-treatment in the same run to ensure that this stage did not introduce random differences in the structure of the specimens used for the isothermal heat-treatments. Comparison of the results from planar films heat-treated at 1250°C for 9 minutes, both with and without a preliminary heat-treatment at 500°C, showed no significant differences. The heattreatment of specimens used in the isothermal analysis was carried out in vacuum (10-4 torr) using a microfurnace of low thermal inertia, permitting fast heat-up times ( < 1 minute) (Presland and White, 1969b). For temperatures above 2200°C, a second microfurnace flushed with dried oxygen-free argon was used (Presland and White, 1969b). Electron diffraction patterns of highly reproducible ( < 1/2%) camera length were obtained in a Siemens Elmiskop I with condenser lenses only excited, and using a large bore projector pole piece. Profiles were obtained with a Jarrell-Ash microphotometer, from plates exposed and developed to a density lying in the region of linear response.



Profile Analysis It is usually assumed in the preparation of replicas for electron microscopy by carbon evaporation that the carbon forms a layer of uniform thickness over the substrate. Direct examination of regions of film bent over both by tilting (using a goniometer stage capable of 22 ° of tilt) and by accidental fracture, indicated that this was in fact the case, and recent work in this laboratory (Presland and Wield, to be published) using similar hemispherical films has provided quantitative confirmation. For hemispherical undulations, the shell walls of the deposited film will have a thickness equal to half that which would be produced by the same volume of material deposited on the equatorial plane. The latter value was 250-300A, and the shell wall thickness was hence adjudged to be 125-150A. Parts of the film lying closely parallel to the electron beam direction were therefore thicker than 1000A, at which value multiple scattering may begin to be of importance (Smith and Burge, 1963). Such regions accounted for approximately 5% only of the total volume, however, and it is assumed that single scattering theory is applicable to the specimens used in this study. The background was subtracted geometrically before measurement of line breadths (White, 1968). The half peak breadth, Bl:2, and two-thirds peak breadth, B2/3, were used in the appropriate Scherrer equations, calculated by Warren and Bodenstein (1966): 1.77 L~-(1) BI: 2 c o s 0


0.94 B2, 3 c o s 0


Instrumental broadening was negligible Ibr all specimens used in the kinetic studies. The calculated Warren profile is not strictly applicable to specimens with crystallite sizes below 50A (Diamond, 1957; Warren and Bodenstein, 1965; Franklin, 1950; Diamond, 1958), and values yielded by equations (1) and (2) require a small correction, for which an approximate method, based on Diamond's data (Diamond, 1957), as interpreted in terms of corrected Scherrer constants by Warren and Bodenstein (1965), was developed (White, 1968). L a values were obtained from breadth measurements made at each of the two extremities of two perpendicular diameters on the pattern. The error in the mean of the four measurements thus obtained was taken to be the root of the variance of these values. RESULTS

Kinetic analysis In diffusion controlled crystal growth processes it is often found that a linear relationship exists between a linear dimension of the crystal and the square root of the heat-treatment time (Norton, 1959; Crank, 1956; Hume-Rothery, 1966). For a heattreatment temperature of 1000°C the plot of L a against t 1/2 was fairly linear (Figure 1) within the limits of the scatter, up to a heat-treatment time of one hour. Higher temperatures gave linear regions which terminated at shorter time (Figures 1 and 2). Since the straight line always gave a positive intercept on the La axis, the relationship tested was of the form : (L, --Lao ) = (K it) 1/2 (3)


P R E S L A N D and W H I T E

L~o can be taken to represent an initial value for L~; a plot of log (I,,--Lao) against log t gave a gradient of one half (Figure 3) where Lao was taken to be 9.7A by extrapolation from the L a versus t 1/2 plot. This analysis was applied separately to the results from each combination of reflections used (10 and 11), and the fraction of the peak height at which breadth measurements were taken (1/2 or 2/3). The four sets of results show closely similar trends, and the graphs shown are quite typical. Values for Kll/2 were found from the gradients of the initial straight line sections of the L, versus 0/2 graphs (Figures 1 and 2). It was expected that K 1 would be of the form : K 1-~K 0 exp (--U1/kT) (4) where U 1 is an activation energy, k is the Boltzmann constant, and T is the absolute temperature. Reasonably linear plots of log K l against 1/T were obtained (Figure 3), and the gradients yielded activation energies of the order of 2eV, as shown in Table 1. TABLE 1

Activation Energies (eV) (10), 1/2

(11), 1/2

(10), 2/3

(11), 2/3

Lavs. t ~





La2vS. t





The accuracy of these values is uncertain. The shortness of the linear region in the L a versus t I/2 plots tbr temperatures above 1000°C, coupled with the large scatter, made the estimation of the K 1 values difficult; the value of K 1 corresponding to heattreatments at 1640°C had to be estimated from the first two points only, an obviously unsatisfactory situation. Since the times involved in this case were very short, the heating-up time may have been significant in this region. The extra work involved in attempting to correct for the heating-up stage would be unjustified without making other improvements in the procedure.

001 Reflections 001 reflections were obtained from all heat-treated undulating films (Figure 5, c.f. Presland and White, 1969a, Figure 3), and attempts were made to measure the interlayer spacing (Table 2). In X-ray studies of graphitisation, the c-spacing is usually considered to be the parameter measureable with the greatest precision, and most kinetic analyses have been based on measurements of this quantity (Fischbach, 1963a, b; Fair and Collins, 1961). No clear correlation was obtained, however, either with the residence time or with the corresponding layer diameter, and this was p, obably a consequence of the lack of precision of the location of the peak position when electron diffraction is used; even at 1640°C the ring profiles were not sharp enough to yield accurate diameter measurements.





°C 1640

t (rains) 1.0 2.3 4.8 5.0 6.8 9.0 15.0 20.0 30.0 40.0 49.0 58.0



(10), 1/2

(10), 2/3

(11), 1/2

(11), 2/3

19.5±0.7 37.5!0.7 40.7±1.1 36.6~2.8 39.1~1.2 26.4~0.6 38.0~1.0 31.8~0.7 25.5~0.2 39.2~2.0 38.7il.4 37.5~1.5

19.4~2.0 33.6~1.1 39.3~3.6 32.9~1.3 34.3~0.6 24.4i0.3 34.1~1.1 29.5~0.9 25.5~0.8 33.8~1.0 36.4~1.5 34.7~1.1

18.0~1.5 38.7~3.9 37.9~7.4 36.2il.2 37.1~1.9 27.8~0.4 37.8~1.7 30.0~1.6 27.6~1.4 38.1~2.2 40.5i2.6 37.9~1.5

16.4i1.1 36.8~1.5 34.7i5.2 32.8i1.1 35.9~1.6 24.1~0.8 34.4~1.9 26.8~1.2 24.0il.3 32.9~1.6 38.2~2.7 36.4~2.0




3.41 3.45 3.45 3.42 3.46 3.47

3.39 3.39 3.40 3.42 3.48 3.48

3.45 3.46

3.44 3.42

L c measurements using basal plane reflections were not attempted, for the following reasons. The steep background in the vicinity of the 002 reflection made measurement of line breadths an extremely difficult task, even for specimens heat-treated at 1640°C and above, while the 004 and higher orders could not be resolved on the densitometer traces.

Electron Microscopy Well-defined features in the electron image were plentiful in specimens heat-treated to high temperatures, and this section concerns principally specimens heat-treated to 2000°C and above. Specimens heat-treated to temperatures in the range used for the kinetic studies often showed features which appeared to be the early stages of development of those described here. Simple dark field electron microscopy, in which the objective aperture is moved away from the instrumental axis to intercept one of the diffracted beams instead of the transmitted beam (bright field) provided interesting results. The use of the 002 reflection to form the image revealed bright patches in the hemispherical shells, consisting of radial lines in those regions of film nearly parallel to the electron beam direction (Figure 6). In view of the smallness of the Bragg angles involved, these patches must clearly be associated with crystallites having basal planes lying closely parallel to the beam. By a separate calibration of the relative rotation between image and diffraction pattern, it was possible to establish the direction of the c-axes of the crystallites contributing to a particular segment of the 002 ring. The crystallites were found to be so oriented within the film as to have their c-axes normal to the local surface, providing confirmatory evidence for the preferred orientation described by Presland and White (1969a). By the use of a tilting stage it was established that the kind of contrast described


P R E S L A N D and W H I T E

above was found whenever the film was suitably oriented relative to the electron beam, so that the features were present in the caps of the hemispheres, and were not confined to the regions near to the equatorial plane. This was confirmed by the observation of regions of film which were broken and bent over. The periodicity over short distances exhibited by the features indicates that an interference effect may be involved. It is suggested that the lines running perpendicular to the surface of the film are in fact rotation moir~ fringes, resulting from interference between two or more crystallites lying side by side in the surface; the basal planes of these crystallites lie parallel to the direction of the electron beam, but the crystallites are tilted slightly relative to one another about an axis parallel to the beam (Figure 7). Measurements of the periodicity of these fringes gave relative misorientation values ranging from less than 2 ° up to 8 °. One would not expect to find fringes corresponding to very small misorientation angles since the fringe spacings would then be larger than the extent of the crystallites in the a-direction (e.g. 1° misorientation corresponds to fringes of spacing 200A approximately). Large misorientations corresponding to small moirfi periodicities cannot be detected due to the limit of resolution of the microscope, and it is possible that the blurred regions of brightness (e.g. Figure 6) contain unresolved fringes. When the moird fringes tail off into blurred regions, this effect is probably caused either by the presence of several adjacent moird patterns from several different pairs of crystallites around the hemispherical surface, or by the spherical aberration which will be present in simple dark field conditions. The corresponding bright field images show features of similar dimensions, but less contrast (e.g. compare Figure 8 with 9). This is in agreement with the proposed moird pattern explanation, since bright field moird patterns rely on the interference between the transmitted beam and a doubly diffracted beam, and favourable conditions for this will not be found in carbon fihns of 1000A thickness or less, due to the small intensity of the doubly diffracted component. Dark field moires can be formed from two singly diffracted beams, however, and can therefore be expected for much thinner regions. Similar features in specimens used in the kinetic analysis showed preferred orientation to have developed at these lower temperatures, but with smaller size and poorer contrast, consistent with the smaller crystallite size. The moird pattern interpretation of the type of feature observed has recently been strikingly confirmed by Heidenreich, Hess and Ban (1968) in their high resolution micrographs of carbon blacks, in which they achieved direct imaging of basal planes. A specimen heat-treated for five minutes in argon at 2400°C was examined in dark field (Figure 10), using the modulated 10 band, and displayed moird patterns similar to those obtained by Jenkins, Turnbull and Williamson (1962) and Turnbull and Williamson (1963). The absence ofmoir~ patterns in the bright field image (Figure 11) is again assumed to be the consequence of insufficient specimen thickness; the etched appearance is thought to be due to surface evaporation or oxidation. By making a tracing of the boundaries in the micrograph it was shown that they correspond to boundaries between neighbouring moird patterns in Figure 10. A typical crystallite diameter as revealed by the moir~ pattern boundaries is approximately 2500A. In view of the fact that such large crystallites had developed, it is hardly surprising to note that the drastic rearrangement of material also resulted in the loss of the undulating nature of the specimen. This was confirmed by the absence



of the 002 reflection in the diffraction pattern, showing that the growth of crystallites perpendicular to the macroscopic plane of the film had been inhibited. That complete preferred orientation had not been attained was evidenced by the resolution of the 1010 and the 1011 reflections and also by the separation of the 1120 and 1122 reflections (Figure 12). The 1120 peak was very narrow, approaching the instrumental line breadth, and an additional hazard in the use of this line to give a value for the basal plane layer diameter was the fact that the film now contained an unknown degree of preferred orientation, and could not be considered to produce a true powder pattern. To obtain a rough estimate for the layer diameter, a Scherrer constant of 0.9 was employed (Presland and White, 1969a) and a simple correction made for instrumental broadening using the "sum of squares" method (Warren, 1941), yielding a value of approximately 1000A. It is curious to note that a high proportion of the moird patterns in Figure 10 have boundaries roughly parallel to one another, with apparent continuity from pattern to pattern over fairly large distances. This is shown more clearly (Figure 13) by using the tilted dark field technique (Hirsch, Howie, Whelan, Pashley and Nicholson, 1965). The crystalline nature of this continuity is clearly shown by the high magnification micrograph of a specimen heat-treated at 2600°C for 3 minutes in argon (Figure 14). There is no evidence for boundary continuity in any other direction, and it is proposed that the observations indicate the development of lath-shaped crystallites several microns long and approximately 2000-3000A wide. This is consistent with the difl]'action evidence for anisotropic growth described by Presland and White (1969a). DISCUSSION The value of the activation energy for the early stages of graphitisation of evaporated carbon of approximately 2eV (46K. cal/mole) is low in comparison with the values obtained in studies of the kinetics of graphitisation in other carbons. (Fischbach, 1963a, b; Mizushima, 1959; Fair and Collins, 1961). It must be emphasised, however, that since diffraction patterns show no evidence for three-dimensional ordering, this low activation energy corresponds to the process of layer-plane growth. An even lower value of 5.8K. cal/mole (0.22eV) for the activation energy has been reported by Hanawa (1964) in a study of the resistivity changes occurring in evaporated carbon films at temperatures well below 1000°C. A range of values of similar magnitude to that found in the present work has also been obtained by McLintock and Orr (1967) from electron spin resonance studies of evaporated carbon films heat-treated also at temperatures below 1000°C. The evidence points to the existence of fairly easy structural rearrangement mechanisms in evaporated carbon films during the early stages of heat-treatment. It is natural to suppose that we are concerned here with the transition from an amorphous to a crystalline state. The existence of a single activation energy, however, is characteristic of a transition between crystalline phases, and it is interesting to consider the model put forward by Kakinoki, Katada and Ino (1960). These workers concluded that approximately half of the carbon in an evaporated carbon film was contained in small regions having a diamond-like structure, the rest being graphitic. It is possible, therefore, that the latter represent the nuclei which grow at the expense of the former.



Little data seems to be available on the thermodynamics of the diamond to graphite transition. Evans and James (1964), however, have demonstrated the development of crystalline graphite on the surface of diamond at 1500°C, while almost complete conversion to graphite was achieved within minutes by heating at 1900°C. The enormous surface area:volume ratio of the diamantine regions in Kakinoki's model for evaporated carbon would presumably facilitate this transformation. An alternative explanation for the relative ease of layer-plane growth derives from the possible presence of gases (e.g. oxygen, water vapour) occluded during condensation in the imperfect vacuum. Such gases, if of an oxidising character, could assist graphitisation by preferential oxidation of cross-links, as suggested by Noda and Inagaki(1964). The fact that the initial linear portion of the kinetic characteristic is limited in extent may be due to impingement of the growing layer-plane nuclei on each other, corresponding to exhaustion of the available non-graphitic carbon. The value of L~ at which this occurs increases with increasing heat-treatment temperature; this implies that the nucleation density is itself a function of the temperature, and that not all the graphite domains in the as-deposited carbon take part in the growth process. It is clear from Figures 1 and 2 that the kinetics of layer-plane growth are very different after mutual impingement has occurred. The average rate of increase in I, a is much smaller, and this is accompanied by a large increase in the scatter from specimen to specimen. The variability may be associated with, or may derive from the same source as, the anisotropic growth already described, the common factor being the presence of local stresses set up during mounting or subsequent heat-trcatment. ACKNOWLEDGMENTS One of us (JRW) would like to thank the Science Research Council for a Research Studentship. We would also like to acknowledge the help of Mr. P. Marlow in some of the experimental work, and the Dow Chemical Co., Michigan, U.S.A., who provided samples of polystyrene latex. REFERENCES AKAMATU, H. and KURODA, H., 1960. On the substructure and the crystallite growth in carbon. Proc. 4th Carbon Conf., 355-369. Pergamon Press, Oxford. CRANK,J., 1956. In: The Mathematics of Diffusion, Section 7, 35 (ii). Oxford University Press. DIAMOND, R., 1957. X-ray diffraction data for large aromatic molecules. Acta Cryst., 10: 359-364. DIAMOND, R., 1958. A least-squares analysis of the diffuse X-ray scattering from carbons. Acta Cryst., 11: 129-138. EVANS, T. and JAMES, P. F., 1964. A study of the transformation of diamond to graphite. Proc. Roy. Soc., A277: 260-269. FAIR, F. V. and COLLINS,F. M., 1963. Effect of residence time on graphitisation at several temperatures. Proc. 5th Carbon Conf., 503-508. Pergamon Press, Oxford. FISCHBACH,D. B., 1963a. Kinetics of graphitisation of a petroleum coke. Nature, 200: 12811283. FISCHBAGH,D. B., 1963b. Kinetics of high-temperature structural transformation in pyrolytic carbons. Applied Phys. Letters, 3: 168-170. FRANKLIN, R. E., 1950. The interpretation of diffuse X-ray diagrams of carbon. Acta Cryst., 3: 107-121.



HANAWA, T., 1964. Heat treatment of arc-evaporated carbon films. Proc. Symposium on Carbon, Session IV--7. Maruzen, Tokyo. HEIDENREICH, R. D., HESS, W. M. and BAN, L. L., 1968. A test object and criteria for high resolution electron microscopy. J. Applied Cryst., 1: 1-19. HIRSCH, P. B., HOWIE, A., NICHOLSON, R. B., PASHLEY, D. W. and WHELAN, M. J., 1965. In : Electron Microscopy of Thin Crystals, Chap. 13. Butterworth, London. HUME-ROTHERY, W., 1966. In: The Structures of Alloys of Iron, p. 176. Pergamon Press, Oxford. JENKINS, G. M., TURNBULL,J. A. and WILLIAMSON, G. K., 1962. Electron microscope studies of graphitisation and deformation in carbon film. J. Nuc. Mats., 7: 215-217. KAKINOKI,J., KATADA,K. and INo, T., 1960. Acta Cryst., 13: 171-179. McLINTOCK, I. S. and ORR, J. C., 1967. Electron spin resonance studies of evaporated carbon films. Carbon, 5: 291-300. MIZUSHIMA, S., 1960. On the crystallite growth of carbon. Proc. 4th Carbon Conf., 417-421. Pergamon Press, Oxford. NODA, T. and INAGAKI, M., 1964. Effect of gas phase on graphitisation of carbon. Carbon, 2: 127-130. NORTON, F. H., 1959. In: Kinetics of High Temperature Processes, ed. Kingery, W. D., p. 116. Tech. Press, M.I.T. and John Wiley, New York. PRESLAND, A. E. B. and WHITE, J. R., 1969a. Graphitisation of evaporated carbon films. Carbon, 7: 77-83. PRESLAND,A. E. B. and WHITE, J. R., 1969b. A high temperature microfurnace for use in vacuum and inert atmospheres. 07. Sei. Inst., 2: 67. SMITH, G. H. and BURGE, R. E., 1963. A theoretical investigation of plural and multiple scattering of electrons by amorphous films, with special reference to image contrast in the electron microscope. Proc. Phys. Soc., 81: 612-632. TURNBULL,J. A. and WILLIAMSON,G. K., 1963. Graphitisation as observed in thin carbon films, and its relation to the mechanical properties of polycrystalline graphite. Trans. Brit. Ceram. Soc., 62: 807-811. WARREN, B. E., 1941. X-ray diffraction methods. J. App. Phys., 13: 375-383. WARREN, B. E. and BODENSTEIN,P., 1965. The diffraction pattern of fine particle carbon blacks. Acta Cryst., 18: 282-286. WARREN, B. E. and BODENSTEIN, P., 1966. The shape of two-dimensional carbon black reflections. Acta Cryst., 20: 602-605. WHITE, J. R., 1968. A study of graphitisation in thin carbon films by electron microscopy and diffraction. Ph.D. Thesis, Univ. of London.




1970, 2:73-88

I.~ measured from breadth ot (11) band at ~3 peak hlight. 23"0 22.0



16"C J250~.

,I 'S'










La measured from breadth of (11)band

u~ ~/3

peak height

. I °'" 16"C







24<3 .








16"0 I





Figures 1 and 2. L , vs. tv~,for heat treatment temperatures in the range 1000°-1640°C.

' i" ttI

if W~ pt







4"0 I~ 5.o t (m.,~)



Micron, 1970, 2:73-88




'_-2 o














1.2 14. LOG~ot






Figure 3. Arrheniusplot derivedfrom Figures 1 and 2.

2'~ 2.0

x/~ I-6 o t.9 O _.j +







Figure 4. Plot of (L.--L.o)



~ log t: L.o 9.7A






Micron, 1970, 2:73-88



(I I)

Figure 5. Electron diffraction pattern and corresponding profile from undulating film, heat-treated at 1640°C. Note the 002 reflection.

Micron, 1970, 2:73-88



F(gure 6. D a r k field 002 m i c r o g r a p h showing direction of c-axis relative to local film topog r a p h y . U n d u l a t i n g film, h e a t - t r e a t e d at 2000°C for 4min. in vacuo. :~, 120,000.




Micron, 1970, 2:73-88


Figure 7. Schematic arrangement ofcrystallites within the film, i represents the beam direction and ~ the misorientation angle.



Figure~ 8 and 9. Bright field (Figure 8) and dark field (Figure 9) 002 micrographs of" overlapping crystallites (same area in each micrograph). T h e specimen was heattreated at 2000°(-I for 4rain. in vacuo. ~<80,000.

Micr:m, 1970 2:73-88





Figure 10. D a r k field m i c r o g r a p h showing moird patterns. Note tile linear a r r a n g e m e n t of Figure Figure

the boundaries. T h e specimen was h e a t - t r e a t e d for 5min. at 2400°C in argon. ~< 16,000. l l. Bright field m i c r o g r a p h of the a r e a shown in F i g u r e 10. × 16,000. 12. Electron diffraction p a t t e r n a n d c o r r e s p o n d i n g profile from an u n d u l a t i n g fihn h e a t - t r e a t e d at 2400°C. Note the absence of 002 reflection a n d the presence of 1 0 i l a n d 1122.

( oT i)





Micron, 1970, 2:73-88

F(¢ure 13. Tilted dark field micrograph, showing lath-shaped crystallites. T h e specimen was heat-treated for 5min. at 2400°C in argon. ,~<16,000.

Figure 14. Anisotropic crystal growth as a result of heat-treatment at 2600°C. × 80,000.