158 BOUNDARY MIGRATION AND GRAIN GROWTH

BOUNDARY MIGRATION AND GRAIN GROWTH * BY WALTER C. MCCRONE

Received 8th February, 1949

It has long been known that metals will show grain growth and that this growth involves a reorientation of metal atoms across grain boundaries in such a way that many grains disappear entirely. This movement of

* Contribution of Armour Research Foundation of Illinois Institute of Technolo,T.

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a b

FIG. I.--TNT during boundary migration a t So” C (a after I min. ; b after 4 min.) ( Y roo) crossed Nicols.

a b

FIG. 2.-DDT showing secondary crystallization due to boundary migration (b is an enlargement ( x 100) of part of a ) . ( x 40) crossed Nicols.

T o face page 1591

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WALTER C. McCRONE I59

grain boundaries led to the term " boundary migration" which will be used here as a synonym for grain growth.

In 1929 Tammann2 published data showing that certain compounds (camphor, pinene hydrochloride and ice) show a behaviour very similar to that observed in metals. showed that some minerals (e.g., anhydrite, fluorite, periclase and corundum) when compressed and heated to temperatures well below the melting point would also show boundary migration similar to metals. In 1949 the study of octachloropropane was suggested as a means of studying boundary migration in metals.

During the past several yeus a number of organic compounds quite dissimilar to octachloropropane in lattice properties have been shown to exhibit boundary migration. For example, Kofler reported in I941 that an organic compound, TNT, shows a somewhat similar behaviour in that crystals once formed undergo a further recrystallization in the solid phase so that one crystal grows into and through its neighbour (Fig. I). DDT has been reported and several other organic compounds (unreported) have been observed to show similar behaviour (Fig. 2). In each of these cases and in contrast with the metals, camphor, fluorite, octachloropropane, etc., it is apparent that these materials show boundary migration in which direction is dependent on the orientation of the crystal lattice within the grains.

Metals, octachloropropane, camphor, pinene hydrochloride, ice, fluorite, anhydrite, etc., show migration of one crystal into another in such a way that the orientation of the lattice cannot be an important factor. On the other hand, boundary migration by TNT, DDT, Vitamin K, etc., is definitely dependent on orientation of the crystals. The crystals will grow in a direction which can be predicted for a given compound from the known relative orientations.

The two types will be described throughout as the DDT type, in which orientation controls the direction of boundary migration ; and the octachloropropane type, in which orientation has little or no effect on the direction of boundary migration.

The DDT type of boundary migration is of particular interest since as stated above the direction of growth is dependent on lattice orientation. Any theory covering the mechanism of boundary migration must take into account, for crystals of this type, the effect of difference in orientation of the two lattices in contact. DDT, for example, grows in such a way that the (001) face will penetrate either the (roo) or (010) planes of adjacent crystals. If, on the other hand, crystals of this type are aligned parallel to each other no growth will occur. Maximum growth will occur, therefore, when crystals elongated parallel to c intersect at 90° angles (Fig. 2).

TNT shows a very similar behaviour although it does not grow as rapidly during boundary migration. It does, however, grow in much the same manner and in such a way that the direction of migration can always be predicted from the orientation of the crystals. In this case the (010) face will always grow into the (001) and (roo) faces (Fig. I).

During the past 20 or 30 years there has been considerable discussion regarding the possible mechanism by which boundary migration occurs.

In 1946 Buerger and Washken

Two different types of boundary migration are therefore recognized.

1 Carpenter and Elam, J . I n s t . Metals, 1920, 24, 133. 2 Tammann, 2. anorg. Chem., 1929, 182, 289. 3 Buerger and Washken, Amer. Miner., 1947, 32, 296. 4 McCrone, J . A@Z. Physics, 1949, 20 (Feb.).

Kofler, 2. physik. Chem. A , 1941, 188, 201. 6 McCrone, Anal. Chem., 1948,20,274.

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160 BOUNDARY MIGRATION AND GRAIN GROWTH

Most of this discussion has been on boundary migration of the octachloro- propane type and most of it has concerned metals. Harker and Parker 7

have advanced the argument that grain shape governs the extent and direction of boundary migration. This results in movement of the grain boundaries in such a way that straight boundaries meet at angles of IZOO.

By this criterion little or no grain growth should occur when these conditions are satisfied. The effect of lattice deformation on boundary migration is not discussed by them, although presumably it would at least affect the angles between grain boundaries. Most other investigators have assumed that strain energy, due to cold-working and resultant plastic deformation, is the driving force.

Two hypothetical questions can be posed as a result of irreconciliation of these two ideas-

I. Can grain growth occur in a sample whose grains meet throughout at 120' angles with straight boundaries but in which the grains possess residual strain energy ?

2. Can grain growth occur in a sample whose grains show curved boundaries and many angles not equal to 120' but in which the grains are strain-free ?

Unfortunately the first of these questions cannot be answered in an un- equivocal fashion. A close approximation to a final answer to the second can, however, be obtained. This is done by comparing the rate of growth in two samples : one with, and the other as nearly as possible without, strain. Experimental data to answer this question are presented below.

A broader problem, however, and one of great interest and importance is to find a more definite relation between boundary migration in metals and in the octachloropropane type of organic compound. It is obvious on examination of photomicrographs showing boundary migration in systems of these two kinds that in superficial appearance there is no difference between the two cases. There is a striking similarity between growth in metals and in octachloropropane and the resulting structures are amazingly similar in appearance before, during and after boundary migration. Furthermore, octachloropropane and other organic compounds of this type show a final structure which agrees entirely with the ideas presented by Harker and Parker. Octachloropropane, for example, during annealing changes progressively toward an ultimate appearance in which all grain boundaries are straight and meet only at angles of 120' (Fig. 3).

An additional effort has been made to relate boundary migration of octachloropropane to that of metals. This is being done by studying the rate of growth at different temperatures and comparing these data with corresponding data for metals systems. Unfortunately little data of the latter type are available and it appears very difficult to accumulate large amounts of such data because of the experimental difficulties. It is possible, on the other hand, to follow boundary migration in organic compounds during annealing of a thin transparent section using polarized light under controlled temperature conditions and to obtain a complete curve with as many experi- mental points as desirable in a few hours.

Some data taken in this way are summarized in Table I. These data were obtained by the following procedures.

Expt. 1-4: A small quantity (5-10 mg.) of octachloropropane (purified by sublimation to a melting point of 168" C) was melted between a cover glass and slide. The fused preparation was quenched quickly to room temperature by placing i t cover-glass side down on a metal block. This preparation was then placed in a previously heated hot-stage set a t the desired temperature. About 10 sec. was required for the slide to become heated and from 3-60 sec. to find

7 Harker and Parker, Trans. Amer. SOC. Metals, 1g45,34, 156.

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FIG. 3.-Boundary migration in octachloropropane, the numbers refer to the same crystal as i t appears at successive times. ( x 100) crossed Nicols.

[To faccpagc 160

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Time (min.)

5 6 7

I 3 16

27 32 41 54 64

I 0

22

I

2

3 5 7

15 28 45 80

140

I 0

I

30 60

I80 240 300

I20

I

I 0 20

I 040 1485 2 I00

3390 F

WALTER C, McCRONE

TABLE I

ISOTHERMAL TIME-RATE DATA FOR OCTACHLOROPROPANE

Expt. I : 136' C

Log Time

0.70 0.78 0.85

1-15

1-34 1'43 1-5 I 1-61 1-73 1.8 I

I '00

1'20

0'00

0.30 0.48 0.60 0.85

1-17

"45 1-65 1-90 2-15

1'00

0'00

1.48 1.78 2-08 2.26 2-38 2.48

0'00 1-00

1.30 3-02 3-18 3'32 3'5 3

Rate Log Rate

0'010

0.007 0.006 0.005

0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003

8.00-10 7-85-10 7' 7 8- I o 7'70-10 7'60-10 7-60-10 7-60-10 7.60-10 7-60-10 7.4 8- 10 7-4 8-1 0

7'48-10

Expt. 2 : 123'C

- - 0'0022 7-34-10

7.20-10 0.00 I 6 0.00 I 5 7-18-10 0'00 I I 7.04- I 0

0'00 I 0 7-00-10

0.0008 6*90-10

- -

0.ooog 6.95-10

Expt. 3 : 115" C

0*0008 6.90-10 0*0007 6-85-10 0.00055 6-74-10 0~00035 6-54-10 0.00025 6-40-10 0'00020 6.30-10 0'00020 6.30-10

Expt. 4 : 103°C

0*00056 6-75-10 0.00033 6052-10 0'00022 6'34-10 0'000 I3 5'1 1-10

0-000 I 3 5-1 1-10 0-000 I 3 5-1 1-10 0~000 I 3 5.1 1-10

161

Log Diam.

2-06 2-07

2-16

2.18 2.29 2.32 2'34 2-42 2-40 2-46 2'54

2-11

2.32 2-36 2.36 2'37 2.38 2-38 2-39 2-42 2'44 2.50 2-58

2'20 2-28 2-30 2'37 2'37 2-41 2.4 I

2.29 2-30 2-3 I 2-38 2-42 2-41 2-45

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162 BOUNDARY MIGRATION AND GRAIN GROWTH

TABLE I-(Continued)

Expt. 5 : 136' C

Time Log Time Rate Log Rate Diam. Log Diam. (min.) (micron)

I

1'5 2.5 4'5 5'5 7'5

I 0

I 5 2 7 40 60 90

140 I 60

I20

4 9

I3 18 23

0'00 0.18 0.40 0.65 0'74 0.88

1-18 1-43 1-60 1-78 1-95 2-08 2-15

1-00

2'20

0.015 0.013

0.0065 0.0055 0.0050

0.0038 0.003 8 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038

0'010

8.18-10 8.1 1-10 8. I O- I o 7-81-10 7-74-10 7-70-1 0

7-58-10 7 -5 8-1 0 7.5 8-10

7'5 8-10

7'5 8-10 7-58-10 7058-1 o 7.58- 10 7'5 8-1 o

1-77 1-83 1-89 2-06

2-13 2-16 2-18 2-32 2-42 2.52 2'55 2-64 2-80 2.89

2'10

Expt. 6 : 159' C

0.60 0.006 7-78-10 185 2-2 7 0.95 0.006 7'78-10 188 2.2 7 1'1 I 0.006 7'7 8- 10 204 2.3 I 1-26 0.006 7.78-10 231 2'36 1-36 0.006 7-78-10 287 2-46

Expt. 7 : 145'C

I 0'00 o.oo08 6.90-10 171 2.23 40 I -60 o*ooo8 6.90- I 0 203 2-3 I

an appropriate field of view. In all experiments zero time indicates the time a t which the preparation was placed in the hot-stage. Most of the readings were started at M = I mjn.

A carefully calibrated Kofler hot-stage was used with a Sola constant voltage transformer. The temperature data are accurate to &I" C and accurately represent the temperature of the field under observation. The data were taken by means of photomjcrography using a Leica with a Speed-O-Copy attachment. The 35 mm. negatives were enlarged to a convenient magnification and the average grain size was determined by measuring the intersections of grain boundaries on a linear scale during a number of regularly spaced linear traverses of the entire field (Fig. 3).

Expt. 5 : A small quantity (5-10 mg.) of octachloropropane (purified as above) was placed between a slide and cover-glass and subjected to 500 psi pressure. This preparation was then placed in a previously heated hot-stage as for Expt. 1-4.

Expt. 6 and 7 : In these two experiments 5-10 mg. of octachloropropane was melted in the usual way between a slide and cover-glass. The preparation was then, however, placed immediately in the previously heated hot-stage so that the temperature of the preparation a t no time fell below 145" C (Expt. 7) or 159" C (Expt. 6).

The average diameters were then determined in the same manner as described above. Fig. 4 shows these average diameters as a function of time for each experiment. These data were then smoothed from these curves and rate of growth data were calculated from the slopes of these smoothed curves. Fig. 5 shows log rate against log time for each experiment. Fig. 6 shows log rate against temperature with a vertical line for each experiment covering the time variable. The actual data points fall on the vertical lines with increasing time downward.

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WALTER C. McCRONE

40

30

10'

IC

1 9-10

FIG. +-Grain growth curves for octachloropropane.

0 STRAINED T H E R M 0 COLD-WORKED 4 UNSTRAINED

)-103k

I 2 3

FIG. 5.-Rate-time curves for grain growth in octachloropropane.

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164 BOUNDARY MIGRATION AND GRAIN GROWTH

9 - I C

a-ic

7- 10

6-10

5 - IC

A

0

B 9 I

0

- - u fl I

TEMPERATURE rC) I I I I I I I

I10 120 130 140 150 160 FIG. 6.-Rate-temperature curves for grain growth in octachloropropane.

Discussion Fig. 4 shows that the slope of the rate curve plotted against time is

constant after an initial period and that the slope increases with increasing temperature. The equations for the linear portions are :

136" C : D = 3.2M + 130 . (1) 123' C : D = I-IM + 230 . (4 115' C : D = o28M + 189 . * (3) 103" C : D = o-ozgM + 205 . (3)

where D is the average grain diameter in microns and M is the time in minutes. The constant in each relation is, of course, fortuitous and depends only on the grain size of the original preparation.

These equations are equivalent to the expression given by Beck : D = K(tg + A)".

where K is the slope and A the imaginary time required for the grains to grow by boundary migration to an average size D at tg. In either case, however, the question is whether K is independent of A or, in the other case, whether S is independent of Di, the intercept on the grain diameter ordinate. The fact that the slope is a linear function of temperature (shown below) as well as the fact that the D against time curves are also linear is strong evidence for the belief that AD/AM is independent of initial grain size.

A plot of the log slope against temperature is also very nearly linear and follows the relation,

where S is the slope, AD/AT, and T is the temperature in O C.

to the same phenomenon in octachloropropane.

log S = 0.063 T + (Z.IO-IO), (5)

These relations show that boundary migration in metals is closely related

8 Beck, J . A p p l . Physics, 1948, 19. 507.

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WALTER C. McCRONE

Expt.

Fig. 4 also shows that two different preparations, one strained thermally (Expt. I) and a second strained mechanically (Expt. 5 ) , show little difference in rate of increase of grain diameter as a function of time. This may have been coincidental in that the amount of strain induced by these two means may have been nearly equal.

The two Expt. 6 and 7 made on nearly unstrained crystals show that these two preparations grew at rates far below those predicted by eqn. (5) on the basis of Expt 1-5.

It is believed that the growth which occurred in Expt. 6 and 7 is partly the result of residual strain and partly of the tendency of the grains to form straight boundaries meeting at 120" angles. Since the interboundary angles for the preparations used in Expt. 6 and 7 are no nearer 120O than those used in Expt. 1-5, the decreased growth in Expt. 6 and 7 must be due to lack of lattice strain. In other words, lattice strain must be the most important factor causing boundary migration in octachloropropane.

TABLE I1

COMPARISON OF OBSERVED AND CALCULATED SLOPES

Temperature

0.8

7'2

7 1 145°C I S

126 I

Slope

Fig. 5 shows the smoothed rate data plotted in log form as a function of log time. These curves illustrate again that the rate is higher in the early stage of annealing and decreases quickly to a constant value. The constant rate is, of course, reached more rapidly the higher the temperature. These curves show again that Expt. 6 and 7, at 159' C and 145O C respectively, are lower than would be expected from an extrapolation of rates in Expt. 1-5. This figure shows the separate curves for Expt. I and 5 which were combined by smoothing in Fig. 4.

These data show that boundary migration in octachloropropane is very similar mathematically to boundary migration in metals. It is suggested that the mechanism by which boundary migration occurs in lattices of these two types is therefore similar and that boundary migration in metals can be studied to great advantage using the much simpler technique involved in studying octachloropropane.

As a result of the above work on octachloropropane it was decided to attempt to determine the effect of lattice strain on boundary migration in compounds of the DDT type. Unfortunately DDT itself could not be used since the crystal habit changes drastically with temperature of crystalliza- tion. However, TNT can be crystallized as broad rods over a wide tempera- ture range. Accordingly an attempt was made to determine the effect of thermally induced lattice strain on boundary migration in TNT. First a small sample (5-10 mg.) of TNT was melted and cooled to about 50°C before crystallization. This preparation was then placed in an already heated hot-stage at 78" C and observed for a period of 40 min. During this time the crystals grew into adjacent crystals a distance of 0.5 mm. Fig. I shows two photomicrographs in this series, one taken at the end of I min., the second at the end of 4 min.

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166 CRYSTAL GROWTH AT HIGH TEMPERATURES

A second preparation of TNT was then melted and placed in the hot-stage at 80" C before crystallization occurred. On seeding, crystals of TNT were made to grow slowly into contact at right-angles. Observation of this and similar preparations over a period of 60 min. showed no sign of boundary migration. The conclusion from this information is that boundary migration in TNT and presumably in DDT and other compounds of this type is entirely due to lattice strain.

Conclusion .-Boundary migration in the octachloropropane and DDT types of crystal lattice is similar in the sense that lattice strain due either to cold working or temperature changes seems to be the principal motivating influence. The two differ, however, in two respects : (i) relative orientations of the neighbouring crystals are important for the DDT type and have little or no effect on compounds of the octachloropropane type; (ii) grain shape is important in controlling grain growth in compounds of the octachloro- propane type and not important in compounds of the DDT type.

This dependence of boundary migration in crystals of the DDT type on relative orientation of the two crystals is more difficult to explain. This, however, has been resolved by the thought that all compounds of the octachloropropane type possess crystal lattices which are either cubic or, at least approximately plastically isotropic. On the other hand, crystals of the DDT type which show boundary migration are highly anisotropic compounds and must be elastically anisotropic. In other words, when crystals of this type, such as DDT, are subjected to pressure or to large temperature changes the resulting strain must be distributed anisotropically throughout the lattice and in such a way that the crystals grow most readily parallel to one definite direction, depending on the anisotropy of elasticity for that lattice.

This work was supported jointly by the Armour Research Foundation and the Research Corporation. Percy T. Cheng made some of these measurements. This help is gratefully acknowledged.

Armour Research Foundation, Illinois Institute of Technology,

Technology Center, Chicago 16, U.S.A. Pu

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