Effect of thermotransport on directionally solidified aluminium-copper eutectic

Effect of thermotransport on directionally solidified aluminium-copper eutectic

Journal of Crystal Growth 28 (1975) 68—76 © North-Holland Publishing Co. EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINIUM-COPPER EUTEC...

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Journal of Crystal Growth 28 (1975) 68—76 © North-Holland Publishing Co.

EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINIUM-COPPER EUTECTIC B. N. BHAT Process Engineering Laboratory, National Aeronautics and Space Administration, Marshall Space Flight Center, Huntsville, Alabama 35812, U.S.A. Received 24 May 1974 Samples of liquid aluminum—copper eutectic alloy (Al—CuAI

2) were directionally solidified in a Bridgman apparatus. The amount of thermotransport was controlled by holding the samples in the temperature gradient for different periods of time. Solidification was interrupted in some samples to study the segregation at solid—liquid interface. The coefficients of thermal2/sec diffusion °Cand D’, 3.57 and xordinary l0~ cm2/sec diffusion respectively. D were determined Thermoand their was transport values observed were found to cause to segregation be 6.21 x 10—8 in thecm directionally solidified eutectic. The amount ofsegregation was a function of process variables such as the time required to start the crystal growth, the temperature gradient and the rate ofsolidification.

1. Introduction Interest in growing composites from the melt by directional solidification has grown considerably in the last decade. Some eutectic composites have been shown to be structurally superior at high temperatures’) while some others have non-structural applications2). Literature on the growth of eutectic grains is rather extensive (see ref. 3). The importance of temperature gradient (G) and rate of growth (R) seems to have been well established. For example, Mollard and Flemings4) have shown that it is possible to obtain eutectic like structures in Pb—Sn alloys at off-eutectic compositions by use of slow rate of growth, steep thermal gradient and essential absence of convection. Similar observations have been made in Al—Cu alloys by Jordan and

transport could lead to a large change in concentration resulting in undesirable microstructure. This paper presents a study of the kinetics of thermotransport in aluminum—copper eutectic alloy and its effect on the microstructure when directionally solidifled. A method is developed to determine the coefficients of thermal diffusion and ordinary diffusion. The results are discussed with reference to the growth of eutectic composites. 2. Phenomenological theory In the absence of convection, diffusion in a liquid binary alloy subjected to a temperature gradient can be described by the following equation 8) J 1

5 Hunt). The effect of thermotransport on the directionally solidified off-eutectic Pb—Sn alloys has been studied by Verhoeven et al. 6) They conclude that thermotransport can lead to significant changes in concentration at high G/R ratios. Similar effect is also predicted theoretically by Yue et al. 7). However, the effect of thermotransport on the growth of directionally solidified eutectic alloys does not seem to have been studied so far. Steep thermal gradients are hard to obtain in practice for large sections and hence one may have to use eutectic composition within narrow limits. In such cases thermo-

—DPL

—i —D’p~x1x2



=

~jlC+JlT,

(1)

where .1, = flux of component 1 in z direction, D = (ordinary) diffusion coefficient, D’ = thermal diffusion coefficient, x1, x2 = atom fractions of components 1 and 2 respectively, T = absolute temperature, PL = density of the liquid alloy. The first term in eq. (1) refers to the flux by ordinary diffusion, J1 ~ due to a concentration gradient. The second term represents the flux due to temperature gradient, J!T. This is known as thermotransport, Soret effect or thermal diffusion. if a homogeneous liquid binary alloy is held in a 68

EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINUM—COPPER EUTECTIC

temperature gradient, segregation generally occurs according to eq. (1). Initially, J1c will be zero and J1 = J~’.As time passes, a concentration gradient will build up because of this flux and the flux will also become appreciable. Finally, a stationary state is reached when the net flux becomes zero; or =



Jtc+J1T

~tC



— —

(2

~lT,

i.e., the flux due to temperature gradient is equal and opposite to the flux due to concentration gradient. Hence, from eq. (1), one obtains at the stationary state, / ( f \ ( /•~ ~ ~ D 1D l,x,x2, ~dx51~T1. ~3, —

~,



~—

The ratio of the two diffusion coefficients is known as Soret coefficient (denoted by s). When the temperatures 8) at the hot and cold ends are known, De Groot obtains, D’/D

(l/AT)ln

=

(4)

(x,Cx2h/xthx2C),

where c and h refer to the cold and hot ends respectively and AT = Tb T~. Thermotransport experiments have been performed 9). by the author aluminum-copper alloys in Copper is foundintoliquid migrate to the colder regions these alloys. The heat of transport, Q*, which is a measure of the segregation, has been determined and is found to be 2800 cal/g-atom for the Al—CuAl 2 eutectic alloy. The values of x~and Xh can be computed for a given AT from the value of Q*. (This is outlined in ref. —

WEIGHT PERCENT, COPPER 5

700

10

15

20

25

~

~

45

9.) When this was done, the Soret coefficient was found to be 3/°C (5) D’/D = 1 74 < loIf aluminum-copper eutectic alloy is held in a temperature gradient such that the cold end is at the eutectic temperature, supersaturate the liquidthermotransport at the cold end will and tend make to it unstable. (Refer to the Al—Cu phase diagram, fig. I.) The excess copper may be expected to precipitate as 0 phase. The rate of precipitation will be determined by the temperature gradient, dT/dz and the thermal diffusion coefficient, D. From eq. (1), ~ J~-r= PLD X~X2dT/dz. (6) This can be integrated over a short period of time, t, to obtain

ft

J, dT

=

tPsXts

—D’tpLxlx

=

2 dT/dz,

°

3. Experimental Samples of aluminum—copper eutectic (Al—CuAl2) alloy were held in a known temperature gradient for different periods of time and directionally solidified. .

Solidification interrupted a series ofofsamples for the purposewas of studying the for precipitation copper

55

6600 650~

___________________

: 5. :

: :

5910/

600

0

__________________________________________C 2.5

17.4

FURNACE ALUMINA TUBE



OUTER CRUCIBLE



• :

INNER CRUCIBLE SAMPLE

o

~



550

32

w

500

a

+

0

EUTECTIC

+

WATER COOLING

HELIUM—~i OUT o

EUTECTIC

450

o

0—RING SEAL 400

0

5

10

15

4

Xe

20

25

30



35

HELIUM IN

ATOMIC PER CENT, COPPER

Fig. 1.

Aluminum-rich end ofAl—Cu phase diagram.

(7)

where r = thickness of 0 precipitate, p~= density of solid 0all phase, x,5 = atom fraction of copper phase. Since the quantities except D’ are known,init0 can be calculated. The value of the ordinary diffusion coefficient can then be obtained from eq. (5).

.

50

69

THERMOCOUPLE TO MOTOR

Fig. 2.

Bridgman apparatus.

70

B. N. BHAT

at the solid—liquid interface. All samples were examined under optical microscope and analyzed. Some samples were also analyzed by use of quantimet and scanning electron microscope. The Bridgman apparatus (made by Metals Research Ltd.) was used for directional solidification (fig. 2). It provided an approximately linear temperature gradient (of 48 °C/cm)for a length of 5 cm. Aluminum-copper eutectic alloy was obtained from Materials Research Corporation and contained less than 10 ppm impurities. The alloy was melted under vacuum (l0-~torr) and filled into graphite molds with 0.32 cm i.d. Each sample was 6.5 cm long. The sample was raised to the hot zone of the Bridgman apparatus and melted. It was then correctly positioned in the furnace so that the desired temperature gradient was applied along the length. Samples were held in that temperature gradient for different periods of time, varying from 1 hr to 6 days. Then they were directionally solidified at the rate of 1.2 cm/hr. It is estimated that the samples were subjected to the temperature gradient for 30 mm before solidification actually began. One sample was solidified with zero holding tinie to serve as a reference. Solidification was interrupted for a series of samples after solidifying for 1.5 cm. The samples were held in that position for different periods of time varying from one hour to nine days. These samples were also solidifled at the rate of 1.2 cm/hr. The samples were mounted, polished and examined in a metallograph. The microstructure was photographed. Some samples were further analyzed in a quantimet and a couple of samples were analyzed in the scanning electron microscope. Chemical analysis employing an atomic absorption spectrometer was used to determine the variation in composition in cases where the structure was dendritic. The procedure for quantimet analysis consisted of the following steps. (1) The sample was polished, but not etched (since etching produced large errors and the measurements were not dependable). The c~phase appeared dark and the 0 phase appeared bright when the samples were not etched. (2) Black and white transparancies were obtamed from selected areas of the samples. These transparencies were reduced to 35 mm slides. (3) Quantimet 720 (by the Image Analyzing Computers Ltd.) was used to determine the proportion of ~ phase.

This was converted into percentage of copper by use of the phase diagramt 0) (fig. 1). All samples did not display the same degree of contrast and this was a source of error. Overall accuracy of quantimet results was estimated to be ± 1 at %. However, the accuracy was better within a sample (±0.6 at %). Chemical analysis had an error of ±1 wt % of copper and hence was more dependable. Scanning electron microscope was used for identifying the different phases. 4. Results 4. 1. SOLIDIFICATION WITHOUT INTERRUPTION The sample which was directionally solidified with minimum of holding in the temperature gradient showed lamellar structure throughout its length. Initially (at the bottom end) transient structure (of the type described by Dean et al.’ 1) was observed for the first half centimeter or so. Multiple grains grew out of this region and one of the grains dominated within a centimeter. The rest of the solid was a single lamellar eutectic grain. The sample which was held in the temperature gradient for one hour showed some 0 phase at the bottom. It generally has facets at 900 angle. Several areas of such precipitates were observed and they were more or less uniformly distributed. This region extended for about half a centimeter. The sapce between the 0 precipitates was filled by irregular lamellar eutectic. Transient eutectic structure was observed adjacent to this region which led to the region of lamellar eutectic structure. This structure continued through the rest of the solid. As the time of holding in the temperature gradient was increased (to 4, 16 and 64 hr) the structure showed more and more 0 phase at the bottom signifying that more copper had migrated to the colder region. The top portion of the sample began to show dendrites of GL phase signifying that it was becoming aluminum rich. The ~ dendrites were much fewer in number and they did not show any facets. They were much larger than the dendrites of 0 phase. The extent of both the aluminum rich and copper rich regions increased with increased holding time. The structure observed at the stationary state is shown in fig. 3. Three different regions could be distinguished: (a) bottom, (b) top and (c) middle. The bottom

EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINUM—COPPER EUTECTIC

(a)

71

(c)

S

+

EUTECTIC

EUTECTIC

(IRREGULAR) (REGULAR)

a + EUTECTIC (REGULAR)

Fig. 3.

Structure of Al—CuAl 2 eutectic alloy held in temperature gradient for 6 days. (a) x 325; (b) x200; (c) x 325.

-—

(b)

region exhibited continuous dendrites of 0 phase in the beginning which thinned down to isolated areas of 0 precipitate leading to regular lamellar structure. The interdendritic eutectic was of transient type. This bottom region was 1.2 cm long. The top region was 2.0 cm long and contained ce dendrites and regular lamellar eutectic, unlike the interdendritic region at the bottom. The middle region consisted of regular lamellar structure characteristic of aluminum-copper eutectic. Quantitative metallographic study of this region was made and the results are shown in fig. 4 which is a plot of percent ~ phase versus composition as calculated from the phase diagram. It can be observed that lamellar structure is obtained over a range of 5 at °,/~copper. This range is not symmetrical about the eutectic point, however. It is shifted towards the

72

B. N. BHAT WEIGHT PER CENT, COPPER 25

26

27

28

29

30

31

32

33

-+

34

35

36

37

38

0.60

Lu

0.50~

0.

~ 0.516 0.50

i&.

0

a 2

0.45





0.40

~~~IIP~” REGULAR LAMELLA

DENDRITES OF a + REGULAR LAMELLAR EUTECTIC

TRUCTURE

/

IDENDRITESOF + IRREGULAR LAME LLAR EUTECTIC

0.35 0.12

0.13

0.14

0.15

0.16

0.17 Xe 0.18

0.19

0.20

0.21

ATOM FRACTION, COPPER Fig. 4.

Relation between percent ~ phase and atom fraction of copper in Al—Cu alloys.

aluminum rich side. The limiting compositions in this range are observed to be 0.193 and 0.143 atom fraction ofcopper. 4.2.

SOLIDIFICATION WITH INTERRUPTION

Fig. 5 shows the general features of the samples which were solidified with an interruption. Five different regions could be distinguished, regions a through e. (a) This is the bottom-most region. It was multigrained, transient eutectic structure, leading to regular lamellar structure of region (b). (b) This region next to the interrupted interface, was generally lamellar and single grained. Interestingly, the interlamellar spacing increased as one approached the interface, almost by a factor of two. Quantimet analysis showed that this area was at the eutectic composition of all the samples. (c) This region consisted of 0 precipitate. The thickness of this precipitate increased with time. Fig. 6 is a plot

of the thickness r of the precipitate versus time of holding. The thickness increased linearly with time for the first 20 hr or so. Then the rate decreased gradually with time and became zero in about 6 days. (This corresponds to the sationary state.) Interestingly, the precipitation of 0 ded not begin until after 1 hr of holding time. Figs. 7, 8, 9 and 10 show the different stages of formation of 0 phase at the interrupted interface. Initially, a mixture of ot and 0, consisting mostly of 5

t ‘-

~

IRREGULAR INTERFACE EUTECTIC ~ (°)

0.

2

LAMELLAR EUTECTIC

Z

d REGULAR LAMELLAR EUTECTIC

a+ e REGULAR LAMELLAR EUTECTIC

Fig. 5. General features of samples which were solidified with an interruption,

3

w

Lu _________________

4

LU

1

0

40

80

120

160

200

240

TIME -+ (HOURS)

Fig. 6. Plot of thickness of 0 precipitate, r, versus time of holding, t.

EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINUM—COPPER EUTECTIC

Fig. 9.

Fig. 7. Solid—liquid interface after 1 temperature gradient. x 180.

Solid—liquid interface after 2 hr of holding in the tern-

perature gradient.

Solid—liquid interface after 8 hr ofholding. x 110.

hr of holding in the ________________________________________________________

Fig. 10.

Fig. 8.

73

>< 150.

8, was obtained. The precipitation began with thickening of 0 lamellae until they touched one another. The ot phase, which was trapped in between the 8 lamellae,

Solid—liquid interface after 46 hr of holding. x 375.

then disappeared slowly. Completely solid 8 phase was formed in 15 hr. (d) This region generally consisted of regular lamellar eutectic structure. Occasionally, the transient structure was also observed. It was a single grain whenever there was a single grain before the interface. Otherwise it was multigrained and became a single grain after some distance. There appeared to be a continuity of structure through the interface (fig. 8). (e) The top region consisted of dendrites of ot and lamellar eutectic. This region was comparable to the top portion of the samples solidified without interruption. The ot dendrites did not begin to form until

74

B. N. BHAT

COMPOSITION PROFIIE

19

AFTERTWDWOURS AFTER TWO DAYS AFTER III DAYS — CALCULATED PROFILE AT STATIDWARY STATE 0

\

~ •

18

.

17

o a

N.

~

0

0

0



0 C,)

p—’ w

0

0

a 16

a

C-)

a

.

w

~15

14

13 10 Fig. 11.

2b

lb

DISTANCE FROM INTERFACE

4b

(mm)

5b

Composition of liquid ahead ofthe interface for different times of holding in the temperature gradient.

after 15 hours of holding. The length of this region increased with time and at the stationary state it occupied about a third of the total length beyond the interface. The regions d and e were analyzed chemically and the results are shown in fig. 11 for different times of holding.

that the partial molar volume is equal to the molar volume for each component and change in volume on melting is 2.5 % for the liquid phase. (The latter part is verified experimentally.) A more accurate value of D’ can be obtained by taking into account the back flux due to ordinary diffusion. From eq. (1),

5. Discussion 5. 1.

INTERRUPTED SOLIDIFICATION

As described in section 2, interruption of solidification of eutectic alloy provides a means of calculating the thermal diffusion and the ordinary diffusion coefficient D. coefficient In the case D’ of Al—CuAI 2 eutectic alloy, the initial rate of solidification is found to be 0.8 mm in 19 hr (fig. 6), after an incubation period of 1 hr. As a first approximation the back flux due to ordinary diffusion is neglected and D’ is obtained from eq. (7): Pst

D







Here, all the quantities except dx~/dTare known and it can be estimated as follows. For a binary alloy8)subjected has ohto a linear temperature gradient, De Groot tamed, for short times, 2D’ AT t a2 ~ (1 —x) ~ ir 2 for t ~ —i-—, (10) xh(l—x) a nD where a is the length of the column of liquid. In the present experimental arrangement, solidification did not begin until after half an hour ofholding in the tern-

X 15

=

(9) D’ x,x2 dT

fiT



PL t X1X2

1 dT/dz

and found to be 5.81 x

(8) 2/sec °C.It is assumed

,

108

cm

. perature gradient. Moreover, precipitation did not rupted. Hence, the melt wasthesubjected to a temperature begin for one hour after solidification was inter.

.

.

.

.

EFFECT OF THERMOTRANSPORT ON DIRECTIONALLY SOLIDIFIED ALUMINUM—COPPER EUTECTIC

gradient of 48 °C/cmfor 1.5 hr before the precipitation began. This would create a concentration gradient according to eq. (10) and cause a diffusion flux, ~1 c away from the interface. Eq. (10) can be evaluated and it is found that

75

at the rate of 0.01 cm/hr, then the contribution from thermotransport is substantial. One could express this in terms of G/R ratio. The amount of component 1 solidifying is PLX!R per sec. The flux of component I due to thermotransport is —D’PLxlx

3 atom fractson, d

Xc~Xh =

dx1

=

4.2x10

Thermal diffusion flux Rate of solidification = D’x 2G/R ~x G/R.



an ~lc/~1iT

2G. Hence, one obtains

(11) —

0.07.

(12)

(14)

Hence, the corrected value of thermal diffusion coeffi- If one arbritrarily chooses 1 as the limiting acceptable cient 15 value of o~,then the upper limit for G/R is 2/sec °C. (13) G/R = 1.95 x l0~°Csec/cm2, (15) D’ = 6.21 x lO_8 cm From eq. (5) the coefficient of ordinary diffusion is now i.e., thermotransport in aluminum-copper eutectic obtained, alloy may be neglected during solidification if the G/R This value compares favorably with the value of ratio is less than 1.95 x i0~CC/cm2. 3.26 x l0 ~ obtained by Jordan and Hunt5) by use of a different technique. 5.2. EFFECT OF MICROSTRUCTURE As the thickness of 8 precipitate increases, the ternIn the present experiments the temperature gradient G perature at the solid—liquid interface also increases and was 48 °C/cm,and the rate of growth (R) was 1.2 cm/hr. this pushes the equilibrium composition of the liquid Hence G/R 1.44 x iO~and the flux due to thermotranto higher copper concentration. This will result in a sport is less than 1 % of the flux due to solidification higher concentration gradient in the liquid and hence a and can be neglected after the solidification begins. larger flux, .J~c’ due to ordinary diffusion. Since this Most of the effect occurs before the solidification, flux is up the temperature gradient, it will cancel the during the period of holding in the temperature grathermal diffusion flux to some extent and hence the rate dient. For short times the amount of segregation is of precipitation will decrease with time. This is ob- given by eq. (10). In practice this is a good approximaserved in the experiments. Finally, at the stationary tion since alloys are seldom held in the temperature state, the two fluxes become equal and opposite. This gradient for more than a few hours. seems to occur in about six days in the present case The sample which was directionally solidified with(fig. 6). out holding in the temperature gradient showed very The type of segregation discussed above may be little segregation. As the time of holding increased, the important in crystal growth processes where a seed is amount of copper at the cold end increased and was employed. Temperature gradients are generally present observed to form dendrites of 8 phase. These dendrites in these processes and the flux due to thermotransport were formed rather readily with a supersaturation of less may be significant, Interestingly, thermotransport has than one atom percent copper. Once the properly the maximum influence when the crystal is not being oriented grains were formed, the lamellar structure was grown, i.e. when the things are allowed to sit for able to accommodate a higher copper content. This stabilization purposes. Once the crystal begins to grow was shown to be the case with the samples which were at a finite rate, thermotransport may assume a minor held in the temperature gradient for longer times. The role depending upon the rate of crystal growth. In the sample in which the stationary state was reached, present case, the rate of precipitation is 0.8 mm/19 hr showed that the lamellar structure could accommodate or 4.2 x 10 ~cm/hr. If the crystal is grown at the rate of as much as 5 at % variation in copper content (fig. 4). I cm/hr, one can afford to neglect thermotransport Dendrites of either 0 or ce were formed beyond this completely. On the other hand, if the crystal is grown range. °,/~

76

B. N. BHAT

5.3. NUCLEATION OF EUTECTIC GRAIN

An interesting feature of the present study is the evidence that it is the El phase which acts as the flucleating site for the A1-CuA12 eutectic, not the ce phase. Whenever there was a 8 dendrite, eutectic grains seem to grow from it on all sides. But no such relationship was observed between ce dendrites and the eutectic grains. In the sample where solidification was interrupted and 0 phase precipitated at the solid—liquid interface, the eutectic grains continued through the interface (fig. 8). In the case where no prior orientation was established, numerous grains were observed to nucleate on the 0 precipitate (fig. 9). There appeared to be a layer of ce phase formed on top ofthe 0 phase before the growth of eutectic grain (fig. 10). observations 12)Such in Pb—Sn system. were made by Hopkins and Kraft An alloy sample containing 25% copper was directionally solidified to see if the ot phase had any influence on nucleating eutectic grain. The solidification was interrupted for 16 hr at a distance of 2 cm from bottom. It was observed that the ce phase had formed at the solid—liquid interface with eutectic next to it. But there was no relation between the eutectic structure and the ot phase. The eutectic was degenerate at the interface and slowly became lamellar after a few centimeters. This was quite in contrast to the 0 phase on which regular lamellar eutectic grain readily nucleated. This supports the view of Hogan’3) who has also observed in his studies that 0 phase is the preferred nucleating site for Al—CuAl 2 eutectic grains. 6. Conclusions When liquid aluminum-copper eutectic alloy is subjected to a temperature gradient, copper migrates to the colder regions. The rate of thermotransport has been determined and the coefficient thermal diffusion is 2/secof°C.Thermotransport found to be 6.21 x 10 8 cm causes segregation in the melt, making it copper rich at

the cold end and aluminum rich at the hot end. This affects the microstructure when directionally solidified. The microstructure changes from regular lamellar to dendritic as the composition deviates from the eutectic point. The extent of segregation depends on the process variables such as the time required to start the crystal growth, the temperature gradient (G) and the rate of solidification (R). The effect of thermotransport can be significant at high G/R ratios. The results also indicate that the eutectic grains nucleate preferentially on the 0 phase. Acknowledgements This work was accomplished while the author held a National Research Council Postdoctoral Research Associateship. The author to thank A. S. Yue of University of wishes California at Los Professor Angeles, Dr. J. D. Hunt of University of Oxford, U.K. and Dr. K. A. Jackson of Bell Laboratories for their useful discussions of the results. References 1) L. P. Jahnke, J. Metals 25 (1973) 15. 2) F. S. Galasso, F. C. Douglas and J. A. Batt, J. Metals 22 (1970) 40. 3) L. M. Hogan, R. W. Kraft and F. D. Lemkey, in: Advances in Materials Research, Vol. 5, Ed. H. Herman (Wiley— Interscience, New York, 1971). 4) F. R. Mollard and M. C. Flemings, Trans. Met. Soc. AIME 239 (1967) 1526, 1534. 5) R. M. Jordan and J. D. Hunt, Met. Trans. 2 (1971) 3401. 6) J. D. Verhoeven, J. C. Warner and E. D. Gibson, Met. Trans. 3 (1972) 1437. 7) A. S. Yue and J. T. Yue, J. Crystal Growth 13/14 (1972) 797. 8) S. R. de Groot, L’Effet Soret (North-Holland, Amsterdam, 1945). 9) B. N. Bhat, Thermotransport in Liquid Aluminum—Copper Alloys, NASA TR R-4I5 (1973). 10) M. Constitution of Binary Alloys (McGraw-Hill, NewHansen, York, 1958), 11) H. Dean and J. E. Gruzleski, J. Crystal Growth 20 (1973) 12) 256. R. H. Hopkins 242 (1968) 1627. and R. W. Kraft, Trans. Met. Soc. AIME 13) L. M. Hogan, J. Australian Inst. Metals 10 (1965) 78.