Microstructural degradation of the Al-Al3Ni directionally solidified eutectic in the presence of a temperature gradient

MICROSTRUCTURAL DEGRADATION OF THE Al-A13Ni DIRECTIONALLY SOLIDIFIED EUTECTIC IN THE PRESENCE OF A TEMPERATURE GRADIENT SI. McLE.0

Di\;ision of Materials Applications. National Physical Laboratory. Teddington. Siiddlesex. England

thermal stability of the directionally solidified Al-AI,Ni eutectic in the presence of a temperature gradient has been studied by both in situ hot-stage electron microscopy and heat treatment of bulk specimens. There was no evidence of the migration of the fibres due to the presence of the temperature gradient, although this has been predicted theoretically. and observations of microstructural degradation are consistent with capillarity motivated spheroidization and coarsening. Abstrrct-The

R&urn&--On a 6tudiC la stabilitC thermique de I’eutectique orient6 Al ‘AI,Ni en prPsence d’un gradient de tempirature par microscopic ilectronique in sirrd B l’aide d’une platine chauffante et par traitement thermique d’&chantillons massifs. On n’a pas pu mettre en evidence la migration des fibres sous I’effet du gradient de temptrature. bien qu’elle ait et6 prevue theoriquement. et les observations de la digradation de la microstructure sont compatibles avec une spherdidisation et un grossissement dus ?I la capillarit6. Zusammenfassung--So\vohl durch Direktbeobachtung im Heiztisch eines Elektronenmikroskopes als such mit der Wiirmebehandlung kompakter Proben rvurde die thermische Stabilitit eines gerichtet erstarrten Eutektikums unter einem Temperaturgradienten untersucht. Es ergab sich kein Hinweis auf die Wanderung der Fibern infolge des Temperaturgradienten;, dies wurde aber theoretisch vorsusgesaet. Die Bzobachtungen dzs mikrostrukturellen Zerfalls sind in C’bereinstimmung mit-durch Kappilarizt begriindete-Sphlroidbildung und Vergriiberung.

1. LVTRODUCTIOS

Directionally solidified eutectic composites continue to show considerable promise as potential structural materials for high temperature applications as. for example, gas turbine blades. Although the mechanical properties of these materials are vkry structure sensitive. many investigators have shown that eutectic composites generally have outstanding microstructural stability during isothermal heat treatments [l. 21. Recently, however, attention has been drawn to the possibility of more rapid microstructural degradation in the presence of a temperature gradient. McLean [3] has suggested that enhanced fibre coarsening will only be significant for mean fibre diameters d > 1 jlrn when mass transport occurs by thermal diffusion through the matrix and he has confirmed this phenomenon in the (Co, Cr)-Cr& systern. Jones [4.5] and Jones and May [6]. on the other hand. propose a model of coarsening due to the impingement and coalescence of fibres Lvhich migrate in the temperature gradient by a mechanism of interfacial diffusion. The latter mechanism should become increasingly dominant as the mean fibre size is reduced. Jones and May [6] have described results on the Al-Al,% system which qualitatively support their model. On the basis of the latter evidence Honeycombe. in a recent review [7]. has suggested that temperature gradient motivated instabilities will

rule out eutectic composites for practical engineering applications. McLean and Loveday [S] have shown that sufliciently high temperature gradients are generated by electron beam heating during hot stage electron microscopy to allow the direct observation of the thermal gradient migration of liquid lead inclusions through a solid aluminium matrix. This technique should in principle be equally applicable to the AlAl,Ni eutectic and consequently provides the possibility of in situ observation of the migration and coalescence of fibres proposed b>- Jones and May [6]. This paper describes the results of t\vo distinct sets of esperiments aimed at characterising the microstructural degradation of the Al-Al,Si eutectic in the presence of temperature gradients. In the first. thin foils of directionally solidified eutectic were heated in an electron microscope hot stage. where a high temperature gradient is known to occur, and the microstructural changes observed it! sin{ Lvere analyzed to determine the dominant mode of degradation. In the second set of experiments bulk specimens of AI-Al,Ni were heat-treated with a temperature gradient normal to the fibre axis for much longer periods and the spatial distribution of fibre radii after the heat treatment were analyzed. following the procedure described by McLean [9]. to determine whether thermal gradient or capillary coarsening were dominant. !09

1210

?IlcLE?IN:

2. ESPERDIENTAI..

5lfCROSTRl_YCTt’RAL ‘---

--

-*----

PROCEDURE

Ingots of the Al-AI,Ni eutectic were prepared by melting elemental material in alumina crucibles and casting, tmder an argon atmosphere, into 12mm diameter copper moutds. The ingots were dir~tiona~y solidified at 63mmh-’ in an atmosphere of flowing argon using a modified Bridgman technique where heating was by radiation from an inductively heated graphite susceptor. and the longitudinal tsmperature gradient was imposed by placing the ingot on a water-cooled copper hearth. Electron microscopy samples were prepared from spark machined shces (- I mm thick) of both longtudinal and transverse sections of the directionally solidified eutectic. The slices were mechanically ground to - 25 pm thick and were then electrochemitally thinned to about S pm in a solution of 18% perchloric acid in ethanol using stainless steel cathodes. These specimens were then heated at various temperatures up to the eutectic melting temperature in a resistively heated stage of the AEI EM7 high voltage electron microscope. The images were recorded on video tape and transferred to 16 mm tine film for subsequent analysis of the degradation of the eutectic microstructure. Small cylinders ( - 10 mm dia. x 10 mm) were spark machined from the directionally solidified ingots so that the AljNi fibre axes were normal to the axis of the cylinder. One end of the cylinder was fixed to a water cooled copper hearth using a high conductivity adhesive and the other placed in contact with nickel-base bar. of high thermal capacity, in a resistively heated furnace. Thermocouples in contact with each end of the cylindrical specimens monitored the temperature gradients throughout the experiments. Typically temperature gradients of - 25K mm- ’ were maintained for approximately 300 h. The heat treated specimens were sectioned normal to the AlsNi fibre axes and the density of fibres determined as a function of distance along the direction of the temperature gradient by conventional metallographic techniques. 3. RESLLTS AI

’ - *---*_

DISCUSSIOS

Part i. Electrcm microscopy Te~~~~~a~ure gmdient. McLean and Loveday [Xl showed that the electron microscope heating stage used in the present study generated a radial temperature gradient, in the plane of the foil, of about 123 K nun-l when heating an AI-Pb alloy to about 600°C. It seems reasonable to assume a similar temperature gradient for the Al-Ni alloy considered here since both materials have a predominantly nickel matrix containing a low volume fraction of second phase. Some confirmation of the presence of a temperature gradient was obtained by melting the specimen and then observing the resolidification of the eutectic liquid film. A typical sequence of micrographs (Fig.

OS

0.045

0-08s

m (a)

yy

01

I 10”

IO“

\J

I

10-1 10-l Growth ratelmmsm’t

1

10

(bt

Fig. 1. (a) Transmission electron micrographs showing the solidification of the AI-Al,Ni eutectic. (b) Comparison of the rod spacing versus growth rate data from the present in situ observations with the published data of Livingston et al. [IO]. la) shows the progression of the solid-liquid interface across the field of view. The direction of the fibres cfearly shows that the tem~rature gradient is in the plane of the specimen. In the sequence shown sotidification proceeds at tOOmmh-’ resulting in a mean fibre radius of 0.09~m. Since a planar interface is maintained during solidification at 2OOmmh-‘, the temperature gradient present must be relatively large. The observed velocity u of the solid-liquid interface and the mean fibre spacing 2 are compared in Fig. I(b) with the interde~ndence of 2 and r described by Livingston et al. [ 103 for the AIJNi-Al system. The present data fall below those of Livingston et al. This is probably because the present observations have been made in situ at the point of solidification whereas previous microstructures, observed after cooling to room temperature. have been subject to post-solidification coarsening as described by Courtney and Garmong Cl I]. ~~e~~ mig~~&ion. Jones and May [6] show that when interface diffusion, with a diffusion coefficient Di, is the dominant mechanism the AlsNi fibres, of radius r, will migrate with a velocity V in the direction of an applied temperature gradient G, where

P _ + Di&Z*G -ZRT2r’ where 6 is the thickness of the boundary layer, Q* is a heat of transport. R is the gas constant and T is the absolute temperature. Taking values of 6 = 1 nm, Q* = 50 KJ mol-’ Di = IO-) mm’s_‘, and T= 883 K, as did Jones and May [S], the fibres of 0.35 pm radius typical of the initial directionally

1lzLEXN:

\fICROSTRL-C-ICR.~L

solidified materials would be expected to migrate nith a velocity of 1.5 rims- I. This would lead to fibrs displacement equal to the fibre radius in under 2 min. The finer microstructure of the eutectic solidified irt sirrl in ths electron microscops would migrate sven more rapidly, -7.5 rims-‘. These are probably overestimates of the respective velocities since the value of Q* assumed is rather high a figure of - 70 KJ mol- ’ being more realistic [2 I]. Hwever. fibres would certainly be expected to move the interfibre spacing in less than 5 min. Ekctror~ wicroscope ohsrrwtions. Various specimens of Al-.Al,Ni, both in the original directionally solidified condition (i -0.35pm) and after it! siru solidification in the electron microscops (F - 0.W jun) wcrz maintained within a few degrees of the eutectic temperature for up to one hour. In no case ivas there any evidence of fibre migration. It is estimated that the present experiment would detect fibrs velocities LO.02 rims- I. ten to a hundred times less th;ln the velocities anticipated. The fibrous microstructure ivas obsevcd to degrade. the severity depending on the scale of fibres. The specimens ivith the coarser microstructux (1.- 0.35 Llrn) were extremely stable at long periods. the only noticeable change being the retraction of fibre terminations as shown in Fig. 2. However. complets spheroidization of the material Lvith fibrcs of small diameter (- 0.09 /lrn) occurred in about ii) s at - 620X’ (Fig. 3). In this case there is evidence of both the retraction of libre terminations and of the detachment of spherical segments from the fibre ends. Discclssiarr. The total lack of mobility of ths .\13Si fibres is surprising. Hobvever. both McLean and Lave-

DEGR.ADATIOS

OF

28s

!‘!l

&I> [S].

and Anthony and Cline [ 121 have esperimcntally identified critical radii below which thermal migration does not occur for liquid Pb inclusions in Al and liquid brine inclusions in KC? respectivel!. Doherty and Strutt [ 131 have recently proposed that. at least in metals. inclusion migration can be inhibited by a dislocation substructure. Essentially the thermodynamic driving force for inclusion migration must escted the line tension of the pinning dislocation before any motion is possible. The driving force F for the migration oi unit length of solid fibre of radius r due to ths prssexe of a temperature gadient G can be estimated. Mowing Nichols[I-l]. to be

where Q* = heat of transport of the rate determining species: R = molecular volume and Tis rhs absolute temperature. If 11 is the dislocation density in the matris. the approsimatz number of dislocations intersecting unit length of fibre - pz and ihese will escrt a force inhibiting fibre motion -iu+‘p*. (I( is the shear modulus and h the Burgers vector.) Fibre migration Lvill onI> occur if the thsrmod!namic driving force for fibrs migration. F. exceeds the anchoring forces of the dislocations (,~h’ p’). Thus 171bremigration c3n oniy occur if Zxr’ Q*G

F = T

T

>r jtl?;t!

12.6s

28.8s L Sw

Fig. 2. Series of transmission

structure

of the Al-Al,N

(3

‘.

For a given temperature gradient G and constant material parameters, fibre migration xill onI>- occur

6.4s

OS I

EUTECTIC

,

elrcrron micrographs showing the progessivr degradation of the mkroeutectic. u-irh an initial mean iibrc radius off 0.33 pm. at OKI C.

SlcLEr\N:

MICROSTRCCTUR.-\L DEGR.4DATION OF ELTECTIC

5um Fig. 3. r\s Fig. 2 for an initial fibre radius of - 0.09 pn when the fibre radius exceeds a critical value rc. Rearranging equation (2) r = ‘pb*p’ ‘RT” c

*

l,~IrrQ*G ,1

Taking il = 2.7 x I010Nm-2. b = 2.86 x 10-‘Om, p = lOL3m-?. R = 10ms m3, Q* = 2 x lO’Jmol_‘, T = 900 K and G = 2.5 x 10’ Km-’ we estimate that for the present experiments r, -0.1 pm.

In view of the approximations involved, this is compatible with the observed lack of mobility of fibres with radii of 0.35 and 0.09 ,um. Indeed it is possible that dislocations could be collected by the fibres giving a higher linear density of dislocations and consequently a higher value of rE. In the present experiments relatively thick foils (S-10lm thick) were used to ensure that the fibres were entrained within the matrix and to approach to bulk behaviour. However, this led to a reduction in resolution of the electron microscope images which prevented the direct observation of any dislocation substructure. This discussion assumes that the temperature gradient G is transverse to the fibres and within the plane of the thin foil specimens. However, the temperature distribution due to heating by the electron beam will be radial, in practice, and will lead to a variation in temperature gradient along the length of each fibre. Consequently, the cooler fibre ends in the low temperature gradients outside the field of view will be immobile. The observed parts of the fibres may either be constrained by the stationary hbre ends or may

migrate causing a distortion of the fibre shape. Thus the failure of the present experiments to observe fibre mobility can be due to the intrinsic anchoring mechanism described in the previous paragraphs or to the inhomogeneous distribution in temperature obtainable in the electron microscope heating stage. No such ambiguity occurs for the spherical particles of Al,Ni which are produced by spheroidization. The lack of mobility of such equiaxed inclusions in the temperature gradients strongly indicate that the anchoring of the phases is indeed intrinsic to the material rather than being an artefact of the experimental technique. ‘Following the approach used by hIcLean [lj] it is possible to use the quantitative observations of fibre retraction and spheroidization to identify the operative mass transport mechanism. Thus the equations describing these two processes when volume and interface diffusion are rate controlling are shown below. (a) fibre retraction -0.33 B

dz dr

volume diffusion,

(3)

interface difTusion.

(4)

r’ = 0.035 Br

volume diffusion,

(5)

rf = %Cr

interface diffusion,

(6)

-=---Y--=--

rC r’

(b) Drop detachment

where r is the mean fibre radius. d: dt is the velocity of the fibre end parallel to the fibre direction, r is

>lcLEAN:

Time,

~~LIICROSTRUCTLR?ILDEGR.+Dz&TION OF ELTECTIC

s

Fig. 4. Plot of the position of the ends of two fibre tcrminations as a function of time for the AI-AISNi eutectic with a mean fibre radius of -0.35 urn.

the characteristic time for drop detachment and C are mobilities. B=.--

and B

cD,_iQ kT

and Di i’Q2

cc-._.__

vkT ’

where c is the concentration of the rate controlling species. D, and Di are volume and interface diffusivities of the rate controlling species, 7 is the interfacial energy, R is the atomic volume, v is mean area of diffusing atom, k is Boltzmann’s constant and T is the absolute temperature. Figure 4 shows data for the retraction of two fibre terminations of relatively large radii at 620°C. These have been analyzed in terms of Equations (3) and (4) to provide estimates of the mobilities B and C associated with volume and interfacial diffusion respectively. The results are shown in Table 1 together with the associated values of the diffusivities D, and Di calculated by taking the following values for the parameters in Equations (1) and (2). (‘i = 250 mJm_‘, R = 10-lOmms v = n2’3 = 464 x 10-t4mm2 and c = 0.015.) t Note that Q is the effective activation energy for volume diffusion in the system and can usually be identified with the slowest diffusing component in a complex alloy. Q is quite different and has no simple relationship to the heat of transport Q* referred to in Part I.

The characteristic time for the detachment of a droplet from 0.09 pm rods at 62O’C. observed to be approximately 10s. was used in conjunction with equations (5) and (6) to obtain alternative estimates of B and C. These are also shown in Table 1 together with the values of D, and Di calculated from them. The values of D, shown in Table I are about a hundred times higher than accepted solid state diffusivities at the melting point. However. the magnitudes of Di shown are quite similar to the interface diffusivities determined by Ho and Weatherly [16] for the Al-CuAlz system. Thus morphological changes of the fibre structure in the present experiments are motivated by capillarity and appear to occur by a mcchanism of interfacial diffusion. Parr II. Bulk experiments Fib-e coarsening. When diffusion in the matrix is the dominant mass transport mechanism, coarsening of the fibrous microstructure can occur, without translation of the fibres. by either an Ostwald ripening mechanism [17] or by the phenomenon of temperature gradient coarsening recently propossd by McLean [3,9], After heat treatment in a temperature gradient, the spatial distributions of fibre radii r(z) parallel to the direction of the applied temperature gradient G are quite different for the two mechanisms.

Osrwald ripening : d In[r(-)-’ - ri] = QG --s+y dz Temperature grdienr

d In[r(:) - ro] QG =-zi-7 d:

Droplet detachment from fibre end

(7)

G

(8)

where r. is the initial radius and Q is the activation energy for volume diffusion.+ Figures 5(a) and (b) show a typical set of data for Al-Al&? annealed for 336 htin a temperature gradient of _ 25 K mm-’ plotted in the forms of equations (7) and (8), respectively. Acceptable linear relationships are obtained enabling values of the diffusional activation energy to be calculated. Q = 131 kJ mol- ‘for Ostwald ripening: Q = 72 kJ mol- ’ for temperature gradient coarsening.

changes in the AIINi-AI eutectic at 62O’C assuming either volume or interface diffusion dominates

Retraction of fibre termination

G

conrser~ing :

Table I. Mobilities and diffusivities associated with morphological

Observation

1’13

Volume diffusion B Dv (m3 s-i) (mm2 s-‘)

Interface diffusion c 4 (m’s_‘) (mm2 s- ‘)

1.78 x IO-“. 1.23 x lo-:’

7 x lo-’ 5 x 1o-J

1.3 x lo-” 6.5 x 10-rS

5.1 x lo-’ 2.7 x lo-’

6.8 x 1o-2’

2.8 x 1O-J

4.2 x IO-=

1.6 x lo-’

MCLEAN:

MICROSTRUCTURAL

femperatur6,

I 0

I

I

I

2

Oistonce

parallel

“C

I 3

I 4

I 3

to temperature

gradient,

Temperature, 6225 (b)

600

’

Distance

575

I

parallel

550

I

1

I 6 I,

7 mm

*C 525

to temperature

500

I

475

1

gradient,

I

2,

mm

Fig. 5. Spatial distribution of mean fibre radii of AI-A13Ni after heat treatments in temperature gradients of 2.5K mm-’ for 336 h plotted as: (a) log (f3 - i,“) vs Z;

(b) log (f - i,,) vs Z.

The value of Q obtained by interpreting the resuIts in terms of temperature gradient coarsening is unrealistically small. On the other hand the Ostwald ripening model gives a value which is close to published activation energies for aluminium self-diffusion [ 181 (126 kJ mol- I). The activation energy For diffusion of Ni in Al is likely to be of a similar ~~itude. The evidence is therefore strong that the capillarity motivated Ostwald ripening dominates any temperature gradient effects in the present experiment. In their recent study of the isothermal coarsening of AI-AI,Ni, Smartt and Courtney r-181 determined an activiation energy of 315 kJ mol-’ which they interpreted as being the sum of the activation energies For diffusion and solution of Ni in Al (231 and 84 kJ mol-’ respectively). The present result is clearly inconsistent with this finding. Bhat~~haryya and Russell [19] have considered the theory of diffusion controlled coarsening of compound precipitates and they have related the activation energy associated with coarsening Q, to the diffusional activation energy QD and the enthalpy of solution of the precipitate + This is an over-estimate in the narrow fibre size distributions encountered in directionally solidified eutectics. However, it pro\+des an approximate measure of the level of con~ntration gradients produced by capillarity

DEGRADATION

OF EUTECTIC

in the matrix AH, They show that the ~ont~bution From AH, can be different in various temperature regimes and indeed in some circumstances Q, 9: QD Whether the apparent discrepancy between our rest&s and those of Smartt and Courtney [lS] is due to different experimental conditions or to the methods of analysis will be resolved in Future studies. It is noteworthy that a relatively low activation energy for coarsening of Al-AI,Ni (- 170-210 kJ mol’-‘) was obtained by Nakagawa and Weatherly [22,23] on reanalysing the early data of Bayles et al. [24]. This was attributed to coarsening proceeding by a process of retraction and annihilation of fibre terminations rather than by Ostwald ripening. We have shown in the earlier part of this paper that such fault migration does indeed occur but probably proceeds by interface diffusion and not by volume diffusion as assumed by Nakagawa and Weatherly [23]. If fault annihilation contributes significantly to fibre coarsening in the present experiments the measured activation energy wilf either be that associated with interface diffusion or will be modified by the interface diffusion contribution. This may well account for the difference between the present results and those of Smartt and Courtney [IS] who took considerable care to ensure their measurements were in a regime of isotropic coarsening. The apparent discrepancy between the present results and those of Jones and May [6] is more difficult to rationalise. However, much higher absolute temperatures were used in the experiments by Jones and May, and in the earlier study by Jones [4] on the Ag-Pb eutectic (_ 0.95 T,,,). Consequently recovery processes close to the melting point might be expected to reduce the density of mat& dislocations and make the fibres more mobile. indeed McLean [9] has shown that the carbide fibres in the (Co,Cr)-Cr& eutectic can become curved due to differential migration rates but this phenomenon was only apparent in materiaf heated to within a few degrees of the melting point. Thus the present results obtained at lower temperatures and in higher temperature gradients are complementary to the earlier study by Jones and May[6] and suggest that fibre migration by interface diffusion is inhibited at the lower temperatures, relative to T,,,, likely to be encountered in engineering applications. Concentration gradients. Particle coarsening by matrix diffusion occurs when a concentration gradient of solute is set up within the matrix. It is instructive to estimate the magnitude of these concentration gradients For the cases of Ostwald ripening and temperature gradient coarsening. Because of the modified solubiiity at a curved interface, described by the Gibbs-~ornp~n equation, a radial concentmtion gradient about a cylindrical inclusion dc/dr is of the order [9]

MCLEAN: MICROSl-RLTCTC’Rr\LDEGRADATION For the present system fi = 10-*on& , c = l.j%,

7 = 250 mJm-‘, T=9OOK and

r = 0.35 q.

Hence dc/dr 5 4 x lo3 at. “/‘,m- I. When a temperature gradient is imposed on a specimen a concentration gradient dc/dz can also be set up in the direction of the imposed gradient [20] dc _=-

dz

Q*cG RT’ ’

where, for the Al-Al,Ni system Q* = 2 x IO’J c = 1.5 at.%, G = 25 x lo3 Km- ’ and mol-‘, T= 900K. Thus dc/dz = 1.1 x lO*at.%m-‘. This latter figure which is a factor of forty less than the concentration gradient which leads to capillarity motivated Ostwald ripening is consistent with our finding that, in the present experimental conditions, the presence of a temperature gradient makes no significant contribution to the driving force for microstructural degradation of the Al-Al,Ni eutectic composite.

4. CONCLUSIONS (1) No phase migration was observed using in siru electron microscopy although relatively large velocities are predicted theoretically. The lack of mobility is probably due to the fibres being anchored by a dislocation substructure. As a consequence some previous assessments [4-73 of the vulnerability of eutectic composites to temperature gradient instabilities are unduly pessimistic. (2) Morphological changes of the A13Ni fibres, observed by in situ electron microscopy are motivated by a reduction in surface energy and occur by diffusion at the interphase boundaries. (3) The coarsening of the microstructure of Al-A13Ni in a ‘temperature gradient can be adequately explained in terms of Ostwald ripening.

OF EUTECTIC

1215

rlcknowvledgements-The author would like to thank M. S. Loveday for assistance in the electron microscopy

and B. E. Hopkins and R. D. Doherty for comments on the paper. REFERENCES 1. J. L. Walter and H. E. Cline, ,Vetall. Trans. 4, 33 (1973). 2. R. W. Kraft. D. L. Albright and J. A. Ford. Trans. metoll. Sot. A.I.,V.E. 227, 540 (1963). 3. M. McLean, Scripra Met. 9, 439 (1975). 4. D. R. H. Jones. .Unter. Sci. Engng. 15, 203 (1974). 5. D. R. H. Jones. .Cfetal Sci. 8. 37 (1974). 6. D. R. H. Jones and G. J. Ma;. A& Mtb. 23. 29 (1975). 7. R. K. Honeycombe, Proceedings of the Rosenhain Centenary Conference, Phil. Trans. R. Sot. 282, 426 (1976). 8. M. McLean and M. S. Loveday. J. muter. Sci. 9, 1la (197J), 9, 2069 (1973). 9. M. McLean, Proc. Conf. in situ Composires II, Bolton Landing, New York. 2-5 September. 1975, (edited by M. R. Jackson. J. L. Walter. F. D. Lemoiex and R. W. Hertzberg), pp. 179-189, Xerox Individialized Publishing (1976). 10. J. D. Livingston, H. E. Cline, E. F. Koch and R. R. Russell, Acta Met. 18, 399 (1970). 11. G. Garmong and T. H. Courtney, Wetall. Trans. (A) 6, 1945 (1975). 12. T. R. Anthony and H. E. Cline, J. appl. Phys. -12. 3380 (1971). 13 R. D. Doherty and T. R. Strutt. J. murer. Sci. 11, 2169 (1976). 14. F. A. Nichols, Acta ?vfer. 20, 207 (1972). 15. M. McLean, Phil. Mug. 27, 1253 (1973). 16. E. Ho and G. C. Weatherly, Acta .C[et. 23, l-151 (1975). 17. H. E. Cline, Acta Met. 19. 481 (1971). 18. H. B. Smartt and T. H. Courtney. Merall. Trans. (A) 7, 123 (1976). 19. S. K. Bhattacharvva and K. C. Russell. ,CletuU. Trans. (A) 3, 2195 (1972j: 20. P. G. Shewmon, Dijiisiorl in Solids. McGraw-Hill, New York (1963). 21. C. J. Meechan and G. W. Lehman. J. appl. Phys. 33, 634 (1967). 22. G. C. Weatherly and Y. G. Nakagawa, Scripta Mer. 5, 777 (1971). 23. Y. G. Nakagawa and G. C. Weatherly, Acra Mer. 20. 345 (1972). 24. B. J. Bayles, J. A. Ford and M. T. Salkind. Trurrs metal

Sot. A.I.M.E.

239, 844 (1967).