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Thermo dynam ic Properties o f M g-G e A lloysY.K . RAO AND G. R. BELTONThe thermod ynamic proper tie s of liquid alloys and two-phase m ixt ures in the Mg-Ge systemhave been investigated in the approxima te tem per atu re range 660 ~ to 1130~ by means of agalvanic cell based on MgCl~ as electrolyte. Derived thermodynamic properties for the ger-man ium -r ich liquid alloys have been found to be in good agreem ent with previous work. Thestandard free energy of formation of solid MgzGe from liquid magnesium and solid germa-nium has been derived from this work, and from p revious studies as:

AF~g2Ge = --29,900 + 7.98 T ca l.valid from 687 ~ to 1115~ The phase d iag ram for the sys tem has been found to differ onlyslightly from that due to Klemm and Westlinning.

TH E Mg-Ge sys tem, for which the phase diagram wasfirs t es tabl ished by Klemm and Westl inning,1 has oneintermetal l ic compound of essentia l ly s to ichiometr iccomposition, Mg2Ge. Gers tein and his coworkers 2 havemeasured the low temperature heat capacity of thiscompound and Beardmore e t a l . 3 h a v e used liquid tinsolut ion calor i metry to determine the heat of formationand heat of fusion. Ere men ko a nd Lu kashenko 4 havemeasured the galvanic cell voltage between solid mag-nesium and the solid mixture Mg2Ge + Ge by usingMgC12 dissolved in molten LiCI-KC1 as an electrolyte.In addition, Smith5 has de termined the vapor pre ssur eof magnesium over th is sol id mixture as well as overthe compound in equil ibr ium with ger man ium -ri ch l iq-uid. The second law heats of formation of the compound(from the soliei element s) from these latte r two stud-ies are , respect ively , -25.1 and- 30. 8 kcal per mole a t900~ These are to be compa red with the cal ori met ricvalues of -27.54 kcal per mole at 273~Activities of magnesium in liquid Mg-Ge alloys havebeen studied by means of an isopiestic equilibrationtechnique by Eldri dge, Mil ler, and Koma rek 6 althoughconsiderable extrapolat ion of resul ts was requir ed toobtain activiti es at a common tempe rat ure . Geffken andMiller 7 combined some of these resul t s with a r edete r-minat ion of the phase diagr am of the Mg-Ge syst em toevaluate activities along the liquidus. The derived ac-tivities were shown to be in good agreement with furthervalues extrapolated from Eldridge e t a l f i Despite thisapparent consis tency, it will be shown in the presen tpaper that the available ther modyn amic evidence andthe new experimental results do not support the largechanges in the liquidus proposed by Geffken and Miller?In the present study, activities in single phase andtwo phase Mg-Ge allo ys, in the te mpe rat ure range 660 ~to 1130~ have been det er mi ne d by mea ns of a galvaniccell involving liquid MgCl2 or MgCI2-CaCIz mixtu resas the electrolyt e. The par ti cul ar design of the cell,the precautions taken, and the experiment al procedurehave been ful ly descr ibed in an e ar l ier publicat ion,a

Y. K. RAO is Assistant Professor, Henry Krumb School of Mines,Columbia University,New York, N.Y.G.R. BELTON is Professor ofMetallurgy and Materials Science, University of Pennsylvania,Phila-delphia, Pa.Manuscript submitted February 22, 1971.

E X P E R I M E N T A LMateria ls

The analyses of magnesium and the electrolyte con-stituents, as well as the method of preparation of theelectrolyte , were as previously descr ibed. 8 The ger -maniu m was semic onduct or grade with a purity in ex-cess of 99.99 pct. Alloys were prepared under a puri-f ied argon atmospher e by induction melt ing in a luminacrucibles contained in a p la t inum suscept or .

P rocedureNo major change in procedure or instrumentat ion

was made from that descr i bed ea r l ie r , a The refere nceelectrode was pure magnesium for all the alloys ex-cept two, 66.2 and 58.6 at. pct Mg. For these highmelt ing point a l loys , the referen ce e lectrode was aMg-AI alloy containing 42.1 at. pct Mg. Extrapolat edresu lts from the study of this alloy 8 were used to con-vert the measured voltages to a magnesium reference.As a check on possible composition changes, additionsof master a l loy were made to the e lectrode compart-ments towards the end of each exper imen tal run. Aft ertherm al equil ibrat ion, the cel l potentia l was found tohave changed by less than 2 my; this being consistentwith the results of chemical analysis of the alloy beads.Six such analyses were performed and it was found thatthe maximum composit ion change which occurre dduring an experimen t was 0.05 at. pct. It would appearthat the film of electrolyte which covered the alloybeads si gnificantly reduced the vap orizati on ofmagnes ium.In addition to the foregoing, an experiment was car-ried out with a pure germanium electrode; the potentialbeing found to be about 1.1 v with res pe ct to magnes iumat about 900~ Since the highest potent ial in the alloystudies was app roximat ely 0.46 v, the poss ibil ity of theoccurr ence of s ignif icant d isplacement react ions ~ hasbeen ignored.

RESULTSThe resul ts obta ined for the ge rma niu m-r ich a l loysare pres ente d in Fig. 1 in the form of mea sur ed cel lvoltage vs temperature. A linear behavior was ob-served in the single phase (liquid) region and, within a

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>-I' ->0. 1 3 0 ~ a r e p r e s e n t e d i n F i g . 8 .A g a i n , w i t h i n a n e x p e r i m e n t a l s c a t t e r o f a b o u t 1 k c a l ,t h e r e s u l t s a r e i n a g r e e m e n t w i t h t h o s e f r o m t h e is o -p i e s t i c s t u d y . 8 T h e m a j o r d i f f e r e n c e i s t h a t E l d r i d g ee t a l . 6 i n t e r p r e t e d t h e i r r e s u l t s a s s h o w i n g a m i n i m u mi n t h e h e a t o f s o l u t i o n c u r v e a t a b o u t 1 8 p c t M g ,w h e r e a s t h e p r e s e n t s t u d y i n d i c a t e s t h e m o r e u s u a lb e h a v i o r , i . e . m o s t n e g a t i v e v a l u e a t i n f in i t e d i l u t i o n .

T h e P h a s e D i a g r a m o f t h e M g - G e S y s t e mT h e li q u i d us t e m p e r a t u r e s , w h i c h w e r e d e t e r m i n e d

f r o m t h e in t e r c e p t s o f t h e s i n g l e p h a s e r e s u l t s w i t h t h ec o m p o s i t i o n i n d e p e n d e n t c u r v e s i n F i g s . 1 , 2 , a n d 3a r e s h o w n in F i g . 9 . T h e r e s u l t s f o r th e p h a s e b o u n d -a r i e s r e p r e s e n t i n g e q u i l i b r i a b e t w e e n s o l i d g e r m a n i u ma n d l i q u i d a n d b e t w e e n M g 2 G e a n d m a g n e s i u m - r i c hl i q u i d a r e i n g o o d a g r e e m e n t w i t h t h e r e s u l t s o f K l e m ma n d W e s t l i n n i n g . ~ F o r t h e g e r m a n i u m - r i c h s i d e ofM g 2 G e , h o w e v e r , t h e p r e s e n t s t u d y y i e l d s a l i q u i d u sa p p r o x i m a t e l y 2 0~ b e l o w t h a t o f t h e s a m e w o r k e r s ;b u t i t s h o u l d b e n o t e d t h a t t h e y r e p o r t e d ~ e x p e r i m e n t a ld i f f i c u l t i e s i n t h i s c o m p o s i t i o n r e g i o n o w i n g to e x c e s -s i v e e v a p o r a t i o n .

T h e t e m p e r a t u r e o f t h e g e r m a n i u m - r i c h e u t e c t i cr e a c t i o n , d e t e r m i n e d f r o m t h e i n t e r s e c t io n o f t h e t woc o m p o s i t i o n i n d e p e n d e n t c u r v e s o f F i g s . 1 a n d 2, i s6 8 7~ w i t h a n u n c e r t a i n t y o f a b o u t 5 ~ T h e e u t e c t i cc o m p o s i t i o n a p p e a r s , s o m e w h a t f o r t u i t o u s l y , t o c o i n -c i d e w i t h t h e r e s u l t s f o r t h e 3 8 .4 p c t M g a l l o y . T h e s ea r e i n r e a s o n a b l e a g r e e m e n t w i t h t h e v a l u e s of K l e m ma n d W e s t l i n n i n g ' f o r t h e e u t e c t i c p o i n t , n a m e l y , 6 8 0~a n d 3 9 p c t M g .

T h e m o s t r e c e n t r e s u l t s o f G e f f k e n a n d M i l l e r 7 a r ea l s o s h o w n i n F i g . 9 , a n d th e m a r k e d d i s a g r e e m e n t o fb e t w e e n 4 0 ~ a n d 6 0 ~ f o r m o s t o f t h e l i q u i d u s t e m p e r -a t u r e s c a n n o t b e r e a d i l y e x p l a i n e d . H o w e v e r , t h e v e r yc l o s e a g r e e m e n t a m o n g t h e t h e r m o d y n a m i c s t u d i e sm u s t s u p p o r t t h e p r e s e n t w o r k . F o r e x a m p l e , i t w a ss h o w n i n a n e a r l i e r s e c t i o n t h a t f o u r i n d e p e n d e n t i n v e s -t i g a t i o n s , 4 '5 '6 i n c l u d i n g t h e p r e s e n t o n e , a r e i n c l o s e

a g r e e m e n t o n t h e s t a n d a r d f r e e e n e r g y o f f o r m a t i o n o fM g z G e ; s i n c e , a s i s s h o w n i n F i g . 7 , t h e w o r k o f E l -d r i d g e e t a l . 6 i s i n a l m o s t e x a c t a g r e e m e n t w i t h t h ep r e s e n t s t u d y a t 1 2 1 0~ i t f o l l o w s t h a t t h e f u n c t i o n

R T I n ( a ~ g ' a G e ) w i l l b e e q u a l to t h e s t a n d a r d f r e ee n e r g y o f f o r m a t i o n o f M g z G e a t e s s e n t i a l l y t h e s a m ec o m p o s i t i o n a s i n t h e p r e s e n t w o r k . I n a d d i t i o n , i n t e r -s e c t i o n s o f a c t i v i t y v s t e m p e r a t u r e c u r v e s f r o m E 1 -d r i d g e e t a l . 8 w i t h t h e c u r v e r e p r e s e n t i n g t h e a c t i v i t yo f m a g n e s i u m i n M g z G e + g e r m a n i u m - r i c h l i q u i d m i x -t u r e s , E q . [3 ] , y i e l d l i q u i d u s t e m p e r a t u r e s w h i c h a g r e et o w i t h i n b e t t e r t h a n + 1 0~ w i t h t h e p r e s e n t w o r k .

I n v i e w o f t h e f o r e g o i n g , t h e w o r k o f G e f f k e n a n dM i l l e r 7 h a s n o t b e e n c o n s i d e r e d i n c o n s t ru c t i n g t h ep h a s e d i a g r a m . T h e w o r k o f R a y n o r ~2 h a s b e e n a s -s u m e d t o b e c o r r e c t f o r t h e m a g n e s i u m - r i c h e u t e c t i c .

I n c o n t r a s t t o t h e w o r k o f K l e m m a n d W e s t l i n n i n g , 1t h e p r e s e n t s t u d y s h o w s a s h a r p p e a k i n t h e l i q u i d u sa t t h e M g z G e c o m p o u n d c o m p o s i t i o n . B y a n a l o g y w i t ht h e b e h a v i o r o f o r g a n i c s y s t e m s a t t h e c o m p o s i t i o n o fa s t a b l e c o m p l e x , H a u f f e a n d W a g n e r 13 h a v e i n t e r p r e t e dt h i s t y p e o f b e h a v i o r a s i n d i c a t i n g a s s o c i a t i o n i n t h el i q u i d s t a t e . A s f a r a s t h e a u t h o r s a r e a w a r e , n o s tr u c -t u r a l s t u d i e s h a v e b e e n c a r r i e d o u t o n t h i s p a r t i c u l a rs y s t e m w h i c h w o u l d c o r r o b o r a t e t h i s i n t e r p r e t a t i o n .H o w e v e r , S t e e b a n d E n t r e s s 14 h a v e d e t e r m i n e d a t o m i cd i s t r i b u t i o n s i n t h e s i m i l a r m a g n e s i u m - g r o u p I V bs y s t e m M g - S n . T h e i r r e s u l t s s h o w t h a t m a r k e d h e t e r o -g e n e o u s c o o r d i n a t i o n e x i s t s i n t h e l i q ui d a l l o y a t c o m -p o s i t i o n s ne ar Mg2Sn and this has led Steeb 5 to clas -sify this system as one showing "liquid compound"formation. Since iquidMg-Ge alloys a re even morestable tha n Mg-Sn alloys,~~ sim ila r interpretationwould appear reaso nable.

A C K N O W L E D G M E N T ST h e p r i n c i p a l s u p p o r t f o r t h is w o r k c a m e f r o m t h e

N a t i o n a l A e r o n a u t i c s a n d S p a c e A d m i n i s t r a t i o n u n d e rg r a n t N s G - 3 1 6 . A d d i t i o n a l s u p p o r t w a s p r o v i d e d b y t h eA d v a n c e d R e s e a r c h P r o j e c t s A g e n c y , O f f i c e o f t h eS e c r e t a r y o f D e f e n s e t h r o u g h t h e L a b o r a t o r y f o r R e -s e a r c h o n t h e S t r u c t u r e o f M a t t e r . T h e a u t h o r s w i s ht o t h a n k t h e B e l l T e l e p h o n e L a b o r a t o r i e s f o r t h e i r g i f to f p u r e g e r m a n i u m .

R E F E R E N C E S1. W. Klemm and H. Westlinning:Z. anorg. Chen~, 1940, vol. 245, pp. 365-80.2. B. C. Gerstein, P. L. Chu ng, and G . C. Danielson:Z Phys. Chem. Solids,1966, vol. 27, pp. 1161-65.3. P. Be ardmore, B. W. Howlett, B. D. Lichter, and M. B. Bever:Trans. TMS-AIME, 1966, vol. 236, pp. 102-8.4. V. N. Eremen ko and G. M. Lukashenko: zv. Akad. Nauk SSSR. Neorg.Mat., 1965, vol. 1, pp. 1296-97.5. J. F. Smith: Io wa State University,Ames, Iowa. Quoted in Ref. 6.6. J. M. Eldridg e, E. Miller,and K. L. Komare k: Trans. TMS-AIME, 1966, vol.236, pp. 1094-98.7. R. Geffk en and E. Miller:Trans. TMS-AIME, 1968, vol. 242, pp. 2323-28.8. G. R. B elton and Y. K. Rao: Trans. TMS-AIME, 1969, vol. 245, pp. 21 8%93.9. C. Wagnerand A. Wemer:Z Electrochem. Soc., 1963, vol. 110, pp. 326-32.10. R. Huttgren, R. L. Orr, P. D. Anderso n, and K . K. Kelley:Selected Values

of Thermodynamic Properties of Metals and Alloys , John Wiley and Sons,New York, I963 , includingsupplements o 1970.11. L. S. Darken: Trans. TMS-AIME, 1967, vol. 239, pp. 80-89.12. G. V. Raynor: J. lnst. Metals, 1940, vol. 66, pp. 403-26 .13. K. Hauffe and C. Wagner:Z. Electrochem., 1940, vol. 46, pp. 160-70.14. S. Steeb and H. Entress:Z. Metalll~, 1966, vol. 57, pp. 803-7.15. S. Steeb:Springer Tracts in Modem Physics, G. Hbhler, ed., vol. 47, p p.1-66, Springer-Verlag,Berlin, 1968.

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