4 . A. Hartman: Int.J. Fract. Mech., 1965,vol. 1, pp. 167-88.5 . F. J. Bradshaw andC. Wheeler: AppL Mater. Res., 1966, vol. 5 , pp . 112-20.6 . R. P .Wei: Int. J. Fract. Mech., 1968, vol. 1, no . 1, pp. 159-70.7 . J. A. Feeney, J. C. McMillan, andR. P .Wei: Met. Trans., 1970, vol. 1, pp. 1741-

57.

(a)

(b)Fig. 3--Effect of r e p l i c a tilt a n g l e on fractographic a p p e a r -ance. (a) Zero d e g t i l t ; (b) 30 d e g til t . Magnification ~5700t i m e s .

a r e k n o w n t o b e q u i t e s e n s i t i v e to t h e e f f e c t o f a t m o s -p h e r i c m o i s t u r e , a n o r d e r o f m a g n i t u d e r e d u c t i o n inc r a c k g r o w t h r a t e a s s o c i a t e d w i t h a c h a n g e in t e s te n v i r o n m e n t , f r o m a i r to v a c u u m , i s p o s s i b l e .4-7 T h es t r i a t i o n s , i f p r e s e n t a t t h e r e d u c e d r a t e o f g r o w t h ,m a y not h a v e b e e n r e s o l v a b l e . T h e s e r e s u l t s , a l o n gw i t h a d d i t i o n a l f r a c t o g r a p h i c r e s u l t s in o t h e r e n v i r o n -m e n t s , s u g g e s t t h a t t h e m e c h a n i s m f o r f a t i g u e - c r a c kg r o w t h in t h e T i - 6 A 1 - 4 V a l l o y i s b a s i c a l l y s i m i l a r( s t r i a t i o n s a r e o b s e r v e d ) f o r a wide r a n g e of e n v i r o n -m e n t s . I n a d d i t i o n to " v a c u u m " , t h e s e e n v i r o n m e n t sinc lude d i s t i l l e d w a t e r , " d r y " a n d " w e t " a i r , " d r y "h y d r o g e n , " d r y " o x y g e n , a n d " d r y " a n d " w e t " a r g o n .

T h e a u t h o r s wish to e x p r e s s t h e i r a p p r e c i a t i o n t oM r . C . M . H u d s o n f o r c a r r y i n g o u t t h e e x p e r i m e n t sin v a c u u m a t NASA L a n g l e y R e s e a r c h C e n t e r , a n d toM r . R . K o r a s t i n s k y f o r e l e c t r o n - m i c r o f r a c t o g r a p h y .S u p p o r t f o r t h i s w o r k by the N a t i o n a l A e r o n a u t i c s a n dS p a c e A d m i n i s t r a t i o n u n d e r G r a n t N G L 3 9 - 0 0 7 - 0 4 0 i sg r a t e f u l l y a c k n o w l e d g e d .

1. R. M. N. Pelloux: J. Eng. Frac. Mech., 1970,vol. 1, no. 4 , pp. 697-704.2 . D. Meyn: Trans. ASM, 1968,vol. 61, no. 1, pp. 52.61.3 . D. Brock: J. Eng. Frac. Mech., 1970,vol. 1, no. 4 , pp. 691-96.

Heat Capacity of Liquid BismuthH O W A R D B E L L A N D R A L P H H U L T G R E N

K N O W L E D G E o f t h e h e a t c a p a c i t y , C p , o f l i q u i db i s m u t h i s n e e d e d f o r i t s p o s s i b l e u s e a s a r e a c t o rc o o l a n t e i t h e r in e l e m e n t a l f o r m o r in a e u t e c t i c w i t hl e a d ; 1 o r a s a n a l l o y w i t h u r a n i u m a s a l i q u i d m e t a lf u e l .2 S c i e n t i f i c a l l y , t h e Cp o f b i s m u t h i s o f i n t e r e s tb e c a u s e o f i t s non c l o s e - p a c k e d s t r u c t u r e in t h e s o l i ds t a t e a n d i t s d e c r e a s e o f v o l u m e o n m e l t i n g .

P r e v i o u s m e a s u r e m e n t s o f t h e h e a t c a p a c i t y ofl i q u i d b i s m u t h d i f f e r c o n s i d e r a b l y , s e e F i g . 1 . C a r -p e n t e r a n d H a r l e3 (1932) f o u n d t h e C~ d e c r e a s e d

- - 4s t e a d i l y to 6 4 4 ° K ; F o r s t e r a n d T s c h e n t k e (1940) ob -t a i n e d r e s u l t s a b o u t 8 pct h i g h e r w i t h Cp d e c r e a s i n gto 6 9 0 ° K , t h e n i n c r e a s i n g a b o v e t h a t t e m p e r a t u r e .P e r s o ns (1848) v e r y e a r l y f o u n d a n i n t e r m e d i a t e v a l u e ,Cp = 7 . 5 9 , c o n s t a n t w i t h T . E n t h a l p y m e a s u r e m e n t s o fU m i n o 8 (1926) l e d to a c o n s t a n t CP = 7 . 8 0 ; w h i l e t h o s eo f W A s t , M e u t h e n , a n d D u r r e r 7 (1918) i n d i c a t e d Cp i n -c r e a s e d w i t h T , f r o m 7 . 1 to 8 . 7 6 a t 1 2 7 3 ° K .

F o r m o s t l i q u i d m e t a l s Cp i s t a b u l a t e d a s c o n s t a n tw i t h t e m p e r a t u r e , s b e c a u s e e n t h a l p y c o n t e n t m e a s u r e -m e n t s a r e not a c c u r a t e e n o u g h to s h o w a t r e n d o f Cpw i t h t e m p e r a t u r e . A f e w p r e c i s e m e a s u r e m e n t s o fl i q u i d m e t a l s s h o w t h a t Cp d e c r e a s e s w i t h t e m p e r a -t u r e . F o r H g , K , a n d N a , t h e d e c r e a s e c o n t i n u e s t o am i n i m u m v a l u e a t a b o u t 2.3 Tm , f o l l o w e d by a n i n -c r e a s e . 14

T h e b i s m u t h u s e d in the e x p e r i m e n t s w a s o b t a i n e df r o m C o n s o l i d a t e d M i n i n g a n d S m e l t i n g C o m p a n y a n dwas r e p o r t e d to be 9 9 . 9 9 9 9 p c t p u r e . S p e c t r o g r a p h i ca n a l y s i s s h o w e d o n l y a s i n g l e i m p u r i t y ; a t r a c e o f i r o n .

T h e l i q u i d t i n s o l u t i o n c a l o r i m e t e r , d e s c r i b e d e l s e -w h e r e , 9 a s m o d i f i e d by H e f f a n ,1° w a s u s e d f o r t h em e a s u r e m e n t s f r o m T m t o 8 0 1 . 8 ° K . Into a l a r g e q u a n -t i t y o f l i q u i d b i s m u t h i s d r o p p e d a s m a l l a m o u n t ofs o l i d b i s m u t h ; t h e t e m p e r a t u r e d r o p i s m e a s u r e d .F r o m t h e h e a t r e q u i r e d to m e l t t h e s o l i d , a n d r a i s e i tt o t h e t e m p e r a t u r e o f t h e l i q u i d , t h e Cp o f b i s m u t h c a nbe c a l c u l a t e d . T h e r e s u l t s a r e s h o w n in T a b l e I a n dF i g . 1 ; s m o o t h e d v a l u e s in T a b l e I I .

T h e e n t h a l p y c o n t e n t of b i s m u t h a t t h e m e l t i n g p o i n t( 4 2 0 0 c a l p e r g - a t o m ) w a s t a k e n f r o m t h e l i t e r a t u r e . ~1

T h e d a t a s h o w a s m o o t h d e c r e a s e in t h e Cp o f l i q u i db i s m u t h , a g r e e i n g f a i r l y we l l w i t h t h o s e of C a r p e n t e ra n d H a r l e~ a n d e x t e n d i n g t h e m t o h i g h e r t e m p e r a t u r e s .O t h e r w o r k e r s f o u n d m u c h h i g h e r v a l u e s .

HOWARD BELL is Assistant Professor of Nuclear Engineering, IowaState University,Ames, Iowa. RALPH HULTGREN is Professor o fMetallurgy, Department of Materials Science and Engineering, Inor-ganic Materials Research Division, Lawrence Berkeley Laboratory, Uni-versity of California, Berkeley, Calif.

Manuscript submitted November 2 , 1970 .

3230-VOLUME 2 , NOVEMBER 1971 METALLURGICAL TRANSACTIONS

Table |. Experimentally Determined Heat Capacity Data for Liquid Bismuth

Cp, Cal/Deg Cp, Cal/DegRun No. T, °K G-Atom Run No. T, °K G-Atom

21 801.7 6.69 8 577.4 7.1320 801.8 6.72 7 577.4 7.1319 755.2 6.83 2 558.5 7.2218 755.3 6.76 1 558.5 7.2117 698.1 6.79 11 545.9 7.3216 698.1 6.86 10 546.6 7.29

12 545.4 7.286 653.4 6.92 13 545.4 7.335 653.4 6.92 9 546.6 7.304 606.3 7.03 15 544.8 7.343 606.8 6.92 14 545.2 7.27

Table II. Selected Data for Liquid Bismuth

T, °K Cal/DegG-Atom HT - H29s, Cal/G-Atom

544.5 (M.P.) - 4200550 7.27(±0.1) 4240600 7.04 4597650 6.93 4946700 6.85 5290750 6.78 5631800 6.72 5969

8 . 0

7.E

o3w .'at a 7 6re' O(.9tl.IO

~E 7:4

"~. 7.Z

S 7.o(J Q&

(J6 . 8

66 IMR540

--.%

z~

flA

AIk

U M I N O A H F=

O THIS INVESTIGATIONrl CARPENTER ond HARLE CpW WLIST, MEUTHEN ond

DURRER AHA F{~RSTER and TSCHENTKE Cp0 PERSON Cp

5 8 0 620 660 700 740 7 8 0 8 2 0T, ° K

Fig. 1--Heat capacity of l iqu id b i smuth .

8 6 0

According to one theory of the liquid state,12'13 theliquid near the melting point consists of aggregates ofa t o m s with lattices s i m i l a r to those in the solid. Asthe temperature is increased, t h e s e aggregates a r ebroken up, absorbing heat and leading to anomalouslyhigh Cp values. This anomaly should grow less im-portant as the temperature r i s e s , finally disappearingaltogether, so the Cp should f i r s t d e c r e a s e , then re-sume a normally increasing v a l u e with temperature.

Numerous X - r a y and electron diffraction patternshave been interpreted on this b a s i s . However, if theseaggregates exist,1~ they should b r e a k up only a fewdegrees above the melting point , giving a much la rge r

anomaly spreading over a limited n u m b e r of d e g r e e s ;not the g radua l effect found.

The experimental Cp c u r v e is more in a c c o r d withthe theory of Kincaid and Eyring, Is who consider thechemica l bonding gradually changes to that in a mort-atomic gas; Cp decreasing toward 5R/2 at high tem-peratures. A statistical mechanical treatment of Chap-man 16 indicates Cv of all liquid m e t a l s should declinewith increasing temperatures. Hg, K, and Na alsofollow this r u l e . The upturn in Cp of t h e s e m e t a l s athigh temperatures is due entirely t o the Cp-Cv t e r m .The six m e t a l s for which t h e r e was sufficient data allfollowed Chapman's equation within +10 pc t . It is hopedthe data for bismuth presented above will provide testsfor this and o t h e r theories of the liquid state.

The experimental work for this paper was supportedby the Office of Ordnance R e s e a r c h , U. S. Army andby the U. S. Atomic Energy Commission and the Inor-ganic Materials R e s e a r c h Division of the L a w r e n c eRadiation Laboratory, Berkeley, California.

1. C. O. Smith:Nuclear Reactor Materials, Addison-Wesley Publishing Co.,Reading, Mass., 1967.

2, A. R. Kaufmann, ed.: Nuelear Reactor Fuel Elements, Interscience Publishers,New York, 1962.

3. L. G. Carpenter and T. F. Hade: Proc. Roy. Soc., London, 1932, vol. 136A,p. 243.

4. F. FSrster and G. Tschentke: Z. Metallk., 1940,vol. 32, p. 191.5. C. C. Person:Ann. Chim. Phys., 1848, vol. 24, p. 128.6. S. Umino: Sci. Rep., Tohoku Imp. Univ., 1926, vol. 15, p. 597,7. A. Wiist, A. Meuthen, and R. Durrer: Forsch. Geb. lngenieurw., 1918,vol.

204, p. 1.8. K. K. Kelley: U.S. Bur.Mines,Bull,, 1960, no. 584.9. R. L. Orr, A. Goldberg, and R. Hultgren: Rev. Sci. Instrum., 1957, vol.28, p.

767.10.H. Heffan: Master's Thesis, University ofCalifornia, 1958.11. R. Hultgren, R. L. Orr, P. O. Anderson, and K. K. Kelley: Selected Values o f

ThermodynamicProperties o fMetal and Alloys, John Wiley &Sons, Inc., NewYork, 1963.

12.A. Latin: J. Inst. Metals, 1940, vol. 66, p. 177.13. A. I. Bublik and A. G. Buntar: Fiz.Metal.Metalloved., 1957,vol. 5, p. 53.14.R. Hultgren and R. L. Orr: Rev. Int. Hautes Temper. R~fract., 1967, vol. 4,

p. 123.15. J. F. Kineaid and H. Eyring:3". Chem. Phys., 1937, vol. 5, p. 587.16.T. W.Chapman: Mater.ScL Eng., 1966, vol. 1, p. 65.

Annihilation of Vacancies by SmallAngle Grain Boundaries DuringSinteringV . K . LINDROOS

T H E explanation b a s e d on the consideration that largeangle gra in boundaries alone could act as effective va-cancy sinks in sintering is open to discussion on ki-netic grounds. As emphasized by Hirth,1 s m a l l anglegra in boundaries, i.e. dislocations, can be more dom-inant than gra in boundaries in controlling sinteringprovided the spacing of the f o r m e r is s m a l l compared

V. K. LINDROOS is Associate Professor, Laboratory of PhysicalMetallurgy, Ins t i tu te of Technology, Otaniemi-Helsinki, Finland.

Manuscript submit ted February 27, 1970.

METALLURGICAL TRANSACTIONS VOLUME 2, NOVEMBER 1971-3231