Volume change accompanying solidification
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Volume Change Accompanying Solidification P. J. WRAY D u r i n g s o l i d i f i c a t i o n the v e l o c i t y and m o r p h o l o g y of the s o l i d - l i q u i d i n t e r f a c e m a y be such that s t r e s s e s a r e induced within both the solid and the liquid, t,2 The d e t e r m i n a t i o n of t h e s e s t r e s s e s r e q u i r e s a knowledge of the v o l u m e change a c c o m p a n y i n g the phase t r a n s P. J. WRAY is Scientist, MechanicalSciencesDivision, Research Laboratory, U.S. Steel Corporation, Monroeville,Pc. 15146. Manuscript submitted March 29, 1974. 2602 - V O L U M E 5, D E C E M B E R 1974
Table I. The Relative Volume Change Accompanying the Solidification of Various Metals ~3F, Pct Element
TF
(,OL)F,g/cm3
(PS)F, g] cm3
19641~
Present
Ag A1 Au Bi Cd Co Cu Fe In Ni Pb Sb Si Sn TI Zn
961 660 1063 271 321 1495 1083 1536 156 1453 327 631 1410 232 303 420
9,323 2.3684 17.28 s 10.0346 7.9987 7.75 ~ 7.9383 7.035 a 7.0177 7.79 s 10.6653,9 6.465 2.5251~ 6.9863,9 11.22 n 6.5771~
9.82,2 2.55013 18.2814 9.70 ~s
5.40 6.37 5.67
5.09 7.14 5.47 -3.40 5.26 5.30 3.16 5.11 -
-
4.00 5.69 4.33 3.58 1.98 6.34 3.56 -0.95 2.9 3,0 2.2 4.08
8.18 s 8.38216 7.265 s 8.21 ~ -
~ o
_
-
-
f o r m a t i o n . F o r f r e e z i n g at t e m p e r a t u r e TF the r e l a tive v o l u m e change is given as
~F :
F
L
vr
JR
~
F'
p being the density. The purpose of this note is to provide up-to-date estimates of ~F for various metallic elements and a portion of the Fe-C alloy system. These estimates will be useful when considering such aspects of casting as stresses in the solid skin, porosity formation, inverse segregation and solidification cracking. The densities of the solid and liquid phases at the f r e e z i n g point, (PS)F and (PL)F, a r e given along with flF in T a b l e I. The d e n s i t y at the f r e e z i n g point has b e e n m e a s u r e d m o r e often for the liquid phase s - n than for the solid phase. P r e s e n t e s t i m a t e s of (PS)F i n T a b l e I a r e s o l e l y due to the d i l a t o m e t r i c m e a s u r e m e n t s of S i m m o n s and Balluffi 12-'4'~6 and the d e n s i t y m e a s u r e m e n t s of Lucas. 8 Also included in T a b l e I a r e the e a r l i e r e s t i m a t e s of/3 F by Lucas. ~~ The p r e s e n t e s t i m a t e s of ~F show the l a r g e s t d i s a g r e e m e n t s a r e for a l u m i n u m , copper and n i c k e l . The v a r i a t i o n in ~3F among the e l e m e n t s i s a p p r e c i a b l e , r e q u i r i n g m o d i f i c a t i o n of C a m p b e l l ' s r e m a r k '7 that /3F is " a b o u t 3 pct for m o s t m e t a l s . " F o r e x a m p l e , the e s t i m a t e d r e l a t i v e v o l u m e change a c c o m p a n y i n g f r e e z i n g is 3 1//2 t i m e s g r e a t e r for a l u m i n u m than for i n d i u m . E s t i m a t e s of the v o l u m e change of a l l o y s d u r i n g f r e e z i n g a r e s c a r c e b e c a u s e of an a b s e n c e of d e n s i t y m e a s u r e m e n t s for the solid phase at
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