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PHASEe q u i l i b r i a of alloy p h a s e s and t h e r m o d y n a m i c data of these p h a s e s a r e c l o s e l y i n t e r r e l a t e d . F o r instance, if we know the f r e e e n e r g i e s of all the alloy p h a s e s in any b i n a r y or t e r n a r y s y s t e m as a function of composition and t e m p e r a t u r e , we can p r e d i c t the phase r e l a t i o n s h i p s in t h i s s y s t e m using t h e r m o d y n a m i c p r i n c i p l e s . On the other hand, from the e x p e r i m e n t a l l y d e t e r m i n e d phase d i a g r a m s , we can often obtain t h e r modynamic information of the alioy p h a s e s . During the past two decades, c o n s i d e r a b l e amount of effort has been done in c o r r e I a t i n g the t h e r m o d y n a m i c p r o p e r t i e s of a l l o y s and phase d i a g r a m s in b i n a r y s y s t e m s by Hultgren and his colleagues.2 F o r t e r n a r y s y s t e m s with no b i n a r y or t e r n a r y i n t e r m e t a l l i c p h a s e s , M e i j e r i n g 2-s and Rudy et al.6 have c o r r e l a t e d the t h e r modynamic p r o p e r t i e s of the a l l o y s and t h e i r phase b e h a v i o r . F o r t e r n a r y t r a n s i t i o n metal b o r i d e s and s i l i e i d e s , B r e w e r et al. 7 have set l i m i t s on the t h e r modynamie s t a b i l R i e s of the b i n a r y t r a n s i t i o n m e t a l b o r i d e s and s i l i c i d e s on the b a s i s of t e r n a r y phase e q u i l i b r i a . More r e c e n t l y , Rudy a developed a t h e r m o dynamic method for caIculating the phase r e l a t i o n s h i p s in t e r n a r y t r a n s i t i o n metal carbon s y s t e m s knowing the t h e r m o d y n a m i c p r o p e r t i e s of the b i n a r y metal c a r b i d e s and a s s u m i n g r e g u l a r b e h a v i o r of the t e r n a r y p h a s e s . Conversely, f r o m the t e r n a r y phase e q u i l i b r i a d e t e r mined e x p e r i m e n t a l l y , this method a l s o allows us to obtain the r e l a t i v e s t a b i l i t i e s of the r e s p e c t i v e b i n a r y t r a n s i t i o n m e t a l c a r b i d e s . The p r i m a r y p u r p o s e of the p r e s e n t p a p e r is to c o r r e l a t e the r e l a t i v e s t a b i l i t i e s of CrCd/2a, CrCs/v, and CrC2/a d e t e r m i n e d from the phase r e l a t i o n s h i p s in t e r n a r y M o - C r - C and W - C r - C s y s t e m s with the t h e r m o d y n a m i c p r o p e r t i e s of t h e s e t h r e e c a r b i d e s d e t e r m i n e d using s e v e r a l d i r e c t t h e r m o c h e m i c a l methods. Since we can d e r i v e only the r e l a t i v e s t a b i l i t i e s of the b i n a r y t r a n s i t i o n m e t a l c a r b i d e s f r o m phase e q u i l i b r i a , we will obtain the f r e e energy v a l u e s of a l l the c a r b i d e p h a s e s b a s e d on the f r e e energy of one of these p h a s e s d e t e r m i n e d d i r e c t l y by conventional t h e r m o c h e m i c a l technique. In p a r t i c u l a r , using this approach,