HETEROGENEOUS EQUILIBRIUM 255 



dt 1 dixj Av^" jx'' — X") — AV" {x» — x") 



d7' " ~ l-x"'dx" A/" At?'" - Ay'^Aij^" 



As before, :; ;; and —77 are necessarily positive. In the 



1 — X ox 



denominator, Av^" is small and may be either positive or nega- 

 tive; Arj"" is positive. In the second term, Av"" is large and 

 positive; Atj"" negative, since by hypothesis the a-form is the 

 high-temperature phase, and hence has greater entropy. The 

 product is negative ; because of the large numerical value of the 

 term Av"", the second term in the denominator predominates, 

 and, being affected by a negative sign, the resultant denomina- 

 tor is always positive. In the numerator the first term is of 

 uncertain sign, but is smaller than the second term. The 

 second term is the dominant one; Av"" is large and positive, 

 and the sign of the numerator, and hence of the entire expres- 

 sion, is determined by, and is the same as, that of the composi- 

 tion difference (x^ — x"). When the high-temperature, or 

 a-form, takes more of the other component into solid solution, 



(x^ — X") is positive, -77; is positive, and the inversion tempera- 

 ture is lowered by solid solution. When the low temperature, 

 or /3-form, takes the greater quantity of the other component 

 into solid solution, the inversion temperature is raised. A 

 well-known example of the second case is the raising of the 

 inversion temperature of the low-temperature form of CaO • SiOj, 

 woUastonite, by solid solution of MgO-Si02. 



The further treatment of equilibria in which there is solid 

 solution is a simple extension of the above methods. The 

 composition of the solid phase is no longer constant, but 

 variable, a circumstance for which allowance is readily made in 

 the discussion. In addition, the entropy and volume are no 

 longer independent of the composition, but this again rarely 

 leads to complications. In the case of solid solution in systems 

 in which both components are volatile all of the coexisting 

 phases in a uni variant equilibrium may be of variable composi- 

 tion, but since compositions come into the equations as differ- 

 ences the detailed application of the equations above presents 

 no difficulty. 



