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# Non-Ideal Solution Behavior

In this section, a simple model for the enthalpy of mixing will be derived. It will be shown that a positive enthalpy of mixing tends to make a system separate and have a miscibility gap at low temperature. A negative enthalpy of mixing tends to favor stable homogeneous solutions.

Consider two neighbors in a solution. The probability that one of the neighbors is an -type or a -type is simply:

 (32-1)

Therefore the probability that a given bond'' is an - type is:

 (32-2)

If each atom has nearest neighbors, the number of bonds, total, is

 (32-3)

The bond density of - type is therefore:

 (32-4)

If the energy per bond is 1then the enthalpy density (due to the - bonds) is:

 (32-5)

Similarly, the bond density of -types is so that . Similarly .

Putting this all together

 (32-6)

 (32-7)

Therefore since, :

 (32-8)

 (32-9)

This is the Regular Solution Model

Next: Behavior of the Regular Up: Lecture_32_web Previous: Lecture_32_web
W. Craig Carter 2002-12-03