Past exam of the quantum condensed matter course of the University of Cambridge / 2006 / Section A / A2 / d

Write $z_c$ for the lattice coordination number and ${ϵ}_{AA},{ϵ}_{BB},{ϵ}_{AB}$ for contact energies. Counting the excess of unlike contacts relative to the unmixed reference gives the Flory interaction parameterUnlike contacts that are less favorable than the mean like contact give $\chi >0$. For temperature-independent contact energies, $\chi$ is proportional to $1/T$, so heating weakens this energetic preference relative to the entropy of mixing. Effective parameters in real solutions can also include entropic terms, often represented schematically by $A/T+B$; the pure contact-energy model does not explain every possible temperature dependence.