Green Function Theory of Short‐Range and Long‐Range Order in Magnetite

For the treatment of short‐range order effects of the extra B‐site electrons in magnetite on the basis of the lattice‐gas model a cluster approximation for Green functions is presented. The short‐range and long‐range (Verwey ordering) order parameters, various correlation functions, configuration probabilities, and thermodynamic functions are calculated self‐consistently as functions of temperature T . At T v a first‐order phase transition to the disordered phase takes place. The system is found to be nearly completely ordered for T < T v and strongly short‐range ordered for T ⪆ T v . For U 2 / U 1 ≈ 0.02 to 0.05 ( U 1 , U 2 Coulomb energies of nearest and further distant neighbours, respectively) both T v and \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop f\limits_{0.9T_v }^{1.05T_v } c_v dT $\end{document} (c v specific heat) have nearly the values measured experimentally.