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Green Function Theory of Short‐Range and Long‐Range Order in Magnetite
Author(s) -
Ihle D.,
Lorenz B.
Publication year - 1974
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220630221
Subject(s) - coulomb , condensed matter physics , magnetite , charge ordering , order (exchange) , lattice (music) , short range order , range (aeronautics) , physics , phase transition , electron , function (biology) , atmospheric temperature range , thermodynamics , chemistry , charge (physics) , quantum mechanics , materials science , finance , evolutionary biology , economics , acoustics , metallurgy , composite material , biology
Abstract 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.