Polaron mean-field model of the Verwey transition
Abstract
An accurate model of the properties of magnetite $(Fe\sb{3(1-\delta)}O\sb4),$ zinc ferrites $(Fe\sb{(3-x)}Zn\sb{x}O\sb4),$ and titanomagnetites $(Fe\sb{3-y}Ti\sb{y}O\sb4)$ in the vicinity of the Verwey Transition (VT) is achieved by adopting a quantum mechanical approach which focuses on quantum states rather than classical concepts, such as particles. Our approach leads to a simple physical picture of the VT which explains all the observed properties at and in the vicinity of the transition. Succinctly stated, the VT is the result of the sudden conversion of trapped states to polaron states. This simple model is capable of explaining all the observed changes which occur in the neighborhood of the transition using only a single order parameter, $\psi.$ The thermodynamic, electron transport, and structural properties as a function of temperature, T, and the nonstoichiometry parameter, $\delta,$ are fully modeled by our polaron mean-field (PMF) theory of the VT. Two approaches are used to obtain the equation of state: Strassler and Kittel mean-field model, and Hijmans and de Boer mean-field order-disorder theory. After careful elucidation of the SK theory, this two state theory is applied to VT. The order parameter and Fermi Dirac statistics are used to compute the number of occupied and empty polaron states. The electron transport properties are then described by the small polaron transport theory of Holstein and Emin. The electron transport properties are shown to be consistent with charge carriers, in the form of small polarons, that move adiabatically by a process called phonon assisted electronic hopping. This is demonstrated by comparison of the theoretically determined values of $\rho(T)$ and $\alpha(T)$ with the measured values of resistivity and the Seebeck coefficient for various values of $\delta.$ The PMF theory is improved by using a more microscopic approach based upon the theory of HB, which treats states as being either occupied polaron states, occupied trapped states, or undistorted vacant states. The three state PMF model gives an improved fit to the measured entropy and the electron transport data.
Degree
Ph.D.
Advisors
Honig, Purdue University.
Subject Area
Particle physics|Atoms & subatomic particles
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