Metal ammonia solutions: A lattice model approach

Abstract

A generalized Falicov-Kimball model is applied to study the phase diagram of metal ammonia solutions. The model includes a fluid-fluid interaction term and an electron-fluid interaction with a hard core and an attractive tail. Mean-field theories are derived for the localized and delocalized electron phases using ideas from the slave-boson approach to the Hubbard model. The attractive force stabilizes both the homogeneous delocalized electron phase and a regime where the electrons localize in cavities devoid of fluid particles. In its absence, the localized states are found to be unstable towards phase separation, in contrast to previous predictions. The Gaussian fluctuations and structure factors derived from this theory suggest the existence of bicontinuous channels percolating through the system. These findings agree qualitatively with experiments and computer simulations.

Flat-band localization in the Anderson-Falicov-Kimball model

“…This model has been applied to mixed valence compounds of rare earth, transition metal oxides, binary alloys and metal ammonia solutions. 16 Its Hamiltonian is…”

Hölder mean applied to Anderson localization

“…The Falicov-Kimball model is, presently, the simplest model to study metal-insulator transitions in mixed valence compounds of rare earth and transition metal oxides, ordering in mixed valence systems, order-disorder transitions in binary alloys, itinerant magnetism, and crystallization. Recently, it was also applied to study the possibility of electronic ferroelectricity in mixed-valence compounds, and also of the phase diagram of metal ammonia solutions [14]. In its most simplified version, namely the static model, it consists in assuming that in the system exist two species of spinless fermions: one of them possess infinite mass and hence does not move while the other one is free to move [15].…”

“…Recently, it was also applied to study the possibility of electronic ferroelectricity in mixed-valence compounds, and also of the phase diagram of metal ammonia solutions [14]. In its most simplified version, namely the static model, it consists in assuming that in the system exist two species of spinless fermions: one of them possess infinite mass and hence does not move while the other one is free to move [15].…”

Thermodynamics of the one-dimensional half-filled-band Falicov-Kimball model

“…Recently, it was also applied to study the possibility of electronic ferroelectricity in mixed-valence compounds, [22][23][24] and also of the phase diagram of metal ammonia solutions. 25 In its most simplified version, namely, static model, it consists in assuming that in the system exist two species of spinless fermions: one of them possess infinite mass and hence does not move while the other one is free to move. This version, in its one-dimensional form for a lattice of N sites, can be written as…”