High-temperature ab initio calculations on FeSi and NiSi

The Fe–Ni–Si system is potentially a very important component of terrestrial planetary cores. However, at present, even the behaviour of the FeSi and NiSi end members is poorly understood, especially at low to moderate pressures—the data for FeSi are contradictory and NiSi has been little studied. For FeSi, there is general agreement that there is a phase transition from the ε-FeSi to the CsCl structure with increasing pressure, but, in experiments, there is disagreement as to the position and slope of the phase boundary and the range of coexistence of the two phases. In this paper we have used ab initio lattice dynamics calculations to determine the phase boundary between the ε-FeSi and CsCl structures as a function of pressure and temperature in both FeSi and NiSi. For FeSi, we find that the transition pressure at zero Kelvin is ~11 GPa and that the boundary between the ε-FeSi and CsCl phases varies little with temperature, having a slight negative Clapeyron slope, going from ~11 GPa at 300 K to ~3 GPa at 2000 K. For NiSi, there is much greater variation of the transition pressure with temperature, with a much shallower negative Clapeyron slope, going from ~156 GPa at 300 K to ~94 GPa at 2000 K

The thermal expansion of (Fe1-y Ni y )Si

We have measured the thermal expansion of (Fe1-y Ni y )Si for y  =  0, 0.1 and 0.2, between 40 and 1273 K. Above ~700 K the unit-cell volumes of the samples decrease approximately linearly with increasing Ni content. Below ~200 K the unit-cell volume of FeSi falls to a value between that of (Fe0.9Ni0.1)Si and (Fe0.8Ni0.2)Si. We attribute this extra contraction of the FeSi, which is a narrow band-gap semiconductor, to the depopulation of the conduction band at low temperatures; in the two alloys the additional electrons introduced by the substitution of Ni lead to the conduction band always being populated. We have fit the unit-cell volume data with a Debye internal energy model of thermal expansion and an additional volume term, above 800 K, to take account of the volumetric changes associated with changes in the composition of the sample. Using the thermophysical parameters of the fit we have estimated the band gap in FeSi to be 21(1) meV and the unit-cell volume change in FeSi associated with the depopulation of the conduction band to be 0.066(35) Å(3)/unit-cell