First-principles investigations on elasticity properties of FeSi under high pressure and temperature
Introduction
The intermetallic compound FeSi has attracted much attention over decades owing to the significant electrical and magnetic properties. It is currently of considerable interest from the functional applications in thermoelectric conversion and solar cells [[1], [2], [3], [4], [5], [6]]. Among these compounds, the elastic property of FeSi at high pressure and temperature has also attracted much scientific attention due to the remarkable application in earth science [[7], [8], [9], [10]].
Nevertheless, some remarkable properties of the phase transition in FeSi are not understood. Two stable structures in FeSi system, B20 phase with P213 symmetry and B2 phase with CsCl structure, were reported via both experiments and calculations at high pressure and temperature. In earlier experiments [[11], [12], [13]], only B20 phase was measured at pressures lower than 10 GPa. Even if the experimental conditions are elevated to 50 GPa and 1500 K, the phase transition from B20 to B2 remains undiscovered in the study of Knittle and Williams [14]. However, subsequent theoretical studies [15,16] showed that B2 phase will become thermodynamically stable compared with B20 phase when pressure is above 20 GPa. Dobson et al. [17] pointed out the reason why previous experimental studies fail to obtain B2 phase at high pressure and temperature is the slightly enriched silicon of the starting sample. By using Fe0.52Si0.48 sample, they found B2 phase is stable at 24 GPa and at the temperatures above 1950 ± 50 K. In the following experimental studies, Lord et al. [18] and Fischer et al. [19] showed sharp boundaries between the two phases at high pressure and temperature, while Geballe and Jeanloz [20] suggested a wide B2+B20 two-phase field. Fischer et al. [19] and Geballe and Jeanloz [20] showed no detectable temperature dependence in the process of phase transformation when temperature is above 1000 K. Nevertheless, the two studies gave two different transition pressure boundaries: ∼42 GPa for Fischer et al. [19] and ∼30 GPa for Geballe and Jeanloz [20]. It should also be noted that refs 17 and 18 do show temperature dependence to the boundary. Computer simulations also provided entirely different transition pressures. Caracas and Wentzcovitch [7] found the B20-B2 transition takes place at ∼40 GPa, whereas Wann et al. [10] reported that the phase transition occurs from ∼11 GPa at 300 K to ∼3 GPa at 2000 K. From these experiments and calculations, there exists only B2 phase at the pressure of more than 50 GPa.
The elasticity simulation of FeSi under high pressure and temperature will help to understand the unusual phenomena of transition metal silicides in deep, such as the phase transition from B20 phase to B2 phase. Despite a great many theoretical and experimental studies performed on FeSi recently, the reports about the elasticity of FeSi under high pressure and temperature are still relatively lacking. This leads us to take an interest in studying the thermoelasticity and thermodynamic properties of B20 and B2 phases of FeSi under high pressure and temperature using the first-principles calculations, in which the effects of temperature are considered by the Quasi harmonic approximation (QHA) [21].
Section snippets
Calculation methods
Most of our calculations are based on density functional theory [22,23] as implemented in the Cambridge Sequential Total Energy Package (CASTEP) [24]. The generalized-gradient approximation (GGA) proposed by Perdew et al. [25] is used to describe exchange-correlation potential. Ultrasoft pseudopotentials are generated on the fly. The electronic wave functions are expanded in a plane wave basis set with a cut-off energy of 800 eV. The K-space integrations are performed using 8 × 8 × 8
Results and discussion
The obtained structural parameters for the two phases of FeSi are presented in Table 1. The obtained zero-pressure lattice constants agree with the experimental values, and the difference is less than one percent. As is known, for the conventional density functional theory (DFT) techniques, local-density approximation (LDA) commonly underestimates crystal structure parameters while generalized-gradient approximation (GGA) commonly overestimates them. However, in our calculation, the lattice
Conclusions
In summary, we have investigated the effect of temperature on the elasticity properties for B20 and B2 phases of FeSi under high pressure via the first-principles calculations combined with the Quasiharmonic approximation. Our results show that the temperature has a little impact on the elasticity of FeSi at high pressures, especially for B2 phase. For example, the anisotropy factor of B2 phase decreases by just 0.01 from 300 K to 2000 K at 160 GPa. The temperature also has an insignificant
Acknowledgement
The authors would like to thank the supports by the National Natural Science Foundation of China (Grant Nos. 41574076, 41704088, and 11604273), the Basic Research of Technology Program of China (Grant No. JSHS2014404B002), the Natural Science Foundation of Sichuan province (Grant No. 15TD0013).
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