Nonlinear elasticity of ɛ -Fe: The pressure effect

Abstract

Description of elasticity of iron at the ultrahigh pressures is a challenging task for physics, with a potential strong impact on other branches of science. In the present work, we calculate the elastic properties of hcp iron in the pressure range of 50-340 GPa beyond the linear elasticity approximation, conventionally assumed in theoretical studies. We define the higher order elastic constants and present expressions for the long-wave acoustic modes Grüneisen parameters of a compressed hcp crystal. We obtain the second and third order elastic constants of the hcp Fe in the considered pressure interval, as well as its Grüneisen parameters for the highsymmetry directions. The latter are directly compared with the Grüneisen parameters derived from the volume dependences of the vibrational frequencies calculated in the quasiharmonic approximation. The obtained results are used for the stability analysis of the hcp phase of iron at high pressures.

High-pressure equations of state and elastic properties of the hcp-Iron

“…While eq. ( 16) is compatible with experimental data [8] up to about 160 GPa pressure and results obtained by the ab initio technique recently reported by Krasilnikov et al [19] show a slight diverge. The results obtained by Equation (13) show much difference from Experimental data [8].…”

“…It is also noticeable that the values of BT, C12, C13 and C44 all increase proportionally with the applied pressure, with BT increasing faster than C12, C13 and C44 as shown in Figure 2. The results for C11, C12, C33 and C44 using Equation ( 17) are well correspond to results obtained by the ab initio technique recently reported by Krasilnikov et al [19]. However, the values of C13 are not much compatible at low pressure yet at high-pressure Equation (17) shows better comprise with the data reported by Krasilnikov et al [19].…”

“…The behavior of hcp-Fe is nonmagnetic and stability has been theoretically predicted up to 5700 GPa [5] and confirmed experimentally to at least 400 GPa [11]. Therefore, experiments [2][3][4][6][7][8] and theoretical study [16][17][18][19][20][21][22] of the elastic moduli of ɛ-Fe under high pressure have a field of significant relevance for researchers. There have been several first-principles calculations of Fe elastic moduli at high pressures [1,[16][17][18][19][20][21][22], most of which are in the zero-temperature.…”

“…Brown [14] pointed out that ɛ-Fe may finish at a triple point near 200 GPa, but experimental results [15] have been inconclusive. Although, it is generally accepted that hcp-Fe is nonmagnetic behavior at room temperature wide range of stability at pressures greater than 50 GPa [16][17][18][19]. The behavior of hcp-Fe is nonmagnetic and stability has been theoretically predicted up to 5700 GPa [5] and confirmed experimentally to at least 400 GPa [11].…”

“…Therefore, experiments [2][3][4][6][7][8] and theoretical study [16][17][18][19][20][21][22] of the elastic moduli of ɛ-Fe under high pressure have a field of significant relevance for researchers. There have been several first-principles calculations of Fe elastic moduli at high pressures [1,[16][17][18][19][20][21][22], most of which are in the zero-temperature. The present model has been successfully employed with the calculation of elastic properties of various solids this paper, we have formulated the elastic moduli for ɛ-Fe using the theory of Bina and Helffrich [26] and the analytical equation of state.…”