Elastic anharmonicity of bcc Fe and Fe-based random alloys from first-principles calculations

We systematically investigate elastic anharmonic behavior in ferromagnetic body-centered cubic (bcc) Fe and Fe1-xMx (M = Al, V, Cr, Co, or Ni) random alloys by means of density-functional simulations. To benchmark computational accuracy, three ab initio codes are used to obtain the complete set of second-and third-order elastic constants (TOECs) for bcc Fe. The TOECs of Fe1-xMx alloys are studied employing the first-principles alloy theory formulated within the exact muffin-tin orbital method in combination with the coherent-potential approximation. It is found that the alloying effects on C-111, C-112, and C-123, which are governed by normal strains only, are more pronounced than those on C-144, C-166, and C-456, which involve shear strains. Remarkably, the magnitudes of all TOECs but C-123 decrease upon alloying with Al, V, Cr, Co, or Ni. Using the computed TOECs, we study compositional effects on the pressure derivatives of the effective elastic constants (dB(ij)/dP), bulk (dK/dP), and shear moduli (dG/dP) and derive longitudinal acoustic nonlinearity parameters (beta). Our predictions show that the pressure derivatives of K and G decrease with x for all solute elements and reveal a strong correlation between the compositional trends on dK/dP and dG/dP arising from the fact that alloying predominantly altersdB(11)/dP. The sensitivity of dB(11)/dP to composition is attributed to intrinsic alloying effects as opposed to lattice parameter changes accompanying solute addition. For Fe and the considered Fe-based alloys, beta along high-symmetry directions orders as beta[111] > beta[100] > beta[110], and alloying increases the directional anisotropy of beta but reduces its magnitude.