First-principles study of elastic properties of Cr- and Fe-rich Fe-Cr alloys

Elastic properties of substitutionally disordered Cr- and Fe-rich Fe-Cr alloys are derived from first-principles calculations using the exact muffin-tin orbitals method and the coherent potential approximation. A peculiarity in the concentration dependence of elastic constants in Fe-rich alloys is demonstrated and related to a change in the Fermi surface topology. Our calculations predict high values for the elastic constants of Cr-rich Fe-Cr alloys, but at the same time show that these alloys could be rather brittle according to the Pugh criterion (the ratio between shear and bulk moduli is calculated to be greater than 0.5).

Figure 1

Lattice parameters of random bcc Fe-Cr alloys: Filled circles are the present EMTO-CPA results, an open square is the result of paramagnetic VASP-PAW calculations made in Ref. 56, a filled square is the low-temperature (LT) experimental lattice parameter used in the elastic constant calculations of Ref. 56 (the elastic constants are presented in Table ), and filled triangles are the experimental data from Ref. 8.

Figure 2

Calculated and experimental elastic properties of Cr-rich Fe-Cr alloys: (a) bulk modulus $B$, Young’s modulus $E$, and shear modulus $G$ (GPa); (b) Poisson’s rato $\nu$, anisotropy constant $A_G$, and $G/B$ ratio (dimensionless); (c) calculated single-crystal elastic constants $C_{44}$ and $C^{\prime }$ (GPa). The elastic properties have been calculated, using the DLM model of paramagnetic state of the alloys, at the room-temperature experimental lattice parameters (Ref. 8) (filled symbols connected by solid lines) and, for the properties sensitive to volume, also at the theoretical equilibrium lattice parameter $a_{\mathrm{calc}}$ (empty symbols connected by dashed lines). Experimental data from Refs. 4 and 6 for paramagnetic Cr and Fe-Cr alloys are shown for comparison (black symbols).

Figure 3

Lattice parameter of disordered bcc Fe-Cr alloys (upper panel) and that relative to the lattice parameter of pure Fe (lower panel). The EMTO-CPA and VASP-PAW results are shown by filled circles and squares, respectively. Empty circles denote the theoretical EMTO-CPA results of Ref. 13. The experimental data from Refs. 10 and 8 are given by filled diamonds and triangles, respectively.

Figure 4

(a) Bulk modulus $B,$ and shear elastic constants (b) $C_{44}$ and (c) $C^{\prime }$ calculated using EMTO-CPA and VASP-PAW methods at experimental and theoretical lattice parameters. Experimental data are from Refs. 3 and 11. The results are also compared with previous EMTO-CPA calculations of Ref. 13. The legend applies to all panels.

Figure 5

Young’s modulus $E$, shear modulus $G$, anisotropy constant $A_G$, and $G/B$ ratio calculated for the experimental and theoretical lattice parameters by the EMTO-CPA and VASP-PAW methods. Experimental data are from Ref. 3. The results are also compared with previous EMTO-CPA calculations of Ref. 13. The legend applies to all panels.

Figure 6

Bulk modulus $B$, elastic constants $C_{44}$ and $C^{\prime }$ calculated in the FM state for the experimental lattice parameters by the EMTO-CPA and VASP-PAW methods for the whole compositional range. Experimental data are from Refs. 3 and 11.