Vibrational Properties of $\alpha$- and $\sigma$-Phase Fe-Cr Alloy

Experimental and theoretical studies, of the Fe-partial phonon density of states (PDOS) for ${\mathrm{Fe}}_{52.5}{\mathrm{Cr}}_{47.5}$ alloy having $\alpha$ and $\sigma$ phases were carried out. The former using the nuclear resonant inelastic x-ray scattering method, and the latter with the direct one. Characteristic features of PDOS, which distinguish one phase from the other, were revealed and successfully reproduced by the theory. Data pertinent to the dynamics such as the Lamb-Mössbauer factor, $f$, the kinetic energy per atom, $E_k$, and the mean force constant, $D$, were directly derived, while vibrational specific heat at constant volume, $C_V$, and vibrational entropy, $S$ were calculated using the Fe partial PDOS. Based on the values of $f$ and $C_V$, we determined Debye temperatures, ${\Theta }_D$. An excellent agreement for some quantities derived from experiment and first-principles theory, like $C_V$ and quite good ones for others like $D$ and $S$ were obtained.

Figure 1

(a) Phonon DOS as measured on ${}^{57}\mathrm{Fe}$ atoms at 298 K for the $\alpha$ (circles) and the $\sigma$ phase (triangles) of the ${\mathrm{Fe}}_{52.5}{\mathrm{Cr}}_{47.5}$ samples. Maximum error bars are shown; (b) measured (circles) and calculated (dots) DOS for the $\alpha \mathrm{\text{−}}{\mathrm{Fe}}_{52.5}{\mathrm{Cr}}_{47.5}$; (c) measured (triangles) and calculated (dots) DOS for the $\sigma \mathrm{\text{−}}{\mathrm{Fe}}_{52.5}{\mathrm{Cr}}_{47.5}$. DOS-curves for particular crystallographic sites are indicated, too.