Positive Vibrational Entropy of Chemical Ordering in FeV

Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to measure phonon spectra of FeV as a $B2$ ordered compound and as a bcc solid solution. The two data sets were combined to give an accurate phonon density of states, and the phonon partial densities of states for V and Fe atoms. Contrary to the behavior of ordering alloys studied to date, the phonons in the $B2$ ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy by $+0.22\pm 0.03k_B/\mathrm{atom}$, which stabilizes the ordered phase to higher temperatures. First-principles calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.

Figure 1

Phonon DOS curves of pure Fe measured by INS and NRIXS (top panel). Neutron-weighted phonon DOS curves of FeV alloys (middle panel), and pure V (bottom panel) measured by INS. Error bars are from counting statistics.

Figure 2

Neutron-weight corrected phonon DOS curves of FeV samples (top panel), along with Fe pDOS curves (middle panel), and V pDOS curves (bottom panel). The Fe pDOS curves were determined directly by NRIXS measurements; the total FeV DOS curves and the V pDOS curves were obtained by combining INS and NRIXS spectra. Error bars are from counting statistics in the Fe pDOS, and propagation of error in the other curves.

Figure 3

Spin-polarized electronic DOS computed from first-principles with VASP for equiatomic FeV in the $B2$ structure, and in a 16-atom SQS. Calculations performed by Johnson et al. [29] using a CPA method are included for comparison. The total eDOS is offset for clarity.