Effects of composition, temperature, and magnetism on phonons in bcc Fe-V alloys

The phonon densities of states of body-centered-cubic Fe-V alloys across the full composition range were studied by inelastic neutron scattering, nuclear resonant inelastic x-ray scattering, and ab initio calculations. The average phonon energy followed the inverse of the electronic heat capacity and the inverse of the electronic density of states at the Fermi level, showing how the interatomic forces depend on electronic screening. These quantities, including phonon energy, changed rapidly near the composition of the paramagnetic-ferromagnetic transition. For Fe- and V-rich alloys, the thermal phonon softening deviated from quasiharmonic behavior but better agreement was found for intermediate compositions. The Fe partial phonon density of states has a distinctly different shape than V for alloys with less than $50\text{at}\text{.}\mathrm{\%}$ Fe.

Figure 1

${}^{57}\text{F}\text{e}$ pDOS curves from NRIXS spectra at 300 K. Curves are offset by integer multiples of $0.03{\text{meV}}^{-1}$.

Figure 2

(Color online) Intensity as a function of energy transfer and momentum transfer for pure Fe (top), ${\text{Fe}}_{0.50}{\text{V}}_{0.50}$ (middle), and pure V (bottom) from neutron scattering at 300 K.

Figure 3

(Color online) Neutron-weighted phonon density of states curves for the alloys measured as a function of temperature. Curves are offset by integer multiples of $0.04{\text{meV}}^{-1}$. The dashed curves up to 10 meV indicate the Debye model fit for the low-energy modes. Error bars are shown and are smaller than the markers. Solid lines (labeled “QH”) show the 300 K DOS shifted in energy using the quasiharmonic model to the volume at 773 K (Sec. 3).

Figure 4

Phonon DOS curves, $g\left(E\right)$, for the alloys at 300 K, after using NRIXS results to correct for neutron weighting. Curves are offset by integer multiples of $0.04{\text{meV}}^{-1}$.

Figure 5

(Color online) (a) Left axis: average phonon energy from inelastic scattering (markers with an “X” for neutron-weighted and open squares for neutron-weight corrected) and from NRIXS for samples measured at 300 K (solid markers with error bars). Dashed lines with markers were obtained from the quasiharmonic predictions using Eq. (3) starting from the volume of pure Fe (diamonds) and pure V (triangles). The QH Fe curve reaches 20.3 meV at pure V and the QH V curve reaches 30.2 at pure Fe. Right axis: inverse of the electronic contribution to the low-temperature heat capacity (Ref. 31) shown as a thick solid line. (b) Lattice parameter of Fe-V alloys from Seki et al. (Ref. 8) at 300 K and from our DFT calculations. Dashed lines are extrapolations of the experimental results from Seki (Ref. 8) on Fe-rich (ferromagnetic) and V-rich (nonmagnetic) alloys. Arrows show the compositions of the Curie temperature at 10, 300, and 773 K [from Andersson (Ref. 13)].

Figure 6

Calculated eDOS for Fe, V, and ordered Fe-V alloys. Nonmagnetic are solid curves with the Fermi level at the diamonds. Magnetic results are dashed curves with the Fermi level at bowties. The curve for V shows the Fermi levels of V and for the other alloys in the rigid band approximation using the total number of electrons, 5, 5.75, 6.5, 7.25, and 8 for V, ${\text{FeV}}_3$, FeV, and ${\text{Fe}}_3\text{V}$, and Fe, respectively. Curves are offset by integer multiples of 5 states/eV/atom.

Figure 7

(Color online) Calculated phonon DOS for ordered bcc-based structures. Inset is the structure of Fe atoms (black) and V atoms (white). The total DOS (thick solid curve) is the concentration-weighted sum of the partial DOS of Fe (diamonds) and V (stars).

Figure 8

(Color online) Calculated neutron-weighted phonon DOS (left) and Fe partial phonon DOS (right) for ordered bcc-based structures convoluted with experimental resolution functions (thick solid curves) and compared to measured curves from disordered alloys.