Effects of composition, temperature, and magnetism on phonons in bcc Fe-V alloys M. S. Lucas, 1,2 J. A. Muñoz, 3 O. Delaire, 1 N. D. Markovskiy, 3 M. B. Stone, 1 D. L. Abernathy, 1 I. Halevy, 3 L. Mauger, 3 J. B. Keith, 3 M. L. Winterrose, 3 Yuming Xiao, 4 M. Lerche, 5 and B. Fultz 3 1 Oak Ridge National Laboratory, 1, Bethel Valley Road, Oak Ridge, Tennessee 37831, USA 2 Air Force Research Laboratory, Wright-Patterson AFB, Ohio 45433, USA 3 California Institute of Technology, W. M. Keck Laboratory, 138-78, Pasadena, California 91125, USA 4 HPCAT, Geophysical Laboratory, Carnegie Institute of Washington, Argonne, Illinois 60439, USA 5 High Pressure Synergetic Consortium, Carnegie Institute of Washington, Argonne, Illinois 60439, USA Received 20 August 2010; published 22 October 2010 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 elec- tronic 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 at. % Fe. DOI: 10.1103/PhysRevB.82.144306 PACS numbers: 63.20.dd, 63.20.kd, 71.20.Be, 75.50.Bb I. INTRODUCTION Phonon thermodynamics underlies the vibrational entropy of materials, which contributes substantially to alloy phase stability and phase transitions. 1 Understanding how compo- sition, structure, temperature, and pressure alter the phonon frequencies has become a rich topic for materials research. 2–7 Unfortunately, simple rules derived from atomic mass, size, electronegativity, electron-to-atom ratio, and bond lengths are at best semiquantitative. Quantitative predictions must address the details of the electronic structure and how it de- pends on nuclear positions. This includes the effects of mag- netism, which alter substantially the electron density at the Fermi level. The body-centered-cubic bcc phase in the Fe-V alloy system spans across the full composition range. 8,9 Systematic changes in magnetic properties with composition make Fe-V alloys interesting for a study of the effects of magnetism on phonon thermodynamics. The magnetic moment decreases linearly from the value of bulk Fe as the V concentration increases until it disappears at about 70 at. % V at low temperature. 10–12 The Curie temperature is 300 K at approxi- mately 58 at. % V. 13,14 First-principles calculations by sev- eral methods have successfully reproduced the trends in the magnetism 15–18 and predict a strong hybridization of the atomic orbitals, charge transfer from the V to the Fe atoms, and the development of an antiparallel moment at the V at- oms. The latter was confirmed by the neutron diffuse scatter- ing measurements of Mirebeau and Parette. 19 The total en- ergy calculations as a function of volume for pure Fe performed by Moruzzi and Marcus, 16 predict the spin- polarized phase to be stable over the nonspin-polarized phase. These calculations showed that the electronic energies vary more with volume in the nonspin-polarized phase, re- sulting in a higher bulk modulus than the ferromagnetic phase. When an atom is displaced from its equilibrium position, the conduction electrons are free to screen the corresponding charge disturbance. The better the screening, the lower the electronic energy and interatomic forces. It is generally ex- pected that a metal with a large electronic density of states eDOS at the Fermi level, nE F , should have phonons of lower average energy than a material with small nE F . 20 The full picture requires details about how the different electron states at the Fermi level respond to atom displacements, and this is complicated for transition metal alloys. Nevertheless, when large, sharp features are present in nE near E F , changes in composition and temperature can alter signifi- cantly the phonon dispersions and the phonon density of states pDOS. For pure V, the adiabatic electron-phonon in- teraction EPI broadens the eDOS, causing a decrease in nE F  with increasing temperature. 21 A consequence is a re- duction in electronic screening with temperature so the pho- non DOS remains anomalously stiff at elevated temperatures. These effects on the phonons are of interest for their own sake but they also have thermodynamically significant ef- fects on the vibrational entropy. Both Fe and V have similar molecular weights, so mass effects from compositional changes are expected to shift phonon frequencies  /  by less than 5%. Larger effects are expected from changes in volume with temperature and perhaps composition. The effects of volume on the phonons are first accounted for with the quasiharmonic QH model. In this model the phonons are assumed harmonic but in- creases in volume owing to thermal expansion cause de- creases in phonon energies in proportion to a Grüneisen parameter. We might expect similar effects from the changes of volume with alloy composition, although this is less direct. The specific volume of Fe 1-x V x alloys increases monotonically with x, where vanadium is 18% larger than Fe. In this study, we explore the effects of alloying and tem- perature on the phonon density of states of bcc Fe 1-x V x across the entire composition range 0  x  1. In what fol- lows we explain the inelastic scattering techniques and their results, present predictions from quasiharmonic theory, and PHYSICAL REVIEW B 82, 144306 2010 1098-0121/2010/8214/1443069 ©2010 The American Physical Society 144306-1