Jorge Munoz

Absence of Long-Range Chemical Ordering in Equimolar FeCoCrNi

Equimolar FeCoCrNi alloys have been the topic of recent research as “high-entropy alloys,” where the name is derived from the high configurational entropy of mixing for a random solid solution. Despite their name, no systematic study of ordering in this alloy system has been performed to date. Here, we present results from anomalous x-ray scattering and neutron scattering on quenched and annealed samples. An alloy of FeNi3 was prepared in the same manner to act as a control. Evidence of long-range chemical ordering is clearly observed in the annealed FeNi3 sample from both experimental techniques. The FeCoCrNi sample given the same heat treatment lacks long-range chemical order.

Temperature and pressure dependence of the Fe-specific phonon density of statesin Ba(Fe_(1−x)Co_x)_2As_2

The ^(57)Fe-specific phonon density of states (DOS) of Ba(Fe_(1−x)Co_x)_2As_2 single crystals (x=0.0,0.08) was measured at cryogenic temperatures and at high pressures with nuclear-resonant inelastic x-ray scattering. Measurements were conducted for two different orientations of the single crystals, yielding the orientation-projected ^(57)Fe-phonon density of states for phonon polarizations in-plane and out-of-plane with respect to the basal plane of the crystal structure. In the tetragonal phase at 300 K, a clear stiffening was observed upon doping with Co. Increasing pressure to 4 GPa caused a marked increase of phonon frequencies, with the doped material still stiffer than the parent compound. Upon cooling, both the doped and undoped samples showed a stiffening and the parent compound exhibited a discontinuity across the magnetic and structural phase transitions. These findings are generally compatible with the changes in volume of the system upon doping, increasing pressure, or increasing temperature, but an extra softening of high-energy modes occurs with increasing temperature. First-principles computations of the phonon DOS were performed and showed an overall agreement with the experimental results, but underestimate the Gruneisen parameter. This discrepancy is explained in terms of a magnetic Gruneisen parameter, causing an extra phonon stiffening as magnetism is suppressed under pressure.

Nonharmonic phonons in α -iron at high temperatures

Phonon densities of states (DOS) of bcc α−^(57)Fe were measured from room temperature through the 1044 K Curie transition and the 1185 K fcc γ-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700 K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born–von Karman model to the experimental phonon spectra using a genetic algorithm optimization. The second-nearest-neighbor fitted axial force constants weakened significantly at elevated temperatures. An unusually large nonharmonic behavior is reported, which increases the vibrational entropy and accounts for a contribution of 35 meV/atom in the free energy at high temperatures. The nonharmonic contribution to the vibrational entropy follows the thermal trend of the magnetic entropy, and may be coupled to magnetic excitations. A small change in vibrational entropy across the α−γ structural phase transformation is also reported.

Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO2

Although the rutile structure of TiO_2 is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000 K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO_2 from 300 to 1373 K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of 3d electrons of Ti and 2p electrons of O atoms. With thermal expansion, the energy variation in this “phonon-tracked hybridization” flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.

Miscibility gap and phonon thermodynamics of Fe-Au alloys studied by inelastic neutron scattering and nuclear-resonant inelastic x-ray scattering

Recent measurements of the phonon spectra of several Au-rich alloys of face-centered-cubic Fe-Au using inelastic neutron scattering and nuclear-resonant inelastic x-ray scattering are summarized. The Wills-Harrison model, accounting for charge transfer upon alloying, is used to explain the observed negative excess vibrational entropy of mixing, which increases the miscibility gap temperature in the system by an estimated maximum of 550 K and we adjudicate to a charge transfer from the Fe to the Au atoms that results in an increase in the electron density in the free-electron-like states and in stronger sd-hybridization. When Au is the solvent, this softens the Fe–Fe bonds but stiffens the Au–Au and Au–Fe bonds which results in a net stiffening relative to the elemental components.

Nonharmonic phonons in alpha-iron at high temperatures

Phonon densities of states (DOS) of bcc α−^(57)Fe were measured from room temperature through the 1044 K Curie transition and the 1185 K fcc γ-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700 K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born–von Karman model to the experimental phonon spectra using a genetic algorithm optimization. The second-nearest-neighbor fitted axial force constants weakened significantly at elevated temperatures. An unusually large nonharmonic behavior is reported, which increases the vibrational entropy and accounts for a contribution of 35 meV/atom in the free energy at high temperatures. The nonharmonic contribution to the vibrational entropy follows the thermal trend of the magnetic entropy, and may be coupled to magnetic excitations. A small change in vibrational entropy across the α−γ structural phase transformation is also reported.

Phonon densities of states of face-centered-cubic Ni-Fe alloys

Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to determine the phonon densities of states of face-centered-cubic Ni-Fe alloys. Increasing Fe concentration results in an average softening of the phonon modes. Chemical ordering of the Ni_(0.72)Fe_(0.28) alloy results in a reduction of the partial vibrational entropy of the Fe atoms but does not significantly change the partial vibrational entropy of the Ni atoms. Changes in the phonon densities of states with composition and chemical ordering are discussed and analyzed with a cluster expansion method.