Positive Vibrational Entropy of Chemical Ordering in FeV

Abstract

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 þ0:22 AE 0:03k B =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. DOI: 10.1103/PhysRevLett.107.115501 PACS numbers: 63.20.dd, 63.20.kd, 64.60.Cn, 71.20.Be At finite temperatures T, the entropy S of a material is dominated by the contribution from atom vibrations. Nevertheless, the relative stabilities of alloy phases depend on differences in their free energies, F ¼ E À TS, and understanding differences in vibrational entropy is an active topic of research [1]. For chemical ordering transitions in alloys, the changes of vibrational entropy can be comparable to the large decrease in configurational entropy that accompanies ordering [2]. Stronger bonds between unlike pairs of atoms lead to ordering, and it is generally expected that such bonds would also be stiffer, reducing the vibrational entropy of the ordered phase [3]. For alloy systems that undergo chemical ordering, the decrease of vibrational entropy destabilizes the ordered phase with respect to the disordered phase [2,[4][5][6][7][8][9]. To our knowledge, there are no experimental reports of an ordered phase that has a larger vibrational entropy than a disordered phase, but here we report that FeV is an exception and we show why.The iron-vanadium alloy system has been investigated extensively, mainly because of its interesting magnetic behavior and chemical order-disorder phase transition. The phase diagram shows that bcc solid solutions are formed at high temperatures for all compositions, while the sigma phase is stable around the equiatomic composition [10,11]. The sigma phase can be avoided easily by quenching from high temperatures. Annealing at moderate temperatures results in B2 order [12,13].We report that the phonons in FeV become softer (shift to lower energies) upon ordering, so the B2 ordered phase has a higher vibrational entropy than the disordered solid solution. First-principles calculations show how better electronic screening can cause a decrease of the average energy of phonons in the ordered phase. At the Fermi energy, the projected electronic density of states (DOS) at the V atoms undergoes a larger increase with ordering than the projected DOS at the Fe atoms, and the phonon partial DOS of V shows a larger softening with ordering than the phonon...

Hysteresis Design of Magnetocaloric Materials—From Basic Mechanisms to Applications

“…The (dis‐)appearance of marked features in the electronic DOS at the Fermi level also has also important consequences for the elastic properties of a material, as the presence of electron states at the highest occupied levels promotes the screening of perturbations arising from the displacement of the ions. This mechanism is discussed in the literature as adiabatic electron–phonon coupling and has been observed, for instance, in narrow‐band‐gap semiconductors and at phase transitions involving chemical ordering . In La–Fe–Si, adiabatic electron–phonon coupling softens the PM phase despite the smaller volume compared to the FM phase and is thus the reason for the unexpected red‐shift of the VDOS and the cooperative change of S lat and S mag at T t .…”

“…For instance, the itinerant electron metamagnet La(Fe x Si 1− x ) 13 , is characterized by a competition of electronic states of Fe with different magnetic moments . Due to this, magnetic disorder leads to an increased DOS at E F , which improves the electronic screening of atomic displacements and thus softens the lattice . The itinerant magnetism of Fe is also observed at the heart of the excellent caloric properties of MnFe(P,Si)‐type materials .…”

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

“…Several results are shown in Table 1. The Wills-Harrison model predicts that the Co-Fe and V-Fe bonds are softer than the average of CoCo and Fe-Fe, and V-V and Fe-Fe bonds, respectively, which is accurate [28,29] and typically results in an ordering tendency [30]. The model predicts that the Au-Fe bond in the fcc structure is softer than the average of Au-Au and FeFe bonds, but Fe-Au is evidently a system with unmixing tendencies.…”

Effects of Short-Range Order on the Magnetic and Mechanical Properties of FeCoNi(AlSi)x High Entropy Alloys

“…In fact, the diversity in atomic radii and the different attractive interactions between the constituent elements will result in a short-range ordered structure [9]. The SRO structures have been found in many engineering materials such as FeV, FeAl and FeCr alloys [10][11][12]. It will significantly affect the structural stability, magnetic and mechanical properties.…”