The magnetic properties of high-entropy alloys based on equimolar FeCoCrNi were investigated using vibrating sample magnetometry to determine their usefulness in high-temperature magnetic applications. Nuclear resonant inelastic x-ray scattering measurements were performed to evaluate the vibrational entropy of the 57 Fe atoms and to infer chemical order. The configurational and vibrational entropy of alloying are discussed as they apply to these high-entropy alloys.
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...
The phonon density of states ͑DOS͒ gives insight into interatomic forces and provides the vibrational entropy, making it a key thermodynamic function for understanding alloy phase transformations. Nuclear resonant inelastic x-ray scattering and inelastic neutron scattering were used to measure the chemical dependence of the DOS of bcc Fe-Co alloys. For the equiatomic alloy, the A2 → B2 ͑chemically disordered→ chemically ordered͒ phase transformation caused measurable changes in the phonon spectrum. The measured change in vibrational entropy upon ordering was −0.02Ϯ 0.02 k B /atom, suggesting that vibrational entropy results in a reduction in the orderdisorder transition temperature by 60Ϯ 60 K. The Connolly-Williams cluster inversion method was used to obtain interaction DOS ͑IDOS͒ curves that show how point and pair variables altered the phonon DOS of disordered bcc Fe-Co alloys. These IDOS curves accurately captured the change in the phonon DOS and vibrational entropy of the B2 ordering transition.
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