The effect of atomic order on the martensitic phase transition and magnetic properties of stoichiometric Ni 2 MnGa has been investigated in a sample quenched from 1000 • C. Magnetization, resistivity and x-ray diffraction measurements indicate that the structural phase transition occurs at ∼103 K, substantially lower than the value reported for samples quenched from 800 • C and ordered in the Heusler L2 1 structure. A small reduction in the ferromagnetic moment was also observed, although the Curie temperature remained largely unaffected. The electronic Sommerfeld coefficient obtained from heat capacity measurements is enhanced but smaller than that observed for the 800 • C quenched sample. The results are consistent with band structure calculations and the electronic changes brought about by atomic disorder.

We performed inelastic neutron scattering measurements on nanophase Fe powders prepared by high-energy ball milling. Neutron energy loss spectra were measured for two states of the material: ͑1͒ as milled, when the material had a characteristic nanocrystallite size of 12 nm; and ͑2͒ annealed, when the material had a characteristic crystallite size of 28 nm. The longitudinal peak in the phonon density of states ͑DOS͒ of the nanophase Fe was broadened, compared to that of the annealed material. We attribute this broadening to short phonon lifetimes in nanocrystals. The nanophase material also showed an enhanced density of states at low energies below 15 meV, which may indicate the presence of intercrystallite vibrations. These differences in phonon DOS should have only a small effect on the difference in vibrational entropy of nanocrystalline and larger-grained Fe.

Inelastic nuclear resonant scattering spectra were measured on alloys of Fe 3 Al that were chemically disordered, partially ordered, and D0 3 ordered. The features in the phonon partial density of states of 57 Fe were found to change systematically with chemical short-range order in the alloy. Changes in the phonon partial density of states were modeled successfully by assigning vibrational spectra to 57 Fe atoms in different first-nearest-neighbor chemical environments. [S0031-9007(98)05811-6] PACS numbers: 76.80. + y, 81.30.Bx Phase diagrams of materials have been subjects of extensive experimental and theoretical research. In recent years, much of the free energies of solid phases have been calculated by elegant combinations of methods for calculating the electronic energy with the local density approximation and methods using cluster approximations for calculating the configurational entropy [1]. The change in vibrational entropy during a solid state phase transition is often thermodynamically important, however. There is now a growing effort to understand the reasons for differences in vibrational entropy between different states of materials [2][3][4][5][6][7][8]. Knowledge of the phonon density of states is central to any understanding of vibrational entropy, at least in the harmonic approximation. Phonons are delocalized excitations on the crystal lattice, so it is not obvious how to include vibrational entropy into methods for phase diagram calculations that are based on the energetic and statistical properties of local clusters of atoms.It would be particularly convenient if changes in the phonon density of states (DOS) could be assigned to changes in local atomic arrangements. The Einstein model for vibrational dynamics is easily included in mean-field calculations of free energy [4]; and vibrational effective cluster interactions, based on local atomic configurations, have been developed recently [6]. There is some evidence that the vibrational contribution to alloy thermodynamics may depend on short-range features of atomic arrangements. The ranges of interatomic force constants, obtained from the shapes of phonon dispersion curves, are typically not much larger than interatomic distances. Although phonons have many wavelengths, most of the phonons in a solid have high frequencies and short wavelengths. Nevertheless, there have been no experimental tests of how the phonon DOS depends on local atomic configurations of alloys. The present investigation was undertaken to measure the phonon partial density of states of 57 Fe atoms in bcc alloys of 57 Fe 3 Al. The alloys had well-characterized differences in chemical short-range order (SRO), so it was possible to correlate the phonon partial DOS to the local chemical environment of the 57 Fe atoms.Previous calorimetric measurements [7] found a difference of ͑0.1 6 0.03͒k B ͞atom in the vibrational entropies of chemically ordered and disordered Fe 3 Al, with the disordered alloy having the larger vibrational entropy. This difference in vibrational entro...

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Inelastic nuclear resonant scattering spectra of 57 Fe atoms were measured on crystalline alloys of Pt 3 57 Fe that were chemically disordered, partially ordered, and L1 2 ordered. Phonon partial density of states curves for 57 Fe were obtained from these spectra. Upon disordering, about 10% of the spectral intensity underwent a distinct shift from 25 to 19 meV. This change in optical modes accounted for most of the change of the vibrational entropy of disordering contributed by Fe atoms, which was (ϩ0.10 Ϯ 0.03͒ k B ͑Fe atom) Ϫ1 .Prospects for parametrizing the vibrational entropy with low-order cluster variables were assessed. To calculate the difference in vibrational entropy of the disordered and ordered alloys, the clusters must be large enough to account for the abundances of several of the atom configurations of the first-nearest-neighbor shell about the 57 Fe atoms.