Cubic scandium trifluoride (ScF 3 ) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF 3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO 9 structure of ScF 3 , and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion. DOI: 10.1103/PhysRevLett.107.195504 PACS numbers: 63.20.Ry, 63.20.DÀ, 65.40.De, 78.70.Nx Nearly all materials expand when heated, so exceptions are interesting. Negative thermal expansion (NTE) of a pure phase has attracted much attention over the past 20 years, driven both by curiosity, and by opportunities to design materials with special thermal properties. For materials like face-centered cubic plutonium and Invar alloys, NTE involves electronic or magnetic excitations. Other types of NTE are structure induced, originating from atom arrangements in the crystal [1]. Several mechanisms of NTE have been proposed, such as deformations of polyhedra, one-or two-dimensional NTE caused by normal thermal expansion of anisotropic bonds, NTE induced by interstitial cations, and NTE associated with transverse motions of linkage atoms (as in Fig. 1) [2,3]. Often NTE is anisotropic, and it usually occurs only in a small range of temperature [4]. Zirconium tungstate (ZrW 2 O 8 ) is a notable exception [5][6][7][8][9][10]. The NTE in ZrW 2 O 8 is associated with under-constrained atom sites in the crystal structure [11]. Although some of the behavior can be understood with a ''quasiharmonic'' model (a harmonic model with interatomic forces adapted to the bond lengths at a given temperature), anharmonic effects are expected, but the full connection between anharmonic lattice dynamics and NTE is obscured by the complexity of the structure [11]. Simplified models like a rigid square [12,13], a 3-atom Bravais lattice [11], and a rigid structure [14] have been used to explain the ''soft-phonon'' NTE mechanism, but accurate lattice dynamics for materials such as ZrW 2 O 8 are not easy to obtain from geometrical models.Very recently, a surprisingly large and isotropic negative thermal expansion was discovered in cubic scandium trifluoride (ScF 3 ) by Greve et al. [15]. It occurs over a wide range of temperature from 10 to about 1100 K, and exceeds À1:0 Â 10 À5 K À1 . Under ambient conditions, ScF 3 has the DO 9 crystal structure of -ReO 3 , shown in Fig. 1, and is stable from 10 to over 1600 K. Although À ReO 3 itself shows modest negative thermal expansion below 300 K [16,17], the ...

We describe the design, construction, calibration, and operation of a relatively simple differential capacitive dilatometer suitable for measurements of thermal expansion and magnetostriction from 300 K to below 1 K with a low-temperature resolution of about 0.05Å. The design is characterized by an open architecture permitting measurements on small samples with a variety of shapes. Dilatometers of this design have operated successfully with a commercial physical property measurement system, with several types of cryogenic refrigeration systems, in vacuum, in helium exchange gas, and while immersed in liquid helium (magnetostriction only) to temperatures of 30 mK and in magnetic fields to 45 T.

Dilation and thermopower measurements on YbAgGe, a heavy-fermion antiferromagnet, clarify and refine the magnetic field-temperature (H-T) phase diagram and reveal a field-induced phase with T-linear resistivity. On the low-H side of this phase we find evidence for a first-order transition and suggest that YbAgGe at 4.5 T may be close to a quantum critical end point. On the high-H side our results are consistent with a second-order transition suppressed to a quantum critical point near 7.2 T. We discuss these results in light of global phase diagrams proposed for Kondo lattice systems

Because of its widespread applications in materials science and geophysics, SiO_{2} has been extensively examined under shock compression. Both quartz and fused silica transform through a so-called "mixed-phase region" to a dense, low compressibility high-pressure phase. For decades, the nature of this phase has been a subject of debate. Proposed structures include crystalline stishovite, another high-pressure crystalline phase, or a dense amorphous phase. Here we use plate-impact experiments and pulsed synchrotron x-ray diffraction to examine the structure of fused silica shock compressed to 63 GPa. In contrast to recent laser-driven compression experiments, we find that fused silica adopts a dense amorphous structure at 34 GPa and below. When compressed above 34 GPa, fused silica transforms to untextured polycrystalline stishovite. Our results can explain previously ambiguous features of the shock-compression behavior of fused silica and are consistent with recent molecular dynamics simulations. Stishovite grain sizes are estimated to be ∼5-30  nm for compression over a few hundred nanosecond time scale.

Phonon densities of states (DOS) of bcc α-57 Fe were measured from room temperature through the 1044K Curie transition and the 1185K 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 700K, 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 Kármán 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.