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.

We combined laser shock compression with in situ x-ray diffraction, to probe the crystallographic state of gold (Au) on it's principal shock Hugoniot. Au has long been recognized as an important calibration standard in diamond anvil cell experiments due to the stability of its face-centered cubic (fcc) structure to extremely high pressures (P >600 GPa at 300 K). This is in contrast to density functional theory and first principles calculations of the high-pressure phases of Au that predict a variety of fcc-like structures with different stacking arrangements at intermediate pressures. In this work, we probe high-pressure and high-temperature conditions on the shock Hugoniot and observe fcc Au at 169 GPa and the first evidence of body-centered cubic (bcc) Au at 223 GPa. Upon further compression, the bcc phase is observed in coexistence with liquid scattering as the Hugoniot crosses the Au melt curve before 322 GPa. The results suggest a triple point on the Au phase diagram that lies very close to the principal shock Hugoniot near ∼ 220 GPa.

The behavior of silicon carbide, SiC, under shock compression is of interest due to its applications as a high-strength ceramic and for general understanding of shock-induced polymorphism. Here we used the Matter in Extreme Conditions beamline of the Linac Coherent Light Source to carry out a series of time-resolved pump-probe x-ray diffraction measurements on SiC laser-shocked as high as 206 GPa. Experiments on single crystals and polycrystals of different polytypes show a transformation from a low-pressure tetrahedral phase to the high-pressure rocksalt-type (B1) structure. We directly observe coexistence of the low-and high-pressure phases in a mixed-phase region and complete transformation to the B1 phase above 2 Mbar. The densities measured by x-ray diffraction are in agreement with both continuum gas-gun studies and a theoretical B1 Hugoniot derived from static-compression data. Time-resolved measurements during shock loading and release reveal a large hysteresis on unloading with the B1 phase retained to as low at 5 GPa. The sample eventually reverts to a mixture of polytypes of the low-pressure phase at late times. Our study demonstrates that x-ray diffraction is an effective means to characterize the time-dependent structural response of materials undergoing shock-induced phase transformations at megabar pressures.

Because of its far-reaching applications in geophysics and materials science, quartz has been one of the most extensively examined materials under dynamic compression. Despite 50 years of active research, questions remain concerning the structure and transformation of SiO2 under shock compression. Continuum gas-gun studies have established that under shock loading quartz transforms through an assumed mixed-phase region to a dense high-pressure phase. While it has often been assumed that this high-pressure phase corresponds to the stishovite structure observed in static experiments, there have been no crystal structure data confirming this. In this study, we use gas-gun shock compression coupled with in situ synchrotron x-ray diffraction to interrogate the crystal structure of shock-compressed α-quartz up to 65 GPa. Our results reveal that α-quartz undergoes a phase transformation to a disordered metastable phase as opposed to crystalline stishovite or an amorphous structure, challenging long-standing assumptions about the dynamic response of this fundamental material.