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 ...

The wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source (SNS) is optimized to provide a high neutron flux at the sample position with a large solid angle of detector coverage. The instrument incorporates modern neutron instrumentation, such as an elliptically focused neutron guide, high speed magnetic bearing choppers, and a massive array of (3)He linear position sensitive detectors. Novel features of the spectrometer include the use of a large gate valve between the sample and detector vacuum chambers and the placement of the detectors within the vacuum, both of which provide a window-free final flight path to minimize background scattering while allowing rapid changing of the sample and sample environment equipment. ARCS views the SNS decoupled ambient temperature water moderator, using neutrons with incident energy typically in the range from 15 to 1500 meV. This range, coupled with the large detector coverage, allows a wide variety of studies of excitations in condensed matter, such as lattice dynamics and magnetism, in both powder and single-crystal samples. Comparisons of early results to both analytical and Monte Carlo simulation of the instrument performance demonstrate that the instrument is operating as expected and its neutronic performance is understood. ARCS is currently in the SNS user program and continues to improve its scientific productivity by incorporating new instrumentation to increase the range of science covered and improve its effectiveness in data collection.

Thermal conductivity of the Earth's lower mantle greatly impacts the mantle convection style and affects the heat conduction from the core to the mantle. Direct laboratory measurement of thermal conductivity of mantle minerals remains a technical challenge at the pressure-temperature (P-T) conditions relevant to the lower mantle, and previously estimated values are extrapolated from low P-T data based on simple empirical thermal transport models. By using a numerical technique that combines first-principles electronic structure theory and Peierls-Boltzmann transport theory, we predict the lattice thermal conductivity of MgO, previously used to estimate the thermal conductivity in the Earth, at conditions from ambient to the core-mantle boundary (CMB). We show that our first-principles technique provides a realistic model for the P-T dependence of lattice thermal conductivity of MgO at conditions from ambient to the CMB, and we propose thermal conductivity profiles of MgO in the lower mantle based on geotherm models. The calculated conductivity increases from 15 -20 W∕K-m at the 670 km seismic discontinuity to 40 -50 W∕K-m at the CMB. This large depth variation in calculated thermal conductivity should be included in models of mantle convection, which has been traditionally studied based on the assumption of constant conductivity.first-principles | phonon transport theory | phonon lifetime | high pressure | Lower Mantle T hermal conductivity (κ) is one of the most important mineral properties in determining the heat budget of the Earth. Heat in the Earth's interior is transferred by convection in the mantle and core and regulated by conduction at thermal boundary layers. As defined by Fourier's law of heat conduction J Q ¼ −κ · ∇T, determines the conducting heat flow density (J Q ) in the presence of a temperature gradient ∇T. κ also appears in the Rayleigh number, which measures the convective vigor of a system. Thus, the thermal conductivity of the lower mantle affects the structure, thickness, and dynamics of the CMB (1, 2), the style and structure of mantle convection (3-5), and the amount of heat conducted from the core to the mantle (6) that in turn influences the generation of the Earth's magnetic field (7).Despite its importance, thermal conductivity remains as one of the least constrained physical properties of minerals, especially at lower-mantle pressures (P) and temperatures (T) and approximately 1,900-4,000 K (9-12). Experimental data at deep mantle conditions are scarce due to the technical difficulty of measuring thermal conductivity at these extremes. Thermal conductivity of lower-mantle minerals is often estimated either by extrapolating data from lower P-T conditions and/or employing theoretical models with parameters fitted with lower P-T data (1, 13). However, direct extrapolation to deep mantle conditions can be unreliable beyond the P-Trange of the measurements, and empirical models are often based on untested assumptions. For example, the sound velocities are used to approximate phonon vel...

Raman spectra of rutile titanium dioxide (TiO 2 ) were measured at temperatures from 100 K to 1150 K. Each Raman mode showed unique changes with temperature. Beyond the volume-dependent quasiharmonicity, the explicit anharmonicity was large. A new method was developed to fit the thermal broadenings and shifts of Raman peaks with a full calculation of the kinematics of 3-phonon and 4-phonon processes, allowing the cubic and quartic components of the anharmonicity to be identified for each Raman mode. A dominant role of phonon-phonon kinematics on phonon shifts and broadenings is reported. Force field molecular dynamics (MD) calculations with the Fourier-transformed velocity autocorrelation method were also used to perform a quantitative study of anharmonic effects, successfully accounting for the anomalous phonon anharmonicity of the B 1g mode.