Structural Relationship between Negative Thermal Expansion and Quartic Anharmonicity of CubicScF3

Abstract

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 ...

Formation of Nets of Corner-Shared Bicapped Gold Squares in SrAu3Ge: How a BaAl4-Type Derivative Reconciles Fewer Valence Electrons and the Origin of Its Uniaxial Negative Thermal Expansion

“…The unique NTE mechanism of SrAu 3 Ge may also be a great playground for further theoretical studies. 15 ■ ASSOCIATED CONTENT…”

“…The simple structure of SrAu 3 Ge, with only four independent atoms in a unit cell, also may be a great playground for further study of NTE in theory. 15 ■ EXPERIMENTAL SECTION Synthesis. All manipulations were performed in a N 2 -filled glovebox (H 2 O < 0.1 ppmv).…”

“…also play pronounced roles in structural stabilization, for example, for CaAu 2 Si 2 (12), CaAuAl 3 (12), RAl 2 Ga 2 (R = rare-earth metal) (15), and SrAl 2 Pb 2 (16). 34 Zheng and Hoffmann 12 have demonstrated by means of EHTB bonding analyses that the CeMg 2 Si 2 type structure is predicted to be more stable than the BaAl 4 type for typical analogues with large vec values (≥15); vice versa, BaAl 4 structures are more stable than CeMg 2 Si 2 at vec ≤ 15.…”

Electronic structure of cubic ScF3 from first-principles calculations

“…The phonon properties of ScF 3 have been studied using a combination of inelastic neutron scattering experiment with ab initio calculations of lattice dynamics [7]. It was shown that a description of NTE within the quasi-harmonic approximation is not reliable in the case of ScF 3 .…”

“…[4]. Two chargetransfer-type satellites, the first one at about 13 eV below the main peaks in the valence-band and the second one with an energy separation of about 9-10 eV, were observed and indicate the strong hybridization effect between Sc 3d and F 2p states [4].The phonon properties of ScF 3 have been studied using a combination of inelastic neutron scattering experiment with ab initio calculations of lattice dynamics [7]. It was shown that a description of NTE within the quasi-harmonic approximation is not reliable in the case of ScF 3 .…”