Soft manifold dynamics behind negative thermal expansion

Entropic elasticity and negative thermal expansion in a simple cubic crystal

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF₃, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.

Negative Thermal Expansion Near the Precipice of Structural Stability in Open Perovskites

Negative thermal expansion (NTE) describes the anomalous propensity of materials to shrink when heated. Since its discovery, the NTE effect has been found in a wide variety of materials with an array of magnetic, electronic and structural properties. In some cases, the NTE originates from phase competition arising from the electronic or magnetic degrees of freedom but we here focus on a particular class of NTE which originates from intrinsic dynamical origins related to the lattice degrees of freedom, a property we term structural negative thermal expansion (SNTE). Here we review some select cases of NTE which strictly arise from anharmonic phonon dynamics, with a focus on open perovskite lattices. We find that NTE is often present close in proximity to competing structural phases, with structural phase transition lines terminating near T=0 K yielding the most prominent displays of the SNTE effect. We further provide a theoretical model to make precise the proposed relationship among the signature behavior of SNTE, the proximity of these systems to structural quantum phase transitions and the effects of phase fluctuations near these unique regions of the structural phase diagram. The effects of compositional disorder on NTE and structural phase stability in perovskites are discussed.

Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation

Negative thermal expansion (NTE) is the phenomenon in which materials shrink rather than expand on heating. Although NTE had been previously observed in a few simple materials at low temperature, it was the realisation in 1996 that some materials have NTE over very wide ranges of temperature that kick-started current interest in this phenomenon. Now, nearly two decades later, a number of families of ceramic NTE materials have been identified. Increasingly quantitative studies focus on the mechanism of NTE, through techniques such as high-pressure diffraction, local structure probes, inelastic neutron scattering and atomistic simulation. In this paper we review our understanding of vibrational mechanisms of NTE for a range of materials. We identify a number of different cases, some of which involve a small number of phonons that can be described as involving rotations of rigid polyhedral groups of atoms, others where there are large bands of phonons involved, and some where the transverse acoustic modes provide the main contribution to NTE. In a few cases the elasticity of NTE materials has been studied under pressure, identifying an elastic softening under pressure. We propose that this property, called pressure-induced softening, is closely linked to NTE, which we can demonstrate using a simple model to describe NTE materials. There has also been recent interest in the role of intrinsic anharmonic interactions on NTE, particularly guided by calculations of the potential energy wells for relevant phonons. We review these effects, and show how anhamonicity affects the response of the properties of NTE materials to pressure.

Probing the Mott physics in κ-(BEDT-TTF)₂X salts via thermal expansion

In the field of interacting electron systems the Mott metal-to-insulator (MI) transition represents one of the pivotal issues. The role played by lattice degrees of freedom for the Mott MI transition and the Mott criticality in a variety of materials are current topics under debate. In this context, molecular conductors of the κ-(BEDT-TTF)2X type constitute a class of materials for unraveling several aspects of the Mott physics. In this review, we present a synopsis of literature results with focus on recent expansivity measurements probing the Mott MI transition in this class of materials. Progress in the description of the Mott critical behavior is also addressed.

Structural relationship between negative thermal expansion and quartic anharmonicity of cubic ScF3

Cubic scandium trifluoride (ScF3) 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 ScF3 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 DO9 structure of ScF3, and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion.

Angular behavior of the Berreman effect investigated in uniform Al2O3 layers formed by atomic layer deposition

Experimental transmission absorbance infrared spectra of γ-Al(2)O(3) showing evidence of the angular dependence of the peaks of surface modes appearing next to the longitudinal optical phonon frequency ω(LO) (the Berreman effect) are collected from heat-treated thin oxide films deposited with thickness uniformity on Si(100) using atomic layer deposition. The peak area of the most intense surface longitudinal optical mode is plotted versus the infrared beam incidence angle θ(0). The experimental points closely follow the sin(4)(θ(0)) function in a broad thickness range. The best match occurs at a critical thickness, where a linear relationship exists between the surface longitudinal optical mode intensity and film thickness. Simulations suggest that below the critical thickness the sin(4)(θ(0)) behavior can be explained by refraction phenomena at the air/thin film and thin film/substrate interfaces. Above the critical thickness, the experimentally obtained result is derived from field boundary conditions at the air/thin film interface. The sin(4)(θ(0)) functional trend breaks down far above the critical thickness. This picture indicates that infrared radiation has a limited penetration depth into the oxide film, similarly to electromagnetic waves in conductors. Consequently, surface longitudinal optical modes are viewed as bulk phonons excited down to the penetration depth of the infrared beam. Comparison with simulated data suggests that the infrared radiation absorptance of surface longitudinal optical modes tends to approach the sin(2)(θ(0)) trend. Reflection phenomena are considered to be the origin of the deviation from the sin(4)(θ(0)) trend related to refraction.

Phonon response in the infrared region to thickness of oxide films formed by atomic layer deposition

Experimental transmission infrared spectra of gamma-Al(2)O(3) and ZnO films are collected from heat-treated thin oxide films deposited with uniform thickness on Si(100) using atomic layer deposition. We show that the Berreman thickness, i.e. the upper limit for a linear relationship between oxide film thickness and phonon absorbance in the infrared region in transmission configuration, is a concept that applies to both transverse and longitudinal optical phonons. We find that for aluminum oxide films the Berreman thickness is 125 nm, and we estimate that it is around approximately 435 nm for zinc oxide films. Combining experiment and simulation, we also show that the Berreman thickness is the maximum distance allowed between interfaces for Snell's law and Fresnel's formulas to determine the optical properties in the infrared region and in transmission configuration for a layer system including an oxide film. Below the Berreman thickness, a Taylor series expansion of the absorbance coefficient determines the linear relationship between phonon absorbance and oxide film thickness t, so that as t --> 0 absorption A(p) is proportional to 4pi omega(ph)t, where omega(ph) indicates optical phonon frequency. Above the Berreman thickness, field boundary conditions at the air/oxide film interface effectively contribute with a single interface in explaining optical phonon absorbance. Preliminary infrared spectra in reflection configuration for gamma-Al(2)O(3)/Si(100) are discussed, and the obtained data support the conclusions reported for the transmission configuration.