On the Thermal Expansion of Solids

Phonon anharmonicity in binary chalcogenides for efficient energy harvesting

Thermoelectric (TE) materials have received much attention due to their ability to harvest waste heat energy. TE materials must exhibit a low thermal conductivity (κ) and a high power factor (PF) for efficient conversion. Both factors define the figure of merit (ZT) of the TE material, which can be increased by suppressing κ without degrading the PF. Recently, binary chalcogenides such as SnSe, GeTe, and PbTe have emerged as attractive candidates for thermoelectric energy generation at moderately high temperatures. These materials possess simple crystal structures with low κ in their pristine forms, which can be further lowered through doping and other approaches. Here, we review the recent advances in the temperature-dependent behavior of phonons and their influence on the thermal transport properties of chalcogenide-based TE materials. Because phonon anharmonicity is one of the fundamental contributing factors for low thermal conductivity in SnSe, Sb-doped GeTe, and related chalcogenides, we discuss complementary experimental approaches such as temperature-dependent Raman spectroscopy, inelastic neutron scattering, and calorimetry to measure anharmonicity. We further show how data gathered using multiple techniques helps us understand and engineer better TE materials. Finally, we discuss the rise of machine learning-aided efforts to discover, design, and synthesize TE materials of the future.

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.

Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so on. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a "perfect" NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

Raman scattering study of InAs nanowires under high pressure

The pressure-dependent phonon modes of InAs nanowires have been investigated by Raman spectroscopy under high pressure up to ∼58 GPa. X-ray diffraction measurements show that InAs nanowires at 21 GPa exhibit a phase transition from a wurtzite to an orthorhombic crystal structure, with a corresponding drastic change in the first-order Raman spectra. In the low-pressure regime, a linear increase in phonon frequencies is observed, whereas splitting between longitudinal and transversal optical phonon modes decreases as a function of applied pressure. The calculated mode Grüneisen parameters and Born's transverse effective charge indicate that the wurtzite InAs nanowires exhibit a more covalent nature under compression.

Temperature variation of the effective Grüneisen parameter in caesium chloride structures

A systematic investigation of the temperature variation of the effective Grüneisen parameter, γ eff. , has been carried out for the caesium chloride structure, on a model incorporating the Coulomb potential between the ions and a nearest neighbour interaction varying as r -n . As the value of n is increased from 8 to 30, the low temperature limit γ 0 of γ eff. is progressively reduced, while the high temperature limit γ ∞ increases. The value of γ 0 — γ ∞ is positive for n ≤ 15 and changes sign for n ≥ 20. Thus the trend and the extent of the temperature variation of γ eff. are sensitive to the value of n in the caesium chloride lattice. On the other hand in the NaCl lattice, the trend of the temperature variation of γ eff. is not affected by a variation of n . For n ≈ 16, the γ eff. value appears to be independent of temperature, though the individual Grüneisen parameters for the lattice frequencies vary widely. This case is an example of a type of perfect Grüneisen solid, the condition for the existence of which was given by Blackman. The Houston method with a constant normalization factor is shown to yield the correct trend of the temperature variation of γ eff. . A more elaborate normalization procedure alters the γ eff. values only slightly. Varying the ratio of the ionic masses has only a slight effect on γ( p ) and γ eff. . From the recently measured elastic data, it appears probable that the value of n pertinent to the caesium halides is about 15. n may increase slightly with increasing size of the anion. If this value of n is correct, the effective Gruneisen parameters for the caesium halides must vary only slightly with temperature. Probably one of the caesium halides will exhibit closely the behaviour of a perfect Grüneisen solid.

Anharmonic interactions in alkali halides. I

Calculations of the Griineisen parameters of individual modes of vibration, of the average Griineisen parameter, and of the temperature dependence of the elastic constants, of sodium iodide and potassium bromide have given reasonable agreement with experiment. The model used was a shell model, obtained from experimental measurements of the dispersion curves, extended in a simple way to include the anharmonicity. Calculations have also been made of the spectral functions of some of the normal modes propagating in the [111] direction. These show qualitative agreement with experiment in that the longitudinal optic modes are particularly temperature dependent. The results are used to discuss the validity and usefulness of a quasi-harmonic approximation in which the frequencies are those measured experimentally. The optical constants and the reflectivity of the crystals have also been calculated and are compared with experiment.

The thermal expansion of alkali halides at low temperatures

Linear thermal expansions of eight alkali halides have been determined at liquid oxygen temperatures and at temperatures from 30 °K down to 2 °K. For temperaturesT≤ θ/20, where θ is the Debye temperature, the expansion coefficients are well represented by α =AT3+BT5. Values are reported for the Grüneisen parameter γ = 3αV/Cx, whereC/Vis the heat capacity per unit volume and x is the compressibility. For CsBr (b.c.c. structure) γ appears to be nearly independent of temperature, with a value of 2·0 but for the other crystals, which have the rock-salt structure, the parameter γ varies with temperature, chiefly betw een θ/10 and θ/5. At room temperature, γ lies between 1·45 and 1·7 but at low temperature this generally decreases to a value γ0which isca.—0·1 for RbI, +0·3 for KCl, KBr and KI and 1·0 for NaCl and Nal; LiF does not show this decrease, γ0being 1·7. The values observed for γ0are compared with those calculated from elastic constants and their pressure derivatives and the general behaviour of γ(T) is observed to conform qualitatively to the predictions of simple theoretical models of Born, Blackman and Barron.

Spectroscopic mode Grüneisen parameters for diamond

Room temperature measurements are reported of the first and second order Raman spectra of diamond in the hydrostatic pressure range 0-2.4 GPa. Values calculated from the data for the optic mode Grüneisen parameters have been fitted in terms of a simple lattice dynamical model for diamond involving volume dependent interatomic forces. The interpolated set of mode Grüneisen parameters are shown to be in substantial agreement with thermodynamic data. The simple model for the anharmonicity of the interatomic forces in the diamond group materials is shown to provide a qualitative explanation for the contrasting low temperature behaviour of the thermal expansion exhibited by these materials.