Thermal conductivity under pressure and through phase transitions in solid alkali halides. I. Experimental results for KCl, KBr, KI, RbCl, RbBr and RbI

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier’s law; (3) Stefan–Boltzmann’s law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (P𝜕V) in a PFES arises from internal interatomic forces, which are linked to Young’s modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: 𝜕ln(cP)/𝜕P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered.

High-Temperature Chloride-Carbonate Phase Change Material: Thermal Performances and Modelling of a Packed Bed Storage System for Concentrating Solar Power Plants

Molten salts eutectics are promising candidates as phase change materials (PCMs) for thermal storage applications, especially considering the possibility to store and release heat at high temperatures. Although many compounds have been proposed for this purpose in the scientific literature, very few data are available regarding actual applications. In particular, there is a lack of information concerning thermal storage at temperatures around 600 °C, necessary for the coupling with a highly efficient Rankine cycle powered by concentrated solar power (CSP) plants. In this contest, the present work deals with a thermophysical behavior investigation of a storage heat exchanger containing a cost-effective and safe ternary eutectic, consisting of sodium chloride, potassium chloride, and sodium carbonate. This material was preliminarily and properly selected and characterized to comply with the necessary melting temperature and latent enthalpy. Then, an indirect heat exchanger was considered for the simulation, assuming aluminum capsules to confine the PCM, thus obtaining the maximum possible heat exchange surface and air at 5 bar as heat transfer fluid (HTF). The modelling was carried out setting the inlet and outlet air temperatures at, respectively, 290 °C and 550 °C, obtaining a realistic storage efficiency of around 0.6. Finally, a conservative investment cost was estimated for the storage system, demonstrating a real possible economic benefit in using these types of materials and heat exchange geometries, with the results varying, according to possible manufacturing prices, in a range from 25 to 40 EUR/kWh.

Exposing the hidden influence of selection rules on phonon-phonon scattering by pressure and temperature tuning

Selection rules act to restrict the intrinsic anharmonic interactions between phonons in all crystals. Yet their influence on phonon propagation is hidden in most materials and so, hard to interrogate experimentally. Using ab initio calculations, we show that the otherwise invisible impact of selection rules on three-phonon scattering can be exposed through anomalous signatures in the pressure (P) and temperature (T) dependence of the thermal conductivities, κ, of certain compounds. Boron phosphide reveals such underlying behavior through an exceptionally sharp initial rise in κ with increasing P, which may be the steepest of any material, and also a peak and decrease in κ at high P. These features are in stark contrast to the measured behavior for many solids, and they occur at experimentally accessible conditions. These findings give a deep understanding of phonon lifetimes and heat conduction in solids, and motivate experimental efforts to observe the predicted behavior.

Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D_∞(T)[1 − exp(−bL)]. When L is several mm, D_∞(T) = FT^−G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D_∞^−0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(c_P)/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.

Non-monotonic pressure dependence of the thermal conductivity of boron arsenide

Recent experiments demonstrate that boron arsenide (BAs) is a showcase material to study the role of higher-order four-phonon interactions in affecting heat conduction in semiconductors. Here we use first-principles calculations to identify a phenomenon in BAs and a related material - boron antimonide, that has never been predicted or experimentally observed for any other material: competing responses of three-phonon and four-phonon interactions to pressure rise cause a non-monotonic pressure dependence of thermal conductivity, κ, which first increases similar to most materials and then decreases. The resulting peak in κ shows a strong temperature dependence from rapid strengthening of four-phonon interactions relative to three-phonon processes with temperature. Our results reveal pressure as a knob to tune the interplay between the competing phonon scattering mechanisms in BAs and similar compounds, and provide clear experimental guidelines for observation in a readily accessible measurement regime.

Thermal properties of materials are driven by complex many-body interactions among thermal atomic vibrations called phonons. Here the authors show, from first-principles, that a full description of the unusual thermal behaviour in boron arsenide requires considering often-neglected four-phonon interactions.

Single-crystal Brillouin spectroscopy with CO2 laser heating and variable q

We describe a Brillouin spectroscopy system integrated with CO2 laser-heating and Raman spectroscopic capabilities. Temperature is determined by measurements of the grey-body thermal radiation emitted by the hot sample, with the system response calibrated relative to a standard tungsten ribbon lamp. High-pressure laser-heating Brillouin scattering measurements of acoustic velocities on liquid water and ice compressed in a diamond-anvil cell were performed at temperatures up to 2500 ± 150 K at high pressure. Single-crystal laser-heating Brillouin measurements were made on the (111) plane of San Carlos olivine at ∼13 GPa, 1300 ± 200 K. The pressure as measured by ruby fluorescence is shown to be within ±0.5 GPa of the pressure on the olivine sample during laser heating when KCl and KBr are used as pressure-transmitting media. In addition, the system is designed for continuously variable scattering angles from forward scattering (near 0° scattering angle) up to near back scattering (∼141°). This novel setup allows us to probe a wide range of wave vectors q for investigation of phonon dispersion on, for example, crystals with large unit cells (on the scale of hundreds of nm).