Ab initio study of mechanical and thermal properties of GeTe-based and PbSe-based high-entropy chalcogenides

GeTe-based and PbSe-based high-entropy compounds have outstanding thermoelectric (TE) performance and crucial applications in mid and high temperatures. Recently, the optimization of TE performance of high-entropy compounds has been focused on reducing thermal conductivity by strengthening the phonon scattering process to improve TE performance. We report a first-principles investigation on nine GeTe-based high-entropy chalcogenide solid solutions constituted of eight metallic elements (Ag, Pb, Sb, Bi, Cu, Cd, Mn, and Sn) and 13 PbSe-based high-entropy chalcogenide solid solutions: Pb0.99-ySb0.012SnySe1-2xTexSx (x = 0.1, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and y = 0) and Pb0.99-ySb0.012SnySe1-2xTexSx (y = 0.05, 0.1, 0.15, 0.2, 0.25 and x = 0.25). We have investigated the mechanical properties focusing on Debye temperature (ΘD), thermal conductivity (κ), Grüneisen parameter (γα), dominant phonon wavelength (λdom), and melting temperature (Tm). We find that the lattice thermal conductivity is significantly reduced when GeTe is alloyed into the following compositions: Ge0.75Sb0.13Pb0.12Te, Ge0.61Ag0.11Sb0.13Pb0.12Bi0.01Te, and Ge0.61Ag0.11Sb0.13Pb0.12Mn0.05Bi0.01Te. This reduction is due to the mass increase and strain fluctuations. The results also show that Ge0.61Ag0.11Sb0.13Pb0.12Bi0.01Te solid solution has the lowest Young's modulus (30.362 GPa), bulk and shear moduli (18.626 and 12.359 GPa), average sound velocity (1653.128 m/sec), Debye temperature (151.689 K), lattice thermal conductivity (0.574 W.m-1.K-1), dominant phonon wavelength (0.692 Å), and melting temperature (535.91 K). Moreover, Ge0.61Ag0.11Sb0.13Pb0.12Bi0.01Te has the highest Grüneisen parameter with a reduced and temperature-independent lattice thermal conductivity. The positive correlation between ΘD and κ is revealed. Alloying of PbSe-based high-entropy by Sb, Sn, Te, and S atoms at the Se and Pb sites resulted in much higher shear strains resulted in the reduction of phonon velocity, a reduced ΘD, and a lower lattice thermal conductivity.

Lattice Softening Significantly Reduces Thermal Conductivity and Leads to High Thermoelectric Efficiency

The influence of micro/nanostructure on thermal conductivity is a topic of great scientific interest, particularly to thermoelectrics. The current understanding is that structural defects decrease thermal conductivity through phonon scattering where the phonon dispersion and speed of sound are assumed to remain constant. Experimental work on a PbTe model system is presented, which shows that the speed of sound linearly decreases with increased internal strain. This softening of the materials lattice completely accounts for the reduction in lattice thermal conductivity, without the introduction of additional phonon scattering mechanisms. Additionally, it is shown that a major contribution to the improvement in the thermoelectric figure of merit (zT > 2) of high-efficiency Na-doped PbTe can be attributed to lattice softening. While inhomogeneous internal strain fields are known to introduce phonon scattering centers, this study demonstrates that internal strain can modify phonon propagation speed as well. This presents new avenues to control lattice thermal conductivity, beyond phonon scattering. In practice, many engineering materials will exhibit both softening and scattering effects, as is shown in silicon. This work shines new light on studies of thermal conductivity in fields of energy materials, microelectronics, and nanoscale heat transfer.

An Ab Initio Study of Pressure-Induced Reversal of Elastically Stiff and Soft Directions in YN and ScN and Its Effect in Nanocomposites Containing These Nitrides

Using quantum-mechanical calculations of second- and third-order elastic constants for YN and ScN with the rock-salt (B1) structure, we predict that these materials change the fundamental type of their elastic anisotropy by rather moderate hydrostatic pressures of a few GPa. In particular, YN with its zero-pressure elastic anisotropy characterized by the Zener anisotropy ratio A Z = 2 C 44 / ( C 11 - C 12 ) = 1.046 becomes elastically isotropic at the hydrostatic pressure of 1.2 GPa. The lowest values of the Young's modulus (so-called soft directions) change from 〈100〉 (in the zero-pressure state) to the 〈111〉 directions (for pressures above 1.2 GPa). It means that the crystallographic orientations of stiffest (also called hard) elastic response and those of the softest one are reversed when comparing the zero-pressure state with that for pressures above the critical level. Qualitatively, the same type of reversal is predicted for ScN with the zero-pressure value of the Zener anisotropy factor A Z = 1.117 and the critical pressure of about 6.5 GPa. Our predictions are based on both second-order and third-order elastic constants determined for the zero-pressure state but the anisotropy change is then verified by explicit calculations of the second-order elastic constants for compressed states. Both materials are semiconductors in the whole range of studied pressures. Our phonon calculations further reveal that the change in the type of the elastic anisotropy has only a minor impact on the vibrational properties. Our simulations of biaxially strained states of YN demonstrate that a similar change in the elastic anisotropy can be achieved also under stress conditions appearing, for example, in coherently co-existing nanocomposites such as superlattices. Finally, after selecting ScN and PdN (both in B1 rock-salt structure) as a pair of suitable candidate materials for such a superlattice (due to the similarity of their lattice parameters), our calculations of such a coherent nanocomposite results again in a reversed elastic anisotropy (compared with the zero-pressure state of ScN).

Theoretical foundations of resonant ultrasound spectroscopy at high pressure

The theory of free-vibration acoustic resonance (FVAR) of solids at high pressure is developed within the framework of nonlinear elasticity and the calculus of variations. The FVAR state is formulated as a generalization of the conventional theory that was originally developed by Rayleigh and Ritz in the sense that it includes geometrical and material nonlinearities as well as the potential energy of external pressure. Magnetic point groups and quasi-harmonic approximation are used so as to obtain a natural extension of normal mode phonons in the high-pressure regime. The numerical analysis of eight different cubic-symmetry crystals reveals that FVAR frequencies depend linearly on the pressure, and the slopes vary with the FVAR modes, including the sign. We estimated the mode Grüneisen parameter up to N =2400 and proved that the high-frequency limit γ ∞ is equivalent to the conventional Grüneisen parameter γ . Quantitative agreement of the parameters demonstrates that nearly the entire third-order elastic constants tensor can be determined from high-pressure ultrasound spectroscopy experiments.