skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Elastic Moduli: a Tool for Understanding Chemical Bonding and Thermal Transport in Thermoelectric Materials
Abstract The elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli—directly tied to sound velocity—is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high‐temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.  more » « less
Award ID(s):
2118463
PAR ID:
10418675
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Angewandte Chemie
Volume:
135
Issue:
12
ISSN:
0044-8249
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Superionic conductors, includingACrX2(A=Ag, Cu; X = S, Se) compounds, have attracted attention due to their low lattice thermal conductivity and high ionic conductivity. These properties are driven by structural characteristics such as anharmonicity, soft bonding, and disorder, which enhance both fast ion transport and thermal resistance. In the present study, we investigate the impact of various factors (e.g.A-site disorder, microstructure, speed of sound and chemical composition) on the thermal conductivity of the compounds CuCrS2, CuCrSe2, AgCrS2and AgCrSe2. The samples were synthesized using solid state reaction, ball milling and subsequent spark plasma sintering, and thermal diffusivity, electrical resistivity, Hall coefficients and Seebeck coefficients were measured as a function of temperature. The selenides were found to behave as degenerate semiconductors, with reasonable thermoelectric figure of merit (up to 0.79 in CuCrSe2), while the sulfides behaved as non-degenerate semiconductors with high electrical resistivity. At room temperature, all samples are in the ordered phase and show low lattice thermal conductivity ranging from 0.60 W m−1-K in AgCrSe2to 1.1 W m−1-K in CuCrSe2. Little reduction in lattice thermal conductivity was observed in the high-temperature phase, despite the increased disorder on the cation site and the onset of superionic conductivity. This suggests that the low lattice thermal conductivity inACrX2compounds is an inherent property of the crystal structure, caused by anharmonic bonding and diffuson dominated transport. 
    more » « less
  2. null (Ed.)
    Accurate density functional theory calculations of the interrelated properties of thermoelectric materials entail high computational cost, especially as crystal structures increase in complexity and size. New methods involving ab initio scattering and transport (AMSET) and compressive sensing lattice dynamics are used to compute the transport properties of quaternary CaAl 2 Si 2 -type rare-earth phosphides RECuZnP 2 (RE = Pr, Nd, Er), which were identified to be promising thermoelectrics from high-throughput screening of 20 000 disordered compounds. Experimental measurements of the transport properties agree well with the computed values. Compounds with stiff bulk moduli (>80 GPa) and high speeds of sound (>3500 m s −1 ) such as RECuZnP 2 are typically dismissed as thermoelectric materials because they are expected to exhibit high lattice thermal conductivity. However, RECuZnP 2 exhibits not only low electrical resistivity, but also low lattice thermal conductivity (∼1 W m −1 K −1 ). Contrary to prior assumptions, polar-optical phonon scattering was revealed by AMSET to be the primary mechanism limiting the electronic mobility of these compounds, raising questions about existing assumptions of scattering mechanisms in this class of thermoelectric materials. The resulting thermoelectric performance ( zT of 0.5 for ErCuZnP 2 at 800 K) is among the best observed in phosphides and can likely be improved with further optimization. 
    more » « less
  3. We introduce a lattice dynamics package which calculates elastic, thermodynamic and thermal transport properties of crystalline materials from data on their force and potential energy as a function of atomic positions. The data can come from density functional theory (DFT) calculations or classical molecular dynamics runs performed in a supercell. First, the model potential parameters, which are anharmonic force constants are extracted from the latter runs. Then, once the anharmonic model is defined, thermal conductivity and equilibrium properties at finite temperatures can be computed using lattice dynamics, Boltzmann transport theories, and a variational principle respectively. In addition, the software calculates the mechanical properties such as elastic tensor, Gruneisen parameters and the thermal expansion coefficient within the quasi-harmonic approximation (QHA). Phonons, elastic constants and thermodynamic properties results applied to the germanium crystal will be illustrated. Using the force constants as a force field, one may also perform molecular dynamics (MD) simulations in order to investigate the combined effects of anharmonicity and defect scattering beyond perturbation theory. 
    more » « less
  4. Abstract This article attempts to summarize our understanding of heat flow in different solid materials and its relationship to atomistic structure of materials. This knowledge can be used to understand and design materials for electricity generation or cooling through the thermoelectric effect. We start with the fundamentals of heat transport in solids: mechanisms of phonon scattering in crystals, the role of interfaces and coherence, and the relationship between chemical bonding and heat transport will be elucidated. Theories used to model thermal conductivity of solids will be exposed next. They include the Green–Kubo formulation, Boltzmann transport equation and its recent quantum extensions, and Allen–Feldman theory of heat diffusion in noncrystalline solids and its recent extensions. In terms of phenomenology, we will distinguish between the kinetic regime based on independent single carriers and the collective or hydrodynamic one which occurs when normal or momentum-conserving processes dominate. Next, we will focus on advanced measurement and characterization techniques, and the knowledge extracted from them. Nanoscale thermal conductivity methods, such as the pump-probe thermoreflectance methods (TDTR/FDTR), have become fairly common allowing researchers to measure thermal conductivity of thin-film thermoelectrics. We will review recent advances of the method: the Gibbs excess approach, which measures thermal resistance across a grain boundary of polycrystals through mapping TDTR/FDTR measurements, and the transient Raman method, where pump-probe Raman spectroscopy realizes in-plane thermal conductivity measurements of two-dimensional materials even on a substrate. We will also review the progress in mode-resolved phonon property measurements, such as inelastic x-ray scattering for thin-film samples, which allows direct observation of the modulation of phonon band and lifetime by nanostructures, and thermal diffuse scattering for quick characterization of phonon dispersion relations. Finally, because the main focus of this issue is thermoelectrics, we will review different classes of materials and strategies to lower their thermal conductivities. Graphical abstract 
    more » « less
  5. Abstract The lattice thermal conductivity ( κ L ) of the monolayers of partial group-VA elements and binary compounds are systemically investigated by the first-principles calculations and phonon Boltzmann transport equation (PBTE), including aW-antimonene, α -arsenene, black phosphorus, α -SbAs, α -SbP and α -AsP. The κ L values decrease with the increasing of atomic mass for these materials with similar geometry and valence structures. It is ascribed to phonon branches softening, low phonon group velocity, and large Grüneisen parameters. Due to the neutralization of phonon group velocity and phonon lifetime, κ L of binary compounds is between their corresponding elements. As the atomic radius and mass increase, the bond strength and the phonon group velocity decreases. Furthermore, the dimensionless parameter γ 2 / A , which comes from the Slack equation and only has the dependence of Grüneisen parameter, grows up with the atomic mass rising, which indicates that a larger anharmonicity is present in the heavier V-V monolayers. For SbAs and SbP compounds, the thermal conductivity anisotropy mainly results from the anisotropy of elastic coefficients along armchair and zigzag directions. Our results highlight the impact of atomic arrangement on the thermal conductivity of group VA binary compounds. This work paves a way to modulate the thermal conductivity of 2D VA elements by incorporation atoms with suitable mass and may guide to improve thermoelectrical performance via the alloying method. 
    more » « less