Inherent Anharmonicity of Harmonic Solids

Journal Article · Fri Apr 29 00:00:00 EDT 2022 · Research

DOI:https://doi.org/10.34133/2022/9786705· OSTI ID:1865989

Agne, Matthias T.  ^[1]; Anand, Shashwat  ^[1]; Snyder, G. Jeffrey  ^[1]

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1. Department Materials Science and Engineering, Northwestern University, Evanston, IL, USA

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest-order, harmonic , approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to nonlinear, anharmonic , interactions. Here, we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter $\gamma$ , which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter as $\gamma \approx \left(3/2\right)\left(3-4x^2\right)/\left(1+2x^2\right)$ , where $x=v_{\text{t}}/v_{\text{l}}$ is the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new material engineering design metrics.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-76SF00515
• OSTI ID: 1865989
• Journal Information: Research, Journal Name: Research Vol. 2022; ISSN 2639-5274
• Publisher: American Association for the Advancement of Science (AAAS)
• Country of Publication: United States
• Language: English