Understanding the origin of the particularly small and anisotropic thermal expansion of MOF-74

TL;DR

This study explains the unusually small and anisotropic thermal expansion in MOF-74 by combining experimental x-ray diffraction with advanced theoretical calculations, revealing phonon contributions and stress-strain interactions.

Contribution

It provides a detailed microscopic understanding of the phonon and stress-strain mechanisms behind MOF-74's unique thermal expansion behavior, combining experimental and theoretical approaches.

Findings

MOF-74 exhibits small negative and positive thermal expansion coefficients.

Thermal expansion is influenced by stress-strain coupling and low mean Gr"uneisen tensor elements.

Only low-frequency phonon modes significantly contribute to thermal expansion.

Abstract

Metal-organic frameworks often display large positive or negative thermal expansion coefficients. MOF-74, a material envisioned for many applications does not display such a behavior. For this system, temperature-dependent x-ray diffraction reveals particularly small negative thermal expansion coefficients perpendicular and positive ones parallel to the hexagonally arranged pores. The observed trends are explained by combining state-of-the-art density-functional theory calculations with the Gr\"uneisen theory of thermal expansion, which allows tracing back thermal expansion to contributions of individual phonons. On the macroscopic level, the small thermal expansion coefficients arise from two aspects: compensation effects caused by the large coupling between stress and strain perpendicular to the pores and the small magnitudes of the mean Gr\"uneisen tensor elements, $\langle\gamma\rangle$, which provide information on how strains in the material influence its phonon frequencies. To understand the small mean Gr\"uneisen tensor in MOF-74, the individual mode contributions are analyzed based on the corresponding atomic motions. This reveals that only the lowest frequency modes up to ~3 THz provide non-negligible contributions, such that $\langle\gamma\rangle$ drops sharply at higher temperatures. These considerations reveal how the details of the anharmonic properties of specific phonon bands determine the magnitude and sign of thermal expansion in a prototypical material like MOF-74.