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 Grüneisen 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 Grüneisen tensor elements, $\langleγ\rangle$, which provide information on how strains in the material influence its phonon frequencies. To understand the small mean Grüneisen 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 $\langleγ\rangle$ 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.
Microscopic Origin of Temperature-Dependent Anisotropic Heat Transport in Ultrawide-Bandgap Rutile GeO2
Technische Universität Berlin（柏林工业大学）；Department of Physics, Universidade Federal do Ceará（塞阿拉联邦大学物理系）；Leibniz-Institut für Kristallzüchtung（莱布尼茨晶体生长研究所）
The electronic-structure origin of the anisotropic thermopower of nanolaminated Ti3SiC2 determined by polarized x-ray spectroscopy and Seebeck measurements
