Compositional dependence of uniaxial zero thermal expansion and zero linear compressibility in metal–organic framework MIL-122 (Al, Ga, In)

Abstract

The responses of MIL-122(Al, Ga, In) to pressure or temperature have been investigated. The findings suggest that the a-axis in the lattice exhibits minimal compressibility, particularly zero linear compressibility (ZLC) behavior observed in MIL-122(In), consistent with experimental reports. Additionally, as the radius of metal atoms increases, the compressibility of the b-axis and c-axis gradually strengthens. There is a notable compositional dependence on volume thermal expansion in MIL-122(Al, Ga, In), where an increase in the metal atom radius leads to gradual weakening of volume thermal expansion. In particular, MIL-122(In) demonstrates pronounced volume negative thermal expansion (NTE) behavior, with the a-axis displaying zero thermal expansion (ZTE) behavior and both the b-axis and c-axis exhibiting NTE behavior. The temperature-dependent relative change in the bulk modulus of MIL-122(Al, Ga, In) has also been explored, revealing abnormal thermal hardening specifically within MIL-122(Ga, In). We attribute these unique uniaxial ZTE and ZLC behaviors in MIL-122(In) to its distinctive wine-rack topology, anomalous phonons (negative Grüneisen parameters), and internal structural flexibility.