First-principles study of elastic mechanical responses to applied deformation of metal-organic frameworks

We use density functional theory to compute the elastic constant tensors of two families of metal-organic frameworks (MOFs) to establish relationships between their structures and mechanical properties. The Zn family consist of Zn4O centers each coordinated by six organic linkers along the < 100 > directions; we studied three linkers of increasing lengths: 1,4-benzenedicarboxylate (BDC), 4,4'-biphenyl-dicarboxylate (BPDC), and 4,4 ''-terphenyl-dicarboxylate. This relatively weak connectivity leads to high anisotropy; in fact, Zn-MOFs exhibit extremely low shear modulus and are near a mechanical instability. In contrast, Zr family studied consists of Zr6O4(OH)(4) centers each linked by fumarate, BDC, and BPDC ligands along the twelve < 110 > directions. The higher structural connectivity results in stiffer frameworks with lower anisotropy. The smallest Zr-MOF exhibits nearly isotropic elasticity with a Zener ratio of 1.06. The stiffest and most compliant directions of both families are directly related to the orientation of the organic linkers. Temperature has a significant effect on elastic moduli; for example, we observed reduction of average Young's modulus and shear modulus by about 30% from 0 K to 300 K in Zn-BPDC even when it exhibits large negative thermal expansion. We find the effect of temperature to be directionally dependent, leading to an increase in anisotropy upon increasing temperature. The predicted effects of temperature and anisotropy help reconcile a longstanding discrepancy between experiments and first principles calculations. Published by AIP Publishing.