Structures of MIL-53(Al)-lp, MIL-47, MIL-122(In), and MIL-140A. Metallic centers are represented as tetrahedra. Color code: C – black, O – red, H – white, Al – cyan, V – brown, In – blue, Zr – green.
Scheme of the directional elastic properties calculated in this work. For each, large red arrows represent the direction of applied stress and smaller green arrows the direction along which the resulting strain is calculated.
(Top) directional Young's modulus for MIL-53(Al)-lp (left) and MIL-47 (right) represented as 3D surfaces, with axes tick labels in GPa. (Bottom) scheme of the Young modulus values for stiffest and softest directions, with Young's modulus values indicated.
Sketch of the three families of metal–organic frameworks exhibiting the wine-rack motif studied in this article.
Directional Young's modulus for MIL-122(In) represented as 3D surfaces, with axes tick labels in GPa.
Directional Young's modulus for MIL-140A represented as 3D surfaces (top), in the Cartesian xy, zx and zy planes (bottom; tick marks correspond to 10 GPa).
Representation of uniaxial strain along the lattice vector [0.05, −0.56, 0.83] on the MIL-140A structure: the relaxed structure is on the left, a strain of +15% is depicted on the right. (Top) viewed along the b axis (a is horizontal, c is vertical); (bottom) viewed along the c axis (a is horizontal, b is vertical). This deformation is included in movie form in the supplementary material. 31
Representation of the inorganic chains of MIL-53(Al)-lp (top; the chain is along the b axis) and MIL-140A (bottom; the chain is along the c axis). Zr: green; Al: purple; O: red; H: white; oxygen atoms of the linkers coordinating the metals are colored orange.
Space group (S.G.), unit cell parameters (a, b, c, and β) and volume (V) of the energy-minimized structures of the MOFs studied in this work.
Minimal and maximal values as well as anisotropy of Young's modulus, shear modulus, linear compressibility, and Poisson's ratio for the MOFs studied, obtained by quantum chemistry calculations. Anisotropy of X is denoted by A X = X max/X min.
Eigenvalues λ i (in GPa) of the stiffness matrix C of the MOFs studied in this work.
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