Extended Data Figure 9: Experimental and simulated data for two metal–organic frameworks, HKUST-1 and MOF-5.
From: Predicting crystal growth via a unified kinetic three-dimensional partition model
a–d, HKUST-1, a porous MOF of copper trimesate, Cu3[(O2C)3C6H3]2(H2O)3. By partitioning the structure with nodes at metal clusters and tile edges along linkers, the HKUST-1 structure consists of three tiles (a) connected in a face-centred cubic lattice (b). Such a partitioning produces simulation results (d) that are in excellent agreement with experiments in terms of both the crystal habit and the terrace topology of the prevalent screw dislocations (c). The simulation predicts that the screw core runs along [110], not perpendicular to the {111} faces because such a screw core would result in multiple spirals (d); ΔUs = 2 kcal mol−1 for small tiles and ΔUs = 5 kcal mol−1 for large tiles. Simulations also allow investigation of the surface termination for this framework (d). Supplementary Video 6 shows the screw dislocation growing and migrating across the surface of the crystal. The approximate size of the crystal shown in d is 0.35 μm × 0.35 μm × 0.35 μm. e–i, MOF-5 (Zn4O(bdc)3, where bdc is 1,4-benzenedicarboxylate), a porous MOF with a simple cubic arrangement of metal centres (red) and linkers (grey), along with a solvent molecule occupying the centre of each cube (purple) (e, left). Treating the structure as a multicomponent molecular crystal in lieu of a standard tile-partition as used in other cases, the framework can also be partitioned into Voronoi polyhedra to demonstrate the interactions between each of the linkers, metal centres and solvent molecules (e, right). Square terracing on the (100) face (f) can be in one of two orientations, depending on the synthesis conditions. The crystal morphology can also be changed to exhibit {111} faces as an octahedral crystal, again depending on synthesis conditions (g, left), as opposed to only {100} faces (g, right) in a cubic crystal. {111} faces exhibited by the crystal are much more isotropic (h) compared to the {100} faces (f) and do not adopt the different orientations demonstrated by the {100} faces. The simple cubic network alone will not permit the development of {111} faces and is immediately an indication of the importance of the solvent N,N′-diethylformamide (DEF) in the preparation. By varying the driving forces for binding of the linker, metal centre and solvent in the final crystal, all crystal habits and surface topologies may be generated (f–h). Double spirals through growth at screw dislocations on the (100) face can also be simulated (i). The estimated sizes of the crystals shown are: f, 0.76 μm × 0.75 μm × 0.75 μm and 0.70 μm × 0.80 μm × 0.80 μm; g, 0.50 μm × 0.50 μm × 0.50 μm and 0.75 μm × 0.75 μm × 0.75 μm; h, 0.50 μm × 0.50 μm × 0.50 μm; and i, 0.75 μm × 0.75 μm × 0.75 μm.
