We describe a general method to model multicomponent ordered crystals using the phase-field-crystal (PFC) formalism. As a test case, a generic B2 compound is investigated. We are able to produce a line of either first-order or second-order order-disorder phase transitions, features that have not been incorporated in existing PFC approaches. Further, it is found that the only elastic constant for B2 that depends on ordering is C_{11}. This B2 model is then used to study antiphase boundaries (APBs). The APBs are shown to reproduce classical mean-field results. Dynamical simulations of ordering across small-angle grain boundaries predict that dislocation cores pin the evolution of APBs.

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Mechanobiological studies of cell assemblies have generally focused on cells that are, in principle, identical. Here we predict theoretically the effect on cells in culture of locally introduced biochemical signals that diffuse and locally induce cytoskeletal contractility which is initially small. In steady-state, both the concentration profile of the signaling molecule as well as the contractility profile of the cell assembly are inhomogeneous, with a characteristic length that can be of the order of the system size. The long-range nature of this state originates in the elastic interactions of contractile cells (similar to long-range “macroscopic modes” in non-living elastic inclusions) and the non-linear diffusion of the signaling molecules, here termed mechanogens. We suggest model experiments on cell assemblies on substrates that can test the theory as a prelude to its applicability in embryo development where spatial gradients of morphogens initiate cellular development.

We introduce a phase-field crystal model that creates an array of complex three-and twodimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order to energetically favor the principal interplanar angles of a target crystal structure. This is achieved via an analysis performed by examining the crystal's structure factor. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF2 crystals. To illustrate the ability of the method to yield a particularly complex and technologically important crystal structure, we show how this three-point correlation function method can be used to generate perovskite crystals.

The reactions of nitrile complexes of the [Re(6)(μ(3)-Se)(8)](2+) core-containing clusters, [Re(6)(μ(3)-Se)(8)(PEt(3))(n)(CH(3)CN)(6-n)](2+) [n = 5 (1); n = 4, cis- (2) and trans- (3); n = 0 (4)], with organic azides C(6)H(5)CH(CH(3))N(3) and C(6)H(5)CH(2)N(3) produced the corresponding cationic imino complexes of the general formula [Re(6)(μ(3)-Se)(8)(PEt(3))(n)(L)(6-n)](2+) [L = PhN=CHCH(3): n = 5 (5); n = 4, cis- (6) and trans- (7); n = 0 (8) and L = HN=CHPh: n = 5 (9); n = 4, cis- (10) and trans- (11)]. These novel complexes were characterized by NMR spectroscopy ((1)H and (31)P) and single-crystal X-ray diffraction. A mechanism involving the migration of one of the groups on the azido α-C atom to the α-N atom of the azido complex, concerted with the photo-expulsion of N(2), was invoked to rationalize the formation of the imino complexes. Density functional theory (DFT) calculations indicated that due to the coordination with and activation by the cluster core, the energy of the electronic transition responsible for the photo-decomposition of a cluster-bound azide is much reduced with respect to its pure organic counterpart. The observed geometric specificity was rationalized by using the calculated and optimized preferred ground-state conformation of the cluster-azido intermediates.