The prototype misfit layer compound (SnS)1.17NbS2 consists of alternatively a metallic triatomic NbS2 layer in which Nb atoms are sandwiched by S atoms and an insulating SnS double-layer of NaCl-type structure. Here we investigate the effect of lattice misfit on the stability and chemical bonding in the misfit layer compound using a first-principles density-functional theory approach. The calculations show that for the (SnS)1+xNbS2 approximants, the most stable one has x = 0.167, close to the experimental observations. Charge analysis finds a moderate charge transfer from the SnS to NbS2. Sn or S vacancies in the SnS part affect the electronic properties and interlayer interactions. The obtained information here helps understand the mechanism of formation and stability of the misfit layer compounds and ferecrystals, and further to design of novel multilayer compounds and emerging van der Waals heterostructures.

An atomic-scale approach is employed to simulate the formation of precipitates with different lattice misfits in the early stages of aging of supersaturated aluminum alloys. Simulation results reveal that the increase of lattice misfit could significantly promote the nucleation rate of precipitates, which results in a larger number and smaller size of the precipitates. The morphologies of the precipitates also vary with the degree of lattice misfit. Moreover, the higher the lattice misfit, the earlier the nucleation of the second phase occurs, which can substantially inhibit the movement of dislocations. The research on the lattice misfit of precipitation can provide theoretical guidance for the design of high-strength aluminum alloy.

Environmentally friendly lead-free K1-xNaxNbO3 (KNN) ceramics possess electromechanical properties comparable to lead-based ferroelectric materials, but cannot meet the needs of device miniaturization, and the corresponding thin films lack of theoretical and experimental studies. To this end, we developed the nonlinear phenomenological theory for ferroelectric materials to study the effects of non-equiaxed misfit strain on the phase structure, electromechanical properties and electrical response of K0.5Na0.5NbO3 epitaxial films and constructed the in-plane misfit strain (u1-u2) phase diagrams. The results show that K0.5Na0.5NbO3 epitaxial film under non-equiaxed in-plane strain can exhibit abundant phase structures, including orthorhombic a1c, a2c and a1a2 phases, tetragonal a1, a2 and c phases, and monoclinic r12 phases. Moreover, in the vicinity of a2c-r12, a1c-c and a1a2-a2 phase boundaries, K0.5Na0.5NbO3 epitaxial films exhibit excellent dielectric constant ε11, while at a2c -r12 and a1c-c phase boundaries large piezoelectric coefficient d15 is observed. It was also found that high permittivity ε33 and piezoelectric coefficients d33 exist near the a2c - a2, r12- a1a2 and a1c-a1 phase boundaries due to the existence of polymorphic phase boundaries (PPB) in the KNN system, which makes it easy to polarize near the phase boundaries, and the polarizability changes suddenly, leading to electromechanical enhancement. In addition, the results show that the K0.5Na0.5NbO3 thin films possess a large electrocaloric response at the phase boundary at the r12-a1a2 and a1c-a1 phase boundaries. And the maximum adiabatic temperature change ∆T is about 3.62 K when the electric field change is 30 MV/m at room temperature, which is significantly enhanced compared with equiaxed strain. This study provides theoretical guidance for obtaining K1-xNaxNbO3 epitaxial thin films with excellent properties.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

We have investigated the interfacial dislocations in InxGa1–xN/GaN (0 ≤ x ≤ 0.20) heterostructures using diffraction contrast analysis in a transmission electron microscopy. The analysis indicate that the structural properties of the interface dislocations depend on the indium composition. For lower indium composition up to x = 0.09, we observed that the screw-type dislocations and dislocation half loops occurred at the interface even though the former do not contributes toward elastic relaxation of the misfit strain in the InGaN layer. With the increase of indium composition (0.13 ≤ x ≤ 0.17), in addition to the network of screw-type dislocations, edge-type misfit dislocations were found generated with their density gradually increasing. For higher indium composition (0.18 ≤ x ≤ 0.20), all the interfacial dislocations are transformed into a network of straight misfit dislocations along the <10-10> directions leading to partially relaxation of the InGaN epilayer. The presence of dislocation half loops may be explained by slip on the basal plane, the formation of misfit dislocations are attributed to punch-out mechanism.