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Register a new userSparse Expansions of Multicomponent Oxide Configuration Energy Using Coherency & Redundancy
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Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.
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The many surface reconstructions of (110)-oriented lanthanum--strontium manganite (La$_{0.8}$Sr$_{0.2}$MnO$_3$, LSMO) were followed as a function of the oxygen chemical potential ($mu_text{O}$) and the surface cation composition. Decreasing $mu_text{O}$ causes Mn to migrate across the surface, enforcing phase separation into A-site-rich areas and a variety of composition-related, structurally diverse B-site-rich reconstructions. The composition of these phase-separated structures was quantified with scanning tunneling microscopy (STM), and these results were used to build a 2D phase diagram of the LSMO(110) equilibrium surface structures.
A methodology for computing expansion basis functions using discrete harmonic modes is presented. The discrete harmonic modes are determined grain-by-grain for virtual polycrystals for which finite element meshes are available. The expansion weights associated with representing field variables over grain domains are determined by exploiting the orthogonality of the harmonic modes. The methodology is demonstrated with the representation of the axial stress distributions during tensile loading of a polycrystalline sample. An open source code, MechMonics, is available to researchers wishing to use the methodology to analyze data.
Graphene oxide membranes show exceptional molecular permeation properties, with a promise for many applications. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of ~9 Angstrom, which is larger than hydrated ion diameters for common salts. The cutoff is determined by the interlayer spacing d ~13.5 Angstrom, typical for graphene oxide laminates that swell in water. Achieving smaller d for the laminates immersed in water has proved to be a challenge.Here we describe how to control d by physical confinement and achieve accurate and tuneable ion sieving. Membranes with d from ~ 9.8 Angstrom to 6.4 Angstrom are demonstrated, providing the sieve size smaller than typical ions hydrated diameters.In this regime, ion permeation is found to be thermally activated with energy barriers of ~10-100 kJ/mol depending on d. Importantly, permeation rates decrease exponentially with decreasing the sieve size but water transport is weakly affected (by a factor of <2). The latter is attributed to a low barrier for water molecules entry and large slip lengths inside graphene capillaries. Building on these findings, we demonstrate a simple scalable method to obtain graphene-based membranes with limited swelling, which exhibit 97% rejection for NaCl.
Many stochastic complex systems are characterized by the fact that their configuration space doesnt grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration space volume in terms of the scaling exponents of the system. These scaling exponents can, in turn, be used to define universality classes that uniquely determine the statistics of a system. Every system belongs to one of these classes. Here we derive the information geometry of scaling expansions of sample spaces. In particular, we present the deformed logarithms and the metric in a systematic and coherent way. We observe a phase transition for the curvature. The phase transition can be well measured by the characteristic length r, corresponding to a ball with radius 2r having the same curvature as the statistical manifold. Increasing characteristic length with respect to the size of the system is associated with sub-exponential sample space growth is associated with strongly constrained and correlated complex systems. Decreasing of the characteristic length corresponds to super-exponential sample space growth that occurs for example in systems that develop structure as they evolve. Constant curvature means exponential sample space growth that is associated with multinomial statistics, and traditional Boltzmann-Gibbs, or Shannon statistics applies. This allows us to characterize transitions between statistical manifolds corresponding to different families of probability distributions.
We developed an inverse design framework enabling automated generation of stable multi-component crystal structures by optimizing the formation energies in the latent space based on reversible crystal graphs with continuous representation. It is demonstrated that 9,160 crystal structures can be generated out of 50,000 crystal graphs, leading to 8,310 distinct cases using a training set of 52,615 crystal structures from Materials Project. Detailed analysis on 15 selected systems reveals that unreported crystal structures below the convex hull can be discovered in 6 material systems. Moreover, the generation efficiency can be further improved by considering extra hypothetical structures in the training. This paves the way to perform inverse design of multicomponent materials with possible multi-objective optimization.
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