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The Li$_2$S-P$_2$S$_5$ pseudo-binary system has been a valuable source of promising superionic conductors, with $\alpha$-Li$_3$PS$_4$, $\beta$-Li$_3$PS$_4$, HT-Li$_7$PS$_6$, and Li$_7$P$_3$S$_{11}$ having excellent room temperature Li-ion conductivity > 0.1 mS/cm. The metastability of these phases at ambient temperature motivates a study to quantify thermodynamic accessibility. Through calculating the electronic, configurational, and vibrational sources of free energy from first principles, a phase diagram of the crystalline Li$_2$S-P$_2$S$_5$ space is constructed. Well-established phase stability trends from experiments are recovered, such as polymorphic phase transitions in Li$_7$PS$_6$ and Li$_3$PS$_4$, and the metastability of Li$_7$P$_3$S$_{11}$ at high temperature. At ambient temperature, it is predicted that all superionic conductors in this space are indeed metastable, but thermodynamically accessible. Vibrational and configurational sources of entropy are shown to be essential towards describing the stability of superionic conductors. New details of the Li sublattices are revealed, and are found to be crucial towards accurately predicting configurational entropy. All superionic conductors contain significant configurational entropy, which suggests an inherent correlation between superionic conductivity and high configurational entropy., Comment: 43 pages, 16 figures

Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate the performance of energy storage. The application of commonly used cluster expansion techniques to model the intercalation thermodynamics of such systems from \textit{ab-initio} is challenged by the combinatorial increase in configurational degrees of freedom as the number of species grows. Such challenges necessitate efficient generation of lattice models without over-fitting and proper sampling of the configurational space under charge balance in ionic systems. In this work, we introduce a combined approach that addresses these challenges by (1) constructing a robust cluster-expansion Hamiltonian using the sparse regression technique, including $\ell_0\ell_2$-norm regularization and structural hierarchy; and (2) implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic configurations using the table-exchange method and an ensemble-average approach. These techniques are applied to a disordered rocksalt oxyfluoride Li$_{1.3-x}$Mn$_{0.4}$Nb$_{0.3}$O$_{1.6}$F$_{0.4}$ (LMNOF) which is part of a family of promising earth-abundant cathode materials. The simulated voltage profile is found to be in good agreement with experimental data and particularly provides a clear demonstration of the Mn and oxygen contribution to the redox potential as a function of Li content.

Monte-Carlo sampling of lattice model Hamiltonians is a well-established technique in statistical mechanics for studying the configurational entropy of crystalline materials. When species to be distributed on the lattice model carry charge, the charge balance constraint on the overall system prohibits single-site Metropolis exchanges in MC. In this article, we propose two methods to perform MC sampling in the grand-canonical ensemble in the presence of a charge-balance constraint. The table-exchange method (TE) constructs small charge-conserving excitations, and the square-charge bias method (SCB) allows the system to temporarily drift away from charge neutrality. We illustrate the effect of internal hyper-parameters on the efficiency of these algorithms and suggest practical strategies on how to apply these algorithms to real applications.

We introduce the $\ell_0\ell_2$-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansion to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The $\ell_2$-norm regularization is used to suppress intrinsic data noise, while $\ell_0$-norm is used to penalize the number of non-zero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged, and effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of $\ell_0\ell_2$-norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation and convergence speed, reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional $\ell_1$-norm regularized cluster expansion model.

With the rapid development of China’s economy, the field positioning and navigation technology has also been continuously developed. The global positioning system(GPS), can provide fast and accurate positioning and navigation for exploration operations in desert areas. In this paper, the developed GPS navigation and positioning software system solves the problem of cooperation between GPS user terminal equipment and exploration site. It also effectively combines image processing, data transmission, data processing, error analysis and other technologies to achieve the goals such as data recording and transmission, field navigation, data browsing and query, coordinate transformation, error analysis, and printing curve. After field test work and post-data processing, the software proved to have the following advantages: convenient operation, accurate coordinate transformation and complete functions. It could meet the requirements for accurate GPS positioning and navigation of the field exploration. Its practical effect is good and can provide reference for future field exploration and navigation mapping.