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Designing thermodynamic conditions to improve (or reduce) the stability of a target material is a key task in materials engineering. For example, during materials synthesis one aims to enhance the stability of a target phase relative to its precursors or competing byproduct phases. If an undesired phase forms in experiment, one aims to destabilize the undesired phase by dissolution or corrosion. When multiple thermodynamic knobs are available to engineer relative stability, it can be difficult to navigate the corresponding high-dimensional phase diagram to identify optimal pathways to promote or destabilize a target phase. We propose that instead of mapping the absolute phase boundaries of a target material, we can invoke a generalized Clausius-Clapeyron relation, which provides a 'compass' to point out which directions on a high-dimensional phase diagram are best to stabilize or destabilize a target phase. Phase boundaries on high-dimensional phase diagrams are also high-dimensional objects, and can represent phase coexistence between numerous phases simultaneously. On a 2D temperature-pressure phase diagram, phase boundaries are 1D lines separating two phases, with a slope given by the Clausius-Clapeyron relation, dP/dT = {\Delta}S/{\Delta}V. Here, we derive a parametric form of the Clausius-Clapeyron relation that readily scales to high-dimensional phase boundaries. The gradient of a phase boundary guides us on how to increase or decrease the relative stability of a target compound, meaning this generalized Clausius-Clapeyron relation enables us to engineer relative stability with respect to multiple thermodynamic conditions simultaneously. Using this approach, we analyze the acid stability of manganese oxide catalysts on a 4-dimensional Pourbaix diagram with axes of pH, redox potential, nanoparticle size, and aqueous [K+] ion concentration.

Modern materials are often synthesized or operated in complex chemical environments, where there can be numerous elemental species, competing phases, and reaction pathways. When analyzing reactions using the Gibbs free energy, which has a natural variable of composition, it is often cumbersome to solve for the equilibrium states of a complicated heterogeneous mixture of phases. However, if one is interested only in the stability of a single target material, it may be easier to reframe the boundary conditions around only the target material-of-interest, with boundary conditions open to chemical exchange with an external reservoir. The corresponding phase diagram would thus have a chemical potential axis for the open volatile species, rather than a composition axis. Here we discuss how to derive, compute, and interpret phase diagrams with chemical potential axes, which are dual to the more common composition phase diagram. In our ambition to construct high-dimensional phase diagrams featuring any thermodynamic variable on its axes, here we examine the duality between extensive and intensive conjugate variables in equilibrium thermodynamics. This duality manifests from the distinction between closed and open boundary conditions of a thermodynamic system, to the relationship between the Internal Energy and its Legendre transformations, to the point-line duality in calculating convex hulls versus half-space intersections. Here we focus on the duality relationships of chemical work, with extensive composition variables, N, and intensive chemical potentials, {\mu}. In particular, we explore mixed composition-chemical potential diagrams for oxynitride synthesis, lithium-ion cathode stability, and oxidation of high-entropy alloys. We further illustrate how chemical potential diagrams reveal the driving forces for non-equilibrium growth and dissolution kinetics.

The intricate nature of time series data analysis benefits greatly from the distinct advantages offered by time and frequency domain representations. While the time domain is superior in representing local dependencies, particularly in non-periodic series, the frequency domain excels in capturing global dependencies, making it ideal for series with evident periodic patterns. To capitalize on both of these strengths, we propose ATFNet, an innovative framework that combines a time domain module and a frequency domain module to concurrently capture local and global dependencies in time series data. Specifically, we introduce Dominant Harmonic Series Energy Weighting, a novel mechanism for dynamically adjusting the weights between the two modules based on the periodicity of the input time series. In the frequency domain module, we enhance the traditional Discrete Fourier Transform (DFT) with our Extended DFT, designed to address the challenge of discrete frequency misalignment. Additionally, our Complex-valued Spectrum Attention mechanism offers a novel approach to discern the intricate relationships between different frequency combinations. Extensive experiments across multiple real-world datasets demonstrate that our ATFNet framework outperforms current state-of-the-art methods in long-term time series forecasting.

Efficient synthesis recipes are needed both to streamline the manufacturing of complex materials and to accelerate the realization of theoretically predicted materials. Oftentimes the solid-state synthesis of multicomponent oxides is impeded by undesired byproduct phases, which can kinetically trap reactions in an incomplete non-equilibrium state. We present a thermodynamic strategy to navigate high-dimensional phase diagrams in search of precursors that circumvent low-energy competing byproducts, while maximizing the reaction energy to drive fast phase transformation kinetics. Using a robotic inorganic materials synthesis laboratory, we perform a large-scale experimental validation of our precursor selection principles. For a set of 35 target quaternary oxides with chemistries representative of intercalation battery cathodes and solid-state electrolytes, we perform 224 reactions spanning 27 elements with 28 unique precursors. Our predicted precursors frequently yield target materials with higher phase purity than when starting from traditional precursors. Robotic laboratories offer an exciting new platform for data-driven experimental science, from which we can develop new insights into materials synthesis for both robot and human chemists.

Visual anomaly detection plays a crucial role in not only manufacturing inspection to find defects of products during manufacturing processes, but also maintenance inspection to keep equipment in optimum working condition particularly outdoors. Due to the scarcity of the defective samples, unsupervised anomaly detection has attracted great attention in recent years. However, existing datasets for unsupervised anomaly detection are biased towards manufacturing inspection, not considering maintenance inspection which is usually conducted under outdoor uncontrolled environment such as varying camera viewpoints, messy background and degradation of object surface after long-term working. We focus on outdoor maintenance inspection and contribute a comprehensive Maintenance Inspection Anomaly Detection (MIAD) dataset which contains more than 100K high-resolution color images in various outdoor industrial scenarios. This dataset is generated by a 3D graphics software and covers both surface and logical anomalies with pixel-precise ground truth. Extensive evaluations of representative algorithms for unsupervised anomaly detection are conducted, and we expect MIAD and corresponding experimental results can inspire research community in outdoor unsupervised anomaly detection tasks. Worthwhile and related future work can be spawned from our new dataset.

Phase diagrams are essential tools of the materials scientist, showing which phases are at equilibrium under a set of applied thermodynamic conditions. Essentially all phase diagrams today are two dimensional, typically constructed with axes of temperature-pressure or temperature-composition. For many modern materials, it would be valuable to construct phase diagrams that include additional forms of thermodynamic work--such as elastic, surface, electromagnetic or electrochemical work, etc.--which grows the free energy of materials into higher (>3) dimensions. Here, we extend Gibbs' original arguments on phase coexistence to derive a generalized Phase Rule, based in the combinatorial geometry of high-dimensional convex polytopes. The generalized Phase Rule offers a conceptual and geometric foundation to describe phase boundaries on high-dimensional phase diagrams, which are relevant for understanding the stability of modern materials in complex chemical environments. We revisit Gibbs arguments on the equilibrium of heterogeneous substances and show that phase coexistence regions in high-dimensional Internal Energy space, U(S,Xi,...,Xj), are simplicial convex polytopes--which are N-dimensional analogues of triangles and tetrahedra. In the first of this three-part series, we examine how the combinatorial relationships between the vertices and facets of simplicial polytopes leads to a generalized high-dimensional description of Gibbs' Phase Rule. Because Gibbs' Phase Rule describes the nature of phase boundaries on phase diagrams, this isomorphism between the physical principles of equilibrium thermodynamics and the geometry of simplicial polytopes provides the foundation to construct generalized phase diagrams, which can exist in any dimension, with any intensive or extensive thermodynamic variable on the axes.

High Entropy Alloys (HEAs) contain near equimolar amounts of five or more elements and are a compelling space for materials design. Great emphasis is placed on identifying HEAs that form a homogeneous solid-solution, but the design of such HEAs is hindered by the difficulty of navigating stability relationships in high-component spaces. Traditional phase diagrams use barycentric coordinates to represent composition axes, which require D = (N - 1) spatial dimensions to represent an N-component system, meaning that HEA systems with N > 4 components cannot be readily visualized. Here, we propose forgoing barycentric composition axes in favor of two energy axes: a formation-energy axis and a 'reaction energy' axis. These Inverse Hull Webs offer an information-dense 2D representation that successfully capture complex phase stability relationships in N > 4 component systems. We use our new diagrams to visualize the transition of HEA solid-solutions from high-temperature stability to metastability upon quenching, and identify important thermodynamic features that are correlated with the persistence or decomposition of metastable HEAs., Comment: 18 pages, 5 figures