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In this work, we present ænet-PyTorch, a PyTorch-based implementation for training artificial neural network-based machine learning interatomic potentials. Developed as an extension of the atomic energy network (ænet), ænet-PyTorch provides access to all the tools included in ænet for the application and usage of the potentials. The package has been designed as an alternative to the internal training capabilities of ænet, leveraging the power of graphic processing units to facilitate direct training on forces in addition to energies. This leads to a substantial reduction of the training time by one to two orders of magnitude compared to the central processing unit implementation, enabling direct training on forces for systems beyond small molecules. Here, we demonstrate the main features of ænet-PyTorch and show its performance on open databases. Our results show that training on all the force information within a dataset is not necessary, and including between 10% and 20% of the force information is sufficient to achieve optimally accurate interatomic potentials with the least computational resources.

Lithium thiophosphates (LPSs) with the composition (Li2S)x(P2S5)1-x are among the most promising prospective electrolyte materials for solid-state batteries (SSBs), owing to their superionic conductivity at room temperature (>10-3 S cm-1), soft mechanical properties, and low grain boundary resistance. Several glass-ceramic (gc) LPSs with different compositions and good Li conductivity have been previously reported, but the relationship among composition, atomic structure, stability, and Li conductivity remains unclear due to the challenges in characterizing noncrystalline phases in experiments or simulations. Here, we mapped the LPS phase diagram by combining first-principles and artificial intelligence (AI) methods, integrating density functional theory, artificial neural network potentials, genetic-algorithm sampling, and ab initio molecular dynamics simulations. By means of an unsupervised structure-similarity analysis, the glassy/ceramic phases were correlated with the local structural motifs in the known LPS crystal structures, showing that the energetically most favorable Li environment varies with the composition. Based on the discovered trends in the LPS phase diagram, we propose a candidate solid-state electrolyte composition, (Li2S)x(P2S5)1-x (x ∼0.725), that exhibits high ionic conductivity (>10-2 S cm-1) in our simulations, thereby demonstrating a general design strategy for amorphous or glassy/ceramic solid electrolytes with enhanced conductivity and stability.

Nanostructured Si is the most promising high-capacity anode material to substantially increase the energy density of Li-ion batteries. Among the remaining challenges is its low rate capability as compared to conventional materials. To understand better what controls the diffusion of Li in the amorphous Li-Si alloy, we use a novel machine-learning potential trained on more than 40,000 ab-initio calculations and nanosecond-scale molecular dynamics simulations, to visualize for the first time the delithiation of entire LiSi nanoparticles. Our results show that the Si host is not static but undergoes a dynamic rearrangement from isolated atoms, to chains, and clusters, with the Li diffusion strongly governed by this Si rearrangement. We find that the Li diffusivity is highest when Si segregates into clusters, so that Li diffusion proceeds via hopping between the Si clusters. The average size of Si clusters and the concentration range over which Si clustering occurs can thus function as design criteria for the development of rate-improved anodes based on modified Si.

Nanostructured Si is the most promising high-capacity anode material to substantially increase the energy density of Li-ion batteries. Among the remaining challenges is its low rate capability as compared to conventional materials. To understand better what controls the diffusion of Li in the amorphous Li-Si alloy, we use a novel machine-learning potential trained on more than 40,000 ab-initio calculations and nanosecond-scale molecular dynamics simulations, to visualize for the first time the delithiation of entire LiSi nanoparticles. Our results show that the Si host is not static but undergoes a dynamic rearrangement from isolated atoms, to chains, and clusters, with the Li diffusion strongly governed by this Si rearrangement. We find that the Li diffusivity is highest when Si segregates into clusters, so that Li diffusion proceeds via hopping between the Si clusters. The average size of Si clusters and the concentration range over which Si clustering occurs can thus function as design criteria for the development of rate-improved anodes based on modified Si.

The atomistic modeling of amorphous materials requires structure sizes and sampling statistics that are challenging to achieve with first-principles methods. Here, we propose a methodology to speed up the sampling of amorphous and disordered materials using a combination of a genetic algorithm and a specialized machine-learning potential based on artificial neural networks (ANNs). We show for the example of the amorphous LiSi alloy that around 1000 first-principles calculations are sufficient for the ANN-potential assisted sampling of low-energy atomic configurations in the entire amorphous LixSi phase space. The obtained phase diagram is validated by comparison with the results from an extensive sampling of LixSi configurations using molecular dynamics simulations and a general ANN potential trained to ∼45 000 first-principles calculations. This demonstrates the utility of the approach for the first-principles modeling of amorphous materials.

The atomistic modeling of amorphous materials requires structure sizes and sampling statistics that are challenging to achieve with first-principles methods. Here, we propose a methodology to speed up the sampling of amorphous and disordered materials using a combination of a genetic algorithm and a specialized machine-learning potential based on artificial neural networks (ANNs). We show for the example of the amorphous LiSi alloy that around 1000 first-principles calculations are sufficient for the ANN-potential assisted sampling of low-energy atomic configurations in the entire amorphous LixSi phase space. The obtained phase diagram is validated by comparison with the results from an extensive sampling of LixSi configurations using molecular dynamics simulations and a general ANN potential trained to ∼45 000 first-principles calculations. This demonstrates the utility of the approach for the first-principles modeling of amorphous materials.

Structure plays a vital role in determining materials properties. In lithium ion cathode materials, the crystal structure defines the dimensionality and connectivity of interstitial sites, thus determining lithium ion diffusion kinetics. In most conventional cathode materials that are well-ordered, the average structure as seen in diffraction dictates the lithium ion diffusion pathways. Here, we show that this is not the case in a class of recently discovered high-capacity lithium-excess rocksalts. An average structure picture is no longer satisfactory to understand the performance of such disordered materials. Cation short-range order, hidden in diffraction, is not only ubiquitous in these long-range disordered materials, but fully controls the local and macroscopic environments for lithium ion transport. Our discovery identifies a crucial property that has previously been overlooked and provides guidelines for designing and engineering cation-disordered cathode materials.

Structure plays a vital role in determining materials properties. In lithium ion cathode materials, the crystal structure defines the dimensionality and connectivity of interstitial sites, thus determining lithium ion diffusion kinetics. In most conventional cathode materials that are well-ordered, the average structure as seen in diffraction dictates the lithium ion diffusion pathways. Here, we show that this is not the case in a class of recently discovered high-capacity lithium-excess rocksalts. An average structure picture is no longer satisfactory to understand the performance of such disordered materials. Cation short-range order, hidden in diffraction, is not only ubiquitous in these long-range disordered materials, but fully controls the local and macroscopic environments for lithium ion transport. Our discovery identifies a crucial property that has previously been overlooked and provides guidelines for designing and engineering cation-disordered cathode materials.

First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent development of compressive sensing approaches for the construction of lattice models has further enabled the systematic construction of sparse physical models without the need for human intuition other than requiring the compactness of effective cluster interactions. However, conventional compressive sensing based on L1-norm regularization is strictly only applicable to certain classes of optimization problems and is otherwise not guaranteed to generate optimally sparse and transferable results, so that the method can only be applied to some materials science applications. In this paper, we illustrate a more robust L0L1-norm compressive-sensing method that removes the limitations of conventional compressive sensing and generally results in sparser lattice models that are at least as predictive as those obtained from L1-norm compressive sensing. Apart from the theory, a practical implementation based on state-of-the-art mixed-integer quadratic programming (MIQP) is proposed. The robustness of our methodology is illustrated for four different transition-metal oxides with relevance as battery cathode materials: Li2xTi2(1-x)O2, Li2xNi2yO2, MgxCr2O4, and NaxCrO2. This method provides a practical and robust approach for the construction of sparser and more predictive lattice models, improving on the compressive sensing paradigm and making it applicable to a much broader range of applications.

First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent development of compressive sensing approaches for the construction of lattice models has further enabled the systematic construction of sparse physical models without the need for human intuition other than requiring the compactness of effective cluster interactions. However, conventional compressive sensing based on L1-norm regularization is strictly only applicable to certain classes of optimization problems and is otherwise not guaranteed to generate optimally sparse and transferable results, so that the method can only be applied to some materials science applications. In this paper, we illustrate a more robust L0L1-norm compressive-sensing method that removes the limitations of conventional compressive sensing and generally results in sparser lattice models that are at least as predictive as those obtained from L1-norm compressive sensing. Apart from the theory, a practical implementation based on state-of-the-art mixed-integer quadratic programming (MIQP) is proposed. The robustness of our methodology is illustrated for four different transition-metal oxides with relevance as battery cathode materials: Li2xTi2(1-x)O2, Li2xNi2yO2, MgxCr2O4, and NaxCrO2. This method provides a practical and robust approach for the construction of sparser and more predictive lattice models, improving on the compressive sensing paradigm and making it applicable to a much broader range of applications.

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

The active phase responsible for low-temperature CO oxidation in nanoparticulate CuO/CeO[subscript 2] catalysts was identified as surface-substituted Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x]. Contrary to previous studies, our measurements on a library of well-defined CuO/CeO[subscript 2] catalysts have proven that the CuO phase is a spectator species, whereas the surface-substituted Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] phase is active for CO oxidation. Using in situ X-ray absorption spectroscopy, we found that the copper ions in Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] remain at high oxidation states (Cu[superscript 3+] and Cu[superscript 2+]) under oxygen-rich catalytic conditions without any evidence for Cu+. Artificial neural network potential Monte Carlo simulations suggest that Cu[superscript 3+] and Cu[superscript 2+] preferentially segregate to the {100} surface of the Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] nanoparticle, which is supported by aberration-corrected electron microscopy measurements. These results pave the way for understanding, at the atomic level, the mechanisms and descriptors pertinent for CO oxidation on these materials and hence the rational design of next-generation catalysts., National Science Foundation (U.S.) (grant number ACI-1053575), United States. Department of Energy. Office of Science (Contract No. DE-AC02- 05CH11231), United States. Department of Energy. Office of Basic Energy Sciences (Contract No. DE-AC02-98CH10886), Philip Morris International, National Science Foundation (U.S.) (Graduate Research Fellowship under Grant No. DGE-1122374), Schlumberger Foundation. Faculty for the Future (fellowship)

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

The active phase responsible for low-temperature CO oxidation in nanoparticulate CuO/CeO[subscript 2] catalysts was identified as surface-substituted Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x]. Contrary to previous studies, our measurements on a library of well-defined CuO/CeO[subscript 2] catalysts have proven that the CuO phase is a spectator species, whereas the surface-substituted Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] phase is active for CO oxidation. Using in situ X-ray absorption spectroscopy, we found that the copper ions in Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] remain at high oxidation states (Cu[superscript 3+] and Cu[superscript 2+]) under oxygen-rich catalytic conditions without any evidence for Cu+. Artificial neural network potential Monte Carlo simulations suggest that Cu[superscript 3+] and Cu[superscript 2+] preferentially segregate to the {100} surface of the Cu[subscript y]Ce[subscript 1–y]O[subscript 2–x] nanoparticle, which is supported by aberration-corrected electron microscopy measurements. These results pave the way for understanding, at the atomic level, the mechanisms and descriptors pertinent for CO oxidation on these materials and hence the rational design of next-generation catalysts., National Science Foundation (U.S.) (grant number ACI-1053575), United States. Department of Energy. Office of Science (Contract No. DE-AC02- 05CH11231), United States. Department of Energy. Office of Basic Energy Sciences (Contract No. DE-AC02-98CH10886), Philip Morris International, National Science Foundation (U.S.) (Graduate Research Fellowship under Grant No. DGE-1122374), Schlumberger Foundation. Faculty for the Future (fellowship)

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.