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Register a new userSupervised deep learning prediction of the formation enthalpy of the full set of configurations in complex phases: the $sigma-$phase as an example
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Machine learning (ML) methods are becoming integral to scientific inquiry in numerous disciplines, such as material sciences. In this manuscript, we demonstrate how ML can be used to predict several properties in solid-state chemistry, in particular the heat of formation of a given complex crystallographic phase (here the $sigma-$phase, $tP30$, $D8_{b}$). Based on an independent and unprecedented large first principles dataset containing about 10,000 $sigma-$compounds with $n=14$ different elements, we used a supervised learning approach, to predict all the $sim$500,000 possible configurations within a mean absolute error of 23 meV/at ($sim$2 kJ.mol$^{-1}$) on the heat of formation and $sim$0.06 Ang. on the tetragonal cell parameters. We showed that neural network regression algorithms provide a significant improvement in accuracy of the predicted output compared to traditional regression techniques. Adding descriptors having physical nature (atomic radius, number of valence electrons) improves the learning precision. Based on our analysis, the training database composed of the only binary-compositions plays a major role in predicting the higher degree system configurations. Our result opens a broad avenue to efficient high-throughput investigations of the combinatorial binary calculation for multicomponent prediction of a complex phase.
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The need for advanced materials has led to the development of complex, multi-component alloys or solid-solution alloys. These materials have shown exceptional properties like strength, toughness, ductility, electrical and electronic properties. Current development of such material systems are hindered by expensive experiments and computationally demanding first-principles simulations. Atomistic simulations can provide reasonable insights on properties in such material systems. However, the issue of designing robust potentials still exists. In this paper, we explore a deep convolutional neural-network based approach to develop the atomistic potential for such complex alloys to investigate materials for insights into controlling properties. In the present work, we propose a voxel representation of the atomic configuration of a cell and design a 3D convolutional neural network to learn the interaction of the atoms. Our results highlight the performance of the 3D convolutional neural network and its efficacy in machine-learning the atomistic potential. We also explore the role of voxel resolution and provide insights into the two bounding box methodologies implemented for voxelization.
Formation energy of the $sigma$-phase in the Fe-Cr alloy system, $Delta E$, was computed versus the occupancy changes on each of the five possible lattice sites. Its dependence on a number of Fe-atoms per unit cell, $N_{Fe}$, was either monotonically increasing or decreasing function of $N_{Fe}$, depending on the site on which Fe-occupancy was changed. Based on the calculated $Delta E$ - values, the average formation energy, $<Delta E>$, was determined as a weighted over probabilities of different atomic configurations. The latter has a minimum in the concentration range where the $sigma$-phase exists. The minimum in that range of composition was also found for the free energy calculated for 2000 K and taking only the configurational entropy into account.
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: aggregation functions. We suggest and examine alternatives to commonly used aggregation functions, including learnable recurrent aggregation functions. Empirically, we show that the Deep Set networks are highly sensitive to the choice of aggregation functions: beyond improved performance, we find that learnable aggregations lower hyper-parameter sensitivity and generalize better to out-of-distribution input size.
Formation energy of the sigma-phase in the Fe-V alloy system, Delta E, was computed in the full compositional range of its occurrence (34 < x < 60) using the electronic band structure calculations by means of the KKR method. Delta E-values were found to strongly depend on the Fe concentration, also its variation with different site occupancies was characteristic of a given lattice site. Calculated magnetic and configuration entropy contributions were used to determine sublattice occupancies for various compositions and temperatures. The results agree well with those obtained from neutron diffraction measurements.
The ability to predict the likelihood of impurity incorporation and their electronic energy levels in semiconductors is crucial for controlling its conductivity, and thus the semiconductors performance in solar cells, photodiodes, and optoelectronics. The difficulty and expense of experimental and computational determination of impurity levels makes a data-driven machine learning approach appropriate. In this work, we show that a density functional theory-generated dataset of impurities in Cd-based chalcogenides CdTe, CdSe, and CdS can lead to accurate and generalizable predictive models of defect properties. By converting any semiconductor + impurity system into a set of numerical descriptors, regression models are developed for the impurity formation enthalpy and charge transition levels. These regression models can subsequently predict impurity properties in mixed anion CdX compounds (where X is a combination of Te, Se and S) fairly accurately, proving that although trained only on the end points, they are applicable to intermediate compositions. We make machine-learned predictions of the Fermi-level dependent formation energies of hundreds of possible impurities in 5 chalcogenide compounds, and suggest a list of impurities which can shift the equilibrium Fermi level in the semiconductor as determined by the dominant intrinsic defects. These dominating impurities as predicted by machine learning compare well with DFT predictions, revealing the power of machine-learned models in the quick screening of impurities likely to affect the optoelectronic behavior of semiconductors.
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