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Register a new userEfficient Construction Method for Phase Diagrams Using Uncertainty Sampling
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We develop a method to efficiently construct phase diagrams using machine learning. Uncertainty sampling (US) in active learning is utilized to intensively sample around phase boundaries. Here, we demonstrate constructions of three known experimental phase diagrams by the US approach. Compared with random sampling, the US approach decreases the number of sampling points to about 20%. In particular, the reduction rate is pronounced in more complicated phase diagrams. Furthermore, we show that using the US approach, undetected new phase can be rapidly found, and smaller number of initial sampling points are sufficient. Thus, we conclude that the US approach is useful to construct complicated phase diagrams from scratch and will be an essential tool in materials science.
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We introduce a massively parallel replica-exchange grand-canonical sampling algorithm to simulate materials at realistic conditions, in particular surfaces and clusters in reactive atmospheres. Its purpose is to determine in an automated fashion equilibrium phase diagrams for a given potential-energy surface (PES) and for any observable sampled in the grand-canonical ensemble. The approach enables an unbiased sampling of the phase space and is embarrassingly parallel. It is demonstrated for a model of Lennard-Jones system describing a surface in contact with a gas phase. Furthermore, the algorithm is applied to Si$_M$ clusters ($M=2, 4$) in contact with an H$_{2}$ atmosphere, with all interactions described at the textit{ab initio} level, i.e., via density-functional theory, with the PBE gradient-corrected exchange-correlation functional. We identify the most thermodynamically stable phases at finite $T, p$(H$_{2}$) conditions.
We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram, for a given potential energy function, efficiently and in a highly automated fashion. The only inputs required are the composition and the desired pressure and temperature ranges, in particular, solid-solid phase transitions are recovered without any a priori knowledge about the structure of solid phases. We benchmark and showcase the algorithm on the periodic Lennard-Jones system, aluminium and NiTi.
Accurate and efficient predictions of the quasiparticle properties of complex materials remain a major challenge due to the convergence issue and the unfavorable scaling of the computational cost with respect to the system size. Quasiparticle $GW$ calculations for two dimensional (2D) materials are especially difficult. The unusual analytical behaviors of the dielectric screening and the electron self-energy of 2D materials make the conventional Brillouin zone (BZ) integration approach rather inefficient and require an extremely dense $k$-grid to properly converge the calculated quasiparticle energies. In this work, we present a combined non-uniform sub-sampling and analytical integration method that can drastically improve the efficiency of the BZ integration in 2D $GW$ calculations. Our work is distinguished from previous work in that, instead of focusing on the intricate dielectric matrix or the screened Coulomb interaction matrix, we exploit the analytical behavior of various terms of the convolved self-energy $Sigma(mathbf{q})$ in the small $mathbf{q}$ limit. This method, when combined with another accelerated $GW$ method that we developed recently, can drastically speed-up (by over three orders of magnitude) $GW$ calculations for 2D materials. Our method allows fully converged $GW$ calculations for complex 2D systems at a fraction of computational cost, facilitating future high throughput screening of the quasiparticle properties of 2D semiconductors for various applications. To demonstrate the capability and performance of our new method, we have carried out fully converged $GW$ calculations for monolayer C$_2$N, a recently discovered 2D material with a large unit cell, and investigate its quasiparticle band structure in detail.
Data science and informatics tools have been proliferating recently within the computational materials science and catalysis fields. This proliferation has spurned the creation of various frameworks for automated materials screening, discovery, and design. Underpinning these frameworks are surrogate models with uncertainty estimates on their predictions. These uncertainty estimates are instrumental for determining which materials to screen next, but the computational catalysis field does not yet have a standard procedure for judging the quality of such uncertainty estimates. Here we present a suite of figures and performance metrics derived from the machine learning community that can be used to judge the quality of such uncertainty estimates. This suite probes the accuracy, calibration, and sharpness of a model quantitatively. We then show a case study where we judge various methods for predicting density-functional-theory-calculated adsorption energies. Of the methods studied here, we find that the best performer is a model where a convolutional neural network is used to supply features to a Gaussian process regressor, which then makes predictions of adsorption energies along with corresponding uncertainty estimates.
Energetic particle irradiation of solids can cause surface ultra-smoothening, self-organized nanoscale pattern formation, or degradation of the structural integrity of nuclear reactor components. Periodic patterns including high-aspect ratio quantum dots, with occasional long-range order and characteristic spacing as small as 7 nm, have stimulated interest in this method as a means of sub-lithographic nanofabrication. Despite intensive research there is little fundamental understanding of the mechanisms governing the selection of smooth or patterned surfaces, and precisely which physical effects cause observed transitions between different regimes has remained a matter of speculation. Here we report the first prediction of the mechanism governing the transition from corrugated surfaces to flatness, using only parameter-free molecular dynamics simulations of single-ion impact induced crater formation as input into a multi-scale analysis, and showing good agreement with experiment. Our results overturn the paradigm attributing these phenomena to the removal of target atoms via sputter erosion. Instead, the mechanism dominating both stability and instability is shown to be the impact-induced redistribution of target atoms that are not sputtered away, with erosive effects being essentially irrelevant. The predictions are relevant in the context of tungsten plasma-facing fusion reactor walls which, despite a sputter erosion rate that is essentially zero, develop, under some conditions, a mysterious nanoscale topography leading to surface degradation. Our results suggest that degradation processes originating in impact-induced target atom redistribution effects may be important, and hence that an extremely low sputter erosion rate is an insufficient design criterion for morphologically stable solid surfaces under energetic particle irradiation.
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