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Development of a Deep Machine Learning Interatomic Potential for Metalloid-Containing Pd-Si Compounds

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Development of a Deep Machine Learning Interatomic Potential for Metalloid-Containing Pd-Si Compounds Ames Laboratory Accepted Manuscripts Ames Laboratory 11-1-2019 Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds Tongqi Wen Ames Laboratory and Northwestern Polytechnical University Cai-Zhuang Wang Iowa State University and Ames Laboratory, [email protected] Matthew J. Kramer Ames Laboratory, [email protected] Yang Sun Ames Laboratory Beilin Ye South China University of Technology See next page for additional authors Follow this and additional works at: https://lib.dr.iastate.edu/ameslab_manuscripts Part of the Condensed Matter Physics Commons Recommended Citation Wen, Tongqi; Wang, Cai-Zhuang; Kramer, Matthew J.; Sun, Yang; Ye, Beilin; Wang, Haidi; Liu, Xueyuan; Zhang, Chao; Zhang, Feng; Ho, Kai-Ming; and Wang, Nan, "Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds" (2019). Ames Laboratory Accepted Manuscripts. 663. https://lib.dr.iastate.edu/ameslab_manuscripts/663 This Article is brought to you for free and open access by the Ames Laboratory at Iowa State University Digital Repository. It has been accepted for inclusion in Ames Laboratory Accepted Manuscripts by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Development of a deep machine learning interatomic potential for metalloid- containing Pd-Si compounds Abstract Interatomic potentials based on neural-network machine learning (ML) approach to address the long- standing challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. Here, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting ot the energies and forces of both liquid and crystal structures first- principles calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in Pd82Si18 and Pd75Si25 liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at Pd3Si and Pd9Si2 composition, the developed ML potential predicts correctly the ground- state structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system. Disciplines Condensed Matter Physics Authors Tongqi Wen, Cai-Zhuang Wang, Matthew J. Kramer, Yang Sun, Beilin Ye, Haidi Wang, Xueyuan Liu, Chao Zhang, Feng Zhang, Kai-Ming Ho, and Nan Wang This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ameslab_manuscripts/ 663 PHYSICAL REVIEW B 100, 174101 (2019) Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds Tongqi Wen ,1,2 Cai-Zhuang Wang,2,3,* M. J. Kramer ,2 Yang Sun ,2 Beilin Ye,4 Haidi Wang,2 Xueyuan Liu,2 Chao Zhang ,2,5 Feng Zhang,2 Kai-Ming Ho,2,3 and Nan Wang 1,† 1MOE Key Laboratory of Materials Physics and Chemistry under Extraordinary Conditions, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an 710072, China 2Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA 3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 4School of Materials Science and Engineering, South China University of Technology, Guangzhou 510641, China 5Department of Physics, School of Opto-electronic Information Science and Technology, Yantai University, Yantai, 264005, China (Received 16 July 2019; revised manuscript received 8 October 2019; published 4 November 2019) Interatomic potentials based on neural-network machine learning (ML) approach to address the long-standing challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. Here, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting to the energies and forces of both liquid and crystal structures first-principles calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in Pd82Si18 and Pd75Si25 liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at Pd3Si and Pd9Si2 composition, the developed ML potential predicts correctly the ground-state structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system. DOI: 10.1103/PhysRevB.100.174101 I. INTRODUCTION coordinates based on one’s chemical and physical insights, such as Lennard-Jones potentials for noble gas and colloidal Molecular-dynamics (MD) simulation has been attracting systems [5,6], Tersoff and Stillinger-Weber potentials [7,8] growing attention in materials science, condensed-matter for covalent systems, and embedded-atom method (EAM) physics, chemical and biological science due to its ability potentials [9] for the metallic systems. Although these to reveal atomic-level structures and dynamics as well as potentials have been widely used in MD simulations and structure-property relationship [1,2]. However, to perform have produced many useful results for better understanding reliable MD simulations, accurate and efficient description the structures and properties of many compounds [10,11], of interatomic forces are critical. Quantum-mechanics limitations for their application in more complex systems calculation based on first-principles density-functional theory have also been noticed. The fixed mathematical function (DFT) can provide accurate description of interatomic for the interatomic interactions inspired by human chemical forces and total energies for many materials, and ab initio and physical insights often cannot provide the balance MD (AIMD) simulations based on DFT have been applied between diverse properties stemming from different bonding extensively to investigate the structures and dynamics in characteristics [12]. New types of potential that can adapt different systems [3,4]. However, due to the expensive to various bonding environments in the same systems are computational demand, AIMD can usually be performed with needed for systems with complex bonding characteristics. smaller size (∼500 atoms) and shorter time (typically less Machine learning (ML) is well-known for its ability in per- than 1 ns) even with the advent of the newest-generation su- forming pattern recognition [13]. Since the energy and forces percomputers. To overcome this limitation, various empirical on an atom in a condensed-matter system are predominately interatomic potential schemes for MD simulations have been dependent on the species of the atom, its valence state, and proposed. Traditionally, interatomic potentials are defined by interactions with its neighbors, interatomic potentials fitting assuming an analytical function with respect to the atomic can be regarded as pattern recognition problem and ML is a promising approach. Under this premise, neural-network potentials (NNPs) were first proposed by Behler and Par- *[email protected] rinello [14] and were applied in MD simulations for systems †[email protected] containing thousands of atoms. In this approach, radial and 2469-9950/2019/100(17)/174101(12) 174101-1 ©2019 American Physical Society TONGQI WEN et al. PHYSICAL REVIEW B 100, 174101 (2019) angular symmetry functions were proposed as the “descrip- with Si composition less than 25 at % where many interesting tors” of the bonding environments to map the atomic coordi- and complex new phases may exist. nates onto the input values of the neural network. The param- The paper is organized as follows. In Sec. II,wefirst eters of the feed-forward neural network were then optimized introduce the ML potential development process including by fitting to the total energies of the system. Based on the the datasets utilized and the detailed parameters used in the Behler-Parrinello approach to construct the NNP, the related DEEPMD-KIT. The training and testing accuracies in compari- research has expanded into a number of different systems, son with the first-principles DFT results are then discussed. such as bulk silicon [14] and carbon [15], TiO2 [16], CaF2 In Sec. III, the liquid structure obtained by NNP-MD is [17], et al. However, the fixed symmetry functions reduce the compared with that by AIMD and the EAM potential from flexibility of the NNPs to describe the complex bonding situ- Sheng [37] through the pair-distribution functions (PDFs) and ations, particularly for systems with many chemical elements. the cluster alignment method [38,39]. Genetic algorithm (GA) Recently,
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