{"title":"计算岩盐和蓝晶锌半导体晶格热导率时交换相关函数的层次结构","authors":"Jiacheng Wei, Zhonghao Xia, Yi Xia, Jiangang He","doi":"10.1103/physrevb.110.035205","DOIUrl":null,"url":null,"abstract":"Lattice thermal conductivity (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>κ</mi><mi mathvariant=\"normal\">L</mi></msub></math>) is a crucial characteristic of crystalline solids with significant implications for thermal management, energy conversion, and thermal barrier coating. The advancement of computational tools based on density functional theory (DFT) has enabled the effective utilization of phonon quasiparticle-based approaches to unravel the underlying physics of various crystalline systems. While the higher order of anharmonicity is commonly used for explaining extraordinary heat transfer behaviors in crystals, the impact of exchange-correlation (XC) functionals in DFT on describing anharmonicity has been largely overlooked. The XC functional is essential for determining the accuracy of DFT in describing interactions among electrons/ions in solids and molecules. However, most XC functionals in solid-state physics are primarily focused on computing the properties that only require small atomic displacements from the equilibrium (within the harmonic approximation), such as harmonic phonons and elastic constants, while anharmonicity involves larger atomic displacements. Therefore, it is more challenging for XC functionals to accurately describe atomic interactions at the anharmonicity level. In this study, we systematically investigate the room-temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>κ</mi><mi mathvariant=\"normal\">L</mi></msub></math> of 16 binary compounds with rocksalt and zinc-blende structures using various XC functionals such as local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), revised PBE for solid and surface (PBEsol), optimized B86b functional (optB86b), revised Tao-Perdew-Staroverov-Scuseria (revTPSS), strongly constrained and appropriately normed functional (SCAN), regularized SCAN (rSCAN), and regularized-restored SCAN (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mrow><mi mathvariant=\"normal\">r</mi></mrow><mn>2</mn></msup><mi>SCAN</mi></mrow></math>) in combination with different perturbation orders, including phonon within harmonic approximation (HA) plus three-phonon scattering (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>HA</mi><mo>+</mo><mrow><mn>3</mn><mi>ph</mi></mrow></mrow></math>), phonon calculated using self-consistent phonon theory (SCPH) plus three-phonon scattering (SCPH <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>+</mo></math> 3ph), and SCPH phonon plus three- and four-phonon scattering (SCPH <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>+</mo></math> 3,4ph). Our results show that the XC functional exhibits strong entanglement with perturbation order and the mean relative absolute error (MRAE) of the computed <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>κ</mi><mi mathvariant=\"normal\">L</mi></msub></math> is strongly influenced by both the XC functional and perturbation order, leading to error cancellation or amplification. The minimal (maximal) MRAE is achieved with revTPSS (rSCAN) at the HA <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>+</mo></math> 3ph level, SCAN (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mrow><mi mathvariant=\"normal\">r</mi></mrow><mn>2</mn></msup><mi>SCAN</mi></mrow></math>) at the SCPH <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>+</mo></math> 3ph level, and PBEsol (rSCAN) at the SCPH <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>+</mo></math> 3,4ph level. Among these functionals, PBEsol exhibits the highest accuracy at the highest perturbation order. The SCAN-related functionals demonstrate moderate accuracy but are suffer from numerical instability and high computational costs. Furthermore, the different impacts of quartic anharmonicity on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>κ</mi><mi mathvariant=\"normal\">L</mi></msub></math> in rocksalt and zinc-blende structures are identified by all XC functionals, attributed to the distinct lattice anharmonicity in these two structures. These findings serve as a valuable reference for selecting appropriate functionals for describing anharmonic phonons and offer insights into high-order force constant calculations that could facilitate the development of more accurate XC functionals for solid materials.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hierarchy of exchange-correlation functionals in computing lattice thermal conductivities of rocksalt and zinc-blende semiconductors\",\"authors\":\"Jiacheng Wei, Zhonghao Xia, Yi Xia, Jiangang He\",\"doi\":\"10.1103/physrevb.110.035205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Lattice thermal conductivity (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mi>κ</mi><mi mathvariant=\\\"normal\\\">L</mi></msub></math>) is a crucial characteristic of crystalline solids with significant implications for thermal management, energy conversion, and thermal barrier coating. The advancement of computational tools based on density functional theory (DFT) has enabled the effective utilization of phonon quasiparticle-based approaches to unravel the underlying physics of various crystalline systems. While the higher order of anharmonicity is commonly used for explaining extraordinary heat transfer behaviors in crystals, the impact of exchange-correlation (XC) functionals in DFT on describing anharmonicity has been largely overlooked. The XC functional is essential for determining the accuracy of DFT in describing interactions among electrons/ions in solids and molecules. However, most XC functionals in solid-state physics are primarily focused on computing the properties that only require small atomic displacements from the equilibrium (within the harmonic approximation), such as harmonic phonons and elastic constants, while anharmonicity involves larger atomic displacements. Therefore, it is more challenging for XC functionals to accurately describe atomic interactions at the anharmonicity level. In this study, we systematically investigate the room-temperature <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mi>κ</mi><mi mathvariant=\\\"normal\\\">L</mi></msub></math> of 16 binary compounds with rocksalt and zinc-blende structures using various XC functionals such as local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), revised PBE for solid and surface (PBEsol), optimized B86b functional (optB86b), revised Tao-Perdew-Staroverov-Scuseria (revTPSS), strongly constrained and appropriately normed functional (SCAN), regularized SCAN (rSCAN), and regularized-restored SCAN (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msup><mrow><mi mathvariant=\\\"normal\\\">r</mi></mrow><mn>2</mn></msup><mi>SCAN</mi></mrow></math>) in combination with different perturbation orders, including phonon within harmonic approximation (HA) plus three-phonon scattering (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>HA</mi><mo>+</mo><mrow><mn>3</mn><mi>ph</mi></mrow></mrow></math>), phonon calculated using self-consistent phonon theory (SCPH) plus three-phonon scattering (SCPH <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>+</mo></math> 3ph), and SCPH phonon plus three- and four-phonon scattering (SCPH <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>+</mo></math> 3,4ph). Our results show that the XC functional exhibits strong entanglement with perturbation order and the mean relative absolute error (MRAE) of the computed <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mi>κ</mi><mi mathvariant=\\\"normal\\\">L</mi></msub></math> is strongly influenced by both the XC functional and perturbation order, leading to error cancellation or amplification. The minimal (maximal) MRAE is achieved with revTPSS (rSCAN) at the HA <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>+</mo></math> 3ph level, SCAN (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msup><mrow><mi mathvariant=\\\"normal\\\">r</mi></mrow><mn>2</mn></msup><mi>SCAN</mi></mrow></math>) at the SCPH <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>+</mo></math> 3ph level, and PBEsol (rSCAN) at the SCPH <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>+</mo></math> 3,4ph level. Among these functionals, PBEsol exhibits the highest accuracy at the highest perturbation order. The SCAN-related functionals demonstrate moderate accuracy but are suffer from numerical instability and high computational costs. Furthermore, the different impacts of quartic anharmonicity on <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mi>κ</mi><mi mathvariant=\\\"normal\\\">L</mi></msub></math> in rocksalt and zinc-blende structures are identified by all XC functionals, attributed to the distinct lattice anharmonicity in these two structures. These findings serve as a valuable reference for selecting appropriate functionals for describing anharmonic phonons and offer insights into high-order force constant calculations that could facilitate the development of more accurate XC functionals for solid materials.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.035205\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.035205","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Hierarchy of exchange-correlation functionals in computing lattice thermal conductivities of rocksalt and zinc-blende semiconductors
Lattice thermal conductivity () is a crucial characteristic of crystalline solids with significant implications for thermal management, energy conversion, and thermal barrier coating. The advancement of computational tools based on density functional theory (DFT) has enabled the effective utilization of phonon quasiparticle-based approaches to unravel the underlying physics of various crystalline systems. While the higher order of anharmonicity is commonly used for explaining extraordinary heat transfer behaviors in crystals, the impact of exchange-correlation (XC) functionals in DFT on describing anharmonicity has been largely overlooked. The XC functional is essential for determining the accuracy of DFT in describing interactions among electrons/ions in solids and molecules. However, most XC functionals in solid-state physics are primarily focused on computing the properties that only require small atomic displacements from the equilibrium (within the harmonic approximation), such as harmonic phonons and elastic constants, while anharmonicity involves larger atomic displacements. Therefore, it is more challenging for XC functionals to accurately describe atomic interactions at the anharmonicity level. In this study, we systematically investigate the room-temperature of 16 binary compounds with rocksalt and zinc-blende structures using various XC functionals such as local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), revised PBE for solid and surface (PBEsol), optimized B86b functional (optB86b), revised Tao-Perdew-Staroverov-Scuseria (revTPSS), strongly constrained and appropriately normed functional (SCAN), regularized SCAN (rSCAN), and regularized-restored SCAN () in combination with different perturbation orders, including phonon within harmonic approximation (HA) plus three-phonon scattering (), phonon calculated using self-consistent phonon theory (SCPH) plus three-phonon scattering (SCPH 3ph), and SCPH phonon plus three- and four-phonon scattering (SCPH 3,4ph). Our results show that the XC functional exhibits strong entanglement with perturbation order and the mean relative absolute error (MRAE) of the computed is strongly influenced by both the XC functional and perturbation order, leading to error cancellation or amplification. The minimal (maximal) MRAE is achieved with revTPSS (rSCAN) at the HA 3ph level, SCAN () at the SCPH 3ph level, and PBEsol (rSCAN) at the SCPH 3,4ph level. Among these functionals, PBEsol exhibits the highest accuracy at the highest perturbation order. The SCAN-related functionals demonstrate moderate accuracy but are suffer from numerical instability and high computational costs. Furthermore, the different impacts of quartic anharmonicity on in rocksalt and zinc-blende structures are identified by all XC functionals, attributed to the distinct lattice anharmonicity in these two structures. These findings serve as a valuable reference for selecting appropriate functionals for describing anharmonic phonons and offer insights into high-order force constant calculations that could facilitate the development of more accurate XC functionals for solid materials.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
-Disordered systems and alloys
-Magnetism
-Superconductivity
-Electronic structure, photonics, and metamaterials
-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter