Jan M. Waack, Nils A. Schäfer, Michael Czerner, Christian Heiliger
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{"title":"立方锌-蓝晶𝑥Ga1-𝑥合金的结构、弹性和电子特性","authors":"Jan M. Waack, Nils A. Schäfer, Michael Czerner, Christian Heiliger","doi":"10.1103/physrevb.110.195201","DOIUrl":null,"url":null,"abstract":"The cubic phase of the ternary <mjx-container ctxtmenu_counter=\"26\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(12 (2 0 1) 10 (8 3 (7 4 5 6)) 11 9)\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,8,9\" data-semantic-content=\"10,11\" data-semantic- data-semantic-owns=\"2 10 8 11 9\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper I n Subscript x Baseline upper G a Subscript 1 minus x Baseline normal upper N\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">I</mjx-c><mjx-c style=\"padding-top: 0.657em;\">n</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,7\" data-semantic- data-semantic-owns=\"3 7\" data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">a</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-owns=\"4 5 6\" data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"7\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> alloy has attracted significant interest as a material for next-generation high-performance electronic and optoelectronic applications. It has recently been demonstrated that epitaxial growth techniques can overcome the miscibility gap in this alloy system, thereby revealing the existence of CuPt-type ordering around <mjx-container ctxtmenu_counter=\"27\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(3 0 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"x almost equals 0.5\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,≈\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>≈</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> [<span>ACS Appl. Mater. Interfaces</span> <b>15</b>, 39513 (2023)]. We present a comprehensive theoretical analysis of the structural and electronic properties of the (In, Ga)N alloy in the zinc-blende structure. This study covers both pure phases of InN and GaN, as well as random alloys of <mjx-container ctxtmenu_counter=\"28\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(12 (2 0 1) 10 (8 3 (7 4 5 6)) 11 9)\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,8,9\" data-semantic-content=\"10,11\" data-semantic- data-semantic-owns=\"2 10 8 11 9\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper I n Subscript x Baseline upper G a Subscript 1 minus x Baseline normal upper N\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">I</mjx-c><mjx-c style=\"padding-top: 0.657em;\">n</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,7\" data-semantic- data-semantic-owns=\"3 7\" data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">a</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-owns=\"4 5 6\" data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"7\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>. Furthermore, it examines the composition of <mjx-container ctxtmenu_counter=\"29\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(9 (2 0 1) 7 (5 3 4) 8 6)\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5,6\" data-semantic-content=\"7,8\" data-semantic- data-semantic-owns=\"2 7 5 8 6\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper I n 0.5 upper G a 0.5 normal upper N\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"9\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">I</mjx-c><mjx-c style=\"padding-top: 0.657em;\">n</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"9\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">a</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> in the ordered phases with CuPt-type ordering and chalcopyrite-type ordering. We establish that the investigated structures are metastable. The results presented include the lattice parameters, elastic constants, and the phononic and electronic band structures. We compare the random phase with the ordered structures and report how the structure affects the properties. This results facilitate the differentiation between the phases in experimental settings.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Structural, elastic, and electronic properties of cubic zinc-blendeIn𝑥Ga1−𝑥Nalloys\",\"authors\":\"Jan M. Waack, Nils A. Schäfer, Michael Czerner, Christian Heiliger\",\"doi\":\"10.1103/physrevb.110.195201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The cubic phase of the ternary <mjx-container ctxtmenu_counter=\\\"26\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(12 (2 0 1) 10 (8 3 (7 4 5 6)) 11 9)\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,8,9\\\" data-semantic-content=\\\"10,11\\\" data-semantic- data-semantic-owns=\\\"2 10 8 11 9\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper I n Subscript x Baseline upper G a Subscript 1 minus x Baseline normal upper N\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.657em;\\\">I</mjx-c><mjx-c style=\\\"padding-top: 0.657em;\\\">n</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,7\\\" data-semantic- data-semantic-owns=\\\"3 7\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.669em;\\\">G</mjx-c><mjx-c style=\\\"padding-top: 0.669em;\\\">a</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic- data-semantic-owns=\\\"4 5 6\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"infixop\\\" size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,−\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" space=\\\"2\\\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> alloy has attracted significant interest as a material for next-generation high-performance electronic and optoelectronic applications. It has recently been demonstrated that epitaxial growth techniques can overcome the miscibility gap in this alloy system, thereby revealing the existence of CuPt-type ordering around <mjx-container ctxtmenu_counter=\\\"27\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(3 0 1 2)\\\"><mjx-mrow data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"x almost equals 0.5\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≈\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\" space=\\\"4\\\"><mjx-c>≈</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">5</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> [<span>ACS Appl. Mater. Interfaces</span> <b>15</b>, 39513 (2023)]. We present a comprehensive theoretical analysis of the structural and electronic properties of the (In, Ga)N alloy in the zinc-blende structure. This study covers both pure phases of InN and GaN, as well as random alloys of <mjx-container ctxtmenu_counter=\\\"28\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(12 (2 0 1) 10 (8 3 (7 4 5 6)) 11 9)\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,8,9\\\" data-semantic-content=\\\"10,11\\\" data-semantic- data-semantic-owns=\\\"2 10 8 11 9\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper I n Subscript x Baseline upper G a Subscript 1 minus x Baseline normal upper N\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.657em;\\\">I</mjx-c><mjx-c style=\\\"padding-top: 0.657em;\\\">n</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,7\\\" data-semantic- data-semantic-owns=\\\"3 7\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.669em;\\\">G</mjx-c><mjx-c style=\\\"padding-top: 0.669em;\\\">a</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic- data-semantic-owns=\\\"4 5 6\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"infixop\\\" size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,−\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑥</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" space=\\\"2\\\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>. Furthermore, it examines the composition of <mjx-container ctxtmenu_counter=\\\"29\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(9 (2 0 1) 7 (5 3 4) 8 6)\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,5,6\\\" data-semantic-content=\\\"7,8\\\" data-semantic- data-semantic-owns=\\\"2 7 5 8 6\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper I n 0.5 upper G a 0.5 normal upper N\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.657em;\\\">I</mjx-c><mjx-c style=\\\"padding-top: 0.657em;\\\">n</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">5</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.669em;\\\">G</mjx-c><mjx-c style=\\\"padding-top: 0.669em;\\\">a</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">5</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" space=\\\"2\\\"><mjx-c>N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> in the ordered phases with CuPt-type ordering and chalcopyrite-type ordering. We establish that the investigated structures are metastable. The results presented include the lattice parameters, elastic constants, and the phononic and electronic band structures. We compare the random phase with the ordered structures and report how the structure affects the properties. This results facilitate the differentiation between the phases in experimental settings.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-11-05\",\"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.110.195201\",\"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.110.195201","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}
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