ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Original Paper

AI-based descriptor for predicting alloy formation energy

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.018
  • Received Date: 27 March 2020
  • Accepted Date: 18 May 2020
  • Rev Recd Date: 18 May 2020
  • Publish Date: 30 June 2020
  • Because of their rich geometric structure and electronic properties, metal alloys have been widely used in catalysis and materials science. Among them, alloys formation energy has an important influence on the formation and catalytic activity of metal alloys. With the development of artificial intelligence and databases in recent years, machine learning has been used to rationally design new materials. Based on the multi-task compressed sensing algotithm in artificial intelligence, the alloy formation energy descriptor of the AB2 alloy formation energy database was investigated. A universal descriptor of the corresponding alloy formation energy was established, and the sensitivity analysis of features revealed the importance of electronic and geometrical properties of metal alloys. The results show that this descriptor has a prediction error lower than 8.10kJ·mol-1 and a better physical interpretation. Finally, the formation energy of a large number of unknown metal alloys was predicted.
    Because of their rich geometric structure and electronic properties, metal alloys have been widely used in catalysis and materials science. Among them, alloys formation energy has an important influence on the formation and catalytic activity of metal alloys. With the development of artificial intelligence and databases in recent years, machine learning has been used to rationally design new materials. Based on the multi-task compressed sensing algotithm in artificial intelligence, the alloy formation energy descriptor of the AB2 alloy formation energy database was investigated. A universal descriptor of the corresponding alloy formation energy was established, and the sensitivity analysis of features revealed the importance of electronic and geometrical properties of metal alloys. The results show that this descriptor has a prediction error lower than 8.10kJ·mol-1 and a better physical interpretation. Finally, the formation energy of a large number of unknown metal alloys was predicted.
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    [2]
    SINFELT J H. Catalysis by alloys and bimetallic clusters [J]. Accounts of Chemical Research, 1977, 10(1): 15-20.
    [3]
    SINFELT J H. Structure of metal catalysts [J]. Reviews of Modern Physics, 1979, 51(3): 569.
    [4]
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    [5]
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    [6]
    PARAMSOTHY M, GUPTA M, SRIKANTH N. Processing, microstructure, and properties of a Mg/Al bimetal macrocomposite[J]. Journal of Composite Materials, 2008, 42(24): 2567-2584.
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    FERNNDEZ J L, WALSH D A, BARD A J. Thermodynamic guidelines for the design of bimetallic catalysts for oxygen electroreduction and rapid screening by scanning electrochemical microscopy. M-Co (M: Pd, Ag, Au)[J]. Journal of the American Chemical Society, 2005, 127(1): 357-365.
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    WANG C P, LIU X J, OHNUMA I, et al. Formation of immiscible alloy powders with egg-type microstructure[J]. Science, 2002, 297(5583): 990-993.
    [15]
    COLINET C. High temperature calorimetry: Recent developments[J]. Journal of Alloys and Compounds, 1995,220(1/2): 76-87.
    [16]
    TOPOR L, KLEPPA O J. Standard molar enthalpy of formation of LaB6 by high-temperature calorimetry[J]. The Journal of Chemical Thermodynamics, 1984, 16(10): 993-1002.
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    KIM G, MESCHEL S V, NASH P, et al. Experimental formation enthalpies for intermetallic phases and other inorganic compounds[J]. Scientific Data, 2017, 4(1): 170162.
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    MIEDEMA A R, CHTEL P F D, BOER F. Cohesion in alloys — fundamentals of a semi-empirical model[J]. Physica B+C, 1980, 100(1): 1-28.
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    MIEDEMA A R, BOER F R, CHATEL P F. Empirical description of the role of electronegativity in alloy formation[J]. Journal of Physics F: Metal Physics, 1973, 3(8): 1558.
    [20]
    ZHANG R F, RAJAN K. Statistically based assessment of formation enthalpy for intermetallic compounds[J]. Chemical Physics Letters, 2014, 612: 177-181.
    [21]
    ZHANG R F, ZHANG S H, HE Z J, et al. Miedema calculator: A thermodynamic platform for predicting formation enthalpies of alloys within framework of Miedema’s Theory [J]. Computer Physics Communications,2016, 209: 58-69.
    [22]
    PALINA N, SAKATA O, KUMARA L, et al. Electronic structure evolution with composition alteration of RhxCuy alloy nanoparticles[J]. Scientific Reports, 2017, 7(1): 1-9.
    [23]
    FOILES S M, BASKES M I, DAW M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys[J]. Physical Review B, 1986, 33(12): 7983.
    [24]
    JOHNSON R A. Alloy models with the embedded-atom method[J]. Physical Review B, 1989, 39(17): 12554.
    [25]
    LEI Y W, SUN X R, ZHOU R L, et al. Embedded atom method potentials for Ce-Ni binary alloy[J]. Computational Materials Science, 2018, 150: 1-8.
    [26]
    WILLIAMS A R, GELATT C D, MORUZZI V L. Microscopic basis of miedema’s empirical theory of transition-metal compound formation[J]. Physical Review Letters, 1980, 44(11): 394-395.
    [27]
    ZHANG Y, KRESSE G, WOLVERTON C. Nonlocal first-principles calculations in Cu-Au and other intermetallic alloys[J]. Physical Review Letters, 2014, 112(7): 75502.
    [28]
    FARSI L, DESKINS N A. First principles analysis of surface dependent segregation in bimetallic alloys[J]. Physical Chemistry Chemical Physics, 2019, 21(42): 23626-23637.
    [29]
    REITH D, PODLOUCKY R. First-principles model study of the phase stabilities of dilute Fe-Cu alloys: Role of vibrational free energy[J]. Physical Review B, 2009, 80(5): 54108.
    [30]
    OU L. The origin of enhanced electrocatalytic activity of Pt-M (M= Fe, Co, Ni, Cu, and W) alloys in PEM fuel cell cathodes: A DFT computational study[J]. Computational and Theoretical Chemistry, 2014, 1048: 69-76.
    [31]
    GUBAEV K, PODRYABINKIN E V, HART G L, et al. Accelerating high-throughput searches for new alloys with active learning of interatomic potentials[J]. Computational Materials Science, 2019, 156: 148-156.
    [32]
    DOAK J W, HAO S, KIRKLIN S, et al. Computational prediction of nanostructured alloys with enhanced thermoelectric properties[J]. Physical Review Materials, 2019, 3(10): 105404.
    [33]
    JAIN A, ONG S P, HAUTIER G, et al. Commentary: The materials project: A materials genome approach to accelerating materials innovation[J]. APL Materials, 2013, 1(1): 11002.
    [34]
    SAAL J E, KIRKLIN S, AYKOL M, et al. Materials design and discovery with high-throughput density functional theory: The open quantum materials database (OQMD)[J]. JOM, 2013, 65(11): 1501-1509.
    [35]
    WU X D, ZHU X Q, WU G Q, et al. Data mining with big data[J]. IEEE Transactions on Knowledge and Data Engineering, 2013, 26(1): 97-107.
    [36]
    ROSCHER R, BOHN B, DUARTE M F, et al. Explainable machine learning for scientific insights and discoveries[J]. IEEE Access, 2020, 8: 42200- 42216.
    [37]
    LI Z, WANG S W, CHIN W S, et al. High-throughput screening of bimetallic catalysts enabled by machine learning[J]. Journal of Materials Chemistry A, 2017, 5(46): 24131-24138.
    [38]
    GHIRINGHELLI L M, VYBIRAL J, LEVCHENKO S V, et al. Big data of materials science: Critical role of the descriptor[J]. Physical Review Letters, 2015, 114(10): 105503.
    [39]
    RUBAN A, HAMMER B, STOLTZE P, et al. Surface electronic structure and reactivity of transition and noble metals[J]. Journal of Molecular Catalysis A: Chemical, 1997, 115(3): 421-429.
    [40]
    ZHAO Z J, LIU S H, ZHA S J, et al. Theory-guided design of catalytic materials using scaling relationships and reactivity descriptors[J]. Nature Reviews Materials, 2019, 4: 792-804.
    [41]
    CHOI K, JANG Y, CHUNG D Y, et al. A simple synthesis of urchin-like Pt-Ni bimetallic nanostructures as enhanced electrocatalysts for the oxygen reduction reaction[J]. Chemical Communications, 2016, 52(3): 597-600.
    [42]
    LI H, WEN P, LI Q, et al. Earth-abundant iron diboride (FeB2) nanoparticles as highly active bifunctional electrocatalysts for overall water splitting[J]. Advanced Energy Materials, 2017, 7(17): 1700513.
    [43]
    YUAN W Y, ZHAO X S, HAO W J, et al. Performance of surface-oxidized Ni3B, Ni2B, and NiB2 electrocatalysts for overall water splitting[J]. ChemElectroChem, 2019, 6(3): 764-770.
    [44]
    ZALUSKA A, ZALUSKI L, STRM-OLSEN J O. Synergy of hydrogen sorption in ball-milled hydrides of Mg and Mg2Ni[J]. Journal of Alloys and Compounds, 1999, 289(1/2): 197-206.
    [45]
    ZHANG L T, CAI Z L, YAO Z D, et al. A striking catalytic effect of facile synthesized ZrMn2 nanoparticles on the de/rehydrogenation properties of MgH2[J]. Journal of Materials Chemistry A, 2019, 7(10): 5626-5634.
    [46]
    OUYANG R H, CURTAROLO S, AHMETCIK E, et al. SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates[J]. Physical Review Materials, 2018, 2: 083802.
    [47]
    OUYANG R H, AHMETCIK E, CARBOGNO C, et al. Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO[J]. Journal of Physics: Materials, 2019, 2(2): 24002.
    [48]
    BARTEL C J, MILLICAN S L, DEML A M, et al. Physical descriptor for the Gibbs energy of inorganic crystalline solids and temperature-dependent materials chemistry[J]. Nature Communications, 2018, 9: 4168.
    [49]
    BARTEL C J, SUTTON C, GOLDSMITH B R, et al. New tolerance factor to predict the stability of perovskite oxides and halides[J]. Science Advances, 2019, 5(2): evva0693.
    [50]
    ANDERSEN M, LEVCHENKO S V, SCHEFFLER M, et al. Beyond scaling relations for the description of catalytic materials[J]. ACS Catalysis, 2019, 9(4): 2752-2759.
    [51]
    OUYANG R H. Exploiting ionic radii for rational design of halide perovskites[J]. Chemistry of Materials,2020, 32(1): 595-604.
    [52]
    HAYNES W M. CRC Handbook of Chemistry and Physics[M]. Boca Raton, FL: CRC Press, 2014.
    [53]
    MEDVEDEV V A, COX J D, WAGMAN D D. CODATA Key Values for Thermodynamics[M]. New York: Hemisphere Publishing Corporation, 1989.
    [54]
    BLUM A L, LANGLEY P. Selection of relevant features and examples in machine learning[J]. Artificial Intelligence, 1997, 97(1/2): 245-271.
    [55]
    BREIMAN L, SPECTOR P. Submodel selection and evaluation in regression. The X-random case[J]. International Statistical Review, 1992, 60(3): 291-319.
    [56]
    RAO R B, FUNG G, ROSALES R. On the dangers of cross-validation. An experimental evaluation[C]// Proceedings of the 2008 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2008:588.
    [57]
    GHIRINGHELLI L M, VYBIRAL J, AHMETCIK E, et al. Learning physical descriptors for materials science by compressed sensing[J]. New Journal of Physics, 2017, 19(2): 23017.
    [58]
    MA X F, LI Z, ACHENIE L E K, et al. Machine-learning-augmented chemisorption model for CO2 electroreduction catalyst screening[J]. The Journal of Physical Chemistry Letters, 2015, 6(18): 3528-3533.
    [59]
    吴春峰, 李慧改, 郑少波, 等. 二元合金热力学模型—Miedema模型[J].上海金属, 2011, 33(4): 1-5.
    [60]
    WATSON R E, BENNETT L H. Optimized predictions for heats of formation of transition-metal alloys II [J]. Calphad, 1984, 8(4): 307-321.)
  • 加载中

Catalog

    [1]
    MITTASCH A, FRANKENBURG W. Early studies of multicomponent catalysts [J]. Advances in Catalysis, 1950, 2(6): 81-104.
    [2]
    SINFELT J H. Catalysis by alloys and bimetallic clusters [J]. Accounts of Chemical Research, 1977, 10(1): 15-20.
    [3]
    SINFELT J H. Structure of metal catalysts [J]. Reviews of Modern Physics, 1979, 51(3): 569.
    [4]
    XU F Y, DENG S B, XU J, et al. Highly active and stable Ni-Fe bimetal prepared by ball milling for catalytic hydrodechlorination of 4-chlorophenol[J]. Environmental Science & Technology, 2012, 46(8): 4576-4582.
    [5]
    HUANG X, LI Y, et al. Synthesis of PtPd bimetal nanocrystals with controllable shape, composition, and their tunable catalytic properties[J]. Nano Letters, 2012, 12(8): 4265-4270.
    [6]
    PARAMSOTHY M, GUPTA M, SRIKANTH N. Processing, microstructure, and properties of a Mg/Al bimetal macrocomposite[J]. Journal of Composite Materials, 2008, 42(24): 2567-2584.
    [7]
    GAO W L, JIN R C, CHEN J X, et al. Titania-supported bimetallic catalysts for photocatalytic reduction of nitrate[J]. Catalysis Today, 2004, 90(3/4): 331-336.
    [8]
    FERNNDEZ J L, WALSH D A, BARD A J. Thermodynamic guidelines for the design of bimetallic catalysts for oxygen electroreduction and rapid screening by scanning electrochemical microscopy. M-Co (M: Pd, Ag, Au)[J]. Journal of the American Chemical Society, 2005, 127(1): 357-365.
    [9]
    STAMENKOVIC V R, FOWLER B, MUN B S, et al. Improved oxygen reduction activity on Pt3Ni(111) via increased surface site availability[J]. Science, 2007, 315(5811): 493-497.
    [10]
    CRISAFULLI C, SCIRE S, MAGGIORE R, et al. CO2 reforming of methane over Ni-Ru and Ni-Pd bimetallic catalysts[J]. Catalysis Letters, 1999, 59(1): 21-26.
    [11]
    DE S, ZHANG J, LUQUE R, et al. Ni-based bimetallic heterogeneous catalysts for energy and environmental applications[J]. Energy & Environmental Science, 2016, 9(11): 3314-3347.
    [12]
    LEE J H, KATTEL S, JIANG Z, et al. Tuning the activity and selectivity of electroreduction of CO2 to synthesis gas using bimetallic catalysts[J]. Nature Communications, 2019, 10(1): 1-8.
    [13]
    SCHWAB G. Some new aspects of the strength of alloys[J]. Transactions of the Faraday Society, 1949, 45:385-396.
    [14]
    WANG C P, LIU X J, OHNUMA I, et al. Formation of immiscible alloy powders with egg-type microstructure[J]. Science, 2002, 297(5583): 990-993.
    [15]
    COLINET C. High temperature calorimetry: Recent developments[J]. Journal of Alloys and Compounds, 1995,220(1/2): 76-87.
    [16]
    TOPOR L, KLEPPA O J. Standard molar enthalpy of formation of LaB6 by high-temperature calorimetry[J]. The Journal of Chemical Thermodynamics, 1984, 16(10): 993-1002.
    [17]
    KIM G, MESCHEL S V, NASH P, et al. Experimental formation enthalpies for intermetallic phases and other inorganic compounds[J]. Scientific Data, 2017, 4(1): 170162.
    [18]
    MIEDEMA A R, CHTEL P F D, BOER F. Cohesion in alloys — fundamentals of a semi-empirical model[J]. Physica B+C, 1980, 100(1): 1-28.
    [19]
    MIEDEMA A R, BOER F R, CHATEL P F. Empirical description of the role of electronegativity in alloy formation[J]. Journal of Physics F: Metal Physics, 1973, 3(8): 1558.
    [20]
    ZHANG R F, RAJAN K. Statistically based assessment of formation enthalpy for intermetallic compounds[J]. Chemical Physics Letters, 2014, 612: 177-181.
    [21]
    ZHANG R F, ZHANG S H, HE Z J, et al. Miedema calculator: A thermodynamic platform for predicting formation enthalpies of alloys within framework of Miedema’s Theory [J]. Computer Physics Communications,2016, 209: 58-69.
    [22]
    PALINA N, SAKATA O, KUMARA L, et al. Electronic structure evolution with composition alteration of RhxCuy alloy nanoparticles[J]. Scientific Reports, 2017, 7(1): 1-9.
    [23]
    FOILES S M, BASKES M I, DAW M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys[J]. Physical Review B, 1986, 33(12): 7983.
    [24]
    JOHNSON R A. Alloy models with the embedded-atom method[J]. Physical Review B, 1989, 39(17): 12554.
    [25]
    LEI Y W, SUN X R, ZHOU R L, et al. Embedded atom method potentials for Ce-Ni binary alloy[J]. Computational Materials Science, 2018, 150: 1-8.
    [26]
    WILLIAMS A R, GELATT C D, MORUZZI V L. Microscopic basis of miedema’s empirical theory of transition-metal compound formation[J]. Physical Review Letters, 1980, 44(11): 394-395.
    [27]
    ZHANG Y, KRESSE G, WOLVERTON C. Nonlocal first-principles calculations in Cu-Au and other intermetallic alloys[J]. Physical Review Letters, 2014, 112(7): 75502.
    [28]
    FARSI L, DESKINS N A. First principles analysis of surface dependent segregation in bimetallic alloys[J]. Physical Chemistry Chemical Physics, 2019, 21(42): 23626-23637.
    [29]
    REITH D, PODLOUCKY R. First-principles model study of the phase stabilities of dilute Fe-Cu alloys: Role of vibrational free energy[J]. Physical Review B, 2009, 80(5): 54108.
    [30]
    OU L. The origin of enhanced electrocatalytic activity of Pt-M (M= Fe, Co, Ni, Cu, and W) alloys in PEM fuel cell cathodes: A DFT computational study[J]. Computational and Theoretical Chemistry, 2014, 1048: 69-76.
    [31]
    GUBAEV K, PODRYABINKIN E V, HART G L, et al. Accelerating high-throughput searches for new alloys with active learning of interatomic potentials[J]. Computational Materials Science, 2019, 156: 148-156.
    [32]
    DOAK J W, HAO S, KIRKLIN S, et al. Computational prediction of nanostructured alloys with enhanced thermoelectric properties[J]. Physical Review Materials, 2019, 3(10): 105404.
    [33]
    JAIN A, ONG S P, HAUTIER G, et al. Commentary: The materials project: A materials genome approach to accelerating materials innovation[J]. APL Materials, 2013, 1(1): 11002.
    [34]
    SAAL J E, KIRKLIN S, AYKOL M, et al. Materials design and discovery with high-throughput density functional theory: The open quantum materials database (OQMD)[J]. JOM, 2013, 65(11): 1501-1509.
    [35]
    WU X D, ZHU X Q, WU G Q, et al. Data mining with big data[J]. IEEE Transactions on Knowledge and Data Engineering, 2013, 26(1): 97-107.
    [36]
    ROSCHER R, BOHN B, DUARTE M F, et al. Explainable machine learning for scientific insights and discoveries[J]. IEEE Access, 2020, 8: 42200- 42216.
    [37]
    LI Z, WANG S W, CHIN W S, et al. High-throughput screening of bimetallic catalysts enabled by machine learning[J]. Journal of Materials Chemistry A, 2017, 5(46): 24131-24138.
    [38]
    GHIRINGHELLI L M, VYBIRAL J, LEVCHENKO S V, et al. Big data of materials science: Critical role of the descriptor[J]. Physical Review Letters, 2015, 114(10): 105503.
    [39]
    RUBAN A, HAMMER B, STOLTZE P, et al. Surface electronic structure and reactivity of transition and noble metals[J]. Journal of Molecular Catalysis A: Chemical, 1997, 115(3): 421-429.
    [40]
    ZHAO Z J, LIU S H, ZHA S J, et al. Theory-guided design of catalytic materials using scaling relationships and reactivity descriptors[J]. Nature Reviews Materials, 2019, 4: 792-804.
    [41]
    CHOI K, JANG Y, CHUNG D Y, et al. A simple synthesis of urchin-like Pt-Ni bimetallic nanostructures as enhanced electrocatalysts for the oxygen reduction reaction[J]. Chemical Communications, 2016, 52(3): 597-600.
    [42]
    LI H, WEN P, LI Q, et al. Earth-abundant iron diboride (FeB2) nanoparticles as highly active bifunctional electrocatalysts for overall water splitting[J]. Advanced Energy Materials, 2017, 7(17): 1700513.
    [43]
    YUAN W Y, ZHAO X S, HAO W J, et al. Performance of surface-oxidized Ni3B, Ni2B, and NiB2 electrocatalysts for overall water splitting[J]. ChemElectroChem, 2019, 6(3): 764-770.
    [44]
    ZALUSKA A, ZALUSKI L, STRM-OLSEN J O. Synergy of hydrogen sorption in ball-milled hydrides of Mg and Mg2Ni[J]. Journal of Alloys and Compounds, 1999, 289(1/2): 197-206.
    [45]
    ZHANG L T, CAI Z L, YAO Z D, et al. A striking catalytic effect of facile synthesized ZrMn2 nanoparticles on the de/rehydrogenation properties of MgH2[J]. Journal of Materials Chemistry A, 2019, 7(10): 5626-5634.
    [46]
    OUYANG R H, CURTAROLO S, AHMETCIK E, et al. SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates[J]. Physical Review Materials, 2018, 2: 083802.
    [47]
    OUYANG R H, AHMETCIK E, CARBOGNO C, et al. Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO[J]. Journal of Physics: Materials, 2019, 2(2): 24002.
    [48]
    BARTEL C J, MILLICAN S L, DEML A M, et al. Physical descriptor for the Gibbs energy of inorganic crystalline solids and temperature-dependent materials chemistry[J]. Nature Communications, 2018, 9: 4168.
    [49]
    BARTEL C J, SUTTON C, GOLDSMITH B R, et al. New tolerance factor to predict the stability of perovskite oxides and halides[J]. Science Advances, 2019, 5(2): evva0693.
    [50]
    ANDERSEN M, LEVCHENKO S V, SCHEFFLER M, et al. Beyond scaling relations for the description of catalytic materials[J]. ACS Catalysis, 2019, 9(4): 2752-2759.
    [51]
    OUYANG R H. Exploiting ionic radii for rational design of halide perovskites[J]. Chemistry of Materials,2020, 32(1): 595-604.
    [52]
    HAYNES W M. CRC Handbook of Chemistry and Physics[M]. Boca Raton, FL: CRC Press, 2014.
    [53]
    MEDVEDEV V A, COX J D, WAGMAN D D. CODATA Key Values for Thermodynamics[M]. New York: Hemisphere Publishing Corporation, 1989.
    [54]
    BLUM A L, LANGLEY P. Selection of relevant features and examples in machine learning[J]. Artificial Intelligence, 1997, 97(1/2): 245-271.
    [55]
    BREIMAN L, SPECTOR P. Submodel selection and evaluation in regression. The X-random case[J]. International Statistical Review, 1992, 60(3): 291-319.
    [56]
    RAO R B, FUNG G, ROSALES R. On the dangers of cross-validation. An experimental evaluation[C]// Proceedings of the 2008 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2008:588.
    [57]
    GHIRINGHELLI L M, VYBIRAL J, AHMETCIK E, et al. Learning physical descriptors for materials science by compressed sensing[J]. New Journal of Physics, 2017, 19(2): 23017.
    [58]
    MA X F, LI Z, ACHENIE L E K, et al. Machine-learning-augmented chemisorption model for CO2 electroreduction catalyst screening[J]. The Journal of Physical Chemistry Letters, 2015, 6(18): 3528-3533.
    [59]
    吴春峰, 李慧改, 郑少波, 等. 二元合金热力学模型—Miedema模型[J].上海金属, 2011, 33(4): 1-5.
    [60]
    WATSON R E, BENNETT L H. Optimized predictions for heats of formation of transition-metal alloys II [J]. Calphad, 1984, 8(4): 307-321.)

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