{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,10]],"date-time":"2026-11-10T12:41:17Z","timestamp":1794314477259,"version":"4.9.0"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T00:00:00Z","timestamp":1641945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Binary chromium carbides display excellent wear resistance, extreme stiffness and oxidation resistance under high temperature. The influence of applied pressure on electronic structure, elastic behavior, Debye temperature and hardness of Cr7C3, Cr3C2 and Cr23C6 have been investigated by the density functional theory (DFT) method. The results reveal that lattice parameters and formation enthalpy display an inverse relationship with applied pressure, and Cr3C2 exhibited optimal structural stability. Moreover, Cr-C orbital hybridization tends to be stronger due to the decreased partial density of states (PDOS) of the Cr atom. The difference in electronic distribution of binary carbides has also been investigated, which confirmed that overall orbital hybridization and covalent characteristics has been enhanced. The theoretical hardness was elevated according to the higher bond strength and bond density. In accordance with structural stability data, Cr3C2 has shown maximum theoretical hardness. Furthermore, the anisotropic nature of hardness has been evaluated with external pressure. Cr3C2, and the highest isotropic hardness behavior along with an increase in hardness values with increasing pressure has been observed. In addition, the variation in Debye temperatures of binary chromium carbides under applied pressure has also been predicted. The results provide a theoretical insight into electronic, mechanical and thermodynamic behavior of three binary chromium carbides and show the potential of these novel carbides in a wide range of applications.<\/jats:p>","DOI":"10.3390\/ma15020558","type":"journal-article","created":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T09:10:36Z","timestamp":1641978636000},"page":"558","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":61,"title":["First Principles Investigation of Binary Chromium Carbides Cr7C3, Cr3C2 and Cr23C6: Electronic Structures, Mechanical Properties and Thermodynamic Properties under Pressure"],"prefix":"10.3390","volume":"15","author":[{"given":"Liang","family":"Sun","sequence":"first","affiliation":[{"name":"National Joint Engineering Research Center for Abrasion Control and Molding of Metal Materials & Henan Key Laboratory of High-Temperature Structural and Functional Materials, Henan University of Science and Technology, Luoyang 471003, China"},{"name":"Key Laboratory of Materials Processing Engineering, College of Materials Science and Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiongshuai","family":"Ji","sequence":"additional","affiliation":[{"name":"Key Laboratory of Materials Processing Engineering, College of Materials Science and Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shaanxi Environmental Protection Group Ecological Construction Management Co., Ltd., Xi\u2019an 710000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenyan","family":"Zhai","sequence":"additional","affiliation":[{"name":"Key Laboratory of Materials Processing Engineering, College of Materials Science and Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liujie","family":"Xu","sequence":"additional","affiliation":[{"name":"National Joint Engineering Research Center for Abrasion Control and Molding of Metal Materials & Henan Key Laboratory of High-Temperature Structural and Functional Materials, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Dong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Materials Processing Engineering, College of Materials Science and Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanmin","family":"Liu","sequence":"additional","affiliation":[{"name":"National Joint Engineering Research Center for Abrasion Control and Molding of Metal Materials & Henan Key Laboratory of High-Temperature Structural and Functional Materials, Henan University of Science and Technology, Luoyang 471003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianhong","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Qinghai University for Nationalities, Xining 810007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1016\/0025-5408(95)00123-9","article-title":"Elaboration, microstructure and reactivity of Cr3C2 powders of different morphology","volume":"30","author":"Laurent","year":"1995","journal-title":"Mater. Res. Bull."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3596","DOI":"10.1016\/j.surfcoat.2006.08.109","article-title":"Resistance of nanoscale multilayer C\/Cr coatings against environmental attack","volume":"201","author":"Kok","year":"2006","journal-title":"Surf. Coat. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.matchar.2007.03.002","article-title":"Microstructure and wear properties of Fe-VC-Cr7C3 composite coating on surface of cast steel","volume":"59","author":"Cheng","year":"2008","journal-title":"Mater. Charact."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2727","DOI":"10.1016\/j.actamat.2005.02.039","article-title":"Atomistic study on the structure and thermodynamic properties of CrC, MnC, FeC","volume":"53","author":"Xie","year":"2005","journal-title":"Acta Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.jallcom.2006.03.102","article-title":"Mechanical-thermal synthesis of chromium carbides","volume":"439","author":"Cintho","year":"2007","journal-title":"J. Alloys Compd."},{"key":"ref_6","unstructured":"Sadangi, R.K., McCandlish, L.E., Kear, B.H., and Seegopaul, P. (June, January 31). Synthesis and characterization of sub-micron vanadium and chromium carbide grain growth inhibitors. Proceedings of the 1998 International Conference on Powder Metallurgy & Particulate Materials Sponsored by the Metal Powder Industries Federation and APMI International, Las Vegas, NV, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.physleta.2004.04.068","article-title":"Electronic structure and mechanical properties of Cr7C3","volume":"326","author":"Music","year":"2004","journal-title":"Phys. Lett. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/S0925-8388(01)01012-X","article-title":"Thermodynamic studies on chromium carbides by the electromotive force (emf) method","volume":"321","author":"Kleykamp","year":"2001","journal-title":"Alloys Compd."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"041909","DOI":"10.1063\/1.2838345","article-title":"First-principles study of structural, elastic, and electronic properties of chromium carbides","volume":"92","author":"Jiang","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_10","first-page":"31","article-title":"Comparison of structural and chemical properties of Cr-based hard coatings","volume":"152","author":"Panjan","year":"2002","journal-title":"Surf. Coat. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/BF02657382","article-title":"High temperature thermodynamic properties of the chromium carbides Cr7C3 and Cr3C2 determined using a galvanic cell technique","volume":"15","author":"Coltters","year":"1984","journal-title":"Metall. Trans. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.msea.2005.02.062","article-title":"Simultaneous synthesis and consolidation of chromium carbides (Cr3C2, Cr7C 3 and Cr23C6) by pulsed electric-current pressure sintering","volume":"399","author":"Hirota","year":"2005","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.surfcoat.2004.08.064","article-title":"Cathodic chromium carbide coatings for molding die applications","volume":"188","author":"Esteve","year":"2004","journal-title":"Surf. Coat. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1007\/s12598-011-0204-x","article-title":"Interfacial microstructure and properties of diamond\/Cu-xCr composites for electronic packaging applications","volume":"30","author":"Zhang","year":"2011","journal-title":"Rare Met."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.wear.2008.12.104","article-title":"Micromechanical properties and erosive wear performance of chromium carbide based cermets","volume":"267","author":"Hussainova","year":"2009","journal-title":"Wear"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/S0921-5093(03)00329-0","article-title":"Influence of Cr23C6 carbides on dynamic recrystallization in hot deformed Nimonic 80a alloys","volume":"359","author":"Tian","year":"2003","journal-title":"Met. Sci. Eng. A"},{"key":"ref_17","unstructured":"Schroder, D.V., and Pribran, J.K. (1999). An Introduction to Thermal Physics, Addison Wesley Longman."},{"key":"ref_18","first-page":"0271","article-title":"First-Principles Calculation Study on the Electronic Structures, Hardness and Debye Temperatures of Chromium Carbides","volume":"41","author":"Min","year":"2012","journal-title":"Rare Met. Mater. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous electron gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. Rev. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized Gradient Approximation Made Simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/S0166-1280(00)00777-6","article-title":"Stability investigation and thermal behavior of a hypothetical silicon nanotube","volume":"539","author":"Fanan","year":"2001","journal-title":"J. Mol. Struct. Theochem."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5188","DOI":"10.1103\/PhysRevB.13.5188","article-title":"Special points for Brillouin-zone integrations","volume":"13","author":"Monkhorst","year":"1976","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"e26231","DOI":"10.1002\/qua.26231","article-title":"Structural, mechanical, electronic, and thermodynamic properties of pure tungsten metal under different pressures: A first-principles study","volume":"120","author":"Jiang","year":"2020","journal-title":"Int. J. Quantum Chem."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"059904","DOI":"10.1103\/PhysRevB.76.059904","article-title":"Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles","volume":"76","author":"Wu","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"085501","DOI":"10.1103\/PhysRevLett.96.085501","article-title":"Hardness of covalent and ionic crystals: First-principle calculations","volume":"96","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","first-page":"929","article-title":"Neue Strukturverfeinerung und Eigenschaften von Cr3C2\/Structure Refinement and Properties of Cr3C2","volume":"58","author":"Glaser","year":"2003","journal-title":"Z. Nat. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"132104","DOI":"10.1103\/PhysRevB.73.132104","article-title":"Hardness of nanocrystalline diamonds","volume":"73","author":"Gao","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_28","first-page":"461","article-title":"\u00c9tudes christallographique des carbures Cr7C3 et Mn7C3","volume":"5","author":"Rouault","year":"1970","journal-title":"Ann. Chim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1107\/S0108768187097957","article-title":"Atom distributions in tau-carbide phases: Fe and Cr distributions in (Cr23\u2212xFex)C6 with x = 0, 0\u00b774, 1\u00b770, 4\u00b713 and 7\u00b736","volume":"43","author":"Yakel","year":"2010","journal-title":"Acta Crystallogr. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2684","DOI":"10.1103\/PhysRevB.59.2684","article-title":"Anomalous behavior of the semiconducting gap in WO3 from first-principles calculations","volume":"59","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4945","DOI":"10.1103\/PhysRevB.39.4945","article-title":"Total energies and bonding for crystallographic structures in titanium-carbon and tungsten-carbon systems","volume":"39","author":"Price","year":"1989","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"115415","DOI":"10.1088\/0022-3727\/42\/11\/115415","article-title":"A comparative study of Cr7C3, Fe3C and Fe2B in cast iron both from ab initio calculations and experiments","volume":"42","author":"Xiao","year":"2009","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"191912","DOI":"10.1063\/1.3026175","article-title":"Carbides in stainless steels: Results from ab initio investigations","volume":"93","author":"Henriksson","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.matchemphys.2008.02.019","article-title":"The first principles study on PtC compound","volume":"111","author":"Deligoz","year":"2008","journal-title":"Mater. Chem. Phys."},{"key":"ref_35","unstructured":"Swain, M. (1994). Structure and Properties of Ceramics, VCH."},{"key":"ref_36","unstructured":"Wang, Y.L. (2003). Performance and Application of Functional Ceramics, The Science Publishing Company."},{"key":"ref_37","unstructured":"Zhou, Y. (1995). Science of Ceramics Material, Harbin Institute of Technology Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1007\/s11661-008-9623-1","article-title":"Effect of tempering on Microstructure, hardness, wear resistance, and fracture toughness of Cr3C2\/steel surface composites fabricated by high-energy electron-beam irradiation","volume":"39","author":"Nam","year":"2008","journal-title":"Metall. Mater. Trans. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.actamat.2011.09.011","article-title":"Anisotropic hardness prediction of crystalline hard materials from the electronegativity","volume":"60","author":"Li","year":"2012","journal-title":"Acta Mater."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1016\/j.commatsci.2009.04.044","article-title":"Structural, elastic and electronic properties of intermetallics in the Pt\u2013Sn system: A density functional investigation","volume":"46","author":"Zhou","year":"2009","journal-title":"Comput. Mater. Sci."},{"key":"ref_41","unstructured":"Born, M., and Huang, K. (1954). Dynamical Theory of Crystal Lattices, Oxford University Press."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1016\/j.scriptamat.2008.06.015","article-title":"Extreme elastic anisotropy of cementite, Fe3C: First-principles calculations and experimental evidence","volume":"59","author":"Nikolussi","year":"2008","journal-title":"Scr. Mater."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1016\/j.commatsci.2008.08.022","article-title":"Substitutional solution of silicon in cementite: A first-principles study","volume":"44","author":"Jang","year":"2009","journal-title":"Comput. Mater. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.jallcom.2009.06.023","article-title":"First-principles calculations of mechanical properties of TiC and TiN","volume":"485","author":"Yang","year":"2009","journal-title":"J. Alloys Compd."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1063\/1.1736249","article-title":"Elastic Constants of TiC and TiB2","volume":"32","author":"Gilman","year":"1961","journal-title":"J. Appl. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.physb.2005.12.264","article-title":"First-principles calculations of elastic properties of LiBC","volume":"381","author":"Liu","year":"2006","journal-title":"Physical B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1590\/1980-5373-mr-2016-0889","article-title":"The effect of Cr3C2 and Ta C additives on microstructures, hardness and fracture toughness of WC-6Co tool material fabricated by spark plasma sintering","volume":"20","author":"Siwark","year":"2017","journal-title":"Mater. Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"6989","DOI":"10.1088\/0953-8984\/14\/29\/301","article-title":"Ab initio calculations of elastic constants and thermodynamic properties of bcc, fcc, and hcp Al crystals under pressure","volume":"14","author":"Smirnow","year":"2002","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/0022-3697(63)90067-2","article-title":"A Simplified Method for Calculating the Debye Temperature from Elastic Constants","volume":"24","author":"Anderson","year":"1963","journal-title":"J. Chem. Solids"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.1088\/0953-8984\/14\/11\/301","article-title":"First-principles simulation: Ideas, illustrations and the CASTEP code","volume":"14","author":"Segall","year":"2002","journal-title":"J. Phys. Condens. 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