Recent Progress in Phase Stability and Elastic Anomalies of Group VB Transition Metals
Abstract
:1. Introduction
2. Phase Stability and Elastic Anomalies in V, Nb, Ta
2.1. Pressure Effect on Structure Stability
2.2. Temperature Effect on Structure Stability
2.3. Elastic Anomalies in V, Nb, Ta
3. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Cezairliyan, A. A dynamic technique for measurements of thermophysical properties at high temperatures. Int. J. Thermophys. 1984, 5, 177–193. [Google Scholar] [CrossRef]
- Liu, Z.L.; Cai, L.C.; Chen, X.R.; Wu, Q.; Jing, F.Q. Ab initio refinement of the thermal equation of state for BCC tantalum: The effect of bonding on anharmonicity. J. Phys. Condens. Matter 2009, 21, 095408. [Google Scholar] [CrossRef] [PubMed]
- Mattheiss, L.F. Electronic structure of niobium and tantalum. Phys. Rev. B 1970, 1, 373. [Google Scholar] [CrossRef]
- Halloran, M.H.; Condon, J.H.; Graebner, J.E.; Kunzier, J.E.; Hsu, F.S.L. Experimental study of the fermi surfaces of niobium and tantalum. Phys. Rev. B 1970, 1, 366. [Google Scholar] [CrossRef]
- Papaconstantopoulos, D.A.; Anderson, J.R.; McCaffrey, J.W. Self-consistent energy bands in vanadium at normal and reduced lattice spacings. Phys. Rev. B 1972, 5, 1214. [Google Scholar] [CrossRef]
- Parker, R.D.; Halloran, M.H. Experimental study of the fermi surface of vanadium. Phys. Rev. B 1974, 9, 4130. [Google Scholar] [CrossRef]
- Laurent, D.G.; Wang, C.S.; Callaway, J. Energy bands, Compton profile, and optical conductivity of vanadium. Phys. Rev. B 1978, 17, 455. [Google Scholar] [CrossRef]
- Papaconstantopoulos, D.A.; Klein, B.M. Calculations of the pressure dependence of the superconducting transition temperature of vanadium. Phys. B 1981, 107, 725–726. [Google Scholar] [CrossRef]
- Anderson, J.R.; Papaconstantopoulos, D.A.; Schirber, J.E. Influence of pressure on the Fermi surface of niobium. Phys. Rev. B 1981, 24, 6790. [Google Scholar] [CrossRef] [Green Version]
- Struzhkin, V.V.; Timofeev, Y.A.; Hemley, R.J.; Mao, H.K. Superconducting Tc and electron-phonon coupling in Nb to 132 GPa: Magnetic susceptibility at megabar pressures. Phys. Rev. Lett. 1997, 79, 4262. [Google Scholar] [CrossRef]
- McMillan, W.L. Transition temperature of strong-coupled superconductors. Phys. Rev. 1968, 167, 331. [Google Scholar] [CrossRef]
- Tse, J.S.; Li, Z.Q.; Uehara, K.; Ma, Y.M.; Ahuja, R. Electron-phonon coupling in high-pressure Nb. Phys. Rev. B 2004, 69, 132101. [Google Scholar] [CrossRef]
- Smith, T.F. Pressure dependence of the superconducting transition temperature for vanadium. J. Phys. F Met. Phys. 1972, 2, 946. [Google Scholar] [CrossRef]
- Brandt, N.B.; Zarubina, O.A. Superconductivity of vanadium at pressures up to 250 kbar. Sov. Phys. Solid State 1974, 15, 3423–3425. [Google Scholar]
- Akahama, Y.; Kobayashi, M.; Kawamura, H. Pressure Effect on Superconductivity of V and V-Cr Alloys up to 50 GPa. J. Phys. Soc. Jpn. 1995, 64, 4049–4050. [Google Scholar] [CrossRef]
- Ishizuka, M.; Iketani, M.; Endo, S. Pressure effect on superconductivity of vanadium at megabar pressures. Phys. Rev. B 2000, 61, 3823. [Google Scholar] [CrossRef]
- Suzuki, N.; Otani, M. Theoretical study on the lattice dynamics and electron-phonon interaction of vanadium under high pressures. J. Phys. Condens. Matter 2002, 14, 10869. [Google Scholar] [CrossRef]
- Landa, A.; Klepeis, J.; Söderlind, P.; Naumov, I.; Velikokhatnyi, O.; Vitos, L.; Ruban, A. Ab initio calculations of elastic constants of the bcc V-Nb system at high pressures. J. Phys. Chem. Solids 2006, 67, 2056–2064. [Google Scholar] [CrossRef] [Green Version]
- Landa, A.; Klepeis, J.; Söderlind, P.; Naumov, I.; Velikokhatnyi, O.; Vitos, L.; Ruban, A. Fermi surface nesting and pre-martensitic softening in V and Nb at high pressures. J. Phys. Condens. Matter 2006, 18, 5079. [Google Scholar] [CrossRef] [Green Version]
- Ding, Y.; Ahuja, R.; Shu, J.; Chow, P.; Luo, W.; Mao, H.K. Structural phase transition of vanadium at 69 GPa. Phys. Rev. Lett. 2007, 98, 085502. [Google Scholar] [CrossRef]
- Nakagawa, Y.; Woods, A.D.B. Lattice Dynamics of Niobium. Phys. Rev. Lett. 1963, 11, 271. [Google Scholar] [CrossRef]
- Koči, L.; Ma, Y.; Oganov, A.R.; Souvatzis, P.; Ahuja, R. Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure. Phys. Rev. B 2008, 77, 214101. [Google Scholar] [CrossRef] [Green Version]
- Cynn, H.; Yoo, C.S. Equation of state of tantalum to 174 GPa. Phys. Rev. B 1999, 59, 8526. [Google Scholar] [CrossRef]
- Ostanin, S.A.; Trubitsin, V.Y.; Savrasov, S.Y.; Alouani, M.; Dreyssé, H. Calculated Nb superconducting transition temperature under hydrostatic pressure. Comput. Mater. Sci. 2000, 17, 202–205. [Google Scholar] [CrossRef]
- Yang, L.H.; Söderlind, P.; Moriarty, J.A. Atomistic simulation of pressure-dependent screw dislocation properties in BCC tantalum. Mater. Sci. Eng. A 2001, 309, 102–107. [Google Scholar] [CrossRef]
- Singh, A.K.; Takemura, K. Measurement and analysis of nonhydrostatic lattice strain component in niobium to 145 GPa under various fluid pressure-transmitting media. J. Appl. Phys. 2001, 90, 3269–3275. [Google Scholar] [CrossRef] [Green Version]
- Louis, C.N.; Iyakutti, K. Electron phase transition and superconductivity of vanadium under high pressures. Phys. Rev. B 2003, 67, 094509. [Google Scholar] [CrossRef]
- Nnolim, N.O.; Tyson, T.A.; Axe, L. Theory of the structural phases of group 5B-6B metals and their transport properties. J. Appl. Phys. 2003, 93, 4543–4560. [Google Scholar] [CrossRef] [Green Version]
- Dewaele, A.; Loubeyre, P.; Mezouar, M. Refinement of the equation of state of tantalum. Phys. Rev. B 2004, 69, 092106. [Google Scholar] [CrossRef] [Green Version]
- Dewaele, A.; Loubeyre, P. Mechanical properties of tantalum under high pressure. Phys. Rev. B 2005, 72, 134106. [Google Scholar] [CrossRef]
- Takemura, K.; Singh, A.K. High-pressure equation of state for Nb with helium-pressure medium: Powder X-ray diffraction experiments. Phys. Rev. B 2006, 73, 224119. [Google Scholar]
- Klepeis, J.E. Electronic topological transitions in high-pressure bcc metals. In APS March Meeting Abstracts; American Physical Society: Washington, DC, USA, 2005; p. L11-010. Available online: http://meetings.aps.org/link/BAPS.2005.MAR.L11.10 (accessed on 28 November 2022).
- Orlikowski, D.; Söderlind, P.; Moriarty, J.A. First-principles thermoelasticity of transition metals at high pressure: Tantalum prototype in the quasiharmonic limit. Phys. Rev. B 2006, 74, 054109. [Google Scholar] [CrossRef]
- Suzuki, N.; Otani, M. The role of the phonon anomaly in the superconductivity of vanadium and selenium under high pressures. J. Phys. Condens. Matter 2007, 19, 125206. [Google Scholar] [CrossRef]
- Luo, W.; Ahuja, R.; Ding, Y.; Mao, H.K. Unusual lattice dynamics of vanadium under high pressure. Proc. Natl. Acad. Sci. USA 2007, 104, 16428–16431. [Google Scholar] [CrossRef] [Green Version]
- Lee, B.; Rudd, R.E.; Klepeis, J.E.; Söderlind, P.; Landa, A. Theoretical confirmation of a high-pressure rhombohedral phase in vanadium metal. Phys. Rev. B 2007, 75, 180101. [Google Scholar] [CrossRef] [Green Version]
- Lee, B.; Rudd, R.E.; Klepeis, J.E.; Becker, R. Elastic constants and volume changes associated with two high-pressure rhombohedral phase transformations in vanadium. Phys. Rev. B 2008, 77, 134105. [Google Scholar] [CrossRef] [Green Version]
- Verma, A.K.; Modak, P. Structural phase transitions in vanadium under high pressure. Europhys. Lett. 2008, 81, 37003. [Google Scholar] [CrossRef] [Green Version]
- Qiu, S.L.; Marcus, P.M. Phases of vanadium under pressure investigated from first principles. J. Phys. Condens. Matter 2008, 20, 275218. [Google Scholar] [CrossRef] [Green Version]
- Bosak, A.; Hoesch, M.; Antonangeli, D.; Farber, D.L.; Fischer, I.; Krisch, M. Lattice dynamics of vanadium: Inelastic X-ray scattering measurements. Phys. Rev. B 2008, 78, 020301. [Google Scholar] [CrossRef]
- Landa, A.; Söderlind, P.; Ruban, A.V.; Peil, A.V.; Vitos, L. Stability in BCC transition metals: Madelung and band-energy effects due to alloying. Phys. Rev. Lett. 2009, 103, 235501. [Google Scholar] [CrossRef]
- Vekilov, Y.K.; Krasil’nikov, O.M. Structural transformations in metals at high compression ratios. Phys. Usp. 2009, 52, 831–834. [Google Scholar] [CrossRef]
- Antonangeli, D.; Farber, D.L.; Said, A.H.; Benedetti, L.R.; Aracne, C.M.; Landa, A.; Söderlind, P.; Klepeis, J.E. Shear softening of tantalum at megabar pressures. Phys. Rev. B 2010, 82, 132101. [Google Scholar] [CrossRef]
- Bondarenko, N.G.; Vekilov, Y.K.; Isaev, E.I.; Krasil’nikov, O.M. Deformation Phase Transition in Vanadium under High Pressure. JETP Lett. 2010, 91, 611–613. [Google Scholar] [CrossRef]
- Klepeis, J.H.P.; Cynn, H.; Evans, W.J.; Rudd, R.E.; Yang, L.H.; Liermann, H.P.; Yang, W. Diamond anvil cell measurement of high-pressure yield strength of vanadium using in situ thickness determination. Phys. Rev. B 2010, 81, 134107. [Google Scholar] [CrossRef] [Green Version]
- Landa, A.; Söderlind, P.; Velikokhatnyi, O.I.; Naumov, I.I.; Ruban, A.V.; Peil, O.E.; Vitos, L. Alloying-driven phase stability in group-VB transition metals under compression. Phys. Rev. B 2010, 82, 144114. [Google Scholar] [CrossRef] [Green Version]
- Jenei, Z.; Liermann, H.P.; Cynn, H.; Klepeis, J.H.P.; Baer, B.J.; Evans, W.J. Structural phase transition in vanadium at high pressure and high temperature: Influence of nonhydrostatic conditions. Phys. Rev. B 2011, 83, 054101. [Google Scholar] [CrossRef] [Green Version]
- Liu, Z.; Shang, J. First principles calculations of electronic properties and mechanical properties of BCC molybdenum and niobium. Rare Met. 2011, 30, 354–358. [Google Scholar] [CrossRef]
- Singh, A.K.; Liermann, H.-P. Strength and elasticity of niobium under high pressure. J. Appl. Phys. 2011, 109, 113539. [Google Scholar] [CrossRef] [Green Version]
- Hu, J.; Dai, C.; Yu, Y.; Liu, Z.; Tan, Y.; Zhou, X.; Tan, H.; Cai, L.; Wu, Q. Sound velocity measurements of tantalum under shock compression in the 10–110 GPa range. J. Appl. Phys. 2012, 111, 033511. [Google Scholar] [CrossRef] [Green Version]
- Yu, Y.; Tan, Y.; Dai, C.; Li, X.; Li, Y.; Wu, Q.; Tan, H. Phase transition and strength of vanadium under shock compression up to 88 GPa. Appl. Phys. Lett. 2014, 105, 201910. [Google Scholar] [CrossRef]
- Krasil’nikov, O.M.; Vekilov, Y.K.; Lugovskoy, A.V.; Mosyagin, I.Y.; Belov, M.P.; Bondarenko, N.G. Structural transformations at high pressure in the refractory metals (Ta, Mo, V). J. Alloys Compd. 2014, 586, 242–245. [Google Scholar] [CrossRef]
- Jing, Q.; Wu, Q.; Xu, J.-A.; Bi, Y.; Liu, L.; Liu, S.; Zhang, Y.; Geng, H. Anomalous softening of yield strength in tantalum at high pressures. J. Appl. Phys. 2015, 117, 055903. [Google Scholar] [CrossRef]
- Wang, Y.X.; Wu, Q.; Xiang, R.; Chen, X.R.; Geng, H.Y. Stability of rhombohedral phases in vanadium at high-pressure and high-temperature: First-principles investigations. Sci. Rep. 2016, 6, 32419. [Google Scholar] [CrossRef] [PubMed]
- Antonangeli, D.; Farber, D.L.; Bosak, A.; Aracne, C.M.; Ruddle, D.G.; Krisch, M. Phonon triggered rhombohedral lattice distortion in vanadium at high pressure. Sci. Rep. 2016, 6, 31887. [Google Scholar] [CrossRef] [PubMed]
- Wang, Y.X.; Geng, H.Y.; Wu, Q.; Chen, X.R.; Sun, Y. First-principles investigation of elastic anomalies in niobium at high pressure and temperature. J. Appl. Phys. 2017, 122, 235903. [Google Scholar] [CrossRef] [Green Version]
- Foster, J.M.; Comley, A.J.; Case, G.S.; Avraam, P.; Rothman, S.D.; Higginbotham, A.; Floyd, E.K.R.; Gumbrell, E.T.; Luis, J.J.D.; McGonegle, D.; et al. X-ray diffraction measurements of plasticity in shock-compressed vanadium in the region of 10-70 GPa. J. Appl. Phys. 2017, 122, 025117. [Google Scholar] [CrossRef] [Green Version]
- Zou, Y.T.; Li, Y.; Chen, H.Y.; Welch, D.; Zhao, Y.S.; Li, B.S. Thermoelasticity and anomalies in the pressure dependence of phonon velocities in niobium. Appl. Phys. Lett. 2018, 112, 011901. [Google Scholar] [CrossRef]
- Xiong, L.; Liu, J. Structural phase transition, strength, and texture in vanadium at high pressure under nonhydrostatic compression. Chin. Phys. B 2018, 27, 036101. [Google Scholar] [CrossRef]
- Jing, Q.M.; He, Q.; Zhang, Y.; Li, S.R.; Liu, L.; Hou, Q.Y.; Geng, H.Y.; Bi, Y.; Yu, Y.Y.; Wu, Q. Unusual softening behavior of yield strength in niobium at high pressures. Chin. Phys. B 2018, 27, 106201. [Google Scholar] [CrossRef]
- Kramynin, S.P.; Akhmedov, E.N. Equation of state and properties of Nb at high temperature and pressure. J. Phys. Chem. Solids 2019, 135, 109108. [Google Scholar] [CrossRef]
- Errandonea, D.; MacLeod, S.G.; Burakovsky, L.; Santamaria-Perez, D.; Proctor, J.E.; Cynn, H.; Mezouar, M. Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions. Phys. Rev. B 2019, 100, 094111. [Google Scholar] [CrossRef] [Green Version]
- Keuter, P.; Music, D.; Schnabel, V.; Stuer, M.; Schneider, J.M. From qualitative to quantitative description of the anomalous thermoelastic behavior of V, Nb, Ta, Pd and Pt. J. Phys. Condens. Matter 2019, 31, 225402. [Google Scholar] [CrossRef] [PubMed]
- Weck, P.F.; Townsend, J.P.; Cochrane, K.R.; Crockett, S.D.; Moore, N.W. Shock compression of niobium from first-principles. J. Appl. Phys. 2019, 125, 245905. [Google Scholar] [CrossRef]
- Errandonea, D.; Burakovsky, L.; Preston, D.L.; MacLeod, S.G.; Santamaría-Perez, D.; Chen, S.P.; Cynn, H.; Simak, S.I.; McMahon, M.I.; Proctor, J.E.; et al. Experimental and theoretical confirmation of an orthorhombic phase transition in niobium at high pressure and temperature. Commun. Mater. 2020, 1, 60. [Google Scholar] [CrossRef]
- Wang, Y.X.; Geng, H.Y.; Wu, Q.; Chen, X.R. Orbital localization error of density functional theory in shear properties of vanadium and niobium. J. Chem. Phys. 2020, 152, 024118. [Google Scholar] [CrossRef] [Green Version]
- Tidholm, J.; Hellman, O.; Shulumba, N.; Simak, S.I.; Tasnádi, F.; Abrikosov, I.A. Temperature dependence of the Kohn anomaly in BCC Nb from first-principles self-consistent phonon calculations. Phys. Rev. B 2020, 101, 115119. [Google Scholar] [CrossRef] [Green Version]
- Weck, P.F.; Kalita, P.E.; Ao, T.; Crockett, S.D.; Root, S.; Cochrane, K.R. Shock compression of vanadium at extremes: Theory and experiment. Phys. Rev. B 2020, 102, 184109. [Google Scholar] [CrossRef]
- Zhang, Y.J.; Tan, Y.; Geng, H.Y.; Salke, N.P.; Gao, Z.P.; Li, J.; Sekine, T.; Wang, Q.M.; Greenberg, E.; Prakapenka, V.B.; et al. Melting curve of vanadium up to 256 GPa: Consistency between experiments and theory. Phys. Rev. B 2020, 102, 214104. [Google Scholar] [CrossRef]
- Yang, F.C.; Hellman, O.; Fultz, B. Temperature dependence of electron-phonon interactions in vanadium. Phys. Rev. B 2020, 101, 094305. [Google Scholar] [CrossRef] [Green Version]
- Wang, Y.X.; Liu, Y.Y.; Yan, Z.X.; Liu, W.; Geng, H.Y.; Chen, X.R. Ab initio dynamical stability and lattice thermal conductivity of vanadium and niobium at high temperature. Solid State Commun. 2021, 323, 114130. [Google Scholar] [CrossRef]
- Wang, H.; Li, J.; Zhou, X.M.; Tan, Y.; Hao, L.; Yu, Y.Y.; Dai, C.D.; Jin, K.; Wu, Q.; Jing, Q.M.; et al. Evidence for mechanical softening-hardening dual anomaly in transition metals from shock-compressed vanadium. Phys. Rev. B 2021, 104, 134102. [Google Scholar] [CrossRef]
- Akahama, Y.; Kawaguchi, S.; Hirao, N.; Ohishi, Y. High-pressure stability of BCC-vanadium and phase transition to a rhombohedral structure at 200 GPa. J. Appl. Phys. 2021, 129, 135902. [Google Scholar] [CrossRef]
- Stevenson, M.G.; Pace, E.J.; Storm, C.V.; Finnegan, S.E.; Garbarino, G.; Wilson, C.W.; McGonegle, D.; Macleod, S.G.; McMahon, M.I. Pressure-induced BCC-rhombohedral phase transition in vanadium metal. Phys. Rev. B 2021, 103, 134103. [Google Scholar] [CrossRef]
- Li, P.; Huang, Y.F.; Wang, K.; Xiao, S.F.; Wang, L.; Yao, S.L.; Zhu, W.J.; Hu, W.Y. Crystallographic-orientation-dependence plasticity of niobium under shock compressions. Int. J. Plasticity 2022, 150, 103195. [Google Scholar] [CrossRef]
- Li, X.H.; Yang, C.; Gan, B.; Huang, Y.Q.; Wang, Q.M.; Sekine, T.; Hong, J.W.; Jiang, G.; Zhang, Y.J. Sound velocity softening in body-centered cubic niobium under shock compression. Phys. Rev. B 2022, 105, 104110. [Google Scholar] [CrossRef]
- Manghnani, M.H.; Nellis, W.J.; Nicol, M.F. Science and technology of high pressure. In Proceedings of the International Conference on High Pressure Sciene and Technology (AIRAPT-17), Honolulu, HI, USA, 25–30 July 1999; University Press: Hyderabad, India, 2000; Volume 1. [Google Scholar]
- Landa, A.; Söderlind, P.; Yang, L.H. Ab initio phase stability at high temperatures and pressures in the V-Cr system. Phys. Rev. B 2014, 89, 020101. [Google Scholar] [CrossRef] [Green Version]
- Dai, C.; Jin, X.; Zhou, X.; Liu, J.; Hu, J. Sound velocity variations and melting of vanadium under shock compression. J. Phys. D Appl. Phys. 2001, 34, 3064. [Google Scholar] [CrossRef]
- Errandonea, D.; Schwager, B.; Ditz, R.; Gessmann, C.; Boehler, R.; Ross, M. Systematics of transition-metal melting. Phys. Rev. B 2001, 63, 132104. [Google Scholar] [CrossRef]
- Landa, A.; Söderlind, P.; Naumov, I.I.; Klepeis, J.E.; Vitos, L. Kohn anomaly and phase stability in group VB transition metals. Computation 2018, 6, 29. [Google Scholar] [CrossRef] [Green Version]
- Haskins, J.B.; Moriarty, J.A. Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases. Phys. Rev. B 2018, 98, 144107. [Google Scholar] [CrossRef] [Green Version]
- Söderlind, P.; Moriarty, J.A. First-principles theory of Ta up to 10 Mbar pressure: Structural and mechanical properties. Phys. Rev. B 1998, 57, 10340. [Google Scholar] [CrossRef]
- Gülseren, O.; Cohen, R.E. High-pressure thermoelasticity of body-centered-cubic tantalum. Phys. Rev. B 2002, 65, 064103. [Google Scholar] [CrossRef]
- Zhang, Y.J.; Yang, C.; Alatas, A.; Said, A.H.; Salke, N.P.; Hong, J.W.; Lin, J.F. Pressure effect on Kohn anomaly and electronic topological transition in single-crystal tantalum. Phys. Rev. B 2019, 100, 075145. [Google Scholar] [CrossRef]
- Bolef, D.I.; Smith, R.E.; Miller, J.G. Elastic Properties of Vanadium. I. Temperature Dependence of the Elastic Constants and the Thermal Expansion. Phys. Rev. B 1971, 3, 4100. [Google Scholar] [CrossRef]
- Ko, C.R.; Salama, K.; Roberts, J.M. Effect of hydrogen on the temperature dependence of the elastic constants of vanadium single crystals. J. Appl. Phys. 1980, 51, 1014. [Google Scholar] [CrossRef]
- Kojima, H.; Shino, M.; Suzuki, T. Effects of hydrogen and deuterium on the temperature dependence of the shear constants C’ of vanadium single crystals. Acta Metall. 1987, 35, 891. [Google Scholar] [CrossRef]
- Trivisonno, J.; Vatanayon, S.; Wilt, M.; Washick, J.; Reifenberger, R. Temperature dependence of the elastic constants of niobium and lead in the normal and superconducting states. J. Low Temp. Phys. 1973, 12, 153. [Google Scholar] [CrossRef]
- Zhang, L.; Geng, H.Y.; Wu, Q. Prediction of anomalous LA-TA splitting in electrides. Matter Radiat. Extremes 2021, 6, 038403. [Google Scholar]
- Zhang, L.; Wu, Q.; Li, S.; Sun, Y.; Yan, X.; Chen, Y.; Geng, H.Y. Interplay of anionic quasi-atoms and interstitial point defects in electrides: Abnormal interstice occupation and colossal charge state of point defects in dense fcc-lithium. ACS Appl. Mater. Interfaces 2021, 13, 6130–6139. [Google Scholar] [CrossRef]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wang, Y.; Wu, H.; Liu, Y.; Wang, H.; Chen, X.; Geng, H. Recent Progress in Phase Stability and Elastic Anomalies of Group VB Transition Metals. Crystals 2022, 12, 1762. https://doi.org/10.3390/cryst12121762
Wang Y, Wu H, Liu Y, Wang H, Chen X, Geng H. Recent Progress in Phase Stability and Elastic Anomalies of Group VB Transition Metals. Crystals. 2022; 12(12):1762. https://doi.org/10.3390/cryst12121762
Chicago/Turabian StyleWang, Yixian, Hao Wu, Yingying Liu, Hao Wang, Xiangrong Chen, and Huayun Geng. 2022. "Recent Progress in Phase Stability and Elastic Anomalies of Group VB Transition Metals" Crystals 12, no. 12: 1762. https://doi.org/10.3390/cryst12121762