Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2014, Vol. 9 Issue (2) : 219-225    https://doi.org/10.1007/s11467-013-0391-z
Concentration-dependent crystal structure, elastic constants and electronic structure of ZrxTi1-x alloys under high pressure
Xiao-Li Yuan1,2,4(), Mi-An Xue2,3, Wen Chen1,2(), Tian-Qing An4
1. College of Mechanics and Materials, Hohai University, Nanjing 210098, China; 2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; 3. College of Harbour Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China; 4. College of Science, Hohai University, Nanjing 210098, China
 Download: PDF(450 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The physical properties of ZrxTi1-x (x = 0.0, 0.33, 0.5, 0.67, 0.75 and 1.00) alloys were simulated by virtual crystal approximation (VCA) methods which is generally used for disordered solid solutions modeling. The elastic constant, electronic structure and thermal Equation of state (EOS) of disordered ZrxTi1-x alloys under pressure are investigated by plane-wave pseudo-potential method. Our simulations reveal increasement of variations of the calculated equilibrium volumes and decreasement of Bulk modulus as a function of the alloy compositions. Lattice parameters a and c of alloys with different Zr concentrations decrease linearly with pressure increasing, but the c/avalues are increasing as pressure increases, indicating no phase transitions under pressure from 0 GPa to 100 GPa. The elastic constants and the Bulk modulus to the Shear modulus ratios (B/G) indicate good ductility of Zr, Zr0.33Ti0.67, Zr0.5Ti0.5, Zr0.75Ti0.25 and Ti, but the Zr0.67Ti0.33 alloy is brittle under 0 K and 0 GPa. The metallic behavior of these alloys was also proved by analyzing partial and total DOS.

Keywords dalloy      density functional theory      virtual crystal approximation (VCA)      mechanics      elastic properties     
Corresponding Author(s): Yuan Xiao-Li,Email:yuanxiaoli0913@163.com; Chen Wen,Email:chenwen@hhu.edu.cn   
Issue Date: 01 April 2014
 Cite this article:   
Xiao-Li Yuan,Mi-An Xue,Wen Chen, et al. Concentration-dependent crystal structure, elastic constants and electronic structure of ZrxTi1-x alloys under high pressure[J]. Front. Phys. , 2014, 9(2): 219-225.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-013-0391-z
https://academic.hep.com.cn/fop/EN/Y2014/V9/I2/219
1 Y. Okazaki, S. Rao, T. Tateishi, and Y. Ito, Cytocompatibility of various metal and development of new titanium alloys for medical implants, Mat. Sci. Eng. A , 1998, 243(1-2): 250
doi: 10.1016/S0921-5093(97)00809-5
2 M. Niinomi, Fatigue performance and cyto-toxicity of low rigidity titanium alloy, Ti-29Nb-13Ta-4.6Zr, Biomaterials , 2003, 24: 2673
doi: 10.1016/S0142-9612(03)00069-3
3 Y. Okazaki, S. Asao, S. Rao, and T. Tateishi, Effect of concentration of Zr, Sn, Nb, Ta, Pd, Mo, Co, Cr, Si, Ni, Fe on the relative growth ratios of bio-cells, J. Jpn. Inst. Met. , 1996, 60: 902
4 D. L. Douglass, The physical metallurgy of zirconium, At. Energy Rev. , 1963, 3: 71
5 H. Ikehata, N. Nagasako, T. Furuta, A. Fukumoto, K. Miwa, and T. Saito, First-principles calculations for development of low elastic modulus Ti alloys, Phys. Rev. B , 2004, 70(17): 174113
doi: 10.1103/PhysRevB.70.174113
6 W. Liu, B. Li, L. Wang, J. Zhang, and Y. Zhao, Elasticity of w-phase zirconium, Phys. Rev. B , 2007, 76(14): 144107
doi: 10.1103/PhysRevB.76.144107
7 M. T. Pérez-Prado and A. P. Zhilyaev, First experimental observation of shear induced hcp to bcc transformation in pure Zr, Phys. Rev. Lett. , 2009, 102(17): 175504
doi: 10.1103/PhysRevLett.102.175504
8 L. Saldana, A. Méndez-Vilas, L. Jiang, M. Multigner, J. L. González-Carrasco, M. T. Pérez-Prado, M. L. González-Martín, L. Munuera, and N. Vilaboa, In vitro biocompatibility of an ultrafine grained zirconium, Biomaterials , 2007, 28(30): 4343
doi: 10.1016/j.biomaterials.2007.06.015
9 N. Stojilovic, E. T. Bender, and R. D. Ramsier, Surface chemistry of zirconium, Prog. Surf. Sci ., 2005, 78(3-4): 101
doi: 10.1016/j.progsurf.2005.07.001
10 M. Long and H. J. Rack, Titanium alloys in total joint replacement-a materials science perspective, Biomaterials , 1998, 19(18): 1621
doi: 10.1016/S0142-9612(97)00146-4
11 J. C. Duthie and D. G. Pettifor, Correlation between d-band occupancy and crystal structure in the rare earths, Phys. Rev. Lett. , 1977, 38(10): 564
doi: 10.1103/PhysRevLett.38.564
12 H. L. Skriver, Crystal structure from one-electron theory, Phys. Rev. B , 1985, 31(4): 1909
doi: 10.1103/PhysRevB.31.1909
13 Z. G. Mei, S. L. Shang, Y. Wang, and Z. K. Liu, Densityfunctional study of the pressure-induced phase transitions in Ti at zero Kelvin, Phys. Rev. B , 2009, 79(13): 134102
doi: 10.1103/PhysRevB.79.134102
14 C. E. Hu, Z. Y. Zeng, L. Zhang, X. R. Chen, L. C. Cai, and D. Alfè, Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal, J. Appl. Phys. , 2010, 107(9): 093509
doi: 10.1063/1.3407560
15 Y. J. Hao, L. Zhang, X. R. Chen, L. C. Cai, Q. Wu, and D. Alfè, Ab initio calculations of the thermodynamics and phase diagram of zirconium, Phys. Rev. B , 2008, 78(13): 134101
doi: 10.1103/PhysRevB.78.134101
16 I. Schnell and R. C. Albers, Zirconium under pressure: Phase transitions and thermodynamics, J. Phys.: Condens. Matter , 2006, 18(5): 1483
doi: 10.1088/0953-8984/18/5/001
17 R. Ahuja, J. M. Wills, B. Johansson, and O. Eriksson, Crystal structures of Ti, Zr, and Hf under compression: Theory, Phys. Rev. B , 1993, 48(22): 16269
doi: 10.1103/PhysRevB.48.16269
18 H. Xia, S. J. Duclos, A. L. Ruoff, and Y. K. Vohra, New highpressure phase transition in zirconium metal, Phys. Rev. Lett. , 1990, 64(2): 204
doi: 10.1103/PhysRevLett.64.204
19 H. Xia, A. L. Ruoff, and Y. K. Vohra, Temperature dependence of the w-bcc phase transition in zirconium metal, Phys. Rev. B , 1991, 44(18): 10374
doi: 10.1103/PhysRevB.44.10374
20 Y. Akahama, M. Kobayashi, and H. Kawamura, Superconductivity and phase transition of zirconium under high pressure up to 50 GPa, J. Phys. Soc. Jpn. , 1990, 59(11): 3843
doi: 10.1143/JPSJ.59.3843
21 Y. Akahama, M. Kobayashi, and H. Kawamura, Highpressure X-ray diffraction study on electronics-d transition in zirconium, J. Phys. Soc. Jpn. , 1991, 60(10): 3211
doi: 10.1143/JPSJ.60.3211
22 Y. Akahama, H. Kawamura, and T. LeBihan, New d (distorted-bcc) titanium to 220 GPa, Phys. Rev. Lett. , 2001, 87(27): 275503
doi: 10.1103/PhysRevLett.87.275503
23 Y. S. Zhao and J. Z. Zhang, Enhancement of yield strength in zirconium metal through high-pressure induced structural phase transition, Appl. Phys. Lett. , 2007, 91(20): 201907
doi: 10.1063/1.2802726
24 Y. K. Vohra and P. T. Spencer, Novel g-phase of titanium metal at megabar pressures, Phys. Rev. Lett. , 2001, 86(14): 3068
doi: 10.1103/PhysRevLett.86.3068
25 I. O. Bashkin, A. Yu. Pagnuev, A. F. Gurov, V. K. Fedotov, G. E. Abrosimova, and E. G. Ponyatovskii, Phase transformations in equiatomic alloy TiZr at pressure up to 70 kbar, Phys. Solid State , 2000, 42(1): 170
doi: 10.1134/1.1131187
26 I. O. Bashkin, A. Yu. Pagnuev, A. F. Gurov, V. K. Fedotov, G. E. Abrosimova, and E. G. Ponyatovsky, Enhanced superconductivity of the Ti-Zr alloys in the high-pressure BCC phase, JETP Lett. , 2001, 73(2): 75
doi: 10.1134/1.1358423
27 I. O. Bashkin, V. K. Fedotov, M. V. Nefedova, V. G. Tissen, E. G. Ponyatovsky, A. Schiwek, and W. B. Holzapfel, Crystal structure and superconductivity of TiZr up to 57 GPa, Phys. Rev. B , 2003, 68(5): 054401
doi: 10.1103/PhysRevB.68.054401
28 V. V. Aksenenkov, V. D. Blank, B. A. Kulnitskiy, and E. I. Estrin, Phys. Met. Metalloved. , 1990, 69: 154
29 J. L. Murray, Phase Diagrams of Binary Titanium Alloys, ASM International, Materials Park, OH , 1987: 340
30 W. F. Ho, W. K. Chen, S. C. Wu, and H. C. Hsu, Structure, mechanical properties, and grindability of dental Ti-Zr alloys, J. Mater. Sci. Mater. Med. , 2008, 19(10): 3179
doi: 10.1007/s10856-008-3454-x
31 H. C. Hsu, S. C. Wu, Y. C. Sung, and W. F. Hod, The structure and mechanical properties of as-cast Zr-Ti alloys, J. Alloy. Comp. , 2009, 488(1): 279
doi: 10.1016/j.jallcom.2009.08.105
32 W. F. Ho, C. H. Cheng, C. H. Pan, S. C. Wu, and H. C. Hsu, Structure, mechanical properties and grindability of dental Ti-10Zr-X alloys, Mater. Sci. Eng. C , 2009, 29(1): 36
doi: 10.1016/j.msec.2008.05.004
33 T. Muto, On the electronic structure of alloys, Sci. Pap. Inst. Phys. Chem. Res. , 1938, 34: 377
34 L. Nordheim, Zur Elektronentheorie der Metalle (I), Ann.Phys. , 1931, 9: 607
doi: 10.1002/andp.19314010507
35 L. L. Sun, Y. Cheng, and G. F. Ji, Elastic and optical propertiesof CeO2 via first-principles calculations, J. At. Mol. Sci. , 2010, 1: 143
36 X. L. Yuan, D. Q. Wei, X. R. Chen, Q. M. Zhang, and Z. Z. Gong, The first-principles calculations for the elastic properties of Zr2Al under compression, J. Alloy. Comp. , 2011, 509(3): 769
doi: 10.1016/j.jallcom.2010.09.084
37 X. L. Yuan, D. Q. Wei, Y. Cheng, J. G. Fu, Q. M. Zhang, and Z. Z. Gong, Pressure effects on elastic and thermodynamic properties of Zr3Al intermetallic compound, Comput. Mater. Sci. , 2012, 58: 125
doi: 10.1016/j.commatsci.2012.02.019
38 X. L. Yuan, D. Q. Wei, Y. Cheng, Q. M. Zhang, and Z. Z. Gong, Thermodynamic properties of Zr2Al under high pressure from first-principles calculations, J. At. Mol. Sci. , 2012, 3: 160
39 X. L. Yuan, M. A. Xue, W. Chen, T. Q. An, and Y. Cheng, Investigations on the structural, elastic and electronic properties of the orthorhombic Zirconium-Nickel alloy under different pressure, Comput. Mater. Sci. , 2012, 65: 127
doi: 10.1016/j.commatsci.2012.07.013
40 X. R. Chen, Z. Y. Zeng, Z. L. Liu, L. C. Cai, and F. Q. Jing, Elastic anisotropy of ?-Fe under conditions at the Earth’s inner core, Phys. Rev. B , 2011, 83(13): 132102
doi: 10.1103/PhysRevB.83.132102
41 H. J. Monkhorst and J. D. Pack, Special points for Brillouinzone integrations, Phys. Rev. B , 1976, 13(12): 5188
doi: 10.1103/PhysRevB.13.5188
42 D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B , 1990, 41(11): 7892
doi: 10.1103/PhysRevB.41.7892
43 B. Hammer, L. B. Hansen, and J. K. Norskov, Improved adsorption energetics within density-functional theory using revised Perdew–Burke–Ernzerhof functionals, Phys. Rev. B , 1999, 59(11): 7413
doi: 10.1103/PhysRevB.59.7413
44 J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B , 1992, 45(23): 13244
doi: 10.1103/PhysRevB.45.13244
45 M. D. Segall, P. J. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark, and M. C. Payne, First-principles simulation: ideas, illustrations and the CASTEP code, J. Phys.: Condens. Matter , 2002, 14(11): 2717
doi: 10.1088/0953-8984/14/11/301
46 F. Birch, Finite elastic strain of cubic crystals, Phys. Rev ., 1947, 71(11): 809
doi: 10.1103/PhysRev.71.809
47 Y. Zhao, J. Zhang, C. Pantea, J. Qian, L. L. Daemen, P. A. Rigg, R. S. Hixson, G. T. Gray, Y. Yang, L. Wang, Y. Wang, and T. Uchida, Thermal equations of state of the a, b, and w phases of zirconium, Phys. Rev. B , 2005, 71(18): 184119
doi: 10.1103/PhysRevB.71.184119
48 B. Olinger and J. C. Jamieson, Zirconium: Phases and compressibility to 120 kilobars, High Temp. High Press. , 1973, 5: 123
49 F. Willaime and C. Massobrio, Development of an N-body interatomic potential for hcp and bcc zirconium, Phys. Rev. B , 1991, 43(14): 11653
doi: 10.1103/PhysRevB.43.11653
50 D. Errandonea, Y. Meng, M. Somayazulu, and D. Hausermann, Pressure-induced αω transition in titanium metal: A systematic study of the effects of uniaxial stress, Physica B , 2005, 355(1-4): 116
doi: 10.1016/j.physb.2004.10.030
52 J. Zhang, Y. Zhao, R. S. Hixson, G. T. Gray, L. P. Wang, W. Utsumi, S. Hiroyuki, and H. Takanori, Thermal equations of state for titanium obtained by high pressure-temperature diffraction studies, Phys. Rev. B , 2008, 78(5): 054119
doi: 10.1103/PhysRevB.78.054119
53 J. P. Poirier, Introduction to the Physics of the Earth’s Interior, New York: Cambridge University Press, 1991
54 X. W. Sun, Q. F. Chen, X. R. Chen, L. C. Cai, and F. Q. Jing, First-principles investigations of elastic stability and electronic structure of cubic platinum carbide under pressure, J. Appl. Phys. , 2011, 110(10): 103507
doi: 10.1063/1.3662143
55 S. F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystaline pure metals, Philos. Mag. , 1954, 45: 823
[1] Zhucheng Zhang, Jiancheng Pei, Yi-Ping Wang, Xiaoguang Wang. Measuring orbital angular momentum of vortex beams in optomechanics[J]. Front. Phys. , 2021, 16(3): 32503-.
[2] Sadegh Imani Yengejeh, William Wen, Yun Wang. Mechanical properties of lateral transition metal dichalcogenide heterostructures[J]. Front. Phys. , 2021, 16(1): 13502-.
[3] Zhi-Yue Zheng, Yu-Hao Pan, Teng-Fei Pei, Rui Xu, Kun-Qi Xu, Le Lei, Sabir Hussain, Xiao-Jun Liu, Li-Hong Bao, Hong-Jun Gao, Wei Ji, Zhi-Hai Cheng. Local probe of the interlayer coupling strength of few-layers SnSe by contact-resonance atomic force microscopy[J]. Front. Phys. , 2020, 15(6): 63505-.
[4] Xiao-Ming Huang, Li-Zhao Liu, Si Zhou, Ji-Jun Zhao. Physical properties and device applications of graphene oxide[J]. Front. Phys. , 2020, 15(3): 33301-.
[5] Thomas Pope, Werner Hofer. Exact orbital-free kinetic energy functional for general many-electron systems[J]. Front. Phys. , 2020, 15(2): 23603-.
[6] Quan Chen (陈泉), Wei Li (李伟), Yong Yang (杨勇). β-PtO2: Phononic, thermodynamic, and elastic properties derived from first-principles calculations[J]. Front. Phys. , 2019, 14(5): 53604-.
[7] Xiao-Bo Yan, He-Lin Lu, Feng Gao, Feng Gao, Liu Yang. Perfect optical nonreciprocity in a double-cavity optomechanical system[J]. Front. Phys. , 2019, 14(5): 52601-.
[8] Jing-Hua Feng (冯景华), Geng Li (李庚), Xiang-Fei Meng (孟祥飞), Xiao-Dong Jian (菅晓东), Zhen-Hong Dai (戴振宏), Yin-Chang Zhao (赵银昌), Zhen Zhou (周震). Computationally predicting spin semiconductors and half metals from doped phosphorene monolayers[J]. Front. Phys. , 2019, 14(4): 43604-.
[9] Xue-Hui Xiao, De-Fang Duan, Yan-Bin Ma, Hui Xie, Hao Song, Da Li, Fu-Bo Tian, Bing-Bing Liu, Hong-Yu Yu, Tian Cui. Ab initio studies of copper hydrides under high pressure[J]. Front. Phys. , 2019, 14(4): 43601-.
[10] Thomas Pope, Werner Hofer. A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules[J]. Front. Phys. , 2019, 14(2): 23604-.
[11] Miao-Miao Zhao, Zhuo Qian, Bang-Pin Hou, Yong Liu, Yong-Hong Zhao. Optomechanical properties of a degenerate nonperiodic cavity chain[J]. Front. Phys. , 2019, 14(2): 22601-.
[12] Jun-Hao Liu, Yu-Bao Zhang, Ya-Fei Yu, Zhi-Ming Zhang. Photon-phonon squeezing and entanglement in a cavity optomechanical system with a flying atom[J]. Front. Phys. , 2019, 14(1): 12601-.
[13] A. S. Sanz. Bohm’s approach to quantum mechanics: Alternative theory or practical picture?[J]. Front. Phys. , 2019, 14(1): 11301-.
[14] Jian Li (李剑), J. Meng (孟杰). Nuclear magnetic moments in covariant density functional theory[J]. Front. Phys. , 2018, 13(6): 132109-.
[15] Longjuan Kong, Kehui Wu, Lan Chen. Recent progress on borophene: Growth and structures[J]. Front. Phys. , 2018, 13(3): 138105-.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed