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Cu掺杂对TiNi合金马氏体相变路径影响的第一性原理研究

严顺涛 姜振益

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Cu掺杂对TiNi合金马氏体相变路径影响的第一性原理研究

严顺涛, 姜振益

First principles study of the effect of Cu doping on the martensitic transformation of TiNi alloy

Yan Shun-Tao, Jiang Zhen-Yi
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  • 不同浓度的Cu元素掺杂会极大地影响TiNi二元合金的物理性质和相变行为.为了解释其中的物理机制,本文通过第一性原理计算,对TiNi和Ti50Ni25Cu25的相变机制和相稳定性进行了计算和讨论.通过计算Cu掺杂前后立方相到正交相、再到单斜相过程中的相变路径和相变势垒,解释了Cu掺杂对二元合金TiNi相变过程的影响.计算结果表明:TiNi合金的正交相和单斜相之间存在一个大小为1.6 meV的相变势垒;而对于Ti50Ni25Cu25,这两个相之间的相变势垒大小至少为10.3 meV,如此大的一个相变势垒意味着Ti50Ni25Cu25合金的正交相很难跨过势垒相变到单斜相.
    As is well known,copper is such an unbelievable element that it can affect the phase transition behaviors of binary TiNi alloy when it displaces Ni element up to near upon 25%.The martensitic transition behaviors of TiNi1-xCux alloys appear from high-temperature cubic B2 phase to intermediate B19 structure with orthorhombic system and then finally to low-temperature B19' phase with monoclinic system with x 10% on cooling,so called two-stage martensitic phase transformation.Whereas,it directly transforms into orthorhombic B19 phase withx 20% on cooling,so called one-stage martensitic phase transformation.The orthorhombic B19 phase becomes final low-temperature phase while monoclinic phase will be unstable on cooling.The electronic structures and the formation energies of various point defects, Mulliken bond orders,etc.are studied for TiNi1-xCuxx alloys,however,the phase transition pathway at an atomic level has not been described at all,and further,the difference in transition pathway between TiNi and Ti1Ni1-xCuxx has not been understood so far.In this work,we optimize the crystal structures of TiNi and Ti50Ni25Cu25 alloys with initial geometry from experimental data.In order to choose the proper positions of Cu atom,we calculate the total energy of each doping system and find the most stable configuration.To study the transformation mechanism of TiNi,we calculate the phonon-dispersion spectra of each phase with both frozen-phonon method and linear response method,and then find the atomic vibrations with the imaginary frequency.Finally,with the help of this atomic vibration direction with negative frequency,we find the intermediate structures by the linear interpolation method and calculate their total energies.The phase transformation of TiNi from cubic to orthorhombic phase is driven by the phonon softening at the M point (0.5,0.5,0) of Brillouin zone.For orthorhombic and monoclinic phase,TiNi has real phonon frequencies for all k points and modes.A barrier of 1.6 meV is calculated between orthorhombic and monoclinic phase while no barrier is found between cubic and orthorhombic phase of TiNi,so it is easy to transform from cubic to orthorhombic and then to monoclinic phase.There exists a potential energy barrier of 10.3 meV at least between orthorhombic and monoclinic phase for Ti50Ni25Cu25,which is too high for its transition to overcome the maximum value of potential energy which corresponds to =93.4.The difference in transition pathway between TiNi and Ti50Ni25Cu25 accords well with the experimental measurement,so that the copper concentration with 25% in binary TiNi alloy will offer a new transition path from cubic to orthorhombic phase.
      Corresponding author: Yan Shun-Tao, yanshuntaofreedom@163.com;jiangzy@nwu.edu.cn ; Jiang Zhen-Yi, yanshuntaofreedom@163.com;jiangzy@nwu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.10647008,50971099,51572219) and the Natural Science Foundation of Shaanxi Province,China (Grant No.2015JM1018).
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    Si L, Jiang Z Y, Zhou B, Chen W Z 2012 Physica B 407 347

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    Otsuka K, Ren X 2005 Prog. Mater Sci. 50 511

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    Hehemann R F, Sandrock G D 1971 Scr. Metall. 5 801

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    Ye Y Y, Chan C T, Ho K M 1997 Phys. Rev. B 2 8

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    Ramachandran B, Tang R C, Chang P C, Kuo Y K, Chien C, Wu S K 2013 J. Appl. Phys. 113 511

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    Kresse G, Furthmller J 1996 Comp. Mater. Sci. 6 15

    [18]

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    [19]

    Blöchl P E 1994 Phys. Rev. B 50 17953

    [20]

    Kresse G, Joubert D 1999 Phys. Rev. B 59 1758

    [21]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [22]

    Nam T H, Saburi T, Nakata Y, Shimizu K I 1990 Mater. Trans. JIM 31 1050

    [23]

    Prokoshkin S, Korotitskiy A, Brailovski V, Turenne S, Khmelevskaya I Y, Trubitsyna I 2004 Acta Mater. 52 4479

    [24]

    Pushin V G, Valiev R Z, Yurchenko L I 2003 J. Phys. IV (Proceedings) 112 709

    [25]

    Huang X, Ackland G J, Rabe K M 2003 Nature Mater. 2 307

    [26]

    Otsuka K, Sawamura T, Shimizu K 1971 Phys. Status Solid A 5 457

    [27]

    Bricknell R H, Melton K N, Mercier O 1979 Metall. Trans. A 10 693

    [28]

    Gou L, Liu Y, Teng Y N 2014 Intermetallics 53 20

    [29]

    Zeng Z Y, Hu C E, Cai L C, Chen X R, Jing F Q 2009 Solid State Commun. 149 2164

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    Chen B H, Franzen H F 1990 J. Alloys Compd. 157 37

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  • [1]

    Huang X, Bungaro C, Godlevsky V, Rabe K M 2001 Phys. Rev. B 65 014108

    [2]

    Parlinski K, Parlinskawojtan M 2002 Phys. Rev. B 66 340

    [3]

    Buehler W J, Gilfrich J, Wiley R 1963 J. Appl. Phys. 34 1475

    [4]

    Eckelmeyer K 1976 Scr. Metall. 10 667

    [5]

    Melton K, Mercier O 1978 Metall. Trans. A 9 1487

    [6]

    Mercier O, Melton K N 1979 Metall. Trans. A 10 387

    [7]

    Luo S H 2003 M. S. Dissertation (Suzhou:Suzhou University) (in Chinese)[骆苏华 2003 硕士学位论文 (苏州:苏州大学)]

    [8]

    Yang H J, Yang G J, Cao J M, Yang H B 2005 Sci. China Mater. 24 27 (in Chinese)[杨宏进, 杨冠军, 曹继敏, 杨华斌 2005 中国材料进展 24 27]

    [9]

    He Z R 1999 The 7th National Conference on Heat Treatment Luoyang, China, October 13-16, 1999

    [10]

    Zhang Z, Elkedim O, Ma Y Z, Balcerzak M, Jurczyk M 2017 Int. J. Hydrogen Energy 42 1444

    [11]

    Si L, Jiang Z Y, Zhou B, Chen W Z 2012 Physica B 407 347

    [12]

    Otsuka K, Ren X 2005 Prog. Mater Sci. 50 511

    [13]

    Hehemann R F, Sandrock G D 1971 Scr. Metall. 5 801

    [14]

    Ye Y Y, Chan C T, Ho K M 1997 Phys. Rev. B 2 8

    [15]

    Ramachandran B, Tang R C, Chang P C, Kuo Y K, Chien C, Wu S K 2013 J. Appl. Phys. 113 511

    [16]

    Teng Y, Zhu S, Wang F, Wu W 2007 Physica B 393 18

    [17]

    Kresse G, Furthmller J 1996 Comp. Mater. Sci. 6 15

    [18]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [19]

    Blöchl P E 1994 Phys. Rev. B 50 17953

    [20]

    Kresse G, Joubert D 1999 Phys. Rev. B 59 1758

    [21]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [22]

    Nam T H, Saburi T, Nakata Y, Shimizu K I 1990 Mater. Trans. JIM 31 1050

    [23]

    Prokoshkin S, Korotitskiy A, Brailovski V, Turenne S, Khmelevskaya I Y, Trubitsyna I 2004 Acta Mater. 52 4479

    [24]

    Pushin V G, Valiev R Z, Yurchenko L I 2003 J. Phys. IV (Proceedings) 112 709

    [25]

    Huang X, Ackland G J, Rabe K M 2003 Nature Mater. 2 307

    [26]

    Otsuka K, Sawamura T, Shimizu K 1971 Phys. Status Solid A 5 457

    [27]

    Bricknell R H, Melton K N, Mercier O 1979 Metall. Trans. A 10 693

    [28]

    Gou L, Liu Y, Teng Y N 2014 Intermetallics 53 20

    [29]

    Zeng Z Y, Hu C E, Cai L C, Chen X R, Jing F Q 2009 Solid State Commun. 149 2164

    [30]

    Chen B H, Franzen H F 1990 J. Alloys Compd. 157 37

    [31]

    Vishnu K G, Strachan A 2010 Acta Mater. 58 745

    [32]

    Kibey S, Sehitoglu H, Johnson D 2009 Acta Mater. 57 1624

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出版历程
  • 收稿日期:  2017-03-27
  • 修回日期:  2017-04-28
  • 刊出日期:  2017-07-05

Cu掺杂对TiNi合金马氏体相变路径影响的第一性原理研究

    基金项目: 国家自然科学基金(批准号:10647008,50971099,51572219)和陕西省自然科学基金(批准号:2015JM1018)资助的课题.

摘要: 不同浓度的Cu元素掺杂会极大地影响TiNi二元合金的物理性质和相变行为.为了解释其中的物理机制,本文通过第一性原理计算,对TiNi和Ti50Ni25Cu25的相变机制和相稳定性进行了计算和讨论.通过计算Cu掺杂前后立方相到正交相、再到单斜相过程中的相变路径和相变势垒,解释了Cu掺杂对二元合金TiNi相变过程的影响.计算结果表明:TiNi合金的正交相和单斜相之间存在一个大小为1.6 meV的相变势垒;而对于Ti50Ni25Cu25,这两个相之间的相变势垒大小至少为10.3 meV,如此大的一个相变势垒意味着Ti50Ni25Cu25合金的正交相很难跨过势垒相变到单斜相.

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