《厦门大学学报（自然科学版）》

通过制备Ti/Ti-7%Sn、Ti/Ti-9%Sn和Ti/Ti-6%Ni扩散偶(7%,9%,6%均为原子分数),利用EPMA(electron probe micro-analyzer)技术测定了扩散偶的摩尔分数-距离曲线,根据摩尔分数-距离曲线用Den Broeder方法计算了Ti-Sn和Ti-Ni二元系中bcc相在1 273,1 373和1 473 K下的互扩散系数.利用DICTRA(diffusion controlled transformation)软件分别优化了Ti-Sn和Ti-Ni二元系中bcc相的扩散迁移率参数,计算结果和实验数据取得了良好的一致性.运用优化得到的扩散迁移率参数计算了扩散偶的摩尔分数-距离曲线,通过计算结果和实验数据比较表明,所优化的扩散迁移率参数具有良好的准确性与有效性.

On the basis of Ti/Ti-7%Sn,Ti/Ti-9%Sn and Ti/Ti-6%Ni diffusion couples(7%,9%,6% were atomic fraction),respectively,interdiffusion coefficients in the bcc Ti-Sn and Ti-Ni binary alloys at the temperature of 1 273,1 373 and 1 473 K were evaluated by means of the Den Broeder method and electron probe micro-analyzer(EMPA).Based on various reported experimental diffusion coefficients and what was measured in this study,accurate atomic mobilities in the bcc Ti-Sn and Ti-Ni alloys were assessed via the diffusion controlled transformation(DICTRA)simulation package.Comparison between the calculated and measured diffusion coefficients indicated that most of the experimental information can be reproduced reasonably.The developed diffusion mobilities were further validated by the prediction of the mole fraction-distance profiles.

引言
1 实验方法及扩散动力学模型
2 结果与讨论
3 结论

表1 Ti-Sn和Ti-Ni二元系扩散偶的热处理工艺<br/>Tab.1 Process of heat treatment in Ti-Sn and Ti-Ni diffusion couples

表1 Ti-Sn和Ti-Ni二元系扩散偶的热处理工艺
Tab.1 Process of heat treatment in Ti-Sn and Ti-Ni diffusion couples

$图1 不同扩散偶在1 473 K时保温不同时间的摩尔分数-距离曲线 Fig.1 Mole fraction profile for different diffusion couple annealed at 1 473 K at different time$

图1 不同扩散偶在1 473 K时保温不同时间的摩尔分数-距离曲线
Fig.1 Mole fraction profile for different diffusion couple annealed at 1 473 K at different time

$图2 本研究实验获得的的互扩散系数与摩尔分数的关系曲线 Fig.2 Mole fraction dependence of interdiffusion coefficients determined in the present work$

图2 本研究实验获得的的互扩散系数与摩尔分数的关系曲线
Fig.2 Mole fraction dependence of interdiffusion coefficients determined in the present work

表2 Ti-Sn二元系中bcc相的扩散迁移率参数<br/>Tab.2 Diffusion mobility parameters of the bcc Ti-Sn binary system

表2 Ti-Sn二元系中bcc相的扩散迁移率参数
Tab.2 Diffusion mobility parameters of the bcc Ti-Sn binary system

$图3 计算的Ti-Sn合金中bcc相在不同温度下互扩散系数与Sn摩尔分数的关系曲线 Fig.3 Calculated interdiffusion coefficients in bcc Ti-Sn alloy dependence on the mole fraction of Sn at different temperature$

图3 计算的Ti-Sn合金中bcc相在不同温度下互扩散系数与Sn摩尔分数的关系曲线
Fig.3 Calculated interdiffusion coefficients in bcc Ti-Sn alloy dependence on the mole fraction of Sn at different temperature

$图4 计算的扩散偶在不同温度和不同保温时间下的摩尔分数-距离曲线 Fig.4 Calculated mole fraction profile for diffusion couple annealed at different temperature and time$

图4 计算的扩散偶在不同温度和不同保温时间下的摩尔分数-距离曲线
Fig.4 Calculated mole fraction profile for diffusion couple annealed at different temperature and time

表3 Ti-Ni二元系中bcc相的扩散迁移率参数<br/>Tab.3 Diffusion mobility parameters of the bcc Ti-Ni binary system

表3 Ti-Ni二元系中bcc相的扩散迁移率参数
Tab.3 Diffusion mobility parameters of the bcc Ti-Ni binary system

$图6 计算的Ti/Ti-6%Ni扩散偶在不同温度和不同保温时间下的摩尔分数-距离曲线 Fig.6 Calculated mole fraction profiles for Ni in the Ti/Ti-6%Ni diffusion couple annealed at different temperatures and time(a)1 273,1 373和1 473 K;(b)1 173,1 323和1 523 K.$

图6 计算的Ti/Ti-6%Ni扩散偶在不同温度和不同保温时间下的摩尔分数-距离曲线
Fig.6 Calculated mole fraction profiles for Ni in the Ti/Ti-6%Ni diffusion couple annealed at different temperatures and time(a)1 273,1 373和1 473 K;(b)1 173,1 323和1 523 K.

$图5 计算的Ti-Ni合金中bcc相在不同温度时的互扩散系数与Ni摩尔分数之间的关系曲线 Fig.5 Calculated interdiffusion coefficients in bcc Ti-Ni alloy dependence on the mole fraction of Ni at different temperatures$

图5 计算的Ti-Ni合金中bcc相在不同温度时的互扩散系数与Ni摩尔分数之间的关系曲线
Fig.5 Calculated interdiffusion coefficients in bcc Ti-Ni alloy dependence on the mole fraction of Ni at different temperatures

[1] EZUGWU E O,WANG Z M.Titanium alloys and their machinability:a review[J].Journal of Materials Processing Technology,1997,68(3):262-274.
[2] 潘兴波,吕小平,胡中铎,等.钛及其合金的应用前景[J].黑龙江电力,2000,22(1):57-59.
[3] 张宝昌.钛合金发展的现状和趋势[J].稀有金属材料与工程,1985,14(4):63-72.
[4] 张喜燕,赵永庆,白晨光.钛合金及应用[M].北京:化学工业出版社,2005:289-302.
[5] 于振涛,余森,张明华,等.外科植入物用新型医用钛合金材料设计、开发与应用现状及进展[J].中国材料进展,2010,29(12):35-51.
[6] OTSUKA K,REN X.Physical metallurgy of Ti-Ni-based shape memory alloys[J].Progress in Materials Science,2005,50(5):511-678.
[7] THAMBURAJA P.Superelastic behavior in tension-torsion of an initially-textured Ti-Ni shape-memory alloy [J].International Journal of Plasticity,2002,18(11):1607-1617.
[8] BORGENSTAM A,HÖGLUND L,ÅGREN J,et al.DICTRA,a tool for simulation of diffusional transformations in alloys[J].Journal of Phase Equilibria,2000,21(3):269-280.
[9] CHEN Y,LI J,TANG B,et al.Computational study of atomic mobility for bcc phase in Ti-Al-Fe system[J].CALPHAD,2014,46(9):205-212.
[10] HUANG L,CUI Y,CHANG H,et al.Assessment of atomic mobilities for bcc phase of Ti-Al-V system[J].Journal of Phase Equilibria and Diffusion,2010,31(2):135-143.
[11] LI W,TANG B,CUI Y W,et al.Assessment of diffusion mobility for the bcc phase of the Ti-Al-Cr system[J].CALPHAD,2011,35(3):384-390.
[12] LIU Y,GE Y,YU D,et al.Assessment of the diffusional mobilities in bcc Ti-V alloys[J].Journal of Alloys and Compounds,2009,470(1):176-182.
[13] LIU Y,PAN T,ZHANG L,et al.Kinetic modeling of diffusion mobilities in bcc Ti-Nb alloys [J].Journal of Alloys and Compounds,2009,476(1):429-435.
[14] LIU Y,ZHANG L,DU Y,et al.Study of atomic mobilities and diffusion characteristics in bcc Ti-Ta and Ta-W alloys[J].CALPHAD,2010,34(3):310-316.
[15] LIU Y,ZHANG L,YU D.Computational study of mobi-lities and diffusivities in bcc Ti-Zr and bcc Ti-Mo alloys[J].Journal of Phase Equilibria and Diffusion,2009,30(4):334-344.
[16] WANG J L,LIU L B,TUO B Y,et al.Computational study of mobilities and diffusion in Ti-Sn alloy[J].Journal of Phase Equilibria and Diffusion,2015,36(3):248-253.
[17] ASKILL J,GIBBS G B.Tracer diffusion in β-titanium[J].Physica Status Solidi(B),1965,11(2):557-565.
[18] IIJIMA Y,LEE S Y,HIRANO K I.Diffusion of silicon,germanium and tin in β-titanium[J].Philosophical Magazine A,1993,68(5):901-914.
[19] ARAKI H,YAMANE T,MINAMINO Y,et al.Effect of pressure on the anomalous diffusion of tin in β-titanium[J].Materials Transactions,JIM,1993,34(9):763-770.
[20] GHOSH G.Thermodynamic and kinetic modeling of the Cr-Ti-V system[J].Journal of Phase Equilibria,2002,23(4):310-328.
[21] GIBBS G B,GRAHAM D,TOMLIN D.Diffusion in titanium and titanium-niobium alloys[J].Philosophical Magazine,1963,8(92):1269-1282.
[22] PEART R F,TOMLIN D H.Diffusion of solute elements in beta-titanium[J].Acta Metallurgica,1962,10(2):123-134.
[23] SHEVCHUK Y A.Interdiffusion in the phases of the Ti-Ni and Ti-Fe systems[J].Inorganic Materials,2004,40(4):376-379.
[24] DEN BROEDER F J A.A general simplification and improvement of the Matano-Boltzmann method in the determination of the interdiffusion coefficients in binary systems[J].Scripta Metallurgica,1969,3(5):321-325.
[25] MATANO C.On the relation between the diffusion-coefficients and concentrations of solid metals(the nickel-copper system)[J].Japanese Journal of Physics,1933,8(3):109-113.
[26] WANG Y,CURTAROLO S,JIANG C,et al.Ab initio lattice stability in comparison with CALPHAD lattice stability[J].CALPHAD,2004,28(1):79-90.
[27] PEARSON W B,VILLARS P,CALVERT L D.Pearson's handbook of crystallographic data for intermetallic phases[M].Ohio:ASM,1985:3258.
[28] ONSAGER L.Theories and problems of liquid diffusion[J].Annals of the New York Academy of Sciences,1945,46(5):241-265.
[29] JÖNSSON B.Ferromagnetic ordering and diffusion of carbon and nitrogen in bcc Cr-Fe-Ni alloys[J].Zeitschrift Für Metallkunde,1994,85(7):498-501.
[30] ANDERSSON J O,ÅGREN J.Models for numerical treatment of multicomponent diffusion in simple phases[J].Journal of Applied Physics,1992,72(4):1350-1355.
[31] JÖNSSON B.Assessment of the mobility of carbon in fcc C-Cr-Fe-Ni alloys[J].Zeitschrift für Metallkunde,1994,85(7):502-509.
[32] REDLICH O,KISTER A T.Thermodynamics of non-electrolyte solutions-x-y-t relations in a binary system[J].Industrial & Engineering Chemistry,1948,40(2):341-345.
[33] ASKILL J.Empirical and semi-empirical diffusion relations[M]∥Tracer diffusion data for metals,alloys,and simple oxides.New York:Springer US,1970:19-26.
[34] DINSDALE A T.SGTE data for pure elements[J].CALPHAD,1991,15(4):317-425.
[35] HAN J J,WANG C P,LIU X J.A modified model to predict self-diffusion coefficients in metastable fcc,bcc and hcp structures[J].Journal of Phase Equilibria and Diffusion,2013,34(1):17-24.
[36] YIN F,TEDENAC J C,GASCOIN F.Thermodynamic modelling of the Ti-Sn system and calculation of the Co-Ti-Sn system[J].CALPHAD,2007,31(3):370-379.
[37] NEUMANN G,TÖLLE V,TUIJN C.On the impurity diffusion in β-Ti[J].Physica B:Condensed Matter,2001,296(4):334-341.
[38] LIU X J,HU H H,HAN J J,et al.Assessment of the diffusional mobilities in fcc Ni-Nb and fcc Ni-Mo alloys[J].CALPHAD,2012,38:140-145.
[39] WANG S Q,ZHOU P,ZHANG W B,et al.Atomic mobility and diffusivity of bcc_A2 phase in the Fe-X(X=Cu,Si,Zn)systems[J].CALPHAD,2012,36:127-134.
[40] DE KEYZER J,CACCIAMANI G,DUPIN N,et al.Thermodynamic modeling and optimization of the Fe-Ni-Ti system[J].CALPHAD,2009,33(1):109-123.
[41] 胡赓祥,蔡珣.材料科学基础[M].3版.上海:上海交通大学出版社,2011:148.
[42] GONG W,ZHANG L,YAO D,et al.Diffusivities and atomic mobilities in fcc Ni-Pt alloys[J].Scripta Materialia,2009,61(1):100-103.

备注

引言

1 实验方法及扩散动力学模型

2 结果与讨论

3 结论

学报简介

备注

引言

1 实验方法及扩散动力学模型

2 结果与讨论

3 结 论

学报简介

3 结论