材料成型外文翻譯 --ti–al–v三元系統(tǒng)中體心立方相的熱力學(xué)和動(dòng)力學(xué)建模（英文）

1、Materials Science and Engineering A 528 (2010) 622–630Contents lists available at ScienceDirectMaterials Science and Engineering Ajournal homepage: www.elsevier.com/locate/mseaThermodynamic and kinetic modeling of bcc ph

2、ase in the Ti–Al–V ternary systemH. Wang, N. Warnken, R.C. Reed ?Department of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UKa r t i c l e i n f oArticle history:Received 7 May 2010

3、Received in revised form 2 September 2010Accepted 2 September 2010Keywords:ThermodynamicMobilityOptimisationTi–Al–Va b s t r a c tA thermodynamic optimisation of the ordered B2 phase in the Ti–Al binary and Ti–Al–V terna

4、ry systemsis carried out, making use of a two-sublattice model (Ti,Al,V):(Ti,Al,V). A self-consistent set of parametersis obtained; it is demonstrated that the available experimental data for the phase equilibria are rep

5、ro-duced accurately. Based upon the thermodynamic driving forces calculated by the new thermodynamicdatabase, interdiffusion in the disordered A2 phase of the ternary Ti–Al–V system is assessed and opti-mised. A set of p

6、arameters describing the atomic mobilities of the disordered A2 phase are given, whichwill be useful for future quantitative models of phase transitions involving this phase.© 2010 Elsevier B.V. All rights reserved.

7、1. IntroductionTi-based alloys exhibit attractive levels of strength and tough-ness, especially when judged on a density-corrected basis.However, the properties of these alloys depend significantly uponthe manner in whic

8、h they are heat treated; for this reason it is vitalto have a good understanding of the microstructure/property rela-tionships in these systems. This is particularly the case for the rangeof high strength, high toughness

9、 titanium alloys which retain signif-icant quantities of the body-centered cubic (bcc) crystal structureat room temperature – known as the ?-alloys – some of which areemerging as candidates for use in the aerospace secto

10、r. Thermody-namic and kinetic data are very helpful for the design of ?-alloys,as indeed for many other engineering alloys, as various kinds ofphase equilibria and phase transformations can be simulated. Thusit is import

11、ant to obtain a complete and comprehensive databasefor the thermodynamics and kinetic mobilities of the bcc phase inthe ternary Ti–Al–V system.So far, there has been only limited analysis carried out byresearchers on thi

12、s system. The phase equilibria of the Ti–Al–Vternary system was assessed by Hayes [1], who presented aschematic liquidus projection, a partial reaction scheme, andisothermal sections at several temperatures. Further phas

13、e equi-libria were considered in the more recent assessment by Raghavan[2] including two full isothermal sections at 600 ?C and 900 ?C; inthis work the ordered B2 phase was considered for the first time.A thermodynamic d

14、atabase for the Ti–Al–V system was optimised? Corresponding author. Fax: +44 121 414 7468.E-mail addresses: r.c.reed@bham.ac.uk, r.reed@bham.ac.uk (R.C. Reed).[3] which lacks any information concerning the ordered B2 pha

15、seunder consideration here (the parameters for disordered A2 phaseare listed in Table 1). Kinetic assessments have also been carried outbased upon experimental measurements of diffusion phenomena.For example, the mobilit

16、ies in the A2 phase have been assessedby Chen et al. [4]. Recently, Takahashi et al. [5] published somenew data for interdiffusion coefficients in the A2 phase, whichrequired the updating of the database. Using these dat

17、a, Huang etal. [6] assessed the atomic mobilities for the A2 phase of Ti–Al–Vsystem. However, their work [6] is based on an extrapolated ther-modynamic database from [7–9] without ternary thermodynamicparameters. In this

18、 work, the thermodynamic parameters wereoptimised for the ordered B2 phase in the Ti–Al binary and theTi–Al–V ternary systems, and kinetic parameters were optimisedfor the disordered A2 phase in the Ti–Al–V system, respe

19、ctively.2. Experimental information2.1. The order/disorder transformationThe A2/B2 order/disorder transformation has been found in theTi–Al–Cr–V quaternary system [10] and some Ti–Al–X (X = Cr [11],Nb [12,13], Mo [13]) t

20、ernary systems. In the Ti–Al–V ternary sys-tem, the ordered B2 phase has been observed using transmissionelectron microscopy [14]. A single phase region of the ordered B2phase has been found at 1200 ?C, and so were the p

21、hase equilib-ria between the B2 phase and other phases (both Ti3Al and TiAl) inthe temperature range of 600–900 ?C. These pieces of experimentalinformation have been used in the modeling work reported here.There is only

22、one binary system of relevance to this prob-lem which contains the A2/B2 order/disorder transformation: the0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2010.09.013624 H.

23、 Wang et al. / Materials Science and Engineering A 528 (2010) 622–630two-sublattice model is used (Ti,Al,V)0.5:(Ti,Al,V)0.5 for B2 phase:GB2 = GA2(xi) + Gord(y1 i y2 i ) ? Gord(xi, xi) (1)where GA2(xi) is the Gibbs energ

24、y of the disordered A2 phase(parameters from [3]), and the difference between the latter twoterms Gord(y1 i y2 i ) and Gord(xi, xi) is the Gibbs energy due to orderingGord(y1 i y2 i ) is determined by:Gord{y1 i y2 i } =2

25、 ?i=13 ?j=i+1[y1 i y2 j Gi:j + y1 j y2 j Gj:i]+2 ?i=13 ?j=i+13 ?k=1y1 i y1 j y2 k[L0 i,j:k + [y1 i ? y1 j ]L1 i,j:k]+2 ?i=13 ?j=i+13 ?k=1y1 i y1 j y2 k[L0 k:i,j + [y1 i ? y1 j ]L1 k:i,j] (2)where i, j, k = Al, Ti, V, and

26、 Gi:j, Gj:i, L? i:j,k, L? k:i,j(? = 0, 1) includeordering parameters optimised here. When y1 i = y2 i = xi, the phaseis disordered.3.2. DiffusivityFor the crystalline phases, the ternary interdiffusion coefficientmatrix

27、is reduced by choosing one element to be dependent on theother two [40], thus:Dn kj = ?i[?ik ? xk]xiMi? ??i ?xj ? ??i?xn?(3)where n, k, j are the dependent, the diffusing and the gradientelement, respectively. The terms

28、xi, ?i, Mi are the mole fraction,chemical potential and mobility of element i, respectively. The term?ik is the Kronecker delta (?ik = 1 if i = k, otherwise ?ik = 0).3.3. MobilityAccording to Jonsson [41], the atomic mob

29、ility in a multicom-ponent phase can be expressed by:MB = M? B exp ? ?QBRT? 1RT (4)where M? B is the frequency factor and QB is the activation enthalpy.The frequency factor is calculated by:M? B = exp[?B] (5)Both ?B and

30、QB generally depend on the composition, tempera-ture and pressure. In the spirit of the Calphad approach [42], thedependence on composition of ?B(?B or QB) is described with aRedlich–Kister polynomial according to:?B = ?

31、ixi?i B + ?i?j>ixixj[m ?r=0r?i,j B [xi ? xj]r]+ ?i?j>i?k>jxixjxk[ ?s?s ijk s?i,j,k B ] (6)where the parameters ?s ijk are obtained by:?s ijk = xs + [1 ? xi ? xj ? xk]3 (7)020040060080010001200140016001800TEMPERA

32、TURE_CELSIUS0 0.2 0.4 0.6 0.8 1.0MOLE_FRACTION AL1415161718191920202121/3122/3222232324242525/2626/2727/28/2928/29/30303111001110112011301140115011601170118011901200TEMPERATURE_CELSIUS0.15 0.20 0.25 0.30 0.35MOLE_FRACTIO

33、N ALTiAl3TiAl2Ti2Al5TiAlTi3AlTi3AlhcpB2A2B2 A2hcphcpLiquidFig. 3. The calculated Ti–Al binary phase diagram by this work versus different data(note some data are for another peritectoid formation of ?2 phase).4. Results

34、and discussion4.1. Phase equilibriaUsing the CALPHAD method, a set of self-consistent thermody-namic parameters for the ordered B2 phase was obtained – seeTable 1 – using the two sublattice model [43] and the experimen-t

35、al data previously mentioned. The phase diagram for the Ti–Albinary system which follows from this dataset is given in Fig. 3. Thedashed line represents the order/disorder transformation betweenthe A2 phase and the B2 ph

36、ase. The transformation temperatureis predicted to change from 1200 ?C to 1400 ?C as the compositionchanges from 20 to 40 at.%Al. The ordered B2 phase is stabilisedto higher temperatures with an increase in Al content, c

37、onsistentwith the positive effect of Al in the tendency for ordering [10].With these optimised binary parameters, the two peritec-toid reactions involving the ordered B2 phase – ? + ˇ → ?2 andˇ + ?2 → ? – can be modeled