How To Calculate The Phase Dagram Of A Bnary System

Transcription

1 CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) Contents lsts avalable at ScenceDrect CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry journal homepage: Thermodynamc descrpton of the system Y.Q. Lu a,b,, Y. Du b a School of Materals Scence and Technology, Chna Unversty of oscences, Bejng, , PR Chna b State Key Laboratory of Powder Metallurgy, Central South Unversty, Changsha, Hunan, , PR Chna a r t c l e n f o a b s t r a c t Artcle hstory: Receved 10 May 2009 Receved n revsed form 22 October 2009 Accepted 3 November 2009 Avalable onlne 17 November 2009 Keywords: system CALPHAD Phase dagram The bnary system was thermodynamcally optmzed usng the CALPHAD method. The lqud phase was descrbed by means of an assocate soluton model. The BCC termnal sold soluton was descrbed by the substtutonal soluton model. The two-sublattce model was used to descrbe the non-stochometrc compounds 3, α 5 3 and β 5 3. The 11 8, and phases were modeled as stochometrc compounds. A set of thermodynamc parameters for the system was obtaned va thermodynamc optmzaton usng assessed expermental data. The calculated phase dagram and thermodynamc propertes agree well wth most of the expermental data Elsever Ltd. All rghts reserved. 1. Introducton Transton metal (TM) germandes possess low room-temperature resstvty, hgh thermal stablty and good adherence to slcon substrates. The bnary TM/ and ternary TM//S systems are of potental mportance n the development of electronc devces [1]. For example, the germandes n the, Cu, T and Co systems have recently been consdered to be promsng canddates for electroncs applcatons, such as the low-resstvty nterconnect lnes and contacts to slcon substrates n S-based semconductor devces [2 5]. Controllng reactons between TM and s of crtcal mportance for the preparaton of robust mcroelectronc devces. Relable thermodynamc data on the relatve stabltes of TMgermandes are essental for establshng the general characterstcs of the nteracton between TM and germanum and solvng problems connected wth the germanum. In ths study, a thermodynamc optmzaton of the system was carred out usng the CALPHAD method appled to the avalable expermental data. 2. Evaluaton of lterature nformaton The expermental phase dagram and thermodynamc data of the system were revewed by Gokhale and Abbaschan [6] n Correspondng author at: School of Materals Scence and Technology, Chna Unversty of oscences, Bejng, , PR Chna. Tel.: ; fax: E-mal addresses: luyuqn@cugb.edu.cn, ms.yuqnlu@gmal.com (Y.Q. Lu) The present assessment takes nto account both the expermental data assessed by Ref. [6] and those publshed later [7 9]. The avalable expermental data n the lterature are summarzed n Table Phase dagram nformaton The phase equlbra n the system have been studed by several groups of authors [10 15]. The most recent nvestgaton on the phase dagram was carred out by Godat and Feschotte [10] n the whole concentraton range. The samples were prepared by meltng 99.99% and % n alumna crucbles under an argon atmosphere, heat-treated n sealed slca tubes and then analyzed usng thermal analyss, X-ray dffracton (XRD), mcrohardness and electron probe mcroanalyss (EPMA). There exst fve compounds wth ncongruent meltng feature. The -rchest phase 3, wth a homogenety range from 20.5 to 25 at.%, decomposes pertectcally at 1564 C. The 5 3 phase, wth a homogenety range from 37.4 to 38.2 at.%, decomposes pertectcally at 1262 C and undergoes an allotropc transformaton at 1002 C. The other three phases, 11 8, and 11 19, are stochometrc and melt pertectcally at 1170 C, 998 C and 928 C, respectvely. The solublty of n the BCC termnal sold soluton vares from 4 at.% (800 C) to the maxmum value of 11 at.% at pertectc temperature 1564 C. s practcally nsoluble n sold at any temperature. The weght losses durng the preparaton of the alloys were determned by spectrophotometrc plasma emsson analyss. Zagryazhsk et al. [11] studed the phase dagram n the whole concentraton range usng mcroscopy, XRD, and dfferental thermal analyses (DTA). The purty of startng materals was 99.98% /$ see front matter 2009 Elsever Ltd. All rghts reserved. do: /j.calphad

2 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) Table 1 Summary of the phase dagram and thermodynamc data for the system. Type of data Reference Expermental method Lqudus: at.% [10] DTA [12] DTA Solublty of n () [10] EPMA [15] Metallography, XRD [11] Metallography, XRD, DTA Homogenety of at.% [10] EPMA at.% [15] Metallography, XRD at.% [6,11] Metallography, XRD, DTA Homogenety of at.% [10] EPMA at.% [11] Metallography, XRD, DTA Enthalpy of mxng of lqud 1773 K, at.% [16] Calormetry Enthalpy of formaton for alloy 1305 K, at.% 1273 K, at.% 1226 K, at.% [7] Drect reacton calormetry Heat capacty of K [17] Adabatc calormetry K for [8] DSC Heat capacty of K [13] Adabatc calormetry K for [8] DSC Heat capacty of, K [13] Adabatc calormetry Heat capacty of 11 19, [13] Adabatc calormetry K Standard enthalpy of formaton at 298 K 3, 5 3 [8] Knudsen effuson mass spectrometry 5 3 [9] Calormetry 3, 11 8,, [18] Potentometrc method Enthalpy dfference between [6] Calculated from C p data 298 K and 0 K for 3, 5 3,, Standard entropy at 298 K [6] Calculated from C p data 3, 5 3,, Entropy of formaton for 11 8 at 1273 K and 1305 K [7] Estmated from drect reacton calormetry results Latent heat of transformaton [10] DTA α 5 3 β 5 3 Actvty of and at 1530 K [8] Knudsen effuson mass spectrometry and 99.99%. The exstence of fve ntermetallc compounds s demonstrated. Among them, 11 19,, 11 8 and 5 3 are formed by pertectc reactons that are consstent wth the result of Godat and Feschotte [10]. However, the temperatures for the equlbrum reactons L (), L and L were found consstently 25 to 27 C hgher than the correspondng ones reported n [6,10] (see Table 3 for detaled nformaton). The dfferences may be due to the fact that the meltng pont of 955 C used for n Ref. [11] s 18 C hgher than 937 C used n Ref. [10]. The second contradcton s that 3 melts congruently at around 1520 C accordng to Zagryazhsk et al. [11] whle Godat and Feschotte [10] reported that 3 s formed va pertectc reacton. Snce the lqudus temperature s somewhat speculatve n Ref. [11] whle Godat and Feschotte [10] measured the lqudus more thoroughly usng thermal analyss wth a reported precson of ±10 C n the -rch sde, ±5 C n the ntermedate composton range and ±4 C n the -rch sde, the fndngs of Ref. [10] are thought to be more relable n ths work. Svechnkov et al. [12] constructed the phase dagram by preparng alloys from sngle crystal and 99.98% electrolytc. Fve ntermetallc compounds and seven nvarant reactons were dentfed from the data of DTA, XRD and mcrostructural analyses. The -rch phase dagram agrees reasonably wth the result of Ref. [10]. In the -rch regon, Svechnkov et al. [12] reported a monotectc reacton L 1 L 2 + BCC at 1565 C and pertectc reacton L + BCC 3 at 1410 C. These results contradcted the observaton of Ref. [10]. Snce the -rch phase equlbra n Ref. [10] were carefully studed at three temperatures 1580 C, 1545 C and 1470 C by mcrostructural analyss and thermal analyss, the monotectc reacton reported n Ref. [12] was not used n ths work. Kalshevch et al. [13] measured the phase relatons usng 99.98% and 99.98% as the startng materals. The mcrostructural and XRD studes revealed that 5 3,, and are formed pertectcally at 1245 C, 995 C and 925 C, respectvely, n agreement wth the fndngs of Ref. [10]. The latter two temperatures agree well wth those of 998 C and 935 C reported by Kawasum et al. [14]. Usng startng materals wth purtes of 99.95% and 99.9%, Rawal and Gupta [15] nvestgated the -rch sde (up to 45 at.% ) of the phase dagram from 700 to 1306 C by XRD and metallography. Three ntermedate compounds, 3, 5 3 and 4 3 ( 11 8 phase), exst n the nvestgated regon. The phase boundares wthn the nvestgated regon agree well wth the result of Ref. [10]. The ndcaton of three lqud sold eutectc reactons by [15] s not relable due to the naccurate lqudus measurement. The lqudus temperatures for the alloys n the composton range of at.% were determned approxmately wth an optcal pyrometer by observng the frst appearance of a sold crust on the melt [6,10] Thermodynamc nformaton The thermodynamc propertes of the system have been nvestgated prevously [6 9,13,16 18]. Yassn and Castanet [7] determned the ntegral enthalpy of formaton for alloys n the -rch sde at three temperatures of 1305 K, 1273 K and 1226 K by means of drect reacton calormetry. The enthalpy of formaton was found to be negatve at any concentraton n good agreement wth those of Shlapak et al. [16], who measured calormetrcally the enthalpy of mxng of lqud alloys from 42 to 93.6 at.% at 1773 K. The deduced enthalpes of formaton for 11 8 at 1305 K and 1273 K relatve to both lqud components are about 28.6 kj/mol-atom and 30.7 kj/mol-atom, respectvely. The heat capactes of ntermedate compounds n the system were also reported [8,13,17]. Kalshevch et al. [13] measured the heat capactes of, 5 3 and n the temperature range of 50 to 300 K by means of adabatc calormetry. The heat capacty of 3 was measured by Surkov et al. [17] usng adabatc calormetry n the temperature range of 5 to 300 K. More recently, the heat capactes of two ntermedate germandes, 3 ( ) and 5 3 ( ), were measured by Zarembo et al. [8] usng DSC n the temperature range of 300 to 700 K. From the reported C p T curve, t can be seen that the reported C p data [8] agree well wth those of [13,17]. Gokhale and Abbaschan [6] calculated the standard entropes and enthalpes of formaton for the 3, 5 3, and compounds by extrapolatng the measured heat capacty data of Refs. [13,17] to absolute zero. We notced that the standard enthalpy of formaton reported n Ref. [6] should be enthalpy dfference between 298 K and 0 K for the ntermedate germandes, whle the standard entropy of formaton should be the standard entropy at 298 K (S 298 ). Kleppa and Yung [9] reported calormetrcally the standard enthalpy of formaton for 5 3 to be 15.7 ± 1.0 kj/mol atom. Lukashenko et al. [18] determned the standard enthalpy of formaton for -germandes by a

3 28 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) potentometrc method usng lqud electrolytes as follows: 3 : 19.12; 11 8 : 10.92; : 10.25; : 7.28 kj/mol atom, referred to both sold components. More recently, Zarembo et al. [8] studed the thermodynamc stabltes of 3 and 5 3 by hgh-temperature Knudsen effuson mass spectrometry (KEMS) and dfferental scannng calormetry (DSC). Actvtes of and were measured over the 3 sngle phase and two-phase mxtures of BCC+ 3 and n a temperature range of approxmately K by hgh temperature KEMS. The standard Gbbs free energy of formaton for -germandes at hgh temperature was determned from the actvty data. The reported standard enthalpes of formaton at 298 K are 19.3 ± 2.5 kj/mol atom for ( 3 ) and 12.3 ± 2.5 kj/mol-atom for ( 5 3 ). Such values were calculated by the thrd-law method usng absolute entropy and estmated hgh-temperature heat capacty from lterature. 3. Thermodynamc model 3.1. Pure elements The Gbbs free energes G ϕ (T) of pure elements and n phase ϕ are taken from the SGTE complaton by Dnsdale [19] and descrbed by the equaton: G ϕ (T) HSER = a + b T + c T ln T + d T 2 + e T 3 + f T 1 + g T 7 + h T 9 (1) where H SER s the molar enthalpy of element at K and 1 atm n ts standard element reference (SER) state, and T s the absolute temperature Lqud phase The lqud phase s descrbed by assocate soluton model [20]. Ths s based on the consderaton that the enthalpy of mxng n the lqud at 1773 K [16] ndcates the exstence of a sharp mnmum. Here, we assume that the assocate 3 1 s formed n the lqud by reacton 3+ = 3 1. The Gbbs free energy for one mole of atoms can be expressed as: [ ] / G Lq = y G 0,Lq + RT y ln y + E G Lq (1 + 3y 3 1 ) (2) where y s the mole fracton of speces n the lqud, represents any of the speces, 3 1,. G 0,Lq and G 0,Lq are the Gbbs free energes of lqud and lqud taken from SGTE complaton [19]. G 0,Lq 3 1 s the Gbbs free energy of 3 1 assocate per mole of formula and can be expressed by G 0,Lq 3 1 = a Lq b Lq 3 1 T + 3G 0,Lq + G 0,Lq (3) where a Lq 3 1 and b Lq 3 1 are related to the formaton enthalpy and entropy of the 3 1 assocate and are evaluated n the optmzaton process. The excess Gbbs free energy for the lqud phase, E G Lq, s expressed by the Redlch Kster polynomal [21] E G Lq = y y j,j,j> n ν=0 ν L Lq,j (y y j ) ν (4) where and j refer to the speces, 3 1,. ν L Lq,j s the vth nteracton parameter between the speces and j and s evaluated n ths work BCC sold soluton The BCC sold soluton s modeled by a substtutonal soluton model and ts Gbbs free energy s descrbed by splttng nto a nonmagnetc contrbuton ( 0 G nmg ) and a magnetc one (G mag ). The nonmagnetc contrbuton s descrbed by 0 G BCC = nmg x 0 G BCC + x 0 G BCC + RT (x ln x cr + x ln x ) where 0 G BCC + x x n =0 and 0 G BCC and BCC, respectvely. L BCC, and expresses as L BCC L BCC, (x x ) (5) are the molar Gbbs free energy of BCC s the -th nteracton parameter =, abcc +b BCC T. a BCC and b BCC are obtaned n ths work durng the optmzaton process. The magnetc contrbuton s gven by means of Hllert Jarl Inden model [22,23]: G BCC mag = RT ln(β + 1)g(τ) (6) n whch τ s T/T c, T c s the crtcal temperature, and β s the average magnetc moment per atom n the alloys. The functon g(τ) s the polynomal derved by Hllert and Jarl [23]. Its complete descrpton s gven n Ref. [23]. The parameters T c and β are usually expressed as a functon of composton as shown by Eqs. (7) and (8): T c = x T 0 c, + x T 0 c, + x x β = x β 0 + x β 0 + x x n T c (x x ) (7) =0 n β (x x ) (8) where T 0 c,, T 0 c,, β0, β0 are the Néel temperature and Bohr magnetons of pure and, respectvely. T c and β are the nteracton parameters to be evaluated Intermedate compounds The ntermedate compounds 11 8, and are modeled as stochometrc compounds. Snce the heat capacty data for the and phases are avalable n the lterature [13], the Gbbs free energy of these two phases s gven by G m n m m + n HSER n m + n HSER = a + bt + ct ln T + dt 2 + et 1 (9) where a, b, c, d, e are the parameters to be evaluated n the optmzaton process. For the stochometrc 11 8 phase, the expermental heat capacty data are not avalable. The reported standard enthalpy of formaton at 298 K by Lukashenko et al. [18] and enthalpy of formaton at 1273 K and 1305 K by Yassn et al. [7] show temperature dependence. Based on ths consderaton, the Gbbs free energy of 11 8 per mol atom s gven by G 11 8 =0 = a b 118 T + c 118 T ln T G BCC G Damond (10) where a 11 8, b 11 8 and c 11 8 are the parameters to be evaluated. 0 G BCC and 0 G Damond are the molar Gbbs free energy of BCC and Damond, respectvely. The nonstochometrc compound 3 has a cp8 structure wth the deal stochometry of 25 at.%, n whch the atoms occupy the 2a Wyckoff poston, and the atoms occupy the 6c Wyckoff poston [24]. The expermental results show that 3

4 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) a b Fg. 1. (a) Calculated phase dagram n the present work, (b) Calculated phase dagram along wth expermental data from the lterature [10 15,28]. on ste substtuton, and nsuffcent avalable expermental data to get the parameters for four sublattce model (, )(, ) 4 (, )(, ) 2, for smplcty, a two-sublattce model (, ) (, ) s used for descrbng the α 5 3 and β 5 3 phases. The Gbbs free energy for the 3, α 5 3 and β 5 3 phases can be expressed as: Fg. 2. Calculated enthalpy of mxng n the lqud at dfferent temperatures. The expermental data from Refs. [7,16] are supermposed for comparson. The sold lne corresponds to 1226 K, whle the dotted lne to 1773 K. The reference state s lqud and lqud. does not exst n deal stochometry but on the composton range around 20.5 to at.% [6,10,11,15]. Snce no further expermental nformaton supports the detaled ste substtuton, for smplcty, the two-sublattce model (, ) 0.75 (, ) 0.25 s used, where the frst sublattce s manly occuped by and the second by. More detaled descrpton of the sublattce model can be found n Ref. [25]. The nonstochometrc 5 3 phase undergoes an allotropc transformaton at 1002 C [10]. The low temperature form α 5 3 has a ti32 structure wth the space group of I4/mcm, n whch the atoms occupy the 4b and 16k Wyckoff poston, and the atoms occupy the 4a and 8h Wyckoff poston [24]. The crystal structure of hgh temperature allotropy β 5 3 s unknown. The homogenety ranges for both the α 5 3 and β 5 3 are 37.4 at.% to 38.2 at.%. Due to the lack of nformaton G ϕ = y y 0 G ϕ + : y y 0 G ϕ + : y y 0 G ϕ : + y y 0 G ϕ + [ ( : RT a y ln y + y ) )] ln y + ( b y ln y + y ln y + y y + y y ( y Lϕ,: + y Lϕ,: ( y Lϕ :, + y Lϕ :, ) ) (11) where the superscrpts and denote the frst and second sublattce, whle y and y are the ste fracton of the speces ( =, ) on the frst and second sublattce, respectvely. The 0 G ϕ :, 0 G ϕ :, 0 G ϕ :, and 0 G ϕ : are the Gbbs free energy of the four end-members () a () b, () a () b, () a () b, () a () b of sublattce model (, ) a (, ) b, respectvely. L ϕ,,: Lϕ,,: Lϕ, :, Lϕ :, are the nteracton parameters between two speces n one sublattce, whch s assumed to be ndependent of the occupaton of other sublattce. Snce heat capacty values n a wde temperature range are avalable for 3 and α 5 3, 0 G ϕ :, for the stochometrc 3 and 5 3, an equaton smlar to Eq. (9) can be used. The parameter 0 G ϕ : relates to the fllng of both sublattces wth antstructure defects and can be estmated by the equaton 0 G ϕ = 0 : G ϕ + 0 : G ϕ 0 : G ϕ :. 4. Results and dscussons The thermodynamc optmzaton of the system was performed usng the PanOptmzer program [26]. The optmzaton process can be dvded nto four steps. In the frst step, the α 5 3 and β 5 3 phases were treated as the same phase and all the ntermedate phases were treated as stochometrc compounds. The optmzaton started wth the lqud phase usng the enthalpy of mxng at 1773 K [16] and the

5 30 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) Table 2 Summary of thermodynamc parameters for the system. a Lqud: (, 3 1, ) 1 G 0,Lq 3 1 = T + 3G 0,Lq 0 L Lq, = T 0 L Lq 3 1, = T 1 L Lq 3 1, = T BCC:(, ) 1 0 L BCC, = T 1 L BCC, = T 0 Tc BCC, = : (, ) 0.75 (, ) G 3 : 0.75HSER 0.25H SER 0 G 3 : 0 G BCC 0 G 3 0 : G Damond 0 G 3 : = 0 G 3 : + 0 G 3 0 : G 3 : 0 L 3 a = T :, 0 L 3,: a = T + G 0,Lq = T T ln T T T K K K α 5 3 : (, ) (, ) K 0 G α 5 3 : H SER H SER = T T ln T T T 1 0 G α 5 3 : 0 G α 5 3 : 0 G BCC 0 G Damond 0 G α 5 3 : = 0 G α 5 3 : + 0 G α 5 3 : 0 G α 5 3 : 0 L α 5 3,: a = T β 5 3 : (, ) (, ) K 0 G β 5 3 : 0.625H SER 0.375H SER = T T ln T T T 1 0 G β 5 3 : 0 G β 5 3 : 0 G BCC 0 G Damond 0 G β 5 3 : = 0 G β 5 3 : + 0 G β 5 3 : 0 G β 5 3 : 0 L β 5 3,: a = T 11 8 : () () G GBCC GDamond : () 0.5 () G 0.5 H SER 0.5 H SER : () () G H SER H SER a Temperature (T ) n Kelvn and Gbbs free energy n J/mol-atom. b The underlned parameters are fxed durng the optmzaton. = T T ln(t) = T T ln T T T 1 = T T ln T T T K K K enthalpy of formaton n the lqud phase regon at 1305 K, 1273 K and 1226 K [7]. For 3, 5 3, and phases, the coeffcents c, d and e n Eq. (10) were estmated from the expermentally determned C p values [8,13,17]. The coeffcents a and b n Eq. (10) were evaluated from the actvty data [8], enthalpy of formaton [8,9,18] and phase dagram data [10 15]. The Gbbs free energes of formaton for 3 and 5 3 at 1530 K reported n Ref. [8] were not ncluded n the optmzaton snce they were deduced from the actvty data [27]. For 11 8 phase, C p data are not avalable. The standard enthalpes of formaton at 298 K [18], enthalpes of formaton for 11 8 at 1305 K and 1273 K [7], and the phase dagrams data [10 15] were used to evaluate the parameters a 11 8, b 11 8 and c 11 8 n Eq. (11). The obtaned coeffcents for the fve ntermedate compounds were subjected to further optmzaton. For the BCC sold soluton, the magnetc contrbuton to the Gbbs free energy was taken nto account. Due to the low solublty of n BCC at low temperatures and nsuffcent expermental data, only T c n Eq. (8) was estmated from the expermental Néel temperature determned by Booth et al. [28] usng a neutron dffracton method. All the parameters obtaned n ths step were further refned n the subsequent optmzaton. In the second step, the homogenety ranges of 3, 5 3 phases were consdered by usng a two-sublattce model. In ths step, all the parameters obtaned n the frst step were fxed. A value of 5000 J/mol atom was assgned to the parameter 0 G ϕ : and 0 G ϕ : and kept fxed durng the whole optmzaton process. The parameter 0 G ϕ : was estmated by the equaton 0 G ϕ : = 0 G ϕ + 0 : G ϕ 0 : G ϕ :. Interacton parameters assocated wth 3, 5 3 phases were evaluated on the bass of expermentally determned homogenety ranges [10,14,15]. In the thrd step, the allotropc transformaton between α 5 3 and β 5 3 s consdered. The parameters of 5 3 obtaned n the second step were consdered to be those of β 5. The expresson 0 G β 5 3 : 0 G α 5 3 : = A 0 + B 0 T was employed n the optmzaton of α 5 3 usng the measured latent heat of transformaton and allotropc transformaton temperature [10].

6 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) Table 3 Summary of the nvarant reactons n the system. Reacton type Temperature ( C) Composton (at.% ) Reference Pertectc L + () ± [10] 1410 [12] Ths work Pertectc L + 3 β ± [10] [11] [12] 1245 [13] Ths work Pertectc L + β ± [10] 1160 ± [11] [12] Ths work Pertectc L ± [10] 1025 ± [11] [12] 995 [13] 998 [14] Ths work Pertectc L ± [10] 955 ± [11] [12] 925 [13] 935 [14] Ths work Eutectc L () 895 ± [10] [11] [12] Ths work Allotropc transformaton α 5 3 β [10] 1002 Ths work a b Fg. 3. Calculated enthalpy of formaton for the alloys at (a) 1305 K, (b) 1273 K. The reference states both components are lqud. The sold lne s the calculated enthalpy of formaton for the equlbrum alloys n ths work, whle the dotted lne s the calculaton for the lqud phase only. The sold square s the expermental measured data from Ref. [7], whle the sold trangle s the deduced enthalpy of formaton for 11 8 compound from Ref. [7]. The ftted H f (T) x curves n Ref. [7] are redrawn n the fgure for comparson, dashed lne referrng to lqud sngle phase regon; dash dotted lne referrng to lqud two phase regon.

7 32 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) Table 4 Comparson of the calculated thermodynamc propertes for the system aganst expermental values. Propertes Phases Values Methods References f H (kj/mol atom) ± 2.5 Knudsen effuson mass spectrometry [8] Potentometrc method [18] Thermodynamc optmzaton Ths work α ± 2.5 Knudsen effuson mass spectrometry [8] 15.7 ± 1.0 Drect calormetry [9] Thermodynamc optmzaton Ths work Potentometrc method [18] Thermodynamc optmzaton Ths work Potentometrc method [18] Thermodynamc optmzaton Ths work Potentometrc method [18] Thermodynamc optmzaton Ths work S (J/mol atom) Estmated from C p data [6] Thermodynamc optmzaton Ths work α Estmated from C p data [6] Thermodynamc optmzaton Ths work Thermodynamc optmzaton Ths work 30.6 Estmated from C p data [6] Thermodynamc optmzaton Ths work Estmated from C p data [6] Thermodynamc optmzaton Ths work f G (kj/mol atom) Knudsen effuson mass spectrometry [8] Thermodynamc optmzaton Ths work Knudsen effuson mass spectrometry [8] Thermodynamc optmzaton Ths work Knudsen effuson mass spectrometry [8] Thermodynamc optmzaton Ths work Latent heat of transformaton α 5 3 β 5 3 (J/mol atom) 1256 Estmated from DTA results [10] 1256 Thermodynamc optmzaton Ths work In the fnal step, the thermodynamc parameters for all phases were optmzed usng all the avalable expermental data. The results of optmzaton are summarzed n Table 2. Fg. 1 presents the calculated phase dagram along wth the expermental data [10 15,28]. In general, the agreement between calculated and expermental phase boundares s good. The temperatures and compostons for all nvarant reactons are summarzed n Table 3. The fve pertectc reactons L + BCC 3, L + 3 β 5 3, L + β , L , L and one eutectc reacton L () as well as the allotropc transformaton α 5 3 β 5 3 are well reproduced. The calculated Néel temperature for the BCC phase s supermposed wth the dotted lne n Fg. 1(b). The calculatons agree well wth the expermental values determned by Booth et al. [28]. Fg. 2 shows the calculated enthalpy of mxng n the lqud at two dfferent temperatures together wth the expermental data [7,16]. The sold lne represents the calculaton result at 1226 K whle the dotted lne at 1773 K. The reference states are lqud and lqud. The expermental values are reproduced well by the calculaton wthn the estmated expermental errors. Fg. 2 ndcates that the enthalpy of mxng n the lqud s nonsymmetrcal wth respect to composton and the locaton of the mnmum pont shfts slghtly to the -rch sde wth a decrease n temperature. Wth the ncrease of temperature, the enthalpy of mxng decreases n magntude because the propertes of alloys wth strong nteratomc nteracton approach those of the deal soluton at hgh temperature. Fg. 4. Calculated RT ln a x curve at 1530 K. The reference states are BCC and lqud. The expermental data from Ref. [8] are supermposed for comparson. Fg. 3(a) and (b) present the calculated enthalpy of formaton, referred to lqud for both components, for the alloys at 1305 K and 1273 K, respectvely. The sold lne s the calculated enthalpy of formaton for the equlbrum alloys, whle the dotted

8 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) a b c Fg. 5. Calculated Gbbs free energes of formaton for the alloys at three dfferent temperatures, (a) 1773 K, (b) 1305 K and (c) 1173 K. The reference states are BCC and damond. lne s the calculaton for lqud phase only. In the sngle-phase lqud regon, the predcted enthalpy of formaton agrees well wth the expermental values [7]. In lqud two phase regon, the consstency s acceptable. The calculated enthalpes of formaton for 11 8 are about 13 kj/mol atom and 11 kj/mol atom more exothermc than those reported by Yassn and Castanet [7] at 1305 K and 1273 K, respectvely. It s worth notng that Yassn and Castanet [7] mathematcally dvded the measured enthalpy of formaton data nto two parts. At 1305 K, the data correspondng to the sngle-phase lqud regon were ftted to equaton H f (1305 K, kj/mol atom) = x x ( x ) and redrawn n Fg. 3(a) as dashed lne, whle the data correspondng to lqud two-phase regon were ftted to H f (1305 K, kj/mol-atom) = x and redrawn n Fg. 3(a) as dash dotted lne. These two curves ntersect at x 0.72, whch dffers greatly from the reported lqud/lqud phase boundares (x 0.63) [6, 10]. At 1273 K, the measured enthalpy of formaton data were ftted to equaton H f (1273 K, kj/mol-atom) = x x ( x ) n the sngle-phase lqud regon (redrawn n Fg. 3(b) as dashed lne) and H f (1273 K, kj/mol-atom) = x n the lqud two-phase regon (redrawn n Fg. 3(b) as dash dotted lne). These two curves ntersect at around x 0.79, whch devates remarkably from the expermentally determned lqud/lqud phase boundares x 0.67 [6,10]. Ths may ntroduce errors to the deduced enthalpy of formaton for Fg. 4 compares the calculated actvty of and at 1530 K aganst expermental data [8]. The reference state s BCC and lqud. In the BCC + 3 two phase regon and 3 sngle phase regon, the calculated RT ln a and RT ln a agrees well wth the expermental values [8]. In the 3 + β 5 3 two phase regon, the consstency s acceptable. Further calculaton shows that the standard Gbbs free energes of formaton for 3 and 5 3 at 1530 K agree well wth the reported values n Ref. [8], as shown n Table 4.

9 34 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) a b c d Fg. 6. Calculated heat capactes of the ntermedate compounds n the system. (a) 3, (b) α 5 3, (c), (d) The measured values [8,13,17] are supermposed for comparson. Fg. 5 shows the calculated Gbbs free energes of formaton, referred to BCC and damond, for the alloys at three temperatures 1773 K, 1305 K and 1173 K. The calculated Gbbs free energes of formaton are negatve n the whole concentraton range. Wth a decrease n temperature, the ntermedate compounds become more stable and the lqud phase becomes less stable. As a result, the solublty of n the BCC sold soluton decreases wth the decrease of temperature, and the concentraton range for the lqud sngle phase regon becomes narrow. The ntermedate compounds β 5 3 and 11 8, whch are not stable at 1773 K, become equlbrum phases at 1305 K. At 1275 K, β 5 3 undergoes allotropc transformaton to α 5 3. Wth a further decrease n temperature (e.g K),, and () become stable phases. The calculated heat capactes of 3, α 5 3,, at dfferent temperatures are shown n Fg. 6(a) (d) n whch the expermental data are supermposed for a comparson. The C p values calculated wth the present thermodynamc parameters are consstent wth the results of [8,13,17]. The relatvely large dfference between the calculated and the expermental C p values at very low temperature arses due to the deducton of T 2 contrbuton from the Gbbs free energy formula (The et 1 term n Eq. (9)). Table 4 presents a comparson between the calculated thermodynamc propertes for ntermedate compounds and the expermental data [6,8 10,18]. The calculated standard enthalpes of formaton at 298 K ( f H ) for 3, α 5 3,, are wthn ±4 kj/mol atom of the expermental values [8,9,18]. For the 11 8 phase, the dfference s about 5.3 kj/mol atom. The calculated standard entropes at 298 K (S 298 ) for the fve ntermedate compounds are n good agreement wth the deduced values by Gokhale and Abbaschan [6]. The predcted standard Gbbs free energes of formaton at 1530 K ( f G ) for two dfferent compostons of 3 phase,.e and , and one composton of β 5 3 phase,.e agree well wth the reported expermental values [8]. The predcted latent heat of

10 Y.Q. Lu, Y. Du / CALPHAD: Computer Couplng of Phase Dagrams and Thermochemstry 34 (2010) transformaton for α 5 3 reported n Ref. [10]. 5. Conclusons β 5 3 agrees well wth that The expermental phase dagram and thermodynamc data avalable for the system were crtcally evaluated. The assocate soluton model was used to descrbe the lqud phase, whle the substtutonal soluton model was used to descrbe the BCC sold soluton. The two-sublattce model was used to descrbe the non-stochometrc compounds 3, α 5 3 and β 5 3. The 11 8, and phases were modeled as stochometrc compounds. A consstent set of thermodynamc parameters was obtaned on the bass of the crtcally evaluated lterature data. The calculated phase dagram and thermodynamc propertes agreed well wth most of the avalable expermental data. Acknowledgements Ths research work s supported by eatve Research Group of Natonal Natural Scence Foundaton of Chna (Grant No ) and the open project of State Key Laboratory of Powder Metallurgy of Central South Unversty. The authors would lke to thank CompuTherm LLC for provdng the Pandat software. Appendx. Supplementary data Supplementary data assocated wth ths artcle can be found, n the onlne verson, at do: /j.calphad References [1] H. Yng, Z. Wang, D.B. Aldrch, D.E. Sayers, R.J. Nemanch, Roman scatterng study of nterface reactons of Co/S, n: R.W. Fathauer, S. Mantl, L.J. Schowalter, K.N. Tu (Eds.), Slcdes, rmandes and ther Interfaces, n: Materals Research Socety Proceedngs, vol. 320, MRS, Pttsburgh, 1994, pp [2] N. Lundberg, M. Ostlng, F.M. d Heurle, Appl. Surf. Sc. 53 (1991) [3] M.A. Borek, S. Oktyabrsky, M.O. Aboelfotoh, J. Narayan, Appl. Phys. Lett. 69 (1996) [4] P.D. Agnelo, V.P. Kesan, M. Tewan, J.A. Ott, J. Electron. Mater. 23 (4) (1994) [5] S.P. Ashburn, M.C. Ozturk, J.J. Wortman, G. Harrs, J. Honeycutt, D.M. Maher, J. Electron. Mater. 21 (1) (1992) [6] A.B. Gokhale, G.J. Abbaschan, Bull. Alloy Phase Dagr. 7 (5) (1986) [7] A. Yassn, R. Castanet, Intermetallcs 7 (1999) [8] S.N. Zarembo, C.E. Myers, R.J. Kematck, P.Y. Zavalj, M.S. Whttngham, E.J. Cotts, J. Alloys Compd. 329 (2001) [9] O.J. Kleppa, W.G. Jung, Hgh Temp. Sc. 29 (1990) [10] D. Godat, P. Feschotte, J. Less-Common Met. 72 (1) (1980) [11] V.L. Zagryazhsk, A.K. Shtol ts, P.V. l d, N.V. Kuz menko, Powder Metall. Met. Ceram. 5 (8) (1966) [12] V.N. Svechnkov, B.F. Kobzenko, Dopov. Akad. Nauk Ukr. RSR 29 (3) (1967) [13] G.I. Kalshevch, V.L. Zagryazhsk, L.V. Shchpanova, N.N. Serebrennkov, P.V. l d, Russ. J. Phys. Chem. 43 (1) (1969) [14] I. Kawasum, S. Konsh, M. Kubota, M. Sakata, Japan J. Appl. Phys. 17 (1978) [15] B. Rawal, K.P. Gupta, J. Less-Common Met. 27 (1972) [16] A.N. Shlapak, E.A. Beloborodova, I.V. Nkolaenko, G.I. Bataln, Ukr. Khm. Zh. 45 (7) (1979) [17] V.I. Surkov, G.I. Kalshevch, P.V. l d, Russ. J. Phys. Chem. 49 (2) (1975) [18] G.M. Lukashenko, L.V. Goncharuk, Tezsy Dokl.-Vses Konf. Khm, Svas Poluprovodn. Polumetall, Akad Nauk Beloruss SSR Ed (1974) 95. [19] A.T. Dnsdale, CALPHAD 15 (1991) [20] U. rlng, M.J. Pool, B. Predel, Z. Metallkd. 74 (1983) [21] O. Redlch, A. Kster, Ind. Eng. Chem. 40 (1948) [22] G. Inden, Proc. Project Meetng, Calphad V, Max Planck Insttute for Metal Research, Dusseldorf, 1976, pp [23] M. Hllert, M. Jarl, CALPHAD 2 (1978) [24] M. Kolenda, J. Stoch, A. Szytula, J. Magn. Magn. Mater. 20 (1980) [25] I. Ansara, N. Dupn, H.L. Lukas, B. Sundman, n: P. Nash, B. Sundman (Eds.), Proc of TMS Conf on Applcatons of Thermodynamcs n the Synthess and Processng of Materals, Warrendale, PA, USA, 1995, pp [26] S.L. Chen, S. Danel, F. Zhang, Y.A. Chang, X.Y. Yan, F.Y. Xe, R. Schmd-Fetzer, W.A. Oates, CALPHAD 26 (2002) [27] R. Schmd-Fetzer, D. Andersson, P.Y. Chevaler, L. Eleno, O. Fabrchnaya, U.R. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, M. Znkevch, CALPHAD 31 (2007) [28] J.G. Booth, M.M.R. Costa, K.R.A. Zebeck, J. Magn. Magn. Mater (1) (1983)