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Thermodynamic assessment of the Ag-Zn system
PII: SO364-5916(98)00024-6
THERMODYNAMIC
calphnd. Vol. 22, No. 2, pp. 203-220, 1998 Science Ltd, All rights reserved. 0384-59161981 $-see front matter
@ 1998Elsevier
Pergamon
ASSESSMENT OF THE Ag-Zn SYSTEM
T. Gomez-Acebo CEIT and Escuela Superior de Ingenieros Industriales (Universidad de Navarra) E-20009 San Sebastian, SPAIN e-mail: [email protected]
ABSTRACT
A thermodynamic assessment of the Ag-Zn system has been done using a computerized CALPHAD (calculation of phase diagrams) technique. The liquid, a, p, rl and E phases are described by a regular solution model, the y phase by a four-sublattice model, and the 5 phase by a two-sublattice model, both based on considerations of their crystal structure and compatibility with the same phase in other systems. A set of parameters describing the Gibbs energy of the different phases is given and calculated phase diagrams are presented.
Introduction The phase equilibria in the Ag-Zn system have been investigated experimentally several times, the oldler measurements are summarised by Hansen [58Han]. The accepted phase diagram was published originally by Andrews et al. [41And] and is established to a high degree of accuracy. Several solid phases are present in this system, between the silver-rich side (a phase) and the zinc side (IJ phase), there are p (ideal composition AgZn, stable at high temperature), 5 (AgZn at low temperature), y (AgsZns) and E (AgZn,). There is also a metastable phase called p’ formed instead of c when quenching from the P-phase domain; this phase has not been taken into account in the present work. No complete thermodynamic assessment has ever been done of this system; Ronka et al. [97Ron] say they have assessed -but still not published- the Ag-Zn system, but based only on data collected by Hultgren et al. [73Hul], and not on real experimental data. In the present work a review of the experimental data available in the literature is made, some models for the intermediate phases are proposed, and a set of thermodynamic parameters describing the entire system is given. The assessment has been carried out using a computer program called PARROT, included in the Thermo-Calc databank system [85&m], for optimisation of parameters in thermodynamic models. All thermodynamic equilibria were calculated using the POLY-3 program, Sal
version received on 10 November 1997,Revised version on 24 April 1998
203
204
T. G6MEZ-ACEBO
included in the same system. The descriptions of the pure solid an liquid elements were taken fi-om [91Din].
Experimental Information Phase Diagram The complete phase diagram of the Ag-Zn system was published originally by Andrews et al. [41And] and since then it has not been modified. Hansen [58Han] reviewed the experimental information available, and concluded that the accepted phase diagram was to be regarded as established to a high degree of accuracy. It is presented in Fig. 1. In addition to the two terminal solid phases, denoted a (Ag-fee) and r\ (Zn-hcp), there are four intermetallic phases, denoted p, L Y and E. The phase diagram from [41And] was obtained using a combination of thermal, microscopic and X-ray methods. It includes temperature and composition of peritectic points, and liquidus and sohdus lines in the whole range of composition. The phase boundaries of solid phases were estimated from measurements of single-phase and two-phase regions. Andrews et al. [41And] give the solubility limits of all phases down to 200 “C. Wiedebach-Nostiz [46Wie] has determined the solid solubility of Ag in q-Zn. There are no direct measurements of tie-lines in any of the binary phase boundaries. The transformation temperature from the p to the < phase has been determined by Noguchi [62Nog], through measurements of the Hall coefficient and the thermoelectric power. The temperatures and compositions of coexisting phases at invariant equilibria as presented by Massalski [90Mas] are shown in Table 1. In the present optimisation, phase boundary limits by [41And] except for the TJ phase, solubility limits of the rl phase by [46Wie], and p/c transformation temperatures by [62Nog] were used. The phase boundaries between solid phases from [41And] were used with care, because they were not obtained as real tie-lines, but as one- and two-phase points. Iwasaki et al. [85Iwa] have measured the pressure-induced transformation between c, p, p’, giving an approximate pressure-temperature phase diagram of the equiatomic ahoy. These data were not used, because no pressure-dependence parameter has been introduced in the present model. Liquid Phase Several researchers have measured the chemical potential (Figs. 2 to 5) or the activity of zinc (Figs. 6 to 8) in Iiquid Ag-Zn alloys [42Sch, 59Kle, 7OYaz, 79Ger, 87Kam]. Schneider and S&mid [42Sch] obtained values of the activity of zinc as its vapour pressure measured by the dew point method. The other researchers give values of the chemical potential of zinc, obtained through measurements of the e.m.f. in a galvanic cell. Kleppa and Thahnayer [59Kle] made their measurements at a constant temperature of 950 K (Fig. 4), and they also measured the dependence of the e.m.f. with temperature, from which partial entropy values of Zn can be deduced (Fig. 5).
THERMODYNAMIC ASSESSMENT OF Ag-Zn
205
TABLE 1 Experimental [9OMas] and Calculated Invariant Equilibria.
- Equilibrium
Temperature, K Experimental Calculated
lX+L+p
983
983
p+L+y
934
933
y+L+&
904
907
&+L+q
704
706
P +a+<
531
53,8
P+r4
547
552
-
-
-
-
-
Phase a P L P Y L Y & L E V L a P 5 P r Y
Composition, at. % Zn Experimental Calculated 32.1 32.5 36.7 37.1 37.5 37.4 58.6 58.2 61.0 60.9 61.8 62.3 64.7 64.6 69.4 69.4 71.0 70.6 89.0 90.3 95.0 96.2 98.0 98.1 40.2 40.3 44.9 45.6 46.0 49.3 50.4 50.1 58.5 58.8
The data from [42Sch] are a bit scattered, as can be seen in Figs. 6 and 8, and were not used in the present optimisation. All the other data agree fairly well, and were used for the calculations. Solid Phases The activity of zinc in the solid phases (Figs. 6 to 9) has been measured mainly by three different methods: dew point [49Bir, SlUnd, 68Str], light absorption method [53Sca] and the isopiestic method [7OMas]. There is a reasonable agreement between all these measurements, except that of Scatchard and Westlund [53Sca], as can be seen in Figs. 7 and 8; these authors give activity values of the alliquid equilibrium that are well above the others. Birchenall and Cheng [49Bir] give activity data for several compositions in the a, p, ‘y, E and liquid phases. Other researchers have measured the activity of Zn in the a [53Sca, 70Mas], p [SlUnd], and E phase [68Str]. The anthalpy of formation of the solid phases (Fig. 10) has been measured using liquid Zn calorimetry [59Wit], and liquid Sn calorimetry [70Bla]. The data from Wittig and Huber [59Wit] are barely endothermic and therefore inconsistent with the others, maybe because of the effect of zinc evaporation, and were not used. Hultgren et al. [73Hul] report some measurements of the enthallpy of formation of a phase; however, they refer to an unpublished work, so it was not possible to check the experimental accuracy of the obtained values, and were not considered in the optimisation.
206
T. GbMEZ-ACEBO
The transformation between p, 6 and j3’ has been studied under several experimental techniques.
Orr and Rove1 [62Orr] give enthalpies of formation of the three phases, measured by liquid-tin calorimetry. Noguchi [62Nog] gives the temperature and enthalpy of transformation between these three phases, the latter obtained through measurements of the specific heat. Only one reference has been found that gives temperature-dependent specific heat values, of the y phase [85Dow], measured for a single composition with a scamring calorimeter (Pig. 11). Wallbrecht et al. [76Wal] give the enthalpy change of a low-temperature transformation of the y phase, by heat capacity measurements. However, this transformation has not been considered, and these data were not taken into account. In this optimisation activity data from [49Bir], [SlUnd], [68Str] and [70Mas], enthalpies from [62Nog], [62Orr] and [70Bla], and heat capacities from [85Dow] were used.
Thermodynamic Models Two different models have been adopted in the present system, the substitutional regular solution model and the sublattice model [7OHil]. The crystal structure of the solid phases is given in Table 2; the metastable p’ phase is not included. TABLE 2
Crystal Structure Data [9 1Vil] Composition, at. % Zn Phase 0 to 40.2 a (Ag) 37 to -51.2 5 (AgZn) 36.7 to 58.6 P (AgZn) 58.5 to 64.7 Y (AgsZng) -66.2 to 89 a (AgZnr) 95 to 100 r\ CW
Pearson symbol cF4 hP9 cI2 ~152 hP2 hP2
Space group FmSm PT ImJm IT3m P63lmmc P63lmmc
Struktur-bericht designation Al A2 082
A3 A3
Prototype cu AgZn W CusZns Mg Mg
The 4 jj E, rj and Liquid Phases The two solid terminal phases (a-Ag and q-Zn), the p, E and the liquid phase were treated using a regular solution model; the molar Gibbs energy per formula unit is: G,$ = xnp”G$, + xZnOG$, + RT(x,s lnx,,+ + x,lnx,,)+EGi
(I)
where $ means the phase considered. The parameters “GA, where M is Ag or Zn, represent the Gibbs energy of pure component M in the same state as the phase considered: fee for the a phase, bee for the p phase, and hcp for IJ and E phases; all were taken corn [91Din], and are reproduced in the Appendix. They are given relative to the enthalpy of selected reference states for the elements at 298.15 K. This state is denoted SER (standard element reference), HiR .
THERMODYNAMIC ASSESSMENT OF Ag-Zn
207
The crystal structure of the hexagonal q and E phases, having both the hcp Mg-type structure, differ in the value of the axial ratio, as was noted by Massalski and King [62Mas]. The ideal value for the close packing of hard spheres is c/u = 1.6330. In the E phase the axial ratio decreases from about 1.58 to 1.55 with increasing concentration of zinc in the region of 67-88 at. %. Conversely, in the r\ phase (which is a solid solution based on zinc) the initial axial ratio is considerably above the ideal value and increases from about 1.78 near the &+q/q boundary to the value of pure Zn (c/u = 1.856) [62Mas]. Taking this into account, Kowalski and Spencer [93Kow] assessed the Cu-Zn system considering that the well-established value of the lattice stability for pure Zn in the fee structure should be used in the thermodynamic description of E. However, in the present work it has been preferred not to change the description of the pure elements. Accordingly, the Gibbs energy of pure zinc in the hexagonal E phase, “G&, has been expressed as
oG;, -- HifiR = GHF
+ A" G&
(2)
where A” G& is a function of temperature, and is the lattice stability of the E phase. The excess Gibbs energy, EGt, depends on the interaction between the two species, Ag and Zn. This interaction is described by a Redlich-Kister polynomial:
For the a, p and liquid phases only the first two parameters were considered; the parameter OL@ &.& was treated as linearly dependent on temperature and 1Lf&Zn as constant. For the 11 phase, the lack of experimental data allowed the calculation of a temperature-independent regular term (“IL)only. For the E phase, it was necessary to evaluate the three parameters of the eq. (3), because of the shape of the solidus and liquidus lines; the regular term (‘L) was treated as temperature-dependent, and the two subregular terms (‘L and 2L) as temperature-independent. The yPha.se The y phase has the same crystalline structure as the Cu-Zn gamma brass. Furthermore, there is a strong similarity between the phase diagrams of the Ag-Zn and the Cu-Zn systems. This considlerations have led to use a thermodynamic model for the y phase that is compatible in both systems. As was noted by Kisi [88Kis], in the ternary system Al-Cu-Zn the gamma brass phase is present both in the Cu-Zn side (prototype structure CuJns, space group 133m) and in the Al-Cu side (prototype structure AL&US, space group P43m). Despite their different crystalline structure, the two phases are the terminal ends of a single phase region in the Al-Cu-Zn alloy system which transects the ternary phase diagram. Kisi [88Kis] has determined the crystalline structure of an ahoy A10.2&~.~8Zr4,0~~ with y-phase structure. Considering this description, Fries et al. [98Fri] have proposed the four-sublattices model for this phase (Al,Cu,Zn)s(Cu)s(Cu,Zn)r@l,Cu,Zn)~~; if we use this model for the Ag-Zn system, with no Al and supposing that Ag occupies Cu
208
T. GblEZ-ACE60
positions, the model is reduced to (Ag,Zn)s(Ag)s(Ag,Zr&(Ag,Zn)~4, (AgJnh(AgMAg,Zn~(Ag,Zn)6.
and after dividing by 4,
This model has eight end-members, being the most stable configuration AgsZns (Zn:Ag:Ag:Zn). The Gibbs energy of each end-member has been calculated referred to the Gibbs energy of pure Ag and Zn in bee state. The correction terms have been calculated associating energies to bonds instead of estimating the Gibbs energy of each end-member as an independent parameter. A temperature-dependent parameter is added to the Gibbs energy of all end-members (& in the Appendix), and an additional positive temperature-independent parameter is added for each sublattice that deviates from the ideal end member Zn:Ag:Ag:Zn (Kr, K3 and K4 in the Appendix). This allows the calculation of 4 model parameters instead of 8. No excess terms have been estimated. The c Phase The 6 phase is the stable low-temperature phase near equiatomic compositions. For this phase a thermodynamic model based upon the crystal structure is used. The crystal structure of the c phase has been determined by Edmunds and Qurashi [5 led]. The space group is CT. The unit cell contains nine atoms; three of the positions are occupied almost exclusively by zinc atoms; the remaining six positions are occupied at random by the remaining atoms (about 75 % silver and 25 % zinc). According to this, the sublattice model proposed may be (Zn)j(Ag,Zn)b, but it can be simplified to (Zn),(Ag,Znh. The Gibbs energy per mole of formula unit is
(6) The Gibbs energy of the Zn:Ag (ZnAgz) end-member is calculated as the sum of that of the pure elements in bee phase, with a temperature-independent correction parameter. The parameter ‘G&,,
has been calculated as three times the Gibbs energy of pure Zn in bee state.
The excess Gibbs energy is given as
and this regular parameter is also temperature-independent.
Method of Optimisation The optimisation was made using a computer program called PARROT included in the ThermoCalc databank system [85Sun], which allows the simultaneous consideration of various types of thermodynamic data. The program works by minimising an error sum where each piece of information used is given a certain weight according to its estimated accuracy. The selection of model parameters and the weights are then changed by trial and error until most of the information is satisfactorily described. As input, selected experimental data together with descriptions of pure solid and liquids by [9 lDin] were used.
THERMODYNAMIC ASSESSMENT OF Ag-Zn
209
For the liquid, a and p phase three parameters have been used in the Redlich-Kister expression, but only one for the q phase, because of the lack of experimental data. For <, E and y phases, some parameters were also optimised for the description of the Gibbs energy of the endmembers.
Results and Discussion All parameters assessed in this work are collected with the data for the pure elements in the Append:.x (expressed in the form of a Thermo-Calc file). Figures 1 to 12 and the comparison of temperatures and compositions of invariant equilibria presented in Table 1 summarize and illustrate the results obtained from the present assessment. There is a very good agreement between calculated and experimental values across the entire system. Phase Diagram The calculated phase diagram is shown in Fig. 1 using the optimised set of parameters describing the binary system presented in the Appendix, compared with the experimental phase diagram [90Mas:j. It can be seen that both the invariant points and the solidus and liquidus lines are well reproduced. However, the calculated solubility of Zn in a is slightly lower than the experimental values: the calculated phase boundaries a/a+p and a+P@ are almost straight lines. This could be avoided by increasing the number of optimising parameters in the Redlich-Kister polynomials, that is, allowing a temperature-dependence on the subregular parameter of both phases (‘L); but it was preferred to optimise only three parameters of these two phases, maintaining the subregular parameter as temperature-independent. In Fig. I.2 the right side of the calculated phase diagram is compared with experimental data used for phase boundaries. The calculated phase boundaries of the FE two-phase field have small deviations from experimental lines. At high temperatures, near the peritectic point, the ?r_& line should be displaced to lower zinc contents, but this effect could not be achieved without increasing the number of optimising parameters of the y-phase, and that was considered reasonable. The only available data for the q phase were some points of the phase boundaries E/E+T\ and &y/q obtained by Andrews et al. [41And], and the solubility limits of Ag in q-Zn [46Wie], i.e. the &+r\/q line. In the present work it has not been possible to reproduce both phase boundaries, even though several combinations of parameters were tried. In the final optimisation, only the E.+TJ/~ data from [46Wie] were used; as can be seen in Fig. 12, they are reasonably well reproduced. Liquid Phase The liquid phase has been modeled with only three parameters, the regular parameter CL) with a temperature dependence, and the subregular parameter (‘L), as temperature-independent. Figs. 2 and 3 snow the calculated chemical potential of several Ag-Zn liquid alloys, compared with data by Yazawa and Gubcova [7OYaz] and Gerling et al. [79Ger], both obtained by e.m.f. techniques. For both figures, the reference state is the liquid phase. It can be seen that the experimental
210
T. G&vlEi!-ACEBO
values are quite well fitted. Some of the data by Yazawa and Gubcova [7OYaz] were also obtained for different solid phases, in particular those with low Zn content. Figs. 4 and 5 show the comparison between the data given by Kleppa and Thalmayer [59Kle] and the calculated values, for the chemical potential and the partial entropy of zinc in liquid alloys at 950 K. Although all the experimental values are referred as obtained for the liquid phase, it can be clearly seen in the phase diagram (Fig. 1) that at the indicated temperature, some points fall into the p and a phases. It has been supposed that the points at Q,, < 0.55 were calculated as an extrapolation from higher temperatures were the liquid phase is the stable one. For the optimisation, that experimental points were calculated as metastable extrapolations of the liquid phase. The dotted lines of Figs. 4 and 5 indicate the extrapolated properties of the liquid phase. It can be seen that the fitting to the experimental values is excellent. Solid Phases Fig. 9 show data given by [49Bir], [SlUnd] and [7OYaz] of the activity of Zn in the p phase at four different compositions as a function of temperature, compared with the calculated activity at the same compositions. The reference state is the liquid phase. The calculated phase boundaries are printed with dotted lines. Data from [7OYaz] were obtained mainly for the liquid phase, but some points belong to solid phases (see Fig. 2); the authors give values of the chemical potential of zinc, but they have been converted to activity for comparison. For the two series of values with lower zinc content (.Q,, = 0.40, 0.434 and 0.50), it can be seen in Fig. 9 that the agree is reasonable. However, for higher Zn content (xz,, = 0.54) the two series of data plotted are not compatible; activity values from [SlUnd] are overestimated. It has not been possible to find a set of parameters for the description of the p phase that adjust at the same time the three series of data given by [ 5 1Und]. These authors report a slight decrease in vapour pressure of Zn when preheating the powders for two days; they suggest that the high values of vapour pressure - and consequently of activity - might be related to surface effects. Taking this into account, together with the reported experimental error of 10 %, the difference in activity for xzn = 0.54 can be explained. These data were given a low weight in the optimisation. Figs. 6, 7 and 8 show the calculated zinc activity at three different temperatures (950 K, 1023 K and 1073 K), compared with some experimental measurements. Data given by [53Sca] and [42Sch] were not used in the optimisation, but they are plotted for comparison. In Fig. 6, the three data given by [59Kle] with lower zinc content were supposed as extrapolated points of the liquid phase from higher temperatures, as was said above. The data given by Hultgren et al. [73Hul] plotted in Fig. 7 are compiled data, not experimental, but are also plotted for comparison. It can be observed at the three temperatures that the agreement between experimental data and calculated values is very good. The calculation of the lattice stability of the E phase, A”G&,
has been done estimating a
hypothetical melting point of pure Zn in the E phase, by graphical extrapolation in the phase diagram of the liquidus and solidus lines up to pure zinc. This has led to an approximate value of 650 K. Considering that the latent heat does not change with temperature, and equating the Gibbs energy of pure Zn in liquid and E phases, ‘G& =‘Ggq at 650 K, the lattice stability was
THERMODYNAMIC ASSESSMENT OF Ag-Zn
211
calculated as A” G&= 0.691 T. The broken lines printed in Fig. 12 indicate the extrapolated solidu,s and liquidus lines of a metastable E phase up to pure Zn. This description of the E phase is proposed to be used in other systems where it is present. Fig. 1lDshows the calculated enthalpy of formation for the solid phases at 623 K, together with some experimental dam. It can be seen that data by [59Wit] are barely endothermic, and are not compatible with the other experimental values; they were not used in the optimisation. Data collected by [73Hul] were plotted for comparison, because they are not experimental data, and were not used in the optimisation. The agreement is quite good. The enthalpy difference between 4 and p phases at three different compositions is presented in Table 3, together with data obtained by Noguchi [62Nog]. The agreement is excellent. These were he only experimental data for c phase, together with solubility limits. TABLE 3
Enthalpy Difference Between c and p Phases, AHyp (J/mol) XZll
0.463 0.486 0.507
Experimental [62Nog] 1330 1216 1119
Calculated 1324 1201 1099
For the y phase few experimental data were available, although the model proposed, having four sublattices, required the calculation of several parameters. It has not been possible to assess the available experimental data estimating 8 parameters, one for each end-member; so four parameters have been set: a temperature-dependent parameter is added to the Gibbs energy of all end-members (& in the Appendix), and an additional positive temperature-independent parameter is added for each sublattice that deviates from the ideal end member Zn:Ag:Ag:Zn (K1, & and K4 in the Appendix). The Ko parameter has a logarithmic dependence of temperature, because a linear dependence could not consider the variation with temperature of the specific heat. For the K1 parameter an arbitrary high positive value has been supposed. The experimental values of specific heat given by [85Dow] for y-phase Ag0,615Znr,385 are plotted in Fig. 11, together with the calculated values. The fitting is not very satisfactory, although the absolute error is relatively small. The increase of the specific heat at temperatures near 400 K [85Dow] can be related to the low-temperature transformation in y-phase reported by [76Wal], who ,noticed an order-disorder transformation in this phase at temperatures ranging between 303 and 407 K, with an enthalpy change of about 177 f 15 J/m01 of Ago.614Zno.3sa.However, the model cannot take into account this effect, so this transformation has not been considered in the prese:nt study. Conclusions A selt of parameters describing the phase equilibria and thermodynamic properties in the Ag-Zn system has been evaluated from experimental data. A comparison between calculated and measured quantities is made, showing a satisfactory agreement, except for some of the phase
212
T. GdMEZ-ACEBO
boundaries. A four-sublattices model for the y phase is used, that considers the properties of the same phase in other different systems.
Acknowledgements This work was done during a three-month stay of the author at the Royal Institute of Technology (Stockholm, Sweden). I wish to thank Dr Bo Sundman for accepting me as a guest researcher in his group, and for many suggestions and critical reading of the manuscript. Valuable discussions with Dr Philip Spencer (about the model for y-phase), Dr Lucia Dumitrescu, Dr Qing Chen and Mrs Alexandra Kusoffsky are gratefully acknowledged.
References 41And: 42Sch: 46Wie: 49Bir: 51Edm: 51Und: 53Sca: 58Han: 59Kle: 59Wit: 62Mas : 62Nog: 62Orr: 68Str: 70Bla: 7OHil: 7oMas: 7OYaz: 73Hul: 76Wal: 79Ger: 85Dow: 851wa: 85Sun: 87Kam: 88Kis: 90Mas: 91Din: 91Vil: 93Kow: 97Ron: 98Fri:
K.W. Andrews, H.E. Davies, W. Hume-Rothery and CR. Oswin, Proc. Roy. Sot. (London), A177, 149-167 (1941). A. Schneider and H. S&mid, Z. Elektrochem., 48 (11) 627-39 (1942). A.v. Wiedebach-Nostiz, Z. MetaZfkunde, 37, 56-60 (1946). C.E. Birchenall and C.H. Cheng, Metals Trans., 185,428-434 (1949). LG. Edmunds and M.M. Qurashi, Acta Cryst., 4,417-425 (1951). E.E. Underwood and B.L. Averbach, J. Metals, 3, 1198-1202 (1951). G. Scatchard and R.A. Westlund, J. Am. Chem. Sot., 75,4189-4193 (1953). M. Hansen, Constitution of binary alloys, 2”d.Ed., pp. 62-66. McGraw-Hill, New York (1958). O.J. Kleppa and C.E. Thalmayer, J. Phys. Chem., 63, 1953-1958 (1959). F.E. Wittig and F. Huber, Z. Elektrochemie, 63 (8) 994-1001 (1959). T.B. Massalski and H.W. King, ActaMet., 10, 1171-1181 (1962). S. Noguchi, J. Phys. Sot. Japan, 17, 1844-1856 (1962). R.L. Orr and J. Rovel, ActaMet., 10,935-939 (1962). J.L. Straalsund and B. Masson, Trans. AZME, 242, 190-195 (1968). G.R. Blair and D.B. Downie,MetalSci. .I, 4, l-5 (1970). M. Hillert and L.I. Staffanson, Acta Chem. Scand., 24,361s (1970). D.B. Mason and J.L. Sheu,Met. Trans., 1, 3005-3009 (1970). A. Yazawa and A. Gubcova, Trans. JIM, 11,419-423(1970). R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleisner, K. Kelley and D.D. Wagman, Selected values of the thermodynamic properties of binary alloys, pp. 115- 121. ASM, Metals Park, Ohio ( 1973). P. Wallbrecht, F. Balck, R. Blachnik and K.C. Mills, ScriptaMet., 10, 579-584 (1976). U. Gerling, M.J. Pool and B. Predel, Z. MetalMe., 70 (4) 224-229 (1979). D.B. Downie and J.F. Martin, J. Chem. Thermodynamics, 17,927-934 (1985). H. Iwasaki, T. Fujimura, M. Ichikawa, S. Endo and M. Wakatsuki, J. Phys. Chem. Sol@ 46 (4) 463468 (1985). B. Sundman, B. Jansson and J.-O. Andersson, CalphadJ, 9 (2) 153-190 (1985). K. Kameda, Trans. Jpn. Inst. Met., 28 (1) 41-47 (1987). E.H. Kisi, Mater. Sci. Forum 27128, 89-94 (1988). T. Massalski, BinaT AIIoys Phase Diagrams, pp. 117-l 18. ASM, Metals Park, Ohio (1990). A. Dinsdale, CalphadJ., 15 (4) 317-425 (1991). P. Vilars and L.D. Calve& Pearson’s Handbook of 0ystaIlogrqhic Data, pp. 645-646. ASM, Metals Park, Ohio (199 1). M. Kowalski and P.J. Spencer, J. Phase Diagrams, 14,432-436 (1993). K.J. Ronka, F.J.J. van Loo and K. Kivilabti, Z. Metallkunde, 88, 3-13 (1997) S.G. Fries, I. Hurtado, T. Jantzen, P.J. Spencer, K.C. Hari Kumar, P. Liang, H.L. L&as, H.J. Seifert and F. Aldinger, J. Alloys Comp., to be published (1998).
THERMODYNAMIC ASSESSMENT OF Ag-Zn
213
APPENDIX Thermodynamic Parameters of the System Ag-Zn (in J/m01 of formula unit). The parameters evaluated in the present work are indicated with *. AU remaining parameters are taken from [91Din]. Liquid (Ag,Z@l oG Liquid _
HSER Ag
Ag
=
11025.076 - 8.89102. T - 1.033905. 1O-2o . T7 + GHF for 298.15 < T< 1234.93 - 3587.111+ 180.964656. T- 33.472.TelnT for 1234.93 < T < 3000.00
0GLiqUid Zn
- H;ER
=
7157.213 - 10.29299. T - 3.58958. lo-l9 . T7 + GH;fiR for 298.15 < T< 692.66 -3620.391+
161.608594.T-31.38.T.lnT
for 692.66 < T < 1700.00 * ‘Ly;;;
=-27400
+ 5.88 T
* 1LLWd __5500 Ag,Zn -
a-phase (Ag, fee)
q-phase (Zn, hcp)
(Ag,Z41 “G& -- Hi?
(Ag,Zn)l ‘G& - H:F
= GHF
‘G& -- Hz,sER = GE; * OLa A@,$”= -24500 + 0.80 T * lLigzn=
= G;T
‘G& - H;fR = GHE * OLQ --18700 Ag,Zn -
0 E-phase (AgZn$
pphase (AgZn, bee) (Ag,Z@l SER =G&= P ‘GAG
P
.- HAg
” GzIl--
SER = Hz,
G&=
(Ag,Zn)l * “GE -Hp=G;T & * “G& _ ,iysER= GHSER Zn +0.691.T Zn * OLigZn =- 17700 - 1.2 T
* oL!&,Zn = -30650 + 2.31 T
* ‘Ligz,
* ‘LigZn = -1920
* 2LEA&Zn =20400
c-phase (AgZn) (Zn)l(.Ag,Zn)2 * OGC -2HiF-H;ER=2G;;+GE-27100 Zn:Ag * oGLs:Zn - 3H;zR = 3G;; * oLirl,Ag Zn =-32500
=26600
214
T. G6MEZ-ACEBO
r-phase (AgsZb) (Ag,znh(Agh(Agtznb(Ag,Zn)6 * oGig:,ig:,,:~g - 13H”
= 13GA7 + K, + 2K, + 6K,
OGY
-1lHr
OG7
-
1OHr
‘4 OGY
-
8Hr
- SH;;’
* OGY
-
7 H;F
- 6H;,ER = 7G~y + 6Gzy + K, + 2K,
l
Zn:Ag:Ag:Ag
t
Ag:Ag:Zn:Ag Zn:Ag:Zn:Ag
Ag:Ag:Ag:Zn
t OGY
Zn:Ag:Ag:Zn
* 0GY
Ag::Ag:Zn:Zn
* OGY
Zn:Ag:Zn:Zn
-5HAg
-2H;ER
=llGA~+2Gz~+K~+6K~
- 3H;fR = 1OGe
SER -8@,ER
+ 3GE
+ K,, + 2K, + 3K, + 6K,
= SGAy + 5Gzy + K, + 3K, + 6K4
=
5GAF + 8Gzy + Ko
-4H;F-9H;F=4Ge+9GE+K,,+2K,+3KJ -
2H;F
- 1 lH;ER = 2Ge
+ 1lGE
+ K,, + 3K,
Functions oG’H;y = -7209.512+118.202013~T-23.8463314.T.InT - 0.001790585. T2 - 3.98587 .10-7 . T3 - 12011/ T for 298.15 < T< 1234.93 -15095.252+190.266404~T-33.472~T~InT+1.411773~1029~T~9 for 1234.93 < T< 3000.00 ‘GH;fiR = -7285.787 + 118.470069. T - 23.7013 14. T. In T -0.001712034.
T2 - 1.264963.10-6. T3
for 298.15 < T < 692.66 -11070.559+172.34566~T-31.38~T~lnT+4.70514~1026~T-9 for 692.66 < T < 1700.00 ‘GE
=‘GHr
o ($2
=‘=(-HSER I Ag +300+0.3’7
’ G,y
=’ GH;ER + 2886.96 - 2.5 104. T
o G fCC
=o
c;HSER
Zn
Zn
+ 3400- 1.05. T
+
2969.82 - 1.56968. T
* KC,= -117900 - 4.72 Tln T * K, = 100000 * K3 = 24200 *Kq=12000
215
THERMODYNAMIC ASSESSMENT OF Ag-Zn
1300
-
.. .
1E!OO P
Calculated Experimental
1100 y 1000 iif
*r;i 3 900 $
800
;
700
I
600 1500
400
A
6
0
0.8
FIG. 1 The calculated phase diagram of the Ag-Zn system, compared with the experimental diagram.
1.0
Mole fraction Zn
FIG. 2 The chemical potential of liquid and solid Ag-Zn alloys referred to liquid phase, as fknction of temperature for different mole fractions of Zn, compared with data from Yazawa and Gubcova [7OYaz]. Dotted lines indicate calculated phase boundaries.
900 L4
1000
1100
Temperature,
K
1200
T. GeMEZ-ACE60
216
0 5 E
-5
2- -10
FIG. 3 The chemical potential of liquid Ag-Zn alloys referred to liquid phase, as function of temperature for different mole fractions of Zn, compared with data from Gerling et al. [79Ger]. Dotted line indicate calculated phase boundary of liquid.
N’
z -15 II
E
Q, -20 -8 58 -25 ._ g -30 5 A
-35 10010
IGO
IlbO
Id50
1200
Temperature, K
FIG. 4 The calculated chemical potential of zinc in liquid Ag-Zn alloys at 950 K, compared with experimental data Corn Kleppa and Thahnayer [59ICle]. The dotted line indicates the extrapolated values for the liquid phase.
0
0.2
0.4
0.6
Mole fraction Zn
0.8
’
J
THERMODYNAMIC ASSESSMENT OF Ag-Zn
I
I
I
217
I
A’..
FIG. 5
‘A.
,_
The calculated partial entropy of zinc in liquid Ag-Zn alloys at 950 K, compared with experimental data from Kleppa and Thahnayer [59Kle]. The dotted line indicates the extrapolated values for the liquid phase.
P \
0
I
0.2
I
0.4
I
0.6
I
0.8
1 .C
Mole fraction Zn
‘I .o
I
I
I
I
0.8 fi 0.6
FIG. 6 The calculated Zn activity at 950 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
0 > 2 0.4 0.2
0.4
0.6
Mole fraction Zn
0.8
218
T. GOMEZ-ACEBO
1.0
0.8
N’ 0.6
FIG. 7 The calculated Zn activity at 1023 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
.z? .-> 2 0.4
0.2
0 A
0.2
0.4
0.6
0.8
1
Mole fraction Zn
1.0
I
I
I
I
0.8
z
0.6
v 79Ger 0 87Kam
FIG. 8 The calculated Zn activity at 1073 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
.z? > 2 0.4
0.2 0 A
0.2
0.4
0.6
Mole fraction Zn
0.8
1
THERMODYNAMIC ASSESSMENT OF Ag-Zn
FIG. 9 The calculated Zn activity referred to the liquid phase, as a function of temperature, at four different compositions (mole fraction of Zn), compared with some experimental data. Dotted lines indicate calculated phase boundaries.
0.1
A
219
0 i 700
I
I
I
800
900
1000
Temperature, K
3
j-@&j-q FIG. 10 Calculated integral enthalpies of the solid phases at 623 K, together with some experimental data.
-6 A =
0
0.2
0.4
0.6
Mole fraction Zn
0.8
1.0
220
T. G&vlEZ-ACEBO
33 32 * z $
31 FIG. 11 Experimental values of the specific heat of the y-phase at constant composition (x~n = 0.6 15) taken from Dowie and Martin [85Dow], compared with the calculated values.
30
2 29 T+.O 28 .k 2 n 27 c0
-I
26,
A
/
25. 300
I
600
9
Temperature, K
FIG. 12 Zinc-rich side of the calculated phase diagram for the Ag-Zn system, together with experimental data. The broken line shows the metastable extrapolation of the liquid/& equilibrium up to pure zinc, indicating an hypothetical melting point of pure Zn as E phase, at 650 K.
x
0.6
0.7 0.8 0.9 Molefraction Zn
1.0
THERMODYNAMIC
calphnd. Vol. 22, No. 2, pp. 203-220, 1998 Science Ltd, All rights reserved. 0384-59161981 $-see front matter
@ 1998Elsevier
Pergamon
ASSESSMENT OF THE Ag-Zn SYSTEM
T. Gomez-Acebo CEIT and Escuela Superior de Ingenieros Industriales (Universidad de Navarra) E-20009 San Sebastian, SPAIN e-mail: [email protected]
ABSTRACT
A thermodynamic assessment of the Ag-Zn system has been done using a computerized CALPHAD (calculation of phase diagrams) technique. The liquid, a, p, rl and E phases are described by a regular solution model, the y phase by a four-sublattice model, and the 5 phase by a two-sublattice model, both based on considerations of their crystal structure and compatibility with the same phase in other systems. A set of parameters describing the Gibbs energy of the different phases is given and calculated phase diagrams are presented.
Introduction The phase equilibria in the Ag-Zn system have been investigated experimentally several times, the oldler measurements are summarised by Hansen [58Han]. The accepted phase diagram was published originally by Andrews et al. [41And] and is established to a high degree of accuracy. Several solid phases are present in this system, between the silver-rich side (a phase) and the zinc side (IJ phase), there are p (ideal composition AgZn, stable at high temperature), 5 (AgZn at low temperature), y (AgsZns) and E (AgZn,). There is also a metastable phase called p’ formed instead of c when quenching from the P-phase domain; this phase has not been taken into account in the present work. No complete thermodynamic assessment has ever been done of this system; Ronka et al. [97Ron] say they have assessed -but still not published- the Ag-Zn system, but based only on data collected by Hultgren et al. [73Hul], and not on real experimental data. In the present work a review of the experimental data available in the literature is made, some models for the intermediate phases are proposed, and a set of thermodynamic parameters describing the entire system is given. The assessment has been carried out using a computer program called PARROT, included in the Thermo-Calc databank system [85&m], for optimisation of parameters in thermodynamic models. All thermodynamic equilibria were calculated using the POLY-3 program, Sal
version received on 10 November 1997,Revised version on 24 April 1998
203
204
T. G6MEZ-ACEBO
included in the same system. The descriptions of the pure solid an liquid elements were taken fi-om [91Din].
Experimental Information Phase Diagram The complete phase diagram of the Ag-Zn system was published originally by Andrews et al. [41And] and since then it has not been modified. Hansen [58Han] reviewed the experimental information available, and concluded that the accepted phase diagram was to be regarded as established to a high degree of accuracy. It is presented in Fig. 1. In addition to the two terminal solid phases, denoted a (Ag-fee) and r\ (Zn-hcp), there are four intermetallic phases, denoted p, L Y and E. The phase diagram from [41And] was obtained using a combination of thermal, microscopic and X-ray methods. It includes temperature and composition of peritectic points, and liquidus and sohdus lines in the whole range of composition. The phase boundaries of solid phases were estimated from measurements of single-phase and two-phase regions. Andrews et al. [41And] give the solubility limits of all phases down to 200 “C. Wiedebach-Nostiz [46Wie] has determined the solid solubility of Ag in q-Zn. There are no direct measurements of tie-lines in any of the binary phase boundaries. The transformation temperature from the p to the < phase has been determined by Noguchi [62Nog], through measurements of the Hall coefficient and the thermoelectric power. The temperatures and compositions of coexisting phases at invariant equilibria as presented by Massalski [90Mas] are shown in Table 1. In the present optimisation, phase boundary limits by [41And] except for the TJ phase, solubility limits of the rl phase by [46Wie], and p/c transformation temperatures by [62Nog] were used. The phase boundaries between solid phases from [41And] were used with care, because they were not obtained as real tie-lines, but as one- and two-phase points. Iwasaki et al. [85Iwa] have measured the pressure-induced transformation between c, p, p’, giving an approximate pressure-temperature phase diagram of the equiatomic ahoy. These data were not used, because no pressure-dependence parameter has been introduced in the present model. Liquid Phase Several researchers have measured the chemical potential (Figs. 2 to 5) or the activity of zinc (Figs. 6 to 8) in Iiquid Ag-Zn alloys [42Sch, 59Kle, 7OYaz, 79Ger, 87Kam]. Schneider and S&mid [42Sch] obtained values of the activity of zinc as its vapour pressure measured by the dew point method. The other researchers give values of the chemical potential of zinc, obtained through measurements of the e.m.f. in a galvanic cell. Kleppa and Thahnayer [59Kle] made their measurements at a constant temperature of 950 K (Fig. 4), and they also measured the dependence of the e.m.f. with temperature, from which partial entropy values of Zn can be deduced (Fig. 5).
THERMODYNAMIC ASSESSMENT OF Ag-Zn
205
TABLE 1 Experimental [9OMas] and Calculated Invariant Equilibria.
- Equilibrium
Temperature, K Experimental Calculated
lX+L+p
983
983
p+L+y
934
933
y+L+&
904
907
&+L+q
704
706
P +a+<
531
53,8
P+r4
547
552
-
-
-
-
-
Phase a P L P Y L Y & L E V L a P 5 P r Y
Composition, at. % Zn Experimental Calculated 32.1 32.5 36.7 37.1 37.5 37.4 58.6 58.2 61.0 60.9 61.8 62.3 64.7 64.6 69.4 69.4 71.0 70.6 89.0 90.3 95.0 96.2 98.0 98.1 40.2 40.3 44.9 45.6 46.0 49.3 50.4 50.1 58.5 58.8
The data from [42Sch] are a bit scattered, as can be seen in Figs. 6 and 8, and were not used in the present optimisation. All the other data agree fairly well, and were used for the calculations. Solid Phases The activity of zinc in the solid phases (Figs. 6 to 9) has been measured mainly by three different methods: dew point [49Bir, SlUnd, 68Str], light absorption method [53Sca] and the isopiestic method [7OMas]. There is a reasonable agreement between all these measurements, except that of Scatchard and Westlund [53Sca], as can be seen in Figs. 7 and 8; these authors give activity values of the alliquid equilibrium that are well above the others. Birchenall and Cheng [49Bir] give activity data for several compositions in the a, p, ‘y, E and liquid phases. Other researchers have measured the activity of Zn in the a [53Sca, 70Mas], p [SlUnd], and E phase [68Str]. The anthalpy of formation of the solid phases (Fig. 10) has been measured using liquid Zn calorimetry [59Wit], and liquid Sn calorimetry [70Bla]. The data from Wittig and Huber [59Wit] are barely endothermic and therefore inconsistent with the others, maybe because of the effect of zinc evaporation, and were not used. Hultgren et al. [73Hul] report some measurements of the enthallpy of formation of a phase; however, they refer to an unpublished work, so it was not possible to check the experimental accuracy of the obtained values, and were not considered in the optimisation.
206
T. GbMEZ-ACEBO
The transformation between p, 6 and j3’ has been studied under several experimental techniques.
Orr and Rove1 [62Orr] give enthalpies of formation of the three phases, measured by liquid-tin calorimetry. Noguchi [62Nog] gives the temperature and enthalpy of transformation between these three phases, the latter obtained through measurements of the specific heat. Only one reference has been found that gives temperature-dependent specific heat values, of the y phase [85Dow], measured for a single composition with a scamring calorimeter (Pig. 11). Wallbrecht et al. [76Wal] give the enthalpy change of a low-temperature transformation of the y phase, by heat capacity measurements. However, this transformation has not been considered, and these data were not taken into account. In this optimisation activity data from [49Bir], [SlUnd], [68Str] and [70Mas], enthalpies from [62Nog], [62Orr] and [70Bla], and heat capacities from [85Dow] were used.
Thermodynamic Models Two different models have been adopted in the present system, the substitutional regular solution model and the sublattice model [7OHil]. The crystal structure of the solid phases is given in Table 2; the metastable p’ phase is not included. TABLE 2
Crystal Structure Data [9 1Vil] Composition, at. % Zn Phase 0 to 40.2 a (Ag) 37 to -51.2 5 (AgZn) 36.7 to 58.6 P (AgZn) 58.5 to 64.7 Y (AgsZng) -66.2 to 89 a (AgZnr) 95 to 100 r\ CW
Pearson symbol cF4 hP9 cI2 ~152 hP2 hP2
Space group FmSm PT ImJm IT3m P63lmmc P63lmmc
Struktur-bericht designation Al A2 082
A3 A3
Prototype cu AgZn W CusZns Mg Mg
The 4 jj E, rj and Liquid Phases The two solid terminal phases (a-Ag and q-Zn), the p, E and the liquid phase were treated using a regular solution model; the molar Gibbs energy per formula unit is: G,$ = xnp”G$, + xZnOG$, + RT(x,s lnx,,+ + x,lnx,,)+EGi
(I)
where $ means the phase considered. The parameters “GA, where M is Ag or Zn, represent the Gibbs energy of pure component M in the same state as the phase considered: fee for the a phase, bee for the p phase, and hcp for IJ and E phases; all were taken corn [91Din], and are reproduced in the Appendix. They are given relative to the enthalpy of selected reference states for the elements at 298.15 K. This state is denoted SER (standard element reference), HiR .
THERMODYNAMIC ASSESSMENT OF Ag-Zn
207
The crystal structure of the hexagonal q and E phases, having both the hcp Mg-type structure, differ in the value of the axial ratio, as was noted by Massalski and King [62Mas]. The ideal value for the close packing of hard spheres is c/u = 1.6330. In the E phase the axial ratio decreases from about 1.58 to 1.55 with increasing concentration of zinc in the region of 67-88 at. %. Conversely, in the r\ phase (which is a solid solution based on zinc) the initial axial ratio is considerably above the ideal value and increases from about 1.78 near the &+q/q boundary to the value of pure Zn (c/u = 1.856) [62Mas]. Taking this into account, Kowalski and Spencer [93Kow] assessed the Cu-Zn system considering that the well-established value of the lattice stability for pure Zn in the fee structure should be used in the thermodynamic description of E. However, in the present work it has been preferred not to change the description of the pure elements. Accordingly, the Gibbs energy of pure zinc in the hexagonal E phase, “G&, has been expressed as
oG;, -- HifiR = GHF
+ A" G&
(2)
where A” G& is a function of temperature, and is the lattice stability of the E phase. The excess Gibbs energy, EGt, depends on the interaction between the two species, Ag and Zn. This interaction is described by a Redlich-Kister polynomial:
For the a, p and liquid phases only the first two parameters were considered; the parameter OL@ &.& was treated as linearly dependent on temperature and 1Lf&Zn as constant. For the 11 phase, the lack of experimental data allowed the calculation of a temperature-independent regular term (“IL)only. For the E phase, it was necessary to evaluate the three parameters of the eq. (3), because of the shape of the solidus and liquidus lines; the regular term (‘L) was treated as temperature-dependent, and the two subregular terms (‘L and 2L) as temperature-independent. The yPha.se The y phase has the same crystalline structure as the Cu-Zn gamma brass. Furthermore, there is a strong similarity between the phase diagrams of the Ag-Zn and the Cu-Zn systems. This considlerations have led to use a thermodynamic model for the y phase that is compatible in both systems. As was noted by Kisi [88Kis], in the ternary system Al-Cu-Zn the gamma brass phase is present both in the Cu-Zn side (prototype structure CuJns, space group 133m) and in the Al-Cu side (prototype structure AL&US, space group P43m). Despite their different crystalline structure, the two phases are the terminal ends of a single phase region in the Al-Cu-Zn alloy system which transects the ternary phase diagram. Kisi [88Kis] has determined the crystalline structure of an ahoy A10.2&~.~8Zr4,0~~ with y-phase structure. Considering this description, Fries et al. [98Fri] have proposed the four-sublattices model for this phase (Al,Cu,Zn)s(Cu)s(Cu,Zn)r@l,Cu,Zn)~~; if we use this model for the Ag-Zn system, with no Al and supposing that Ag occupies Cu
208
T. GblEZ-ACE60
positions, the model is reduced to (Ag,Zn)s(Ag)s(Ag,Zr&(Ag,Zn)~4, (AgJnh(AgMAg,Zn~(Ag,Zn)6.
and after dividing by 4,
This model has eight end-members, being the most stable configuration AgsZns (Zn:Ag:Ag:Zn). The Gibbs energy of each end-member has been calculated referred to the Gibbs energy of pure Ag and Zn in bee state. The correction terms have been calculated associating energies to bonds instead of estimating the Gibbs energy of each end-member as an independent parameter. A temperature-dependent parameter is added to the Gibbs energy of all end-members (& in the Appendix), and an additional positive temperature-independent parameter is added for each sublattice that deviates from the ideal end member Zn:Ag:Ag:Zn (Kr, K3 and K4 in the Appendix). This allows the calculation of 4 model parameters instead of 8. No excess terms have been estimated. The c Phase The 6 phase is the stable low-temperature phase near equiatomic compositions. For this phase a thermodynamic model based upon the crystal structure is used. The crystal structure of the c phase has been determined by Edmunds and Qurashi [5 led]. The space group is CT. The unit cell contains nine atoms; three of the positions are occupied almost exclusively by zinc atoms; the remaining six positions are occupied at random by the remaining atoms (about 75 % silver and 25 % zinc). According to this, the sublattice model proposed may be (Zn)j(Ag,Zn)b, but it can be simplified to (Zn),(Ag,Znh. The Gibbs energy per mole of formula unit is
(6) The Gibbs energy of the Zn:Ag (ZnAgz) end-member is calculated as the sum of that of the pure elements in bee phase, with a temperature-independent correction parameter. The parameter ‘G&,,
has been calculated as three times the Gibbs energy of pure Zn in bee state.
The excess Gibbs energy is given as
and this regular parameter is also temperature-independent.
Method of Optimisation The optimisation was made using a computer program called PARROT included in the ThermoCalc databank system [85Sun], which allows the simultaneous consideration of various types of thermodynamic data. The program works by minimising an error sum where each piece of information used is given a certain weight according to its estimated accuracy. The selection of model parameters and the weights are then changed by trial and error until most of the information is satisfactorily described. As input, selected experimental data together with descriptions of pure solid and liquids by [9 lDin] were used.
THERMODYNAMIC ASSESSMENT OF Ag-Zn
209
For the liquid, a and p phase three parameters have been used in the Redlich-Kister expression, but only one for the q phase, because of the lack of experimental data. For <, E and y phases, some parameters were also optimised for the description of the Gibbs energy of the endmembers.
Results and Discussion All parameters assessed in this work are collected with the data for the pure elements in the Append:.x (expressed in the form of a Thermo-Calc file). Figures 1 to 12 and the comparison of temperatures and compositions of invariant equilibria presented in Table 1 summarize and illustrate the results obtained from the present assessment. There is a very good agreement between calculated and experimental values across the entire system. Phase Diagram The calculated phase diagram is shown in Fig. 1 using the optimised set of parameters describing the binary system presented in the Appendix, compared with the experimental phase diagram [90Mas:j. It can be seen that both the invariant points and the solidus and liquidus lines are well reproduced. However, the calculated solubility of Zn in a is slightly lower than the experimental values: the calculated phase boundaries a/a+p and a+P@ are almost straight lines. This could be avoided by increasing the number of optimising parameters in the Redlich-Kister polynomials, that is, allowing a temperature-dependence on the subregular parameter of both phases (‘L); but it was preferred to optimise only three parameters of these two phases, maintaining the subregular parameter as temperature-independent. In Fig. I.2 the right side of the calculated phase diagram is compared with experimental data used for phase boundaries. The calculated phase boundaries of the FE two-phase field have small deviations from experimental lines. At high temperatures, near the peritectic point, the ?r_& line should be displaced to lower zinc contents, but this effect could not be achieved without increasing the number of optimising parameters of the y-phase, and that was considered reasonable. The only available data for the q phase were some points of the phase boundaries E/E+T\ and &y/q obtained by Andrews et al. [41And], and the solubility limits of Ag in q-Zn [46Wie], i.e. the &+r\/q line. In the present work it has not been possible to reproduce both phase boundaries, even though several combinations of parameters were tried. In the final optimisation, only the E.+TJ/~ data from [46Wie] were used; as can be seen in Fig. 12, they are reasonably well reproduced. Liquid Phase The liquid phase has been modeled with only three parameters, the regular parameter CL) with a temperature dependence, and the subregular parameter (‘L), as temperature-independent. Figs. 2 and 3 snow the calculated chemical potential of several Ag-Zn liquid alloys, compared with data by Yazawa and Gubcova [7OYaz] and Gerling et al. [79Ger], both obtained by e.m.f. techniques. For both figures, the reference state is the liquid phase. It can be seen that the experimental
210
T. G&vlEi!-ACEBO
values are quite well fitted. Some of the data by Yazawa and Gubcova [7OYaz] were also obtained for different solid phases, in particular those with low Zn content. Figs. 4 and 5 show the comparison between the data given by Kleppa and Thalmayer [59Kle] and the calculated values, for the chemical potential and the partial entropy of zinc in liquid alloys at 950 K. Although all the experimental values are referred as obtained for the liquid phase, it can be clearly seen in the phase diagram (Fig. 1) that at the indicated temperature, some points fall into the p and a phases. It has been supposed that the points at Q,, < 0.55 were calculated as an extrapolation from higher temperatures were the liquid phase is the stable one. For the optimisation, that experimental points were calculated as metastable extrapolations of the liquid phase. The dotted lines of Figs. 4 and 5 indicate the extrapolated properties of the liquid phase. It can be seen that the fitting to the experimental values is excellent. Solid Phases Fig. 9 show data given by [49Bir], [SlUnd] and [7OYaz] of the activity of Zn in the p phase at four different compositions as a function of temperature, compared with the calculated activity at the same compositions. The reference state is the liquid phase. The calculated phase boundaries are printed with dotted lines. Data from [7OYaz] were obtained mainly for the liquid phase, but some points belong to solid phases (see Fig. 2); the authors give values of the chemical potential of zinc, but they have been converted to activity for comparison. For the two series of values with lower zinc content (.Q,, = 0.40, 0.434 and 0.50), it can be seen in Fig. 9 that the agree is reasonable. However, for higher Zn content (xz,, = 0.54) the two series of data plotted are not compatible; activity values from [SlUnd] are overestimated. It has not been possible to find a set of parameters for the description of the p phase that adjust at the same time the three series of data given by [ 5 1Und]. These authors report a slight decrease in vapour pressure of Zn when preheating the powders for two days; they suggest that the high values of vapour pressure - and consequently of activity - might be related to surface effects. Taking this into account, together with the reported experimental error of 10 %, the difference in activity for xzn = 0.54 can be explained. These data were given a low weight in the optimisation. Figs. 6, 7 and 8 show the calculated zinc activity at three different temperatures (950 K, 1023 K and 1073 K), compared with some experimental measurements. Data given by [53Sca] and [42Sch] were not used in the optimisation, but they are plotted for comparison. In Fig. 6, the three data given by [59Kle] with lower zinc content were supposed as extrapolated points of the liquid phase from higher temperatures, as was said above. The data given by Hultgren et al. [73Hul] plotted in Fig. 7 are compiled data, not experimental, but are also plotted for comparison. It can be observed at the three temperatures that the agreement between experimental data and calculated values is very good. The calculation of the lattice stability of the E phase, A”G&,
has been done estimating a
hypothetical melting point of pure Zn in the E phase, by graphical extrapolation in the phase diagram of the liquidus and solidus lines up to pure zinc. This has led to an approximate value of 650 K. Considering that the latent heat does not change with temperature, and equating the Gibbs energy of pure Zn in liquid and E phases, ‘G& =‘Ggq at 650 K, the lattice stability was
THERMODYNAMIC ASSESSMENT OF Ag-Zn
211
calculated as A” G&= 0.691 T. The broken lines printed in Fig. 12 indicate the extrapolated solidu,s and liquidus lines of a metastable E phase up to pure Zn. This description of the E phase is proposed to be used in other systems where it is present. Fig. 1lDshows the calculated enthalpy of formation for the solid phases at 623 K, together with some experimental dam. It can be seen that data by [59Wit] are barely endothermic, and are not compatible with the other experimental values; they were not used in the optimisation. Data collected by [73Hul] were plotted for comparison, because they are not experimental data, and were not used in the optimisation. The agreement is quite good. The enthalpy difference between 4 and p phases at three different compositions is presented in Table 3, together with data obtained by Noguchi [62Nog]. The agreement is excellent. These were he only experimental data for c phase, together with solubility limits. TABLE 3
Enthalpy Difference Between c and p Phases, AHyp (J/mol) XZll
0.463 0.486 0.507
Experimental [62Nog] 1330 1216 1119
Calculated 1324 1201 1099
For the y phase few experimental data were available, although the model proposed, having four sublattices, required the calculation of several parameters. It has not been possible to assess the available experimental data estimating 8 parameters, one for each end-member; so four parameters have been set: a temperature-dependent parameter is added to the Gibbs energy of all end-members (& in the Appendix), and an additional positive temperature-independent parameter is added for each sublattice that deviates from the ideal end member Zn:Ag:Ag:Zn (K1, & and K4 in the Appendix). The Ko parameter has a logarithmic dependence of temperature, because a linear dependence could not consider the variation with temperature of the specific heat. For the K1 parameter an arbitrary high positive value has been supposed. The experimental values of specific heat given by [85Dow] for y-phase Ag0,615Znr,385 are plotted in Fig. 11, together with the calculated values. The fitting is not very satisfactory, although the absolute error is relatively small. The increase of the specific heat at temperatures near 400 K [85Dow] can be related to the low-temperature transformation in y-phase reported by [76Wal], who ,noticed an order-disorder transformation in this phase at temperatures ranging between 303 and 407 K, with an enthalpy change of about 177 f 15 J/m01 of Ago.614Zno.3sa.However, the model cannot take into account this effect, so this transformation has not been considered in the prese:nt study. Conclusions A selt of parameters describing the phase equilibria and thermodynamic properties in the Ag-Zn system has been evaluated from experimental data. A comparison between calculated and measured quantities is made, showing a satisfactory agreement, except for some of the phase
212
T. GdMEZ-ACEBO
boundaries. A four-sublattices model for the y phase is used, that considers the properties of the same phase in other different systems.
Acknowledgements This work was done during a three-month stay of the author at the Royal Institute of Technology (Stockholm, Sweden). I wish to thank Dr Bo Sundman for accepting me as a guest researcher in his group, and for many suggestions and critical reading of the manuscript. Valuable discussions with Dr Philip Spencer (about the model for y-phase), Dr Lucia Dumitrescu, Dr Qing Chen and Mrs Alexandra Kusoffsky are gratefully acknowledged.
References 41And: 42Sch: 46Wie: 49Bir: 51Edm: 51Und: 53Sca: 58Han: 59Kle: 59Wit: 62Mas : 62Nog: 62Orr: 68Str: 70Bla: 7OHil: 7oMas: 7OYaz: 73Hul: 76Wal: 79Ger: 85Dow: 851wa: 85Sun: 87Kam: 88Kis: 90Mas: 91Din: 91Vil: 93Kow: 97Ron: 98Fri:
K.W. Andrews, H.E. Davies, W. Hume-Rothery and CR. Oswin, Proc. Roy. Sot. (London), A177, 149-167 (1941). A. Schneider and H. S&mid, Z. Elektrochem., 48 (11) 627-39 (1942). A.v. Wiedebach-Nostiz, Z. MetaZfkunde, 37, 56-60 (1946). C.E. Birchenall and C.H. Cheng, Metals Trans., 185,428-434 (1949). LG. Edmunds and M.M. Qurashi, Acta Cryst., 4,417-425 (1951). E.E. Underwood and B.L. Averbach, J. Metals, 3, 1198-1202 (1951). G. Scatchard and R.A. Westlund, J. Am. Chem. Sot., 75,4189-4193 (1953). M. Hansen, Constitution of binary alloys, 2”d.Ed., pp. 62-66. McGraw-Hill, New York (1958). O.J. Kleppa and C.E. Thalmayer, J. Phys. Chem., 63, 1953-1958 (1959). F.E. Wittig and F. Huber, Z. Elektrochemie, 63 (8) 994-1001 (1959). T.B. Massalski and H.W. King, ActaMet., 10, 1171-1181 (1962). S. Noguchi, J. Phys. Sot. Japan, 17, 1844-1856 (1962). R.L. Orr and J. Rovel, ActaMet., 10,935-939 (1962). J.L. Straalsund and B. Masson, Trans. AZME, 242, 190-195 (1968). G.R. Blair and D.B. Downie,MetalSci. .I, 4, l-5 (1970). M. Hillert and L.I. Staffanson, Acta Chem. Scand., 24,361s (1970). D.B. Mason and J.L. Sheu,Met. Trans., 1, 3005-3009 (1970). A. Yazawa and A. Gubcova, Trans. JIM, 11,419-423(1970). R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleisner, K. Kelley and D.D. Wagman, Selected values of the thermodynamic properties of binary alloys, pp. 115- 121. ASM, Metals Park, Ohio ( 1973). P. Wallbrecht, F. Balck, R. Blachnik and K.C. Mills, ScriptaMet., 10, 579-584 (1976). U. Gerling, M.J. Pool and B. Predel, Z. MetalMe., 70 (4) 224-229 (1979). D.B. Downie and J.F. Martin, J. Chem. Thermodynamics, 17,927-934 (1985). H. Iwasaki, T. Fujimura, M. Ichikawa, S. Endo and M. Wakatsuki, J. Phys. Chem. Sol@ 46 (4) 463468 (1985). B. Sundman, B. Jansson and J.-O. Andersson, CalphadJ, 9 (2) 153-190 (1985). K. Kameda, Trans. Jpn. Inst. Met., 28 (1) 41-47 (1987). E.H. Kisi, Mater. Sci. Forum 27128, 89-94 (1988). T. Massalski, BinaT AIIoys Phase Diagrams, pp. 117-l 18. ASM, Metals Park, Ohio (1990). A. Dinsdale, CalphadJ., 15 (4) 317-425 (1991). P. Vilars and L.D. Calve& Pearson’s Handbook of 0ystaIlogrqhic Data, pp. 645-646. ASM, Metals Park, Ohio (199 1). M. Kowalski and P.J. Spencer, J. Phase Diagrams, 14,432-436 (1993). K.J. Ronka, F.J.J. van Loo and K. Kivilabti, Z. Metallkunde, 88, 3-13 (1997) S.G. Fries, I. Hurtado, T. Jantzen, P.J. Spencer, K.C. Hari Kumar, P. Liang, H.L. L&as, H.J. Seifert and F. Aldinger, J. Alloys Comp., to be published (1998).
THERMODYNAMIC ASSESSMENT OF Ag-Zn
213
APPENDIX Thermodynamic Parameters of the System Ag-Zn (in J/m01 of formula unit). The parameters evaluated in the present work are indicated with *. AU remaining parameters are taken from [91Din]. Liquid (Ag,Z@l oG Liquid _
HSER Ag
Ag
=
11025.076 - 8.89102. T - 1.033905. 1O-2o . T7 + GHF for 298.15 < T< 1234.93 - 3587.111+ 180.964656. T- 33.472.TelnT for 1234.93 < T < 3000.00
0GLiqUid Zn
- H;ER
=
7157.213 - 10.29299. T - 3.58958. lo-l9 . T7 + GH;fiR for 298.15 < T< 692.66 -3620.391+
161.608594.T-31.38.T.lnT
for 692.66 < T < 1700.00 * ‘Ly;;;
=-27400
+ 5.88 T
* 1LLWd __5500 Ag,Zn -
a-phase (Ag, fee)
q-phase (Zn, hcp)
(Ag,Z41 “G& -- Hi?
(Ag,Zn)l ‘G& - H:F
= GHF
‘G& -- Hz,sER = GE; * OLa A@,$”= -24500 + 0.80 T * lLigzn=
= G;T
‘G& - H;fR = GHE * OLQ --18700 Ag,Zn -
0 E-phase (AgZn$
pphase (AgZn, bee) (Ag,Z@l SER =G&= P ‘GAG
P
.- HAg
” GzIl--
SER = Hz,
G&=
(Ag,Zn)l * “GE -Hp=G;T & * “G& _ ,iysER= GHSER Zn +0.691.T Zn * OLigZn =- 17700 - 1.2 T
* oL!&,Zn = -30650 + 2.31 T
* ‘Ligz,
* ‘LigZn = -1920
* 2LEA&Zn =20400
c-phase (AgZn) (Zn)l(.Ag,Zn)2 * OGC -2HiF-H;ER=2G;;+GE-27100 Zn:Ag * oGLs:Zn - 3H;zR = 3G;; * oLirl,Ag Zn =-32500
=26600
214
T. G6MEZ-ACEBO
r-phase (AgsZb) (Ag,znh(Agh(Agtznb(Ag,Zn)6 * oGig:,ig:,,:~g - 13H”
= 13GA7 + K, + 2K, + 6K,
OGY
-1lHr
OG7
-
1OHr
‘4 OGY
-
8Hr
- SH;;’
* OGY
-
7 H;F
- 6H;,ER = 7G~y + 6Gzy + K, + 2K,
l
Zn:Ag:Ag:Ag
t
Ag:Ag:Zn:Ag Zn:Ag:Zn:Ag
Ag:Ag:Ag:Zn
t OGY
Zn:Ag:Ag:Zn
* 0GY
Ag::Ag:Zn:Zn
* OGY
Zn:Ag:Zn:Zn
-5HAg
-2H;ER
=llGA~+2Gz~+K~+6K~
- 3H;fR = 1OGe
SER -8@,ER
+ 3GE
+ K,, + 2K, + 3K, + 6K,
= SGAy + 5Gzy + K, + 3K, + 6K4
=
5GAF + 8Gzy + Ko
-4H;F-9H;F=4Ge+9GE+K,,+2K,+3KJ -
2H;F
- 1 lH;ER = 2Ge
+ 1lGE
+ K,, + 3K,
Functions oG’H;y = -7209.512+118.202013~T-23.8463314.T.InT - 0.001790585. T2 - 3.98587 .10-7 . T3 - 12011/ T for 298.15 < T< 1234.93 -15095.252+190.266404~T-33.472~T~InT+1.411773~1029~T~9 for 1234.93 < T< 3000.00 ‘GH;fiR = -7285.787 + 118.470069. T - 23.7013 14. T. In T -0.001712034.
T2 - 1.264963.10-6. T3
for 298.15 < T < 692.66 -11070.559+172.34566~T-31.38~T~lnT+4.70514~1026~T-9 for 692.66 < T < 1700.00 ‘GE
=‘GHr
o ($2
=‘=(-HSER I Ag +300+0.3’7
’ G,y
=’ GH;ER + 2886.96 - 2.5 104. T
o G fCC
=o
c;HSER
Zn
Zn
+ 3400- 1.05. T
+
2969.82 - 1.56968. T
* KC,= -117900 - 4.72 Tln T * K, = 100000 * K3 = 24200 *Kq=12000
215
THERMODYNAMIC ASSESSMENT OF Ag-Zn
1300
-
.. .
1E!OO P
Calculated Experimental
1100 y 1000 iif
*r;i 3 900 $
800
;
700
I
600 1500
400
A
6
0
0.8
FIG. 1 The calculated phase diagram of the Ag-Zn system, compared with the experimental diagram.
1.0
Mole fraction Zn
FIG. 2 The chemical potential of liquid and solid Ag-Zn alloys referred to liquid phase, as fknction of temperature for different mole fractions of Zn, compared with data from Yazawa and Gubcova [7OYaz]. Dotted lines indicate calculated phase boundaries.
900 L4
1000
1100
Temperature,
K
1200
T. GeMEZ-ACE60
216
0 5 E
-5
2- -10
FIG. 3 The chemical potential of liquid Ag-Zn alloys referred to liquid phase, as function of temperature for different mole fractions of Zn, compared with data from Gerling et al. [79Ger]. Dotted line indicate calculated phase boundary of liquid.
N’
z -15 II
E
Q, -20 -8 58 -25 ._ g -30 5 A
-35 10010
IGO
IlbO
Id50
1200
Temperature, K
FIG. 4 The calculated chemical potential of zinc in liquid Ag-Zn alloys at 950 K, compared with experimental data Corn Kleppa and Thahnayer [59ICle]. The dotted line indicates the extrapolated values for the liquid phase.
0
0.2
0.4
0.6
Mole fraction Zn
0.8
’
J
THERMODYNAMIC ASSESSMENT OF Ag-Zn
I
I
I
217
I
A’..
FIG. 5
‘A.
,_
The calculated partial entropy of zinc in liquid Ag-Zn alloys at 950 K, compared with experimental data from Kleppa and Thahnayer [59Kle]. The dotted line indicates the extrapolated values for the liquid phase.
P \
0
I
0.2
I
0.4
I
0.6
I
0.8
1 .C
Mole fraction Zn
‘I .o
I
I
I
I
0.8 fi 0.6
FIG. 6 The calculated Zn activity at 950 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
0 > 2 0.4 0.2
0.4
0.6
Mole fraction Zn
0.8
218
T. GOMEZ-ACEBO
1.0
0.8
N’ 0.6
FIG. 7 The calculated Zn activity at 1023 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
.z? .-> 2 0.4
0.2
0 A
0.2
0.4
0.6
0.8
1
Mole fraction Zn
1.0
I
I
I
I
0.8
z
0.6
v 79Ger 0 87Kam
FIG. 8 The calculated Zn activity at 1073 K, referred to liquid phase, compared with some experimental data. Values at different temperatures only when indicated.
.z? > 2 0.4
0.2 0 A
0.2
0.4
0.6
Mole fraction Zn
0.8
1
THERMODYNAMIC ASSESSMENT OF Ag-Zn
FIG. 9 The calculated Zn activity referred to the liquid phase, as a function of temperature, at four different compositions (mole fraction of Zn), compared with some experimental data. Dotted lines indicate calculated phase boundaries.
0.1
A
219
0 i 700
I
I
I
800
900
1000
Temperature, K
3
j-@&j-q FIG. 10 Calculated integral enthalpies of the solid phases at 623 K, together with some experimental data.
-6 A =
0
0.2
0.4
0.6
Mole fraction Zn
0.8
1.0
220
T. G&vlEZ-ACEBO
33 32 * z $
31 FIG. 11 Experimental values of the specific heat of the y-phase at constant composition (x~n = 0.6 15) taken from Dowie and Martin [85Dow], compared with the calculated values.
30
2 29 T+.O 28 .k 2 n 27 c0
-I
26,
A
/
25. 300
I
600
9
Temperature, K
FIG. 12 Zinc-rich side of the calculated phase diagram for the Ag-Zn system, together with experimental data. The broken line shows the metastable extrapolation of the liquid/& equilibrium up to pure zinc, indicating an hypothetical melting point of pure Zn as E phase, at 650 K.
x
0.6
0.7 0.8 0.9 Molefraction Zn
1.0