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A thermodynamic evaluation of the copper-phosphorus system
Vol. 14, No. 3, pp. 265-274, Printed in the USA.
CALPHAD
1990
0364-5916190 $3.00 + .OO (c) 1990 Pergamon Press plc
A THERMODYNAMIC EVALUATION OF THE COPPER-PHOSPHORUS
SYSTEM
Sabine an Mey, Philip J. Spencer Lehrstuhl fiirTheoretische Hiittenkunde und Metallurgic der Kernbrennstoffe, RNTH Aachen D-5100 Aachen, Germany
ABSTRACT. A critical thermodynamic evaluation of available, experimental information for the system Cu-P has been carried out. The representation of measured data by optimised coefficients of a polynomial function in composition and temperature leads to an analytical description of the thermodynamic properties of Cu-P, which allows both thermodynamic functions or phase equilibria for the system to be calculated. The extent of the agreement between calculated and measured properties is discussed.
1.
Introduction
A knowledge of the thermodynamic properties of the copper-phosphorus system is of importance for Cu-metallurgy, P being present in a number of commercially-important copper alloys. This work provides a theoretical basis for calculations related to the application of such alloys as well as for calculations in higher-order systems involving Cu and P. 2. Method of Calculation Experimental information on phase equilibria in the Cu-P system, together with results from thermodynamic measurements on Cu-P alloys, were used as input for a computer-aided evaluation procedure which results in the optimised analytical description of the system presented below. As described on several previous occasions (e.g. 10, 14, 15) the program written by Lukas et al. (11) was again used in the present work. No further discussion of the method will therefore be given here. The analytical expression used for the Gibbs energy of the pure elements and the stoichiometric compound phases was 3 G(T) = a + bT + CT In T + dT2 + eT + f/T while for the excess-properties of the solution phases the excess Gibbs energy of mixing was described by the Redlich-Kister equation AG~(x~,T)
=
xi
xj
f u=o
(x
i
-
x.1 3
3
Lw ij
with i = Cu; j = P. ____________________-----Received 22 August 1989.
265
(T)
S. AN
MEY andP.J. SPENCER
3. Exnerimental Information from the Literature The analytical description for pure Cu was derived from the Janaf Tables (6) (see table 1). Considerable confusion has arisen in the literature over the years due to choice of either white or red phosphorus by different data compilers as reference state for tabulated enthalpies of formation of phosphides. This has led to incorrectly reported values in many subsequent publications where the authors concerned have not taken the appropriate reference state into account. In this work, red phosphorus has been chosen as reference state since it is the form used in experimental enthalpy measurements on copper phosphides. No change in reference state is necessary, therefore, in treating the experimental numbers. Gibbs energy data for red-phosphorus were given by Kubaschewski (9). TABLE 1 Gibbs free energy of the pure elements G(T) =a+bT+cTlnT+dT'
+eT
3 +f$
phase
a
b
Cu-Liq P-Liq
-48.7 9041.4
173.91101
-31.380000
135.12040
-26.317400
8:
Cu-fee P-fee P(K)
-8044.1 31167.1 -5651.9
135.25700 106.86710
-24.853001 -16.736000 -16.736000
-.189325 -.744750 -.744750
93.72910
C
J/m01
d.102
e
f 8:
0. 0. 0.
69455. 8:
Measurement of properties of the Cu-P system for concentrations above xp = 0.25 are complicated by the high phosphorus partial pressures in this region. A phase diagram for the W-rich region of the Cu-P system is presented by Hansen (4), who reviewed experimental information for compositions up to XP = 0.25. For higher P-concentrations Hansen simply presents a vaporisation curve. In 1971 Ugai et al. (17) investigated the concentration region between 0.25 < XP < 0.667 using thermal analysis with the aid of a Kurnakov pyrometer. They published a T-x-projection of the Cu-P phase diagram at equilibrium pressure. As this phase diagram provides the only experimental indication of the liquidus in this region, it was included in the experimental input data used for the optimisation program. Even the extrapolated liquidus (up to pure P) presented by these authors was accepted, although with considerably less weight. In the Cu-P system, the compounds Cu3P, Cup2 and more recently, Cu2P7 have been found to exist (3, 4, 12, 13, 16, 18). Ugai (17) found that Cu3P has a homogenity range which extends to XP = 0.275 at 973 K, while Olofsson (13) reports that Cup2 has a "very small homogenity range". In the present work, all compounds are treated as stoichiometric. Ugai (16, 17) has reported melting temperatures for Cu3P and Cup2 and Gordienko et al. (3) have determined the enthalpies of formation of these two compounds at 298 K using mass-spectrometric analysis. Kubaschewski (8) cites older calorimetric values for&98 of Cu3P and Cup2 and has additionally estimated S2g8 values for both compounds. These data have been included with a lower weighting in the present evaluation.
THERMODYNAMIC EVALUATION OF THE Cu-P SYSTEM
267
No information for the melting temperature or for the enthalpy of formation of Cu2P7 has been found. The only thermodynamic information for the liquid phase is provided by experimental determinations of the activity of P in Cu-rich alloys (5,7). Krams et al. (7) used an isopiestic method to determine activities at about 1473 K and 0.25 < XP ( 0.30 with white phosphorus as reference state. Iwad et al. (5) determined activities at 1473, 1523 and 1573 K for alloys up to x = 0.01 using a solid-oxide galvanic cell. 4. Results and Discussiop There are very large inaccuracies in the available experimental information for the Cu-P system at compositions greater than xp = 0.25. Although this was taken into consideration during the optimisation procedure, it was not possible to obtain a satisfactory representation of the more reliable experimental results in the Cu-rich part of the phase diagram and at the same time obtain thermodynamically sensible results on the P-rich side of the system. Two sets of coefficients have therefore been derived, one which provides an optimum representation of data in the region up to xp = 0.25, and a second set which represents a compromise description of all the experimental information. The first description is particularly important in relation to practical applications in Cu-metallurgy. However, it should not be applied to concentrations xp ? 0.25. The second description represents a thermodynamic survey of the entire system. In this case, greater discrepancies on the Curich side had to be accepted to enable all the experimental information mentioned above to be included in the evaluation. The Gibbs energy coefficients for the compounds obtained from the two evaluations are listed in Table 2; the coefficients for the excess Gibbs energies of the liquid and Cu-fee phase are given in Table 3. TABLE 2 Gibbs free energies of the compounds in the Cu-P system J/m01 of atoms G(T) = a * b T + c T In T + d T2 +eT3+ phase
a
b
C
d 102
Evaluated coefficients from a consideration of the Cu3P -19777.7 119.25207 -22.832895 -.328180 CUP2 -32551.0 92.88499 -17.459452 -.559625 C"2p7 -26411.3 92.27973 -17.439720 -.621335
f-
1
T
e
f
entire system: 0.
52091.5
0. 0.
23151.5 15434.5
Evaluated coefficients from a consideration of Cu-rich alloys only: Cu3P -25251.7 114.52276 -21.680485 -.418400 0. 0.0
268
SAN MEYand PJ.SPENCER
TABLE 3 Excess Gibbs energies of the solution phases in the Cu-P system J/m01 AcE
= xcu xP
v
(v) LcuP
+ Bg;
T
(x cu - xP'
with (VI LcuP = L;;;(T) = Ag; Description Entire system
phase Liq Cu-fee
Cu-rich alloys
Liq Cu-fee
V -;;_ 1 2 0
(VI ACuP
(9) BCuP
:
-71364.8 -34678.3 -39831.5 -25827.2 -34523.3 -29849.3
+3.88871 +44.11335 0.00000 +48.30795 -82.73254 0.00000
0 1 2 0 1 2
-115660.2 -63275.0 83061.8 -95074.4 -905.6 0.0
66.84010 -59.09494 0.0 -55.84886 42.44433 0.0
Figures 1 and 2 present comparisons of the calculated and measured phase diagram and relative chemical potential of P in the liquid phase at 1473 K for the coefficient set corresponding to the Cu-rich region of the system. Figures 3 and 4 show the calculated enthalpy and entropy of mixing curves for the liquid phase (ref. state: liq) for that description. FIG. 1 Calculated phase diagram of the Curich region of the system Cu-P in comparison with experimental data +(4)
THERMODYNAMIC
EVALUATION OF THE Cu-P SYSTEM
FIG.
2
Calculated and measured relative chemical potential of P in the liquid phase at 1473 K + (5)
-:t
26 XP
FIG. 3 Calculated enthalpy of mixing of the liquid phase at 1473 K (Ref.: liq)
-10.8 -
-3&B-35.8 " 0.0
0
)
0 6.1
I( XP
1
" 6.2
1 0.26
Comparison of the calculated phase equilibria with the diagram presented by Hansen (4) shows excellent agreement. The calculated eutectic lies at 978.5 K and xGu = 0.039, xbig = 0.154, which represents a deviation of less than 0.5 K and 0.5 at % from the experimental information. The melting temperature of Cu3P is calculated to be 1269.9 K as compared with the experimental value of 1295 K (17). The 25 K difference has been accepted in view of the limited and inconsistent experimental information. 0.1
FIG. 4 Calculated entropy of mixing of Cu-rich liquid Cu-P alloys at 1473 K (Ref.: liq)
-16.0 -
J 6.2
il. I XP
6.26
Activities of P determined by Iwase (5) were well reproduced by this analytical description, as shown in Figure 2.
270
S. AN MEY
andP.J. SPENCER
For information with respect to higher phosphorus concentration ranges the second coefficient set must be used. Figure 5 shows a comparison of the complete calculated phase diagram with the experimental phase boundary information presented by Hansen (4) and by Ugai (17). This second description leads to a copper-rich eutectic at 978.8 K, xf;u = 0.037 and xbiq = 0.140. The difference between the calculated and experimental liquidus in equilibrium with Cu3P is perhaps less serious than might appear, because the measured liquidus temperatures lead to an improbably sharp peak at the melting point of Cu3P. This is not consistent with thermodynamic requirements. Calculated melting temperatures and three-phase equilibria in the system are listed in table 4, which includes a comparison with experimental information. Figures 6 and 7 show the good agreement between calculated and measured chemical potentials of Cu and P in the liquid phase at 1473 X. Figures 8 to 10 present the calculated thermodynamic mixing functionsAG, AH andAS for the liquid phase at the same temperature. WhileAG and AH are negative over the whole composition range,AS shows significant positive values at higher P-concentrations. This can possibly be attributed to the breaking up of stable Pg-type bonding in liquid phosphorus when it is alloyed with copper. FIG. 5 Calculated phase diagram of Cu-P in comparison with data from the literature +(4), x(17) (The dashed curve indicates vapour pressure of 1 bar.)
IAl x
x
x
,
*
1
#.Y
*
8.6 XP
a.0
I.1
FIG. 6 Chemical potential of Cu and P in the liquid at 1473 K in comparison with the measured values (Ref.: liq) +(5), x(7)
THERMODYNAMIC
EVALUATION OF THE Cu-P SYSTEM
271
FIG. 7 Relative chemical potential of phosphorus in the Cu-rich liquid at 1473 K +(5)
:::i.....
i3.e
0.62
6.66
6.6u
0.06
6. lff
XP
FIG.
B
Gibbs free energy of mixing of liquid Cu-P alloys at 1473 K (Ref.: liq)
-25.0 -
.r.d
e.0
3
’ 0.2
’
t 0-u
*
g 0.6
’
’ 0.6
s
’
I.0
XP
FIG.
9
Enthalpy of mixing of liquid Cu-P at 1473 K
XP
272
S.ANMEYandF'.J.SPENCER
FIG. 10 Entropy of mixing of liquid Cu-P at 1473 K
6.1 -
:
6.U-
.T u :
1.6-
7 \
:2.a-
i;;
.:I: ‘0.n
6.2
0.u
XP
8.6
0. II
l.u
The coefficient set for the entire system includes three compounds, the coefficients of which are given in Table 2. The resulting standard enthalpies and entropies of formation as well as enthalpies of fusion are listed in Table 5. Comparison with Bf data reported by Gordienko (3) for Cu3P and Cup2 shows good agreement, the deviation being about 4000 J/g-at. This lies within the limits of experimental error. Agreement with the values given by Kubaschewski (8) is less satisfactory, but this may be due to confusions in the standard state used for phosphorus, as referred to earlier. The calculated S298 value for CUP is in excellent agreement with the value proposed by Kubaschewski while S 296 for Cu3P shows a discrepancy of 6.4 or 3.4 J/K g-atom respectively. To check the phosphorus partial pressures implied by the present evaluation of the Cu-P system, thermodynamic data for the P4, P2 and P gas species were taken from the Barin-Knacke Tables (1). These were combined with the data set for the entire system to carry out total equilibrium calculations using the program SAGE (2). It was found that the gas phase reaches a pressure of 1 bar at approximately 2200 K in Cu-rich alloys, at about 1900 K for xp 3 0.2 and at 1400 K for xp = 0.4. The calculated 1 bar total pressure curve at higher concentrations is included in the phase diagram (figure 5). The calculated phosphorus pressures lie within the error limits of experimentally reported values (3, 7, 171, reaching 18 atm at xp = 0.666 and 1164 K (17) or pP2 = 0.2 atm at xP = 0.291 and T = 1475 K (7).
THERMODYNAMIC
EVALUATION
OF THE Cu-P SYSTEM
TABLE
273
4
Characteristic equilibria in the Cu-P system calculated using the coefficients set for the entire system in comparison with experimental information Equilibrium
X’
x’
0.140 0.157 0.250
0.037 0.035 0.250
0.250 0.250
0.400 0.490 0.667 0.667 0.667 0.778 0.954
0.250 0.250 0.667 0.667 0.771 0.778 0.778
0.667 0.667
liq = fee + Cu3P liq = Cu3P liq = Cu3P + CUP2 liq = Cup2 liq = CUP2 + CU2P7 liq = cu2p7 liq = Cu2P7 + P(R)
’
x’
I
I
0.778 1.000
T/K 978.8 987. 1271 .l 1295. 1042.9 1106. 1182.4 1164. 1125.8 1126.1 824.3 863.
Ref. * (4) * (4) * (17) * (17) * * * (17)
* this work TABLE 5 Enthalpies of formation and of fusion and entropy values in comparison with literature data in J, mol of atoms, Ref. state: red P phase Cu3P
T/K 298 298 298 298
AHf
ASf
-12329. -18420 -16300. -27900.
5.7 2.6
s
Cu2p7
298 298 298 1182 298 1126 work,
Ref.
36.2 33.2 29.8
1271 1270
CUP2
a*fus
7374. 7713. -26693.
1.4
-22300. -18400.
27.6 27.2
28897. -20556
3.3
28.4
25662.
e tire * thi syste ** this work, description for Cu-rich alloys
5. Summary A thermodynamic evaluation of the Cu-P system has been carried out using experimental thermodynamic and phase diagram information. Two sets of optimised coefficients are presented in this work. The first set provides a good description of all measured properties for Cu-rich alloys, while the second represents a more general analytical description of the entire system. Calculated data using both sets of coefficients are compared with experimental information. Acknowledaement The financial support of the Deutsche Forschungsgemeinschaft contract Sp 23313-l is greatfully acknowledged.
under
274
S. AN MEV
andP.J. SPENCER
Reference8 1. I. Barin, 0. Xnacke, 0. Xubaschewski, Thermochemical properties of inorganic substances, Suppl. Springer Verlag, Berlin, Heidelberg, New York (1977) Erfksson, IC.Hack, to be published in Calphad
2.
G.
3.
S.P.
Gordienko, G.Sh. Viksman, Soviet. Powder Metall. 2, 573 - 575 (1985)
4. M. Hansen, X. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York (1958) 5. M. Jwask, E. Ichise, N. Yamada, Steel Research j&
319 - 326 (1985)
6. JANAF, Thermochemical Tables, Distributed by Clearinghouse for Federal and Technical Information, Addendum (1966) 7. J. Xramss, M.G. Frohberg, J. Pijtschke,2. Metallkde. $,& 532 - 536 (1971) 8. 0. Xubaschewski, C.B. Alcock, Metallurgical Thermochemistry, 5th Ed., Pergamon Press, O~ford/N.Y./Toronto/Sydney/Paris/Frankfurt (1979) 9. 0. Xubaschewski, piv. communication, 1987 10. D. Liidecke,X. Hack, 2. Metallkde. x,
145 - 151 (1986)
11. H.L. Lukas, E.-Th. Henig, B. Zinunermann,Calphad I, 225 - 236 (1979.) 12.
M.H. lvrijller, W. Yeitschko, 2. anorg. allg. Chem. m,
225 - 236 (1982)
13. 0. Olofsson, Acta Chem. Stand. 19, 229 - 241 (1965) 14.
S.
an Mey,
K.
Hack, 2. Metallkde. 77, 454 - 459 (1986)
15. P.J. Spencer, Calphad 1Q, 175 - 185 (1986) 16. Ya.A. Ugai, O.Ya. Gukov, Izv. Akad. Nauk SSSR, Neorg. Mater., -
599 (1969)
1 i3),
17. Y~.A. Hgai, V.R. Pshestanchik, O.Ya. Gukov, V.Z. Anokhin, Akad. Nauk SSSR, Neorg. Mater., 8 (61, 1015 - 1018 (1972) 18, F. weibke, G. Schrag, 2. Elektrochem. 42, 228 - 238 (1941)
598
CALPHAD
1990
0364-5916190 $3.00 + .OO (c) 1990 Pergamon Press plc
A THERMODYNAMIC EVALUATION OF THE COPPER-PHOSPHORUS
SYSTEM
Sabine an Mey, Philip J. Spencer Lehrstuhl fiirTheoretische Hiittenkunde und Metallurgic der Kernbrennstoffe, RNTH Aachen D-5100 Aachen, Germany
ABSTRACT. A critical thermodynamic evaluation of available, experimental information for the system Cu-P has been carried out. The representation of measured data by optimised coefficients of a polynomial function in composition and temperature leads to an analytical description of the thermodynamic properties of Cu-P, which allows both thermodynamic functions or phase equilibria for the system to be calculated. The extent of the agreement between calculated and measured properties is discussed.
1.
Introduction
A knowledge of the thermodynamic properties of the copper-phosphorus system is of importance for Cu-metallurgy, P being present in a number of commercially-important copper alloys. This work provides a theoretical basis for calculations related to the application of such alloys as well as for calculations in higher-order systems involving Cu and P. 2. Method of Calculation Experimental information on phase equilibria in the Cu-P system, together with results from thermodynamic measurements on Cu-P alloys, were used as input for a computer-aided evaluation procedure which results in the optimised analytical description of the system presented below. As described on several previous occasions (e.g. 10, 14, 15) the program written by Lukas et al. (11) was again used in the present work. No further discussion of the method will therefore be given here. The analytical expression used for the Gibbs energy of the pure elements and the stoichiometric compound phases was 3 G(T) = a + bT + CT In T + dT2 + eT + f/T while for the excess-properties of the solution phases the excess Gibbs energy of mixing was described by the Redlich-Kister equation AG~(x~,T)
=
xi
xj
f u=o
(x
i
-
x.1 3
3
Lw ij
with i = Cu; j = P. ____________________-----Received 22 August 1989.
265
(T)
S. AN
MEY andP.J. SPENCER
3. Exnerimental Information from the Literature The analytical description for pure Cu was derived from the Janaf Tables (6) (see table 1). Considerable confusion has arisen in the literature over the years due to choice of either white or red phosphorus by different data compilers as reference state for tabulated enthalpies of formation of phosphides. This has led to incorrectly reported values in many subsequent publications where the authors concerned have not taken the appropriate reference state into account. In this work, red phosphorus has been chosen as reference state since it is the form used in experimental enthalpy measurements on copper phosphides. No change in reference state is necessary, therefore, in treating the experimental numbers. Gibbs energy data for red-phosphorus were given by Kubaschewski (9). TABLE 1 Gibbs free energy of the pure elements G(T) =a+bT+cTlnT+dT'
+eT
3 +f$
phase
a
b
Cu-Liq P-Liq
-48.7 9041.4
173.91101
-31.380000
135.12040
-26.317400
8:
Cu-fee P-fee P(K)
-8044.1 31167.1 -5651.9
135.25700 106.86710
-24.853001 -16.736000 -16.736000
-.189325 -.744750 -.744750
93.72910
C
J/m01
d.102
e
f 8:
0. 0. 0.
69455. 8:
Measurement of properties of the Cu-P system for concentrations above xp = 0.25 are complicated by the high phosphorus partial pressures in this region. A phase diagram for the W-rich region of the Cu-P system is presented by Hansen (4), who reviewed experimental information for compositions up to XP = 0.25. For higher P-concentrations Hansen simply presents a vaporisation curve. In 1971 Ugai et al. (17) investigated the concentration region between 0.25 < XP < 0.667 using thermal analysis with the aid of a Kurnakov pyrometer. They published a T-x-projection of the Cu-P phase diagram at equilibrium pressure. As this phase diagram provides the only experimental indication of the liquidus in this region, it was included in the experimental input data used for the optimisation program. Even the extrapolated liquidus (up to pure P) presented by these authors was accepted, although with considerably less weight. In the Cu-P system, the compounds Cu3P, Cup2 and more recently, Cu2P7 have been found to exist (3, 4, 12, 13, 16, 18). Ugai (17) found that Cu3P has a homogenity range which extends to XP = 0.275 at 973 K, while Olofsson (13) reports that Cup2 has a "very small homogenity range". In the present work, all compounds are treated as stoichiometric. Ugai (16, 17) has reported melting temperatures for Cu3P and Cup2 and Gordienko et al. (3) have determined the enthalpies of formation of these two compounds at 298 K using mass-spectrometric analysis. Kubaschewski (8) cites older calorimetric values for&98 of Cu3P and Cup2 and has additionally estimated S2g8 values for both compounds. These data have been included with a lower weighting in the present evaluation.
THERMODYNAMIC EVALUATION OF THE Cu-P SYSTEM
267
No information for the melting temperature or for the enthalpy of formation of Cu2P7 has been found. The only thermodynamic information for the liquid phase is provided by experimental determinations of the activity of P in Cu-rich alloys (5,7). Krams et al. (7) used an isopiestic method to determine activities at about 1473 K and 0.25 < XP ( 0.30 with white phosphorus as reference state. Iwad et al. (5) determined activities at 1473, 1523 and 1573 K for alloys up to x = 0.01 using a solid-oxide galvanic cell. 4. Results and Discussiop There are very large inaccuracies in the available experimental information for the Cu-P system at compositions greater than xp = 0.25. Although this was taken into consideration during the optimisation procedure, it was not possible to obtain a satisfactory representation of the more reliable experimental results in the Cu-rich part of the phase diagram and at the same time obtain thermodynamically sensible results on the P-rich side of the system. Two sets of coefficients have therefore been derived, one which provides an optimum representation of data in the region up to xp = 0.25, and a second set which represents a compromise description of all the experimental information. The first description is particularly important in relation to practical applications in Cu-metallurgy. However, it should not be applied to concentrations xp ? 0.25. The second description represents a thermodynamic survey of the entire system. In this case, greater discrepancies on the Curich side had to be accepted to enable all the experimental information mentioned above to be included in the evaluation. The Gibbs energy coefficients for the compounds obtained from the two evaluations are listed in Table 2; the coefficients for the excess Gibbs energies of the liquid and Cu-fee phase are given in Table 3. TABLE 2 Gibbs free energies of the compounds in the Cu-P system J/m01 of atoms G(T) = a * b T + c T In T + d T2 +eT3+ phase
a
b
C
d 102
Evaluated coefficients from a consideration of the Cu3P -19777.7 119.25207 -22.832895 -.328180 CUP2 -32551.0 92.88499 -17.459452 -.559625 C"2p7 -26411.3 92.27973 -17.439720 -.621335
f-
1
T
e
f
entire system: 0.
52091.5
0. 0.
23151.5 15434.5
Evaluated coefficients from a consideration of Cu-rich alloys only: Cu3P -25251.7 114.52276 -21.680485 -.418400 0. 0.0
268
SAN MEYand PJ.SPENCER
TABLE 3 Excess Gibbs energies of the solution phases in the Cu-P system J/m01 AcE
= xcu xP
v
(v) LcuP
+ Bg;
T
(x cu - xP'
with (VI LcuP = L;;;(T) = Ag; Description Entire system
phase Liq Cu-fee
Cu-rich alloys
Liq Cu-fee
V -;;_ 1 2 0
(VI ACuP
(9) BCuP
:
-71364.8 -34678.3 -39831.5 -25827.2 -34523.3 -29849.3
+3.88871 +44.11335 0.00000 +48.30795 -82.73254 0.00000
0 1 2 0 1 2
-115660.2 -63275.0 83061.8 -95074.4 -905.6 0.0
66.84010 -59.09494 0.0 -55.84886 42.44433 0.0
Figures 1 and 2 present comparisons of the calculated and measured phase diagram and relative chemical potential of P in the liquid phase at 1473 K for the coefficient set corresponding to the Cu-rich region of the system. Figures 3 and 4 show the calculated enthalpy and entropy of mixing curves for the liquid phase (ref. state: liq) for that description. FIG. 1 Calculated phase diagram of the Curich region of the system Cu-P in comparison with experimental data +(4)
THERMODYNAMIC
EVALUATION OF THE Cu-P SYSTEM
FIG.
2
Calculated and measured relative chemical potential of P in the liquid phase at 1473 K + (5)
-:t
26 XP
FIG. 3 Calculated enthalpy of mixing of the liquid phase at 1473 K (Ref.: liq)
-10.8 -
-3&B-35.8 " 0.0
0
)
0 6.1
I( XP
1
" 6.2
1 0.26
Comparison of the calculated phase equilibria with the diagram presented by Hansen (4) shows excellent agreement. The calculated eutectic lies at 978.5 K and xGu = 0.039, xbig = 0.154, which represents a deviation of less than 0.5 K and 0.5 at % from the experimental information. The melting temperature of Cu3P is calculated to be 1269.9 K as compared with the experimental value of 1295 K (17). The 25 K difference has been accepted in view of the limited and inconsistent experimental information. 0.1
FIG. 4 Calculated entropy of mixing of Cu-rich liquid Cu-P alloys at 1473 K (Ref.: liq)
-16.0 -
J 6.2
il. I XP
6.26
Activities of P determined by Iwase (5) were well reproduced by this analytical description, as shown in Figure 2.
270
S. AN MEY
andP.J. SPENCER
For information with respect to higher phosphorus concentration ranges the second coefficient set must be used. Figure 5 shows a comparison of the complete calculated phase diagram with the experimental phase boundary information presented by Hansen (4) and by Ugai (17). This second description leads to a copper-rich eutectic at 978.8 K, xf;u = 0.037 and xbiq = 0.140. The difference between the calculated and experimental liquidus in equilibrium with Cu3P is perhaps less serious than might appear, because the measured liquidus temperatures lead to an improbably sharp peak at the melting point of Cu3P. This is not consistent with thermodynamic requirements. Calculated melting temperatures and three-phase equilibria in the system are listed in table 4, which includes a comparison with experimental information. Figures 6 and 7 show the good agreement between calculated and measured chemical potentials of Cu and P in the liquid phase at 1473 X. Figures 8 to 10 present the calculated thermodynamic mixing functionsAG, AH andAS for the liquid phase at the same temperature. WhileAG and AH are negative over the whole composition range,AS shows significant positive values at higher P-concentrations. This can possibly be attributed to the breaking up of stable Pg-type bonding in liquid phosphorus when it is alloyed with copper. FIG. 5 Calculated phase diagram of Cu-P in comparison with data from the literature +(4), x(17) (The dashed curve indicates vapour pressure of 1 bar.)
IAl x
x
x
,
*
1
#.Y
*
8.6 XP
a.0
I.1
FIG. 6 Chemical potential of Cu and P in the liquid at 1473 K in comparison with the measured values (Ref.: liq) +(5), x(7)
THERMODYNAMIC
EVALUATION OF THE Cu-P SYSTEM
271
FIG. 7 Relative chemical potential of phosphorus in the Cu-rich liquid at 1473 K +(5)
:::i.....
i3.e
0.62
6.66
6.6u
0.06
6. lff
XP
FIG.
B
Gibbs free energy of mixing of liquid Cu-P alloys at 1473 K (Ref.: liq)
-25.0 -
.r.d
e.0
3
’ 0.2
’
t 0-u
*
g 0.6
’
’ 0.6
s
’
I.0
XP
FIG.
9
Enthalpy of mixing of liquid Cu-P at 1473 K
XP
272
S.ANMEYandF'.J.SPENCER
FIG. 10 Entropy of mixing of liquid Cu-P at 1473 K
6.1 -
:
6.U-
.T u :
1.6-
7 \
:2.a-
i;;
.:I: ‘0.n
6.2
0.u
XP
8.6
0. II
l.u
The coefficient set for the entire system includes three compounds, the coefficients of which are given in Table 2. The resulting standard enthalpies and entropies of formation as well as enthalpies of fusion are listed in Table 5. Comparison with Bf data reported by Gordienko (3) for Cu3P and Cup2 shows good agreement, the deviation being about 4000 J/g-at. This lies within the limits of experimental error. Agreement with the values given by Kubaschewski (8) is less satisfactory, but this may be due to confusions in the standard state used for phosphorus, as referred to earlier. The calculated S298 value for CUP is in excellent agreement with the value proposed by Kubaschewski while S 296 for Cu3P shows a discrepancy of 6.4 or 3.4 J/K g-atom respectively. To check the phosphorus partial pressures implied by the present evaluation of the Cu-P system, thermodynamic data for the P4, P2 and P gas species were taken from the Barin-Knacke Tables (1). These were combined with the data set for the entire system to carry out total equilibrium calculations using the program SAGE (2). It was found that the gas phase reaches a pressure of 1 bar at approximately 2200 K in Cu-rich alloys, at about 1900 K for xp 3 0.2 and at 1400 K for xp = 0.4. The calculated 1 bar total pressure curve at higher concentrations is included in the phase diagram (figure 5). The calculated phosphorus pressures lie within the error limits of experimentally reported values (3, 7, 171, reaching 18 atm at xp = 0.666 and 1164 K (17) or pP2 = 0.2 atm at xP = 0.291 and T = 1475 K (7).
THERMODYNAMIC
EVALUATION
OF THE Cu-P SYSTEM
TABLE
273
4
Characteristic equilibria in the Cu-P system calculated using the coefficients set for the entire system in comparison with experimental information Equilibrium
X’
x’
0.140 0.157 0.250
0.037 0.035 0.250
0.250 0.250
0.400 0.490 0.667 0.667 0.667 0.778 0.954
0.250 0.250 0.667 0.667 0.771 0.778 0.778
0.667 0.667
liq = fee + Cu3P liq = Cu3P liq = Cu3P + CUP2 liq = Cup2 liq = CUP2 + CU2P7 liq = cu2p7 liq = Cu2P7 + P(R)
’
x’
I
I
0.778 1.000
T/K 978.8 987. 1271 .l 1295. 1042.9 1106. 1182.4 1164. 1125.8 1126.1 824.3 863.
Ref. * (4) * (4) * (17) * (17) * * * (17)
* this work TABLE 5 Enthalpies of formation and of fusion and entropy values in comparison with literature data in J, mol of atoms, Ref. state: red P phase Cu3P
T/K 298 298 298 298
AHf
ASf
-12329. -18420 -16300. -27900.
5.7 2.6
s
Cu2p7
298 298 298 1182 298 1126 work,
Ref.
36.2 33.2 29.8
1271 1270
CUP2
a*fus
7374. 7713. -26693.
1.4
-22300. -18400.
27.6 27.2
28897. -20556
3.3
28.4
25662.
e tire * thi syste ** this work, description for Cu-rich alloys
5. Summary A thermodynamic evaluation of the Cu-P system has been carried out using experimental thermodynamic and phase diagram information. Two sets of optimised coefficients are presented in this work. The first set provides a good description of all measured properties for Cu-rich alloys, while the second represents a more general analytical description of the entire system. Calculated data using both sets of coefficients are compared with experimental information. Acknowledaement The financial support of the Deutsche Forschungsgemeinschaft contract Sp 23313-l is greatfully acknowledged.
under
274
S. AN MEV
andP.J. SPENCER
Reference8 1. I. Barin, 0. Xnacke, 0. Xubaschewski, Thermochemical properties of inorganic substances, Suppl. Springer Verlag, Berlin, Heidelberg, New York (1977) Erfksson, IC.Hack, to be published in Calphad
2.
G.
3.
S.P.
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319 - 326 (1985)
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225 - 236 (1982)
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1 i3),
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598