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Coupled phase diagrams and thermochemical data for transition metal binary systems-III
CALPHAD Vo1.2, No.2, pp.117-146. 8 Pergamon Press Limited, 1978. Printed in Great Britain.
COUPLEDPHASE DIAGRAMSAND THERMOCHEMICAL DATA FOR TRANSITION METAL BINARY SYSTEMS-III* Larry Kaufman ManLabs, Inc., 21 Erie Street Cambridge, Massachusetts 02139, USA
ABSTRACT.
A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper, which is part of a series, details the following twelve binary systems: titanium-manganese, chromium-manganese, iron-manganese, cobalt-manganese, manganese-nickel, copper-manganese, titanium-copper, cobalt-copper, copper-chromium, iron-copper, nickel-copper and niobium-copper. This brings the total of such systems covered to thirty-seven. This paper together with the past and projected contributions will cover other binary members in order to permit calculation of a sufficiently wide range of ternary systems. 1.
Introduction
Previous papers in the current series (l-3) provide descriptive information covering twenty-five binary systems composed of titanium, chromium, iron, cobalt, nickel, niobium, molybdenum and tungsten. The present paper includes binary systems containing manganese and copper thus enlarging the data base. Future contributions will extend this list to cover carbon, aluminum and silicon. Thus lattice stability descriptions of manganese and copper are presented below which when coupled with those presented earlier (l-3) and with excess free energy and compound formation data permit characterization of specific ternary systems. 2.
Lattice
Stability
Values
Tables 1 and 2 provide lattice stability values for manganese and copper as well as the elements discussed earlier with respect to the P(8Mn) and K(aMn) structures. The current series of binary systems display wide ranges of temperature and composition over which the P(8Mn) and K(oMn) structures are stable. As a consequence, it is necessary to treat these phases as solutions and to specify the lattice stability of the P and K structures for the binary partners of manganese. These lattice stabilities, which are shown in Tables 1 and 2 for copper, titanium, chromium, iron, cobalt and nickel were obtained by analyses of their respective binary systems and are the first such estimates developed for the metals in question. Accordingly, they will be treated as provisional values and will be modified in the future as required. Comparison of the numerical values shown in Tables 1 and 2 for the lattice stability of the P and K structures (as compared with the fee, bee or hcp forms) does not disclose any unusual behavior.
*
This work has been sponsored by the Metallurgy Program, Metallurgy and Materials Section, Division of Materials Research, National Science Foundation, Washington D.C. under Grant DMR76-08453.
117
L. Kaufman
118
TABLE
1
LATTICE STABILITY VALUES FOR THE ELEMENTS* (4) _=-=_=-=-=_=-=_=-=-=_ (Units of J/mol and J/m01 K will be used throughout)
(L=Liquid. P=Primative Cubic-8Mn, K=Complex Cubic-aMn)
Element
o&o&-=
Mn
cu
*
E-m
=
Temperature Range (K)
14644-9.6233
1220 < T
oGL_oGhcp =
9205-7.1131
1220 < T
.&_op
=
16401-10.8781
1220 < T
oGbcc_yp
=
3975-2.887T
1220 < T
OGP_$ =
2259-2.259T
1220 < T
oGfcc_oGbcc =
1477-0.51400T-2.7420(E-3)T2+1.6534(E-6)T3
400 < T < 1220
opt _OGP =
611+13.101T-2.1240(E-2)T2+0.8396(E-5)T3
400 < T < 1220
o&o&-
6778-6.2761
300 c T
oGbcc_oGfcc =
6276-3.347T
300 < T
o$cp_o(;bcc =
-5648+4.602T
300 < T
0CfCC_OCP =
-2218
300 < T
yP_yK
-3640+2.510T
300 < T
=
10srn
=
=
119
TRANSITION METAL BINARY SYSTEMS - III
TABLE
2
LATTICE STABILITY VALUES FOR THE ELEMENTS*
(Units of J/m01 and J/m01 K will be used throughout)
Element
(P=PrimativeCubic-8Mn, K=Complex Cubic-aMn) .CfCC - OCP =
Ti
-4184
300 < T
=
2929
300 < T
0G-P =
-5439
300 < T
OCP _ OCK
OGfCC-
Cr
Fe
co
Ni
*
E-m
Temperature Range (K)
yp _ OGK =
4812 - 2.0921
300 < T
0CfCC - OCP =
-1151 - 0.837T
300 < T
OCP _ OCK
-418 + 0.167T
300 < T
.CfCC _ OCP =
-4443-9.045T+1.7218(E-2)T2-0.67509(E-5)T3
300 < T
OCP - OCK
-3347 + 1.841T
300 < T
0CfCC - OCP =
-2092
300 < T
OCP - OCK
-1464
300 < T
=
I,,-”
=
=
=
-6874
Ti0.333?0.667
(LavesPhase)
-3870
TiO.5oo”“o. 500
AH = H-x&~~~-x&~&
AS =
-xTix14,,1569
KC&l
Compound
0
-xTi~10042
P(BW
3.530
3.421
xTik9.205
0
-xTih2720
fee
0
0
0
+R[~i'~i+~~~I
ES+ = S&TioS;i-~oS~
xTik23012
0
-xTix14J2552
EH9 = H$Ti'H&4n"I$n
hcp
bee
Liquid
Phase 0
~LYTICAL DESCRIPTIONOF TEE TIT~I~-THESE
TABLE 3
x& = 0.333
qi = 0.500
Composition
O
o
06x&l
ki&l
0$x&l
O
Composition Range
SYSTEM
8 = hcp
8 = bee
Comments
400,
lOOO
1200.sT,<1500 ' Refers to fee
400,
800
1400cT~2000 'Refersto Liquid
Comments
z
=I H
k? I
F;:
!!
!j
E
g
4
E E ..
Cro.210Mno.790
1.862
1.388
-3332
-3316
xk
x&
= 0.790
= 0.667
Composition
AS = S-X&$,-X~~S~
O-'h-'l
' AH = H-x& OH' Cr_x* ~ oHMn
Cr0.333Mn0.667
Compound
+xCrb6.276
-xCrk3096
o
O-
-xCrxMn10.46
-xcrxMn17573
fee
O
Composition Range
-xCrk3096
-xCrxMn10.46
-xCrxMn8786
bee
-xCrxMn10.46
+R[xC,Q-lxCr+s~~n$J
ES@ = SO_"Cr~S$Mn%~
-xCrx&2552
EH$ = H$CroH$Mno$
Liquid
Phase 10
ANALYTICAL DESCRIPTION OF THE CHROMIUM-MANGANESE SYSTEM
TABLE 4
e = bee
f3= bee
Comments
400
8006 T& 1500 o Refers to 8Mn
12006 T,<1500 o Refers to fee
400$T,< 2200 o Refers to bee
lSOO\
Comments
L. Kaufman
122
The Titanium-Manganese
3.
System
Table 3 shows the analytical description of the titanium-manganese system which can be coupled with the lattice stability values to compute the The former is shown in Figure 1 phase diagram and thermochemical properties. where it is compared with the observed diagram (5-8). The present analytical description supercedes an earlier version (9) which dealt with a limited porThe latter was used successfully to calculate the ternary tion of the system. system Ti-Mn-Mo in-good agreement with observations (9). The Chromium-Manganese
4.
System
Table 4 displays the analytical description of the chromium-manganesl system which can be employed to compute the phase diagram shown in Figure 2 fo. As in the forgoing titanium comparison with the observed phase diagram [S-8). thermochemical data could be located for commanganese case, no experimental parison with the values which can be computed on the basis of the analytical description shown in Table 4. 5.
The Iron-Manganese
System
The iron-manganese system is characterized by extensive solid solufee, bcc,.BMn(P) and.oMn(K) phases are stable. Prc tion ranges where the liquid, vious analyses (10,ll) have considered only limited composition ranges or deal. Experimental thermochemical with no more than three of the stable phases. data are available for the fee and liquid phases. Table 5 summarizes the experimental thermochemical data (8) provided by the compilation of Hultgren, et.al. The analytical description of the liquid, bee, fee, BMn(P) and oMn(K) phases of the iron-manganese system presented in Table 6 can be employed to calculate the thermochemical properties and the phase diagram which is compared with the observed phase diagram (5-8) in Figure 3. The computed ironmanganese phase diagram shown in Figure 3 is obtained by coupling the free energy of mixing equations specified in Table 6 with the lattice stability values for the liquid, bee, fcc,P and K forms of manganese and iron provided ir Tables 1 and 2 above and in the earlier referenced work (1,2). Recent experimental work by Hayes (12), who measured the vapor pressure of fee iron-manganese alloys at 1350K suggests that the minimum excess Gibbs energy of formation This value is more negative than either in this system is about -800 J/mol. the experimental thermochemical results listed in Table 5 or the values calculated from the analytical expressions given in Table 6. Both sets of result! suggest that the excess free energy of mixing of fee iron-manganese alloys at 1350K is positive with a maximum excess of free energy of mixing near 1000 J/mol. The difference between this result and the value suggested by Hayes (12) lies within the stated uncertainty limits shown in Table 5. TABLE 5 DATA FOR IRON-MANGANESE EXPERIMENTALTHERMOCHEMICAL ALLOYS (8)
0.1 00.: 0:4 ^ _ :::
EHfcc -___-1314 -3431 -2456
(145OK)______:___ -1.238 -3.167 -2.297
-4204 -4728?1674 -4925 -4690 -3895 -2389
-3.837 -4.255+0.837 -4.372 -4.113 -3.381 -2.054
EGL (13$3K) 703 924 1054 1100?1674 1054 924 703 397
L. Kaufman
123
124
L. Kaufman
xFex&-9665xFe-5021xJ
K(ati)
.~ . -.--___
xFex&-18870)
EH' = H$-xFeoH;e-x&&
fee
bee
Liquid
Phase 0
L
,*I
.___,_
._._
..
.I
.1..
-
.”
.-,
-_-u
-
-.I
__L, ,“,
400< T,<1200 'Refers to aMn
06X
xFek[-7.782xFe-2.510%]
-2.9204x10-3T]
800~T<1500 'Refers to 8Mn O,
xFexh[-11.326xFe-5.217%
300,
300&T< 2000 'Refers to bee
1500&T,< 2000 ORefers to Liquid
Comments
O,
O,
Composition Range
-xFeh16.987
-xFeh16.987
ES+ = S@_x FeoS~e-xMnos!& +R]xFe~nxFe+~an~]
ANALYTICAL DESCRIPTION OF THE IRON-MANGANESE SYSTEM
TABLE 6
126
L. Kaufman
a
127
TRANSITION METAL BINARY SYSTEMS - III
6.
The Cobalt-Manganese System
Experimental thermochemical data for coablt-manganese alloys (8) is shown in Table 7. Table 8 provides an analytical description of the system which can be coupled with the lattice stability provided earlier to calculate the thermochemical properties as well as the phase diagram shown in Figure 4 for comparison with the observed phase diagram (5-8). TABLE
7
EXPERIMENTAL THERMOCHEMICAL DATA FOR COBALT-MANGANESE ALLOYS AT 1023K (8) xcoCofCC
+
xMnMnP-+ CoxcoMn~~~
(0.1
xcoCofcc
+
xMnMnP-+ CoxCoMnzMn
(0.64
P = 8Mn Structure
XMn
AG
AG
'Mn
0.10
-4904
0.20 0.30 0.40
AG
XMn
0.50
-11498
0.70
-10397
-7941
0.60
-11305
0.80
-8289
-9912 -11054+1464
0.63 0.64
-11125 -11054
0.90
-4979
Recent experimental measurement of the excess free energy of mixing of fee Co-Mn alloys by Hayes (12) suggests that the minimum excess free energy of formation of Co-Mn alloys at 1350 is -4500 J/mol. This compares with a value of -5577 J/mol derived from the analytical descriptions in Tables 1 and 8. The experimental values at 1023K shown in Table 7 yield a minimum excess free energy of formation of -5594 J/mol. 7.
The Manganese-Nickel System
Table 9 summarizes the experimental thermochemical data available for the manganese-nickel system (8). Table 10 displays the analytical description of the liquid, fee, bee, P, K and compound phases which can be coupled with the lattice stability values presented earlier to compute the phase diagram shown in Figure 5 and the thermochemical properties. The former is compared with the experimental phase diagram (5-8) in Figure 5. TABLE
9
EXPERIMENTAL THERMOCHEMICAL- DATA FOR MANGANESE-NICKEL ALLOYS AT 1050K (8) xMnMnP+ xNiNi
fee
NifCC
-+Mn 'Mn
XNi 0.21 0.30 0.40
AG -10669 -13765 -16339
AH -3573 -6791 -10711
XNi 0.42 0.57 0.60
(P = %Mn structure)
'Ni AG
-16786 -17820 -17602
AH -18318 -14489 -14393
XNi 0.70 0.80 0.90
AG -15882 -12050 -7527
AH -12966 -9272 -5418
128
L.
Kaufman
Figure
CO
-
c
4.
The
Calculated
Cobalt-Manganese
(a)
System.
1000
fee
1500
2000
2500
‘T°K
(b)
Observed
Liquid
(S-8)
bee
Mn
-
Compound
fee
Liquid
Phase Q
x$ si
-0.557 -2.040
-16777
"I%
+1.360
si
"ii
= 0.750
= 0.667
= 0.500
= 0.333
= 0.250
Composition
06xNi61
o*xNixl
-18891
+1.302
-17.730
e AS = S-x* OS8 Mn Mn-%iosNi
-xMnxNi17.991
-xMnxN.#3178xMn+39330xNi]
AH = H-x&'&-xii?-&
-xMnxNi17.991
-xMnxNi[63178xh+39330xNi]
O
e = fee
e = fee
8 = bee
8 = fee
8 = K(aMn)
Comments
400
7006T<1500 o Refers to @tn
300< Td1800 ' Refers to fee
1200
06Si61
-xMnxNi3.640
-.xMnXNi10.878
1200qT,<1800 o Refers to Liquid
Comments
OCxNi'l
Composition Range
.xMnxNi10.878
+R[xMnKnxMn+xNillnxNil
Es@ = s%MnOs~-xNi's~i
-xMnxNiW32xMn+64434xNi]
EHe = HI$xMnO&-xNioH&
ANALYTICAL DESCRIPTION OF THE MANGANESE-NICKEL SYSTEM
TABLE 10
Figure
5.
The Manganese-Nickel
Liquid
System.
1000
1500
2000
2500
T”K
(b)
Observed
(5-8)
L. Kaufman
132
8. The Copper-ManganeseSystem Table 11 summarizes the experimental thermochemicaldata for the copper-manganesesystem (8). Table 12 shows the analytical description of the solution phases in this system which can be coupled with the lattice stability values to compute the thermochemicalproperties and the phase diagram which is compared in Figure 6 with the observed phase diagram (S-8). The starting point for the present analysis was the discussion presented in reference (4). TABLE 11 EXPERIMENTAL THERMOCHEMICALDATA FOR COPPER-MANGANESEALLOYS (8) xMn 0.1 0.2 0.3 0.4 0.5
EHfcc (1100K) 1004 1908 2544 2933 3197k418
EGfcc (UOOK) -118 -50 276 720tl464 1209
9.
EGL (1500K) -473 -267 +405 +1222 +1992*418
EHfcc EGfcc EGL (1100K) (11OOK) (1550K) +2632 0.6 3644 1669 +3020 0.7 4221 1987 +2958 0.8 4586 2004 -*-0.885 3012 1606 ------+513 0.9 'Mn
The Copper-TitaniumSystem
Table 13 summarizes the limited experimental thermochemicaldata currently available for the copper-titaniumsystem. The analytical description shown in Table 14 when coupled with the lattice stability values provided nreviouslv nermits calculation of the thermochemicalproperties as well as the-phase d&gram which is shown in Figure 7 where it is compared with the observed phase diagram (5-8). TABLE 13 EXPERIMENTAL THERMOCHEMICALDATA FOR COPPER-TITANIUM ALLOYS (8) xCuCuL + xTiTiL + 0.1 TiL xCu 'Ti 'Ti 0.86 0.93
(L = Liquid)
AG (1800K) -5891*167 -3924
xCuCufcc + xTiTibCC + CuxCuTi~~~
XTi 0.905 0.950
AG (1473K) -3234+105 -2092
TRANSITION METAL BINARY SYSTEMS - III
8 w
r
133
134
L. Kaufman
0
0
-9310
-5055
AS = S-X~~~S~~-X*~~~S~~
-1.580
AH = H-x;~~H;~-x&~H;~
Compound
-9142
xTixCu [‘6O’I
fee 0
“&I
“&I
0.333
= 0.770
= 0.500
“&l =
Composition
o
OCXcu"l
0
hcp
O-
0
xTixCu [s’s’1
bee
Osxcu
Composition Range
0
+R[xTiLnxTi+xCulnxCu]
$ ES@ = S$_x .yj._x Ti Ti CuosC"
xTixCu[-17573XTi_11715xcu]
EH+ = HI$-xTiOl$i-xCuOH~u
Liquid
Phase 0
TABLE 14 ANALYTICAL DESCRIPTION OF THE TITANIUM-COPPER SYSTEM
8 = fee
e = fee
6 = bee
Comments
300
300xT<1400 "Refers to hcp
800
lOOO
Comments
136
L. Kaufman
TRANSITION METAL BINARY SYSTEMS - III
10.
137
The Cobalt-Copper System
Table 15 shows the experimental thermochemical data presently available for cobalt-copper alloys (8). The analytical description shown in Table 16 when combined with the lattice stability values provided earlier permits calculation of the thermochemical properties and the phase diagram. The latter, shown in Figure 8, is compared with the observed phase diagram (5-8). TABLE
15
EXPERIMENTAL THERMOCHEMICAL DATA FOR COBALT-COPPER ALLOYS (8)
xcu
ECfcc
EHL
(1300K)
(14733) ___
0.050
1636
0.093
2778
0.947 0.950
1652*418 -_11.
1565+628
The Copper-Chromium System
Table 17 provides the analytical description of the copper-chromium system which can be employed to compute the thermochemical properties and the phase diagram. The latter which is compared in Figure 9 with the observed phase diagram (5-8) shows a miscibility gap in the liquid with a critical point at 1947K and 58% Cr. 12.
The Iron-Copper System
Table 18 displays the experimental thermochemical data presently available for the iron-copper system (8). Recently, Kubaschewski, Smith and Bailey (14) carried out an extensive analysis of this system. Their analytical description of the system is shawn in Table 19. Combination of the latter with the lattice stability values presented earlier permits calculation of the thermochemical properties and the phase diagram shown in Figure 10 (14). TABLE
18
EXPERIMENTAL THERMOCHEMICAL DATA FOR IRON-COPPER ALLOYS AT 1823K (8) xcu
EHL
0.1
3975
0.548
ESL
0.2
6535
0.757
0.3
8021
0.774
0.4
8757
0.728
0.5
8920?418
0.678kO.334
0.6
8506
0.590
0.7
7485
0.460
0.8
5803
0.305
0.9
3364
0.159
0
xcoxcu[29288xco+31798xcu]
fee
xcuxcr104600
~~u~~~104600
fee
-1.67912T+4.24914x10-4T2)]
+2.83276~10-~T~)+6778Ox~~]
bee
~~ux~~[16.736x~~+x~u(1613.6
xCuxCr]xCu(1032150-0.83956T2
Liquid
0
0
+R[xCu~nxCu+xCr~nxCrl
EsQ = &XCuOS~u-xcrOS~,
EH' = H$xCuoH;u-xCroH;,
Phase +
ANALYTICAL DESCRIPTION OF THE COPPER-CHROMIUM SYSTEM
TABLE 17
0
xcoxcu[29288xco+31798xcu]
xcoxcu[8.368xco+16.736xcu]
+R[xCo~nxCo+xCu~nxCul
$ ES@ = S _x + co"Sco-xcuoScu
bcp
= ~-xCoO~~o-xCuO~~u
xcoxcu[40166xco+53555xcu]
E$ H
Liquid
Phase * $
ANALYTICAL DESCRIPTION OF THE COBALT-COPPER SYSTEM
TABLE 16
Cr"
06 XCrGl
O
o
Composition Range
OQXCu\
o
O
Composition Range
400
lOOO
1300,
Comments
a Refers to fee 400cTc1800
o Refers to hcp 400*:T<8DO
o Refers to Liquid 1300~T61800
Comments
TRANSITION METAL BINARY SYSTEMS - III
+
+
139
140
L. Kaufman
141
TRANSITION METAL BINARY SYSTEMS - III
It is interesting to compare the analyses of the fee copper-iron (14) with those described in CALPHAD 1 phase presented by Kubaschewski et.al. Reference to Table 19 shows that 37-40,1977 by Hillert (15) and Brewer (16). th excess free energy of mixing of the fee phase of the iron-copper system, ECycc, can be described by Equation (1) as ECfcc
the
= xFexCu[(54124-13.4637T)xFe
The analysis performed following description shown ECfcc
= xFexCu[
Brewer’s ECfcc
+(42288-3.429T)xCU]
by Harvig, by Equation
Kirchner (2)
and Hillert
(41119-4.376T)xFe+(58290-14.47T)xCU]
result
(16)
is
given
by Equation
(J/mol) (15)
(1) yields
(J/mol)
(2)
(3)
= ~F~~C~[(37620-2.13T)~F~+(41800-2.13T)xC~]
(J/mol)
(3)
ECfcc by the three individual analyses Although the Equations for evaluation of the numerical coefficients of the xFe and xCu terms differ, within the braces at 1250K do not differ substantially, thus Equation (1) yields 37294 and 38001 respectively while Equation (2) yields 35647 and 40207 and Equation (3) yields 34953 and 39133. (1) - (3) should yield Thus, Equations nearly the same numerical values for the excess free energy of mixing of the fee iron-copper phase in the temperature range of interest. 13.
The Copper-Nickel
System
Table 20 summarizes the experimental thermochemical data for nickel-copper alloys (8). An analytical description for the liquid and fee phases in this system is given in Table 21. The latter can be combined with the lattice stability values provided earlier to compute the phase diagram shown in Figure 11 as well as the thermochemical properties. The calculated miscibility gap critical point at 615K and 32% Cu is in reasonable agreement with the critical point calculated at 595K and 20% Cu by Elford, Mueller and Kubaschewski (17). Figure 11 compares the calculated diagram with the observed phase diagram (5-8). 14.
The Niobium-Copper
System
Table 22 displays the analytical description of the niobium-copper system. Combining these results with the lattice stability values provided earlier, permits calculation of the thermochemical properties and the phase diagram which is compared in Figure 12 with the observed phase diagram (5-8).
h
02
QL Q6 0,8 Mole Fraction. NFe
Fe
Comparison of the calculated equilibrium diagram Mid lines) with experimental data for the binary F&u system. 0 Hansen phase diagram’) (bars in range 0.3 d NFs B 0.7 indicate k 15Kl Figure 10 (14) A Spaich at al.
j’=fCC=E , cr=bcc=d,
LIQ=Liquid
~~~~~_[36134x~~+32508xC,
Liquid
fee
xFe+j8070xCu
xFexCu[54124xFe+42288xCU]
-0.21597T2+1.74832x10-4T3
-xFex&33930
+7565(xFe-xCu)2+2418(xFe-xCJ3]
EH+ = Hkx M FeoH!e-XCuoHk
Phase +
bee
19
xFexCu[13.4637xFe+3.4292xCU]
+2.62248~10-~T~-0.5326xlO-~T~]
-xFexCu[217.482xFe+238.754xC,-0.43194T
(~~~-x~J~+2.34777(x~~-x~~)~]
xFexCu[3.50012xFe+0.21758xCu+2.58626times
+RtxFeanxFe+xCuLnxCul
Es+ = S~-xFeOS;e-XC"OS~u
ANALYTICAL DESCRIPTION OF THE IRON-COPPER SYSTEM (14)
TABLE
cu
41
o\
06X
O&XCu"l
Composition Range
400~ T\<1800 o Refers to fee
1041\
1300s T,<1900 o Refers to Liquid
Comments
E
TABLE
22
&lx ] +R[xNi&nx Ni+XCu Cu
0 ES@ = S@ _x .o,$ Ni NimXCuoSCu
EHe = ~-xNbo~b-xC~ 00 NC_
XNbXCul11294
xNbxCu46024
98742 xNbxCu
Liquid
bee
fee
41.84 'NbXCu
0
xNbxCu41.84
+R[x knx ] NbanxNb+XCu Cu
Es4= s+-xNb%~b-xcuos~u
ANALYTICAL DESCRIPTION OF THE NIOBIUM-COPPER SYSTEM
xNixcu[11632xNi+2469xcu]
+' EH@ = H+-x .'H@__x M Ni Ni Cu'HCu
Phase Ip
fCC
Liquid
Phase QI
21
ANALYTICAL DESCRIPTION OF THE NICKEL-COPPER SYSTEM
TABLE
xcu’<
1
1
0$X
cu
$1
OQXCu"c1
OSXCu
Composition Range
0-S xcu’<
04
Composition Range
300dT,<1400 'Refers to fee
3004 T,<2800 "Refers to bee
1200,
Comments
300,
1200~ Tc1800 'Refers to Liquid
Comments
E
144
L. Kaufman
145
TRANSITION METAL BINARY SYSTEMS - III
,
I
146
L. Kaufman
TABLE
20
EXPERIMENTAL THERMOCHEMICAL DATA FOR NICKEL-COPPER ALLOYS (a)
xCU
EHfcc
ESfcc (973K)
EGL (18233)
0.1
971
-0.602
1092
0.2
1582
-0.962
1941
0.3
la79
-1.125
2548
0.4
1929
-1.146
2912
0.5
177ak418
-1.067+0.460
3033*418
0.6
1485
-0.925
2900
0.7
1109
-0.749
2494
0.8
694
-0.519
1820
0.9
310
-0.272
958
(L=Liquid)
References 1.
L. Kaufman, CALPHAD L
2.
L. Kaufman and H. Nesor, CALPHAD 2, 59 (1978).
7 (1977).
3.
L. Kaufman and H. Nesor, CALPHAD 2, 81 (1978).
4.
L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams Academy Press, New York (1970).
5.
M. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw Hill, New York, (1958).
6.
R. P. Elliott and F. Shunk, First and Second Supplements (Ibid) (1965), (1969).
7.
D. T. Hawkins and R. Hultgren, Metals Handbook S 251 American Society for Metals, Metals Park, Ohio (1973).
a.
R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser and K. K. Kelly, Selected Values of the Thermodynamic Properties of Metals (and of Binary Alloys) (2 Volumes) ASM, Metals Park, Ohio (1973).
9.
L. Kaufman and H. Nesor, Annual Review of Materials Science, R. A. Huggin R. H. Bube and R. W. Roberts, Editors 3, (1973). Annual Reviews Inc., Palo Alto, California.
10.
J. F. Breedis and L. Kaufman, Met. Trans. 2. 2359 (1971).
11.
G. Kirchner, T. Nishazawa and B. Uhrenius, Met. Trans. 4, 167 (1973).
12.
F. H. Hayes, CALPHAD 1, 295 (1977).
13.
J. M. Vitek and H. Warlimont, Metal Science (1976)pp7-13
14.
0. Kubaschewski, J. F. Smith and D. M. Bailey, Zeit. f. Metallkunde -68 495 (1977).
15.
H. Harvig, G. Kirchner and M. Hillert, Met. Trans. 2 329 (1972).
16.
L. Brewer, CALPHAD 1, 39 (1977).
17.
L. Elford, F. Mueller and 0. Kubaschewski, Ber Bunsenger Physik Chem., -73 601 (1969).
COUPLEDPHASE DIAGRAMSAND THERMOCHEMICAL DATA FOR TRANSITION METAL BINARY SYSTEMS-III* Larry Kaufman ManLabs, Inc., 21 Erie Street Cambridge, Massachusetts 02139, USA
ABSTRACT.
A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper, which is part of a series, details the following twelve binary systems: titanium-manganese, chromium-manganese, iron-manganese, cobalt-manganese, manganese-nickel, copper-manganese, titanium-copper, cobalt-copper, copper-chromium, iron-copper, nickel-copper and niobium-copper. This brings the total of such systems covered to thirty-seven. This paper together with the past and projected contributions will cover other binary members in order to permit calculation of a sufficiently wide range of ternary systems. 1.
Introduction
Previous papers in the current series (l-3) provide descriptive information covering twenty-five binary systems composed of titanium, chromium, iron, cobalt, nickel, niobium, molybdenum and tungsten. The present paper includes binary systems containing manganese and copper thus enlarging the data base. Future contributions will extend this list to cover carbon, aluminum and silicon. Thus lattice stability descriptions of manganese and copper are presented below which when coupled with those presented earlier (l-3) and with excess free energy and compound formation data permit characterization of specific ternary systems. 2.
Lattice
Stability
Values
Tables 1 and 2 provide lattice stability values for manganese and copper as well as the elements discussed earlier with respect to the P(8Mn) and K(aMn) structures. The current series of binary systems display wide ranges of temperature and composition over which the P(8Mn) and K(oMn) structures are stable. As a consequence, it is necessary to treat these phases as solutions and to specify the lattice stability of the P and K structures for the binary partners of manganese. These lattice stabilities, which are shown in Tables 1 and 2 for copper, titanium, chromium, iron, cobalt and nickel were obtained by analyses of their respective binary systems and are the first such estimates developed for the metals in question. Accordingly, they will be treated as provisional values and will be modified in the future as required. Comparison of the numerical values shown in Tables 1 and 2 for the lattice stability of the P and K structures (as compared with the fee, bee or hcp forms) does not disclose any unusual behavior.
*
This work has been sponsored by the Metallurgy Program, Metallurgy and Materials Section, Division of Materials Research, National Science Foundation, Washington D.C. under Grant DMR76-08453.
117
L. Kaufman
118
TABLE
1
LATTICE STABILITY VALUES FOR THE ELEMENTS* (4) _=-=_=-=-=_=-=_=-=-=_ (Units of J/mol and J/m01 K will be used throughout)
(L=Liquid. P=Primative Cubic-8Mn, K=Complex Cubic-aMn)
Element
o&o&-=
Mn
cu
*
E-m
=
Temperature Range (K)
14644-9.6233
1220 < T
oGL_oGhcp =
9205-7.1131
1220 < T
.&_op
=
16401-10.8781
1220 < T
oGbcc_yp
=
3975-2.887T
1220 < T
OGP_$ =
2259-2.259T
1220 < T
oGfcc_oGbcc =
1477-0.51400T-2.7420(E-3)T2+1.6534(E-6)T3
400 < T < 1220
opt _OGP =
611+13.101T-2.1240(E-2)T2+0.8396(E-5)T3
400 < T < 1220
o&o&-
6778-6.2761
300 c T
oGbcc_oGfcc =
6276-3.347T
300 < T
o$cp_o(;bcc =
-5648+4.602T
300 < T
0CfCC_OCP =
-2218
300 < T
yP_yK
-3640+2.510T
300 < T
=
10srn
=
=
119
TRANSITION METAL BINARY SYSTEMS - III
TABLE
2
LATTICE STABILITY VALUES FOR THE ELEMENTS*
(Units of J/m01 and J/m01 K will be used throughout)
Element
(P=PrimativeCubic-8Mn, K=Complex Cubic-aMn) .CfCC - OCP =
Ti
-4184
300 < T
=
2929
300 < T
0G-P =
-5439
300 < T
OCP _ OCK
OGfCC-
Cr
Fe
co
Ni
*
E-m
Temperature Range (K)
yp _ OGK =
4812 - 2.0921
300 < T
0CfCC - OCP =
-1151 - 0.837T
300 < T
OCP _ OCK
-418 + 0.167T
300 < T
.CfCC _ OCP =
-4443-9.045T+1.7218(E-2)T2-0.67509(E-5)T3
300 < T
OCP - OCK
-3347 + 1.841T
300 < T
0CfCC - OCP =
-2092
300 < T
OCP - OCK
-1464
300 < T
=
I,,-”
=
=
=
-6874
Ti0.333?0.667
(LavesPhase)
-3870
TiO.5oo”“o. 500
AH = H-x&~~~-x&~&
AS =
-xTix14,,1569
KC&l
Compound
0
-xTi~10042
P(BW
3.530
3.421
xTik9.205
0
-xTih2720
fee
0
0
0
+R[~i'~i+~~~I
ES+ = S&TioS;i-~oS~
xTik23012
0
-xTix14J2552
EH9 = H$Ti'H&4n"I$n
hcp
bee
Liquid
Phase 0
~LYTICAL DESCRIPTIONOF TEE TIT~I~-THESE
TABLE 3
x& = 0.333
qi = 0.500
Composition
O
o
06x&l
ki&l
0$x&l
O
Composition Range
SYSTEM
8 = hcp
8 = bee
Comments
400,
lOOO
1200.sT,<1500 ' Refers to fee
400,
800
1400cT~2000 'Refersto Liquid
Comments
z
=I H
k? I
F;:
!!
!j
E
g
4
E E ..
Cro.210Mno.790
1.862
1.388
-3332
-3316
xk
x&
= 0.790
= 0.667
Composition
AS = S-X&$,-X~~S~
O-'h-'l
' AH = H-x& OH' Cr_x* ~ oHMn
Cr0.333Mn0.667
Compound
+xCrb6.276
-xCrk3096
o
O-
-xCrxMn10.46
-xcrxMn17573
fee
O
Composition Range
-xCrk3096
-xCrxMn10.46
-xCrxMn8786
bee
-xCrxMn10.46
+R[xC,Q-lxCr+s~~n$J
ES@ = SO_"Cr~S$Mn%~
-xCrx&2552
EH$ = H$CroH$Mno$
Liquid
Phase 10
ANALYTICAL DESCRIPTION OF THE CHROMIUM-MANGANESE SYSTEM
TABLE 4
e = bee
f3= bee
Comments
400
8006 T& 1500 o Refers to 8Mn
12006 T,<1500 o Refers to fee
400$T,< 2200 o Refers to bee
lSOO\
Comments
L. Kaufman
122
The Titanium-Manganese
3.
System
Table 3 shows the analytical description of the titanium-manganese system which can be coupled with the lattice stability values to compute the The former is shown in Figure 1 phase diagram and thermochemical properties. where it is compared with the observed diagram (5-8). The present analytical description supercedes an earlier version (9) which dealt with a limited porThe latter was used successfully to calculate the ternary tion of the system. system Ti-Mn-Mo in-good agreement with observations (9). The Chromium-Manganese
4.
System
Table 4 displays the analytical description of the chromium-manganesl system which can be employed to compute the phase diagram shown in Figure 2 fo. As in the forgoing titanium comparison with the observed phase diagram [S-8). thermochemical data could be located for commanganese case, no experimental parison with the values which can be computed on the basis of the analytical description shown in Table 4. 5.
The Iron-Manganese
System
The iron-manganese system is characterized by extensive solid solufee, bcc,.BMn(P) and.oMn(K) phases are stable. Prc tion ranges where the liquid, vious analyses (10,ll) have considered only limited composition ranges or deal. Experimental thermochemical with no more than three of the stable phases. data are available for the fee and liquid phases. Table 5 summarizes the experimental thermochemical data (8) provided by the compilation of Hultgren, et.al. The analytical description of the liquid, bee, fee, BMn(P) and oMn(K) phases of the iron-manganese system presented in Table 6 can be employed to calculate the thermochemical properties and the phase diagram which is compared with the observed phase diagram (5-8) in Figure 3. The computed ironmanganese phase diagram shown in Figure 3 is obtained by coupling the free energy of mixing equations specified in Table 6 with the lattice stability values for the liquid, bee, fcc,P and K forms of manganese and iron provided ir Tables 1 and 2 above and in the earlier referenced work (1,2). Recent experimental work by Hayes (12), who measured the vapor pressure of fee iron-manganese alloys at 1350K suggests that the minimum excess Gibbs energy of formation This value is more negative than either in this system is about -800 J/mol. the experimental thermochemical results listed in Table 5 or the values calculated from the analytical expressions given in Table 6. Both sets of result! suggest that the excess free energy of mixing of fee iron-manganese alloys at 1350K is positive with a maximum excess of free energy of mixing near 1000 J/mol. The difference between this result and the value suggested by Hayes (12) lies within the stated uncertainty limits shown in Table 5. TABLE 5 DATA FOR IRON-MANGANESE EXPERIMENTALTHERMOCHEMICAL ALLOYS (8)
0.1 00.: 0:4 ^ _ :::
EHfcc -___-1314 -3431 -2456
(145OK)______:___ -1.238 -3.167 -2.297
-4204 -4728?1674 -4925 -4690 -3895 -2389
-3.837 -4.255+0.837 -4.372 -4.113 -3.381 -2.054
EGL (13$3K) 703 924 1054 1100?1674 1054 924 703 397
L. Kaufman
123
124
L. Kaufman
xFex&-9665xFe-5021xJ
K(ati)
.~ . -.--___
xFex&-18870)
EH' = H$-xFeoH;e-x&&
fee
bee
Liquid
Phase 0
L
,*I
.___,_
._._
..
.I
.1..
-
.”
.-,
-_-u
-
-.I
__L, ,“,
400< T,<1200 'Refers to aMn
06X
xFek[-7.782xFe-2.510%]
-2.9204x10-3T]
800~T<1500 'Refers to 8Mn O,
xFexh[-11.326xFe-5.217%
300,
300&T< 2000 'Refers to bee
1500&T,< 2000 ORefers to Liquid
Comments
O,
O,
Composition Range
-xFeh16.987
-xFeh16.987
ES+ = S@_x FeoS~e-xMnos!& +R]xFe~nxFe+~an~]
ANALYTICAL DESCRIPTION OF THE IRON-MANGANESE SYSTEM
TABLE 6
126
L. Kaufman
a
127
TRANSITION METAL BINARY SYSTEMS - III
6.
The Cobalt-Manganese System
Experimental thermochemical data for coablt-manganese alloys (8) is shown in Table 7. Table 8 provides an analytical description of the system which can be coupled with the lattice stability provided earlier to calculate the thermochemical properties as well as the phase diagram shown in Figure 4 for comparison with the observed phase diagram (5-8). TABLE
7
EXPERIMENTAL THERMOCHEMICAL DATA FOR COBALT-MANGANESE ALLOYS AT 1023K (8) xcoCofCC
+
xMnMnP-+ CoxcoMn~~~
(0.1
xcoCofcc
+
xMnMnP-+ CoxCoMnzMn
(0.64
P = 8Mn Structure
XMn
AG
AG
'Mn
0.10
-4904
0.20 0.30 0.40
AG
XMn
0.50
-11498
0.70
-10397
-7941
0.60
-11305
0.80
-8289
-9912 -11054+1464
0.63 0.64
-11125 -11054
0.90
-4979
Recent experimental measurement of the excess free energy of mixing of fee Co-Mn alloys by Hayes (12) suggests that the minimum excess free energy of formation of Co-Mn alloys at 1350 is -4500 J/mol. This compares with a value of -5577 J/mol derived from the analytical descriptions in Tables 1 and 8. The experimental values at 1023K shown in Table 7 yield a minimum excess free energy of formation of -5594 J/mol. 7.
The Manganese-Nickel System
Table 9 summarizes the experimental thermochemical data available for the manganese-nickel system (8). Table 10 displays the analytical description of the liquid, fee, bee, P, K and compound phases which can be coupled with the lattice stability values presented earlier to compute the phase diagram shown in Figure 5 and the thermochemical properties. The former is compared with the experimental phase diagram (5-8) in Figure 5. TABLE
9
EXPERIMENTAL THERMOCHEMICAL- DATA FOR MANGANESE-NICKEL ALLOYS AT 1050K (8) xMnMnP+ xNiNi
fee
NifCC
-+Mn 'Mn
XNi 0.21 0.30 0.40
AG -10669 -13765 -16339
AH -3573 -6791 -10711
XNi 0.42 0.57 0.60
(P = %Mn structure)
'Ni AG
-16786 -17820 -17602
AH -18318 -14489 -14393
XNi 0.70 0.80 0.90
AG -15882 -12050 -7527
AH -12966 -9272 -5418
128
L.
Kaufman
Figure
CO
-
c
4.
The
Calculated
Cobalt-Manganese
(a)
System.
1000
fee
1500
2000
2500
‘T°K
(b)
Observed
Liquid
(S-8)
bee
Mn
-
Compound
fee
Liquid
Phase Q
x$ si
-0.557 -2.040
-16777
"I%
+1.360
si
"ii
= 0.750
= 0.667
= 0.500
= 0.333
= 0.250
Composition
06xNi61
o*xNixl
-18891
+1.302
-17.730
e AS = S-x* OS8 Mn Mn-%iosNi
-xMnxNi17.991
-xMnxN.#3178xMn+39330xNi]
AH = H-x&'&-xii?-&
-xMnxNi17.991
-xMnxNi[63178xh+39330xNi]
O
e = fee
e = fee
8 = bee
8 = fee
8 = K(aMn)
Comments
400
7006T<1500 o Refers to @tn
300< Td1800 ' Refers to fee
1200
06Si61
-xMnxNi3.640
-.xMnXNi10.878
1200qT,<1800 o Refers to Liquid
Comments
OCxNi'l
Composition Range
.xMnxNi10.878
+R[xMnKnxMn+xNillnxNil
Es@ = s%MnOs~-xNi's~i
-xMnxNiW32xMn+64434xNi]
EHe = HI$xMnO&-xNioH&
ANALYTICAL DESCRIPTION OF THE MANGANESE-NICKEL SYSTEM
TABLE 10
Figure
5.
The Manganese-Nickel
Liquid
System.
1000
1500
2000
2500
T”K
(b)
Observed
(5-8)
L. Kaufman
132
8. The Copper-ManganeseSystem Table 11 summarizes the experimental thermochemicaldata for the copper-manganesesystem (8). Table 12 shows the analytical description of the solution phases in this system which can be coupled with the lattice stability values to compute the thermochemicalproperties and the phase diagram which is compared in Figure 6 with the observed phase diagram (S-8). The starting point for the present analysis was the discussion presented in reference (4). TABLE 11 EXPERIMENTAL THERMOCHEMICALDATA FOR COPPER-MANGANESEALLOYS (8) xMn 0.1 0.2 0.3 0.4 0.5
EHfcc (1100K) 1004 1908 2544 2933 3197k418
EGfcc (UOOK) -118 -50 276 720tl464 1209
9.
EGL (1500K) -473 -267 +405 +1222 +1992*418
EHfcc EGfcc EGL (1100K) (11OOK) (1550K) +2632 0.6 3644 1669 +3020 0.7 4221 1987 +2958 0.8 4586 2004 -*-0.885 3012 1606 ------+513 0.9 'Mn
The Copper-TitaniumSystem
Table 13 summarizes the limited experimental thermochemicaldata currently available for the copper-titaniumsystem. The analytical description shown in Table 14 when coupled with the lattice stability values provided nreviouslv nermits calculation of the thermochemicalproperties as well as the-phase d&gram which is shown in Figure 7 where it is compared with the observed phase diagram (5-8). TABLE 13 EXPERIMENTAL THERMOCHEMICALDATA FOR COPPER-TITANIUM ALLOYS (8) xCuCuL + xTiTiL + 0.1 TiL xCu 'Ti 'Ti 0.86 0.93
(L = Liquid)
AG (1800K) -5891*167 -3924
xCuCufcc + xTiTibCC + CuxCuTi~~~
XTi 0.905 0.950
AG (1473K) -3234+105 -2092
TRANSITION METAL BINARY SYSTEMS - III
8 w
r
133
134
L. Kaufman
0
0
-9310
-5055
AS = S-X~~~S~~-X*~~~S~~
-1.580
AH = H-x;~~H;~-x&~H;~
Compound
-9142
xTixCu [‘6O’I
fee 0
“&I
“&I
0.333
= 0.770
= 0.500
“&l =
Composition
o
OCXcu"l
0
hcp
O-
0
xTixCu [s’s’1
bee
Osxcu
Composition Range
0
+R[xTiLnxTi+xCulnxCu]
$ ES@ = S$_x .yj._x Ti Ti CuosC"
xTixCu[-17573XTi_11715xcu]
EH+ = HI$-xTiOl$i-xCuOH~u
Liquid
Phase 0
TABLE 14 ANALYTICAL DESCRIPTION OF THE TITANIUM-COPPER SYSTEM
8 = fee
e = fee
6 = bee
Comments
300
300xT<1400 "Refers to hcp
800
lOOO
Comments
136
L. Kaufman
TRANSITION METAL BINARY SYSTEMS - III
10.
137
The Cobalt-Copper System
Table 15 shows the experimental thermochemical data presently available for cobalt-copper alloys (8). The analytical description shown in Table 16 when combined with the lattice stability values provided earlier permits calculation of the thermochemical properties and the phase diagram. The latter, shown in Figure 8, is compared with the observed phase diagram (5-8). TABLE
15
EXPERIMENTAL THERMOCHEMICAL DATA FOR COBALT-COPPER ALLOYS (8)
xcu
ECfcc
EHL
(1300K)
(14733) ___
0.050
1636
0.093
2778
0.947 0.950
1652*418 -_11.
1565+628
The Copper-Chromium System
Table 17 provides the analytical description of the copper-chromium system which can be employed to compute the thermochemical properties and the phase diagram. The latter which is compared in Figure 9 with the observed phase diagram (5-8) shows a miscibility gap in the liquid with a critical point at 1947K and 58% Cr. 12.
The Iron-Copper System
Table 18 displays the experimental thermochemical data presently available for the iron-copper system (8). Recently, Kubaschewski, Smith and Bailey (14) carried out an extensive analysis of this system. Their analytical description of the system is shawn in Table 19. Combination of the latter with the lattice stability values presented earlier permits calculation of the thermochemical properties and the phase diagram shown in Figure 10 (14). TABLE
18
EXPERIMENTAL THERMOCHEMICAL DATA FOR IRON-COPPER ALLOYS AT 1823K (8) xcu
EHL
0.1
3975
0.548
ESL
0.2
6535
0.757
0.3
8021
0.774
0.4
8757
0.728
0.5
8920?418
0.678kO.334
0.6
8506
0.590
0.7
7485
0.460
0.8
5803
0.305
0.9
3364
0.159
0
xcoxcu[29288xco+31798xcu]
fee
xcuxcr104600
~~u~~~104600
fee
-1.67912T+4.24914x10-4T2)]
+2.83276~10-~T~)+6778Ox~~]
bee
~~ux~~[16.736x~~+x~u(1613.6
xCuxCr]xCu(1032150-0.83956T2
Liquid
0
0
+R[xCu~nxCu+xCr~nxCrl
EsQ = &XCuOS~u-xcrOS~,
EH' = H$xCuoH;u-xCroH;,
Phase +
ANALYTICAL DESCRIPTION OF THE COPPER-CHROMIUM SYSTEM
TABLE 17
0
xcoxcu[29288xco+31798xcu]
xcoxcu[8.368xco+16.736xcu]
+R[xCo~nxCo+xCu~nxCul
$ ES@ = S _x + co"Sco-xcuoScu
bcp
= ~-xCoO~~o-xCuO~~u
xcoxcu[40166xco+53555xcu]
E$ H
Liquid
Phase * $
ANALYTICAL DESCRIPTION OF THE COBALT-COPPER SYSTEM
TABLE 16
Cr"
06 XCrGl
O
o
Composition Range
OQXCu\
o
O
Composition Range
400
lOOO
1300,
Comments
a Refers to fee 400cTc1800
o Refers to hcp 400*:T<8DO
o Refers to Liquid 1300~T61800
Comments
TRANSITION METAL BINARY SYSTEMS - III
+
+
139
140
L. Kaufman
141
TRANSITION METAL BINARY SYSTEMS - III
It is interesting to compare the analyses of the fee copper-iron (14) with those described in CALPHAD 1 phase presented by Kubaschewski et.al. Reference to Table 19 shows that 37-40,1977 by Hillert (15) and Brewer (16). th excess free energy of mixing of the fee phase of the iron-copper system, ECycc, can be described by Equation (1) as ECfcc
the
= xFexCu[(54124-13.4637T)xFe
The analysis performed following description shown ECfcc
= xFexCu[
Brewer’s ECfcc
+(42288-3.429T)xCU]
by Harvig, by Equation
Kirchner (2)
and Hillert
(41119-4.376T)xFe+(58290-14.47T)xCU]
result
(16)
is
given
by Equation
(J/mol) (15)
(1) yields
(J/mol)
(2)
(3)
= ~F~~C~[(37620-2.13T)~F~+(41800-2.13T)xC~]
(J/mol)
(3)
ECfcc by the three individual analyses Although the Equations for evaluation of the numerical coefficients of the xFe and xCu terms differ, within the braces at 1250K do not differ substantially, thus Equation (1) yields 37294 and 38001 respectively while Equation (2) yields 35647 and 40207 and Equation (3) yields 34953 and 39133. (1) - (3) should yield Thus, Equations nearly the same numerical values for the excess free energy of mixing of the fee iron-copper phase in the temperature range of interest. 13.
The Copper-Nickel
System
Table 20 summarizes the experimental thermochemical data for nickel-copper alloys (8). An analytical description for the liquid and fee phases in this system is given in Table 21. The latter can be combined with the lattice stability values provided earlier to compute the phase diagram shown in Figure 11 as well as the thermochemical properties. The calculated miscibility gap critical point at 615K and 32% Cu is in reasonable agreement with the critical point calculated at 595K and 20% Cu by Elford, Mueller and Kubaschewski (17). Figure 11 compares the calculated diagram with the observed phase diagram (5-8). 14.
The Niobium-Copper
System
Table 22 displays the analytical description of the niobium-copper system. Combining these results with the lattice stability values provided earlier, permits calculation of the thermochemical properties and the phase diagram which is compared in Figure 12 with the observed phase diagram (5-8).
h
02
QL Q6 0,8 Mole Fraction. NFe
Fe
Comparison of the calculated equilibrium diagram Mid lines) with experimental data for the binary F&u system. 0 Hansen phase diagram’) (bars in range 0.3 d NFs B 0.7 indicate k 15Kl Figure 10 (14) A Spaich at al.
j’=fCC=E , cr=bcc=d,
LIQ=Liquid
~~~~~_[36134x~~+32508xC,
Liquid
fee
xFe+j8070xCu
xFexCu[54124xFe+42288xCU]
-0.21597T2+1.74832x10-4T3
-xFex&33930
+7565(xFe-xCu)2+2418(xFe-xCJ3]
EH+ = Hkx M FeoH!e-XCuoHk
Phase +
bee
19
xFexCu[13.4637xFe+3.4292xCU]
+2.62248~10-~T~-0.5326xlO-~T~]
-xFexCu[217.482xFe+238.754xC,-0.43194T
(~~~-x~J~+2.34777(x~~-x~~)~]
xFexCu[3.50012xFe+0.21758xCu+2.58626times
+RtxFeanxFe+xCuLnxCul
Es+ = S~-xFeOS;e-XC"OS~u
ANALYTICAL DESCRIPTION OF THE IRON-COPPER SYSTEM (14)
TABLE
cu
41
o\
06X
O&XCu"l
Composition Range
400~ T\<1800 o Refers to fee
1041\
1300s T,<1900 o Refers to Liquid
Comments
E
TABLE
22
&lx ] +R[xNi&nx Ni+XCu Cu
0 ES@ = S@ _x .o,$ Ni NimXCuoSCu
EHe = ~-xNbo~b-xC~ 00 NC_
XNbXCul11294
xNbxCu46024
98742 xNbxCu
Liquid
bee
fee
41.84 'NbXCu
0
xNbxCu41.84
+R[x knx ] NbanxNb+XCu Cu
Es4= s+-xNb%~b-xcuos~u
ANALYTICAL DESCRIPTION OF THE NIOBIUM-COPPER SYSTEM
xNixcu[11632xNi+2469xcu]
+' EH@ = H+-x .'H@__x M Ni Ni Cu'HCu
Phase Ip
fCC
Liquid
Phase QI
21
ANALYTICAL DESCRIPTION OF THE NICKEL-COPPER SYSTEM
TABLE
xcu’<
1
1
0$X
cu
$1
OQXCu"c1
OSXCu
Composition Range
0-S xcu’<
04
Composition Range
300dT,<1400 'Refers to fee
3004 T,<2800 "Refers to bee
1200,
Comments
300,
1200~ Tc1800 'Refers to Liquid
Comments
E
144
L. Kaufman
145
TRANSITION METAL BINARY SYSTEMS - III
,
I
146
L. Kaufman
TABLE
20
EXPERIMENTAL THERMOCHEMICAL DATA FOR NICKEL-COPPER ALLOYS (a)
xCU
EHfcc
ESfcc (973K)
EGL (18233)
0.1
971
-0.602
1092
0.2
1582
-0.962
1941
0.3
la79
-1.125
2548
0.4
1929
-1.146
2912
0.5
177ak418
-1.067+0.460
3033*418
0.6
1485
-0.925
2900
0.7
1109
-0.749
2494
0.8
694
-0.519
1820
0.9
310
-0.272
958
(L=Liquid)
References 1.
L. Kaufman, CALPHAD L
2.
L. Kaufman and H. Nesor, CALPHAD 2, 59 (1978).
7 (1977).
3.
L. Kaufman and H. Nesor, CALPHAD 2, 81 (1978).
4.
L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams Academy Press, New York (1970).
5.
M. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw Hill, New York, (1958).
6.
R. P. Elliott and F. Shunk, First and Second Supplements (Ibid) (1965), (1969).
7.
D. T. Hawkins and R. Hultgren, Metals Handbook S 251 American Society for Metals, Metals Park, Ohio (1973).
a.
R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser and K. K. Kelly, Selected Values of the Thermodynamic Properties of Metals (and of Binary Alloys) (2 Volumes) ASM, Metals Park, Ohio (1973).
9.
L. Kaufman and H. Nesor, Annual Review of Materials Science, R. A. Huggin R. H. Bube and R. W. Roberts, Editors 3, (1973). Annual Reviews Inc., Palo Alto, California.
10.
J. F. Breedis and L. Kaufman, Met. Trans. 2. 2359 (1971).
11.
G. Kirchner, T. Nishazawa and B. Uhrenius, Met. Trans. 4, 167 (1973).
12.
F. H. Hayes, CALPHAD 1, 295 (1977).
13.
J. M. Vitek and H. Warlimont, Metal Science (1976)pp7-13
14.
0. Kubaschewski, J. F. Smith and D. M. Bailey, Zeit. f. Metallkunde -68 495 (1977).
15.
H. Harvig, G. Kirchner and M. Hillert, Met. Trans. 2 329 (1972).
16.
L. Brewer, CALPHAD 1, 39 (1977).
17.
L. Elford, F. Mueller and 0. Kubaschewski, Ber Bunsenger Physik Chem., -73 601 (1969).