Calculation of superalloy phase diagrams: Part III
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HE earlier papers in this series 1' 2 illustrated methods for calculating ternary systems based on the explicit definition of the free energy of solution and compound phases in terms of lattice stability, solution and compound parameters. In this paper several ternary systems are computed based on the description of binary systems published earlier 3-9 in accordance with o-iz and thermochemical observed phase diagram' 13-15 In addition, a series of cobalt-based binary data. systems are analyzed to provide the basis for future computation of cobalt-based ternary systems.
rium in the Nb-Cr system"2 at 1973 K and 2173 K are in better agreement with the calculated results shown in Fig. 2 than with the results observed by Kornilov et al.' 7 In spite of these differences the
1. CALCULATION OF Ni -Nb-W ISOTHERMAL SECTIONS Previous analyses of the Nb-Ni 5 and Ni -W 9 systems were employed to synthesize the Ni -Nb-W ternary system. The excess free energy of mixing of the bcc and liquid phases in the Nb-W system were assumed identical with those in the Nb -Mo system. $ The free energy of ternary solutions is defined from a knowledge of the component binary systems on the basis of the Koehler 2 ' s -8 No ternary terms are added! Equation." Fig. 1 compares calculated sections at 2073 K and 2173 K with those observed by Allibert, Wicker, Driole and Bonnier 16 who presented ternary tie lines in addition to phase boundaries. The comparison between calculated and observed results shown in Fig. 1 is excellent over the entire composition range except at the nickel rich end of the L/L+BCC field on the W -Ni edge. The latter discrepancy is due to inaccuracy in the calculation s which is the result of ignoring the shallow maximum in the FCC/LIQUID trajectory in the NiW system 1° and approximating the FCC/LIQUID/BCC equilibrium by a peritectic.
III
Fig. 1—Comparison of calculated and observed 16 isothermal sections in the Ni -Nb-W system.
2. CALCULATION OF THE Nb-Cr-Ti SYSTEM The analyses of the Nb-Ti, 3 ' 4 Nb-Cr 5 and Ti-Cr 5 systems performed earlier were combined to calculate isothermal sections in the Nb-Cr-Ti system shown in Figs. 2 and 3. The latter are compared with experimental results reported by Kornilov, Shakhova and Budberg. 17 It should be pointed out that the most recent experimental studies of the BCC/LIQUID equilib-
RG 1973 ° K (talc.)
BCC
METALLURGICAL TRANSACTIONS A
Cobs.)
BCC a= (Nb,ri)cr Zx=(rm,Ti)crZ L*T
LIQUID
LARRY KAUFMAN is Director of Research and HARVEY NESOR is Senior Scientist, both at Manlabs, Inc., Cambridge, Mass. 02139. Manuscript submitted January 31, 1975.
1973°K
Ti
LIQUID +BCC
L+a LIQDID+BCC
Cr
Fig. 2—Comparison of calculated and observed 17 isothermal sections in the Nb-Cr-Ti system. VOLUME 6A, NOVEMBER 1975-2115
m
Cr
Nb
Cr
BCC 1773°K (obs.)
1700°K
1500°K
(cal c.)
(talc.)
X+L +BCC
BCC
n BCC+1
L
X+L +BCC
BCC
BCC +L
BCC +L+L
DIS
BCC L BCC
FCC 1 1
L
BCC+L+a
Fe
Cr
L
r
^I Ti(Fe,Cr)2
1573 ° K Cobs.)
1273K (c o ls.)
BCC
a
1273°K (obs.)
^(
&BCC u+r+BCC
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