Computation of thermodynamic properties of multi-component solutions: Extension of toop model
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Fig. 2 - - G e n e r a l nature of migration markings in a sample initially subjected to eight cycles at 583 K followed by four additional cycles with an intermediate hold time 10 min. DE represents the position of the boundary prior to migration.
leads to serrated boundary profiles in pure metals in the absence of second phase particles. Previous investigations on high temperature fatigue have also reported observations of serrated boundaries in C u 6'7 and Pb. 8 Snowden 7 observed serrated boundaries at 500 ~ in commercial purity copper after 104 cycles at a strain amplitude of - 0 . 1 0 pct. The serrations were associated with the intersection of slip bands with grain boundaries. Saegusa and Weertman 6 resolved finer serrations (5 to 15 /xm) in fatigued copper than the ones observed by Snowden, using replicas and electron microscopy. Under the conditions employed in this study, slip bands were largely absent and therefore this mechanism for the development for serrations is not considered important here. The second important conclusion is based on the demonstration that the serrated profile of the boundary is retained in the course of cyclic deformation. This conclusion is also valid for the situation when an intermediate hold time at the test temperature is included in the test schedule.
REFERENCES 1. C.H. White: The Nimonic Alloys, W. Betteridge and J. Heslop, eds., Edward Arnold, London, 1974, p. 82. 2. J.M. Larson and S. Floreen: Metall. Trans. A, 1977, vol. 8A, p. 51. 3. J. Beddoes and W. Wallace: Metallography, 1980, vol. 13, p. 85. 4. A. K. Koul and D. D. Morphy: Microstruct. Sci., 1982, vol. 11, p. 79. 5. A. K. Koul and R. Thamburaj: Metall. Trans. A, 1985, vol. 16A, p. 17. 6. T. Saegusa and J.R. Weertman: Scripta Met., 1978, vol. 12, p. 187. 7. K.U. Snowden: Metals Forum, 1981, vol. 4, p. 106. 8. K. U. Snowden: Phil. Mag., 1966, vol. 14, p. 1019.
Thermodynamic properties of systems which are made up of more than three components are difficult and time consuming to determine experimentally. Since most systems of interest commercially, such as slags, are multi-component systems, and since the number of systems that can be formed from a given number of components is very large, methods of computing rather than measuring their thermodynamic properties are required. Toop 1 developed a model for computing the thermodynamic properties of ternary, nonregular solutions from the knowledge of the thermodynamic properties of the three corresponding binary solutions. Toop used the composition paths shown in Figure 1 which are defined by:
Xc = constant XA/Xs = constant
[ 1]
The Toop equation for the excess integral property of a ternary solution G ~ c is given by:
rxac.
G~c = i l -Xc
Ac + 1
2
X_"x]
c Ggc Xc
E
+ (1 - Xc) [GAs]XA/XB
[21
C
X
A/
X A/X a
B
Fig. 1 - - Ternary system showing path of constant mole fraction of component C and path of constant ratio of mole fractions of A and B.
E. JIRAN, formerly Undergraduate Student at the University of Toronto, is Graduate Student in the Department of
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