Advances in Chemical Physics, Vol.11 (Interscience, 1967) by I. (editor) Prigogine

By I. (editor) Prigogine

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POINT-DEFECT INTERACTIONS I N SOLIDS 21 exist semi-invariants M,(xl) and M,(x2), then from Eq. (45) + + Mn(x, 4 Mn(4 Mn(4 (48) Therefore in the semi-invariant expansion of two independent variables there appear no cross terms in any semi-invariant Mn(xl + x 2 ) . The result is easily generalized to n independent variables. In Eq. (42) F may be considered as a random variable in the coordinates of the N, defects. The distribution law is that every defect can take up any one of the sites on its sublattice with equal probability and independently of the positions s f the other defects.

Comparison of Eqs. 38 A. R. 24 eV in order that the two correction terms differ by less than 10%. g. 0 eV in copper) the correction due to the vacancy-pair term is unimportant for much smaller values of -F21 so that differences are not practically very important. The terms of order ( c t ) 3 are more difficult to compare and the numerical values depend on the relative magnitudes of F ( 2 )and F((123}),as can be seen by noting that the sum of products of f-functions in B3 is equivalent to exp (pF({123))) - [ f 1 2 f 1 3 f f l 2 f 2 3 + f23f31 + + + + 1' fi2 f23 f31 whereas the mass action expression (Eq.

The interaction energies F(n)appearing in Eq. (67)are all zero when two of the defects of n are on the same site. 2a A. R. ALLNATT B. Other Thermodynamic Functions Once the cluster expansion of the partition function has been made the remaining thermodynamic functions can be obtained as cluster expansions by taking suitable derivatives. Of particular interest are the expressions for the equilibrium concentrations of intrinsic point defects for the various types of lattice disorder. Since the partition function is a function of N,, N,, V , and T , it is convenient for the derivation of these expressions to introduce defect chemical potentials for each of the species in the set (N, + N,) defined, by analogy with ordinary Gibbs chemical potentials (cf.

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