ISSN:
0032-3888
Keywords:
Chemistry
;
Chemical Engineering
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
This paper is a sequel to an earlier one on the applicability of classical nucleation theory to second-order transitions in the Ehrenfest sense (1). In each case the approach was to obtain the critical size rc and energy barrier ΔGc for the growth of a nucleus of β-phase in an α-phase matrix by a Maclaurin series expansion of the free-energy-density g = (Gβ - Gα)/vβ as a function of θ (in BC-I) and of ΔP and Δσ in this paper where θ = (T - Tt) is the degree of undercooling and ΔP and Δσ are analogous terms for the hydrostatic pressure shift and tensile stress shift away from the equilibrium transition. The expansion coefficients were determined by the use of thermodynamic relationships. For second-order transitions, rc = 4γvβ Tt/ΔCpθ2, rc = 4γ/Δβ(Δp)2, and rc = 4γ/YαYβ(Δσ)2, respectively, for the three cases. The terms ΔCp, Δβ, and ΔY denote the differences in heat capacity, compressibility, and Young's modulus, e.g., ΔY = Yβ - Yα. The interfacial energy γαβ is denoted by γ. The activation energy barriers for the cases developed in this paper were ΔGc = (16π/3)γ3/(Δβ)2 (Δp)4 and ΔGc = (64π/3)γ3Yα2Yβ2/(ΔY)2(Δσ)4. More complicated expressions are given in the paper for the rc and ΔGc for first-order transitions. In the long run, these expressions may prove more useful than the ones for second-order because of the modifications expressions for the kinetics of transformations.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pen.760251709
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