Thermal Effects of Phase Transformations: A General Approach
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0979-HH02-01
Thermal Effects of Phase Transformations: A General Approach Alex Umantsev Natural Sciences, Fayetteville State University, 1200 Murchison Rd., Fayetteville, NC, 28301
ABSTRACT All stages of phase transformations in materials, nucleation, growth, and coarsening, are subjected to thermal effects that stem from the redistribution of energy in the system like, release of latent heat and heat conduction. The thermal effects change the rate and outcome of the transformation and may result in appearance of unusual states or phases, in particular in nanosystems. This paper is not a complete account of the theory of thermal effects; it is rather a guide through many seemingly unrelated effects in different phase transformations, which in fact have unified origin. Although the dynamical Ginzburg-Landau approach will be used for the analysis of the effects, they are robust and independent of the employed theoretical methods. Another purpose of this review is to bring these effects to the attention of experimenters and motivate them on conducting new experiments in the area of phase transitions. INTRODUCTION Phase transitions in materials occur due to symmetry changes as a result of changing external conditions, temperature, pressure, or chemical potential, and are among the most important factors that influence properties of materials. The ‘purpose’ of the transition is to achieve thermodynamic equilibrium in the system under the new external conditions. Depending on the type of symmetry changes in the system, there can be identified two types of transitions: discontinuous (first-order) and continuous (second-order), which differ in dynamics and final outcome. A very convenient way of addressing general problems of transitions is the Landau paradigm where one assumes that the free energy, in addition to temperature T, pressure and composition, is a continuous function of a set of internal parameters {ηi} associated with the symmetry changes, which are usually called the long-range order parameters (OP) [1]. The concept of OP helps one to define a phase as a locally stable state of matter homogeneous in OP. As a continuous function of its variables the free energy density f(T,η) can be expanded in powers of the OP where only terms compatible with the symmetry of the system are included: f(T,η) = f0(T) + 12 aη2 + 13bη 3 + 14 cη 4 + (1) The presence of defects (e.g. interfaces) makes the system essentially inhomogeneous even at equilibrium and imposes a certain penalty on the system in the form of the “gradient energy” contribution into the free energy:
L
F = ∫{f(T,η)+ 12κ(∇ η )2}d 3 x
(2)
Here the gradient energy is represented in the Ginzburg-Landau-Cahn-Hilliard form [1, 2] and κ is called the gradient energy coefficient. In compliance with the Zeroth law of thermodynamics, the expression for the free energy functional cannot include gradients of temperature.
(δ F)T ≡ (∂ f )T − κ ∇ 2η = 0 δη ∂η
(3)
T = const
The equilibrium states η =Ξ(T) are the extremals of the free energy functional, Eq.(2). The hom
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