Thermodynamics of Interface Motion

An interface has an effective driving pressure if its displacement decreases the total system s free energy. This effective pressure can derive from any mechanism by which a material stores energy, but for many cases it arises from only two sources the volumetric free-energy differences between the interface s adjacent phases, and mechanical pressure differences due to reduction of the interfacial energy. 

The conditions and kinetic equations for phase transformations are treated in Chapters 17 and 20 and involve local changes in free-energy density. The quantification of thermodynamic sources for kinetically active interface motion is approximate for at least two reasons. First, the system is out of equilibrium (the transformations are not reversible). Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic case) can exist and because the thermal con- 

Kinetics of Materials. By Robert W. Balluffi, Samuel M. Allen, and W. Craig Carter. 285 Copyright 2005 John Wiley Sons, Inc. 

For a liquid/crystal interface that moves as the undercooled liquid crystallizes at temperature T, a model for nphase trans can be developed. Using AG(T) = AH(T) — T AS(T) and treating the volumetric heat capacities as temperature independent, AS(Tm) = AH(Tm)/Tm, leads to the approximation 

The surface energy per area, 7, has the same units as a force per length and for some interfacial geometries can lead to an interfacial net force that is balanced by a difference in pressure between the two adjacent phases. If 7 is isotropic, this pressure difference is directly proportional to the interfacial curvature through the the Gibbs-Thomson equation (see Sections C.2.1 and C.4.1), 

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