Free Energy Results

The majority of free energy calculations in the literature have relied on very crude methods to estimate the error in the free energy results. Basically, a simulation is repeated several times, sometimes in the "forward" (0—>1) and "reverse" (1—>0) X directions, sometimes only in one direction or the other. Each simulation is performed with a different (but equivalent)... 

Recrystallization occurs when a crystalline material is plastically deformed at a relatively low temperature and then heated [1]. The as-deformed material possesses excess bulk free energy resulting from a high density of dislocations and point-defect debris produced by the plastic... 

Nevertheless, we see already from Fig. 9 that, for the current example, the robustness of the results to the addition of extra moment densities provides a reasonable qualitative check of the accuracy of the coexistence curves. To study the convergence of the moment free energy results to the exact ones more quantitatively, especially in cases where the latter are not available for comparison, we need a measure of the deviation between ptot((r) and p (dimensionless quantity that does not scale with die overall density of the parent, we consider the normalized distributions nMt(a) — Ptot(ff) / Ptot and (a) = /c/°) (cr) / pW and define as our measure of deviation... 

A stable structure may but need not be a structure of minimum free energy. Results obtained for kinetically determined structures are essentially the same. 

In a third step the counterions are released from the surface. Stimulated by thermal fluctuations, they partially diffuse away from the surface and form the diffuse double layer. The entropy and, at the same time, the energy increases. One can show that both terms compensate, so that in the third step no contribution to the Gibbs free energy results. 

Instead of (20.11), we have for. the change in free energy resulting from the process of mixing the components 1 and 2 at constant temperature, to form a non-ideal solution ... 

---