Gibbs-Thompson

Although, for obvious reasons, classical thermod5mamics caimot provide a quantitative account of the vast variety of phenomena occurring on the nanoscale, it does make some useful semiquantitative predictions in the scalable size interval. For example, based on the Gibbs-Thompson relation, Pheth predicted that for a metal composed of small particles, the redox potential E d) of the transition... 

D. Dependence of on Lamellar Thickness (Gibbs-Thompson Equation)... 

If 8L/L0 is small, as observed experimentally, perhaps due to very slow kinetics of chain rearrangements, then the relationship between Lq and Tc is the same as the Gibbs-Thompson equation ... 

After certain duration of time, let the lamella have thickened by a factor of p so that L = LoP- According to the Gibbs-Thompson equation, Eq. (1.28), the melting temperature of the thickened lamella is... 

In a spherical nucleus, AG is associated to the supercooling, T, and the surface free energy at the crystal/ melt interface, o, through the Gibbs-Thompson equation (Eq.2) ... 

To correlate with the usual macroscopic observations, the Gibbs-Thompson equation may be Introduced to describe the dependence of the Surface free energy on parameters of the surface being analyzed U6). 

Introduction of the Gibbs-Thompson equation results in

po + 2Citr... 

Further, A5, Gb and Gi denote thermal conductivities and temperature gradients in the liquid and solid, and D the solute diffusivity in the liquid. m = dTjdCoo and k are volumetric latent heat of fusion, liquidus slope and interfacial distribution coefficient. G o is the concentration far from the interface and F = Tmlsi/Ly the Gibbs-Thompson parameter based on the solid liquid interfacial energy 7 / and melting temperature Tm is the solidification velocity and uj = 27t/A the wave number of a perturbation. 

The growth of the clusters is governed by the Gibbs-Thompson equation... 

The Gibbs-Thompson equation relates the mean-field concentration and the mean particle size. 

Here q is the molecular volume of the adatoms. The flux of adatoms to and from a crystallite is estimated by considering local equilibrium at the surface via the Gibbs-Thompson equation and resorting to the mean-field approximation for the concentration far from the crystallites. The Gibbs-Thompson equation relates the radius of curvature of a particle with the concentration of adatoms in equilibrium with it. It is given by... 

Here c, is the concentration at the curved interface, Cpi is the concentration at the planar interface, M is the molecular weight, E is the interfacial energy, and p is the density. Thus the concentration in equilibrimn for a curved smface differs from that for a flat surface. This result is not due just to the reduction of surface area. This phenomenon is known as the Gibbs-Thompson effect. 

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