Analytical studies of Gibbs-Thomson effect on the diffusion controlled spherical phase growth in a subcooled medium

Abstract

By using a small-time series expansion technique, the thermal effect of surface tension (Gibbs-Thomson effect) on the early-stage phase growth of a spherical nucleus immersed in an infinite subcooled liquid is studied in this paper. The result shows that surface tension greatly reduces the incipient growth rate of the solid nucleus. Critical value of surface tension is found beyond which the decreasing of the phase growth rate with time becomes non-monotonic. Analytical expression for the phase growth rate in terms of relevant physical parameters is also derived under the condition of small degree of undercooling.

Growth of YbVO4 crystals evolved from hot corrosion reactions of Yb2Zr2O7 against V2O5 and Na2SO4+V2O5

“…Ostwald ripening is the dominant mechanism of the nanorods growth: the formation of tiny crystalline nuclei in a supersaturated medium occurs at first, and this is followed by crystal growth [28]. The larger particles grow at the cost of the smaller particles; reduction in surface energy is the primary driving force for crystal growth and morphology evolution, due to the difference in solubility between the larger particles and the smaller particles, according to the Gibbs-Thomson law [29]. The nucleation and growth mechanisms of rod-like YbVO 4 is a complex process of simultaneous chemical reactions and self-assembly.…”

Patterning Configuration of Surface Hydrophilicity by Graphene Nanosheet towards the Inhibition of Ice Nucleation and Growth

“…According to the Gibbs-Thomson effect [43,62], the surface curvature of ice would cause additional pressure on the ice-water interface, resulting in an external resistance for the further growth of the ice nucleus. [42,63]. Hence, the free energy barrier for ice growth increases, and the freezing point of liquid water is decreased.…”

Surface Area Limited Model for Predicting Anisotropic Coarsening of Faceted Nanoparticles

“…where R is the radius, AERae is the mean radial distribution, D S is the surface diffusion coefficient, γ is a parameter which contains the interfacial surface tension and atomic volume of the solute, K is the step growth rate, V m is the molecular volume of the species, C 0 is the concentration of the vapor or solution, k B is Boltzmann's constant, T is the absolute temperature, and t is time. Both incorporate the Gibbs-Thomson relation 39 and utilize Fick's law of diffusion, and an in depth analysis can be obtained from refs 40-42. In the second instance, the greatest conceptual insight given by the Burton, Cabrera, and Frank (BCF) theory is that the growth at the surface of a crystal, or any nanostructure, is heavily influenced by the existence of steps and kinks, which provide preferable sites for the attachment of adatoms (or growth monomers). This step-flow theory results in a rate equation of the growth of steps (K) on a crystal surface which evolves either as a basic step island or as a spiral:…”

“…Soon after, Wagner introduced the opposing case, in which the vapor is in equilibrium but the cluster/vapor interface is held in a nonequilibrium state; this phenomena has been termed the reaction limited theory (eq ). normald R normald t = D normalS R .25em 2 normalγ V normalm 2 C 0 k normalB T ( 1 false⟨ R false⟩ − 1 R ) normald R normald t = D normalS R .25em 2 K normalγ V normalm 2 C 0 k normalB T ( false⟨ R false⟩ false⟨ R 2 false⟩ − 1 false⟨ R false⟩ ) where R is the radius, ⟨ R ⟩ is the mean radial distribution, D S is the surface diffusion coefficient, γ is a parameter which contains the interfacial surface tension and atomic volume of the solute, K is the step growth rate, V m is the molecular volume of the species, C 0 is the concentration of the vapor or solution, k B is Boltzmann’s constant, T is the absolute temperature, and t is time. Both incorporate the Gibbs−Thomson relation and utilize Fick’s law of diffusion, and an in depth analysis can be obtain...…”