Thermodynamics -for understanding crystal growth-

Abstract

To understand what entropy is, thermodynamical entropy was derived from Boltzmann's entropy formula. After defining the Helmholtz and the Gibbs free energies, we calculated the formation Gibbs free energies of an equilibrium and a non-equilibrium nucleus following Toschev's approach taking a water droplet as an example. It is demonstrated that the Gibbs free energy for the formation of a cluster takes the maximum as the cluster radius is increased. The cluster at this maximum is called critical nucleus.Thermodynamics is also a useful tool to obtain the rate of crystal growth in a vapor phase. The partial pressures of all gaseous species are calculated by solving equations given by the law of mass action and the initial conditions. The mathematical formulas to give the growth rates in a closed tube and in a gas flow system are derived.