Improvement of Nucleation Theory

It should be possible to describe nucleation by using a basic equation of stochastic processes, yet it remains 

It has been long believed that a fundamental kinetic equation. Equation (4.1), with respect to J N, t) proposed by CNT can describe the nucleation process correctly. However, this section explains that/(V, t) and the kinetic equation in CNT do not satisfy the normalized condition and the mass conservation law, respectively. Hence,/(V, i) is not a proper distribution function. 

If we regard the nucleation process as the phase transition from 100% supercooled melt to 100% crystal, that is, formation of a single crystal or polycrystal, clearly, f N, t) should satisfy the following relationship, 

is a maximum of N. As the f(N, t) does not satisfy the requested normalized conditions of Equation (4.33) for the distribution function of a stochastic process, we cannot consider f N, t) as a distribution function. Since f N, t) and f N -t 1, t) do not mean any number of particles, / defined by Equation (4.1) cannot mean net flow in any stochastic process. Hence, the fundamental kinetic equation of CNT given by Equation (4.1) cannot satisfy the mass conservation law. Therefore, the fundamental kinetic equation cannot be a basic equation of a stochastic process [31]. 

The next section, which introduces a mass distribution function Q N, i), also describes a new basic equation of the mass conservation law based on the introduction of the net flow j N, t). We directly observe Q N, i) and obtain the overall crystalUnify during nano-nucleation in the bulk melt, which confirms our proposed nucleation theory. 

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