When concentration of vacancies in a CZ silicon crystal is defined by molar fraction $X_{B}$, the degree for supersaturation $sigma$ is given by $[X_{B}-X_{BS}]/X_{BS}=X_{B}/X_{BS}-1=ln(X_{B}/X_{BS})$ because $X_{B}/X_{BS}$ is nearly equal to unity. Here, $X_{BS}$ is the saturated concentration of vacancies in a silicon crystal and $X_{B}$ is a little larger than $X_{BS}$. According to Bragg-Williams approximation, the chemical potential of the vacancies in the crystal is given by ${mu}_{B}={mu}^{0}+RT$ ln $X_{B}+RT$ ln ${gamma}$, where R is the gas constant, T is temperature, ${mu}^{0}$ is an ideal chemical potential of the vacancies and ${gamma}$ is and adjustable parameter similar to the activity of solute in a solute in a solution. Thus, ${sigma}(T)$ is equal to $({mu}_{B}-{mu}_{BS})/RT$. Driving force of nucleation for the vacancy agglomeration will be proportional to the chemical potentialdifference $({mu}_{B}-{mu}_{BS})/RT$ or ${sigma}(T)$, while growth of the vacancy agglomeration is proportaional to diffusion of the vacancies and grad ${mu}_{B}$.