The surface work of the critical dimension nucleus formation.

In the formation of the crystallization nucleus, the part of the energy is released when the bulk phase occurs, and part of the work is spent on creating the surface partition, the system resists, prevents the formation of the interface. We substitute rкр values into the energy balance formula:

If the amount of energy released by the passage of the certain volume of a liquid phase with a large level of free energy into the solid phase with a lower level of free energy would be equal to the amount of energy spent on the formation of the interface, then ΔG would be equal to zero. If the energy was released (allocated) more than was expended, then ΔG would be less than zero. In our case, ΔG is positive and equal to 1/3A of the nucleus formation. This means that the system allocates only 2/3A of the nucleus’s formation, and 1/3A of the nucleus formation is lacking. But experience shows that the germinal centers are formed, therefore, the system finds the missing part of the energy due to energy fluctuations. The energy fluctuations are understood as the deviation of the energy of individual particles from its mean value. The frequency dependence of the energy of individual particles can be represented by a graph (Fig. 1).

The less fluctuation of energy is required for the formation of germinal centers, the more easily its system is sought. The higher the degree of supercooling of DT, the smaller the critical size of the nucleus rкр, the less the work of its formation Акр and the smaller the energy fluctuations, hence the number of germinal centers increases with increasing degree of supercooling. But with the increase in the degree of supercooling of DT, the number of germinal centers does not increase all the time, but passes along a curve with the maximum (Fig. 2).

This dependence is explained as follows. With the increase in the supercooling degree ΔT, the mobility of atoms decreases, the viscosity of the medium increases, and the number of atoms whose energy is equal to or greater than the activation energy of the process decreases. Thus, the probability of the transition of atoms from the liquid phase into a solid is equal to:

The probability of the critical dimension nucleus formation is equal to:

The probability of the occurrence of a number of germinal centers is equal to the product of two probabilities:

where  k  –  the coefficient of proportionality;

Азар – the magnitude of the energy fluctuation necessary for the critical dimension nucleus formation;

R – the gas constant;

T- the absolute temperature.

Thus, the greater the degree of cooling, the greater the difference in the free energies, the smaller the critical size of the nucleation nucleus, and the W1 of the transition of one phase to another, W2 decreases, since the work for the formation of a critical size nucleus is smaller and smaller than the energy fluctuation (Fig. 3).

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