Assuming homogeneous nucleation, please draw in schematic the temperature dependence of the following quantities: (1) the number of stable nuclei; (2) the frequency of attachment of an atom to a nuclei; (3) nucleation rate. Use the melting temperature (T_m) as a reference.

Schematic is describe below: (Please draw the following schematic)

Here is a schematic diagram using the melting temperature (Tm) as a reference to demonstrate how the number of stable nuclei, frequency of atoms attaching to nuclei, and nucleation rate for homogeneous nucleation is all temperature-dependent:

The melting temperature (Tm) is the reference point for the x-axis in this diagram, which indicates temperature. The various quantities of importance are represented on the y-axis.

(1) The number of stable nuclei: Due to the greater driving force for nucleation, the number of stable nuclei rises exponentially as the temperature falls below Tm. As the temperature falls below Tm, the curve demonstrates a sharp increase in the number of stable nuclei.

(2) The frequency with which an atom attaches to a nucleus: As the temperature falls below Tm, the frequency with which an atom attaches to a nucleus declines as the activation energy necessary for attachment rises. As the temperature falls below Tm, the curve depicts a steady decline in the frequency of attachment.

(3) Nucleation rate: The sum of the number of stable nuclei and the frequency of connection is the nucleation rate. Consequently, the nucleation rate curve peaks at a temperature just below Tm, where the frequency of attachment is still not too low, and the number of stable nuclei is high. Despite an increase in the number of stable nuclei, the nucleation rate diminishes as the temperature drops further due to a decrease in the frequency of attachment.

Although the precise shapes of these curves rely on the material's unique characteristics and the circumstances surrounding the nucleation process, the general trends are as described above.