Visualizing Critical Energy and Free Energy in Nucleation
Prompt
An informative illustration depicting the principles of critical energy and critical free energy for nucleation within a material. This visualization represents the critical energy as the minimum energy barrier that must be overcome for a new phase or nucleus to form within the material. Correspondingly, the critical free energy is shown as the minimum free energy barrier required to form a new phase or nucleus. Additionally, the image illustrates the relationship between the total free energy, volume free energy, and surface free energy as a function of the nucleation radius. Namely, the total free energy is depicted as the sum of the volume and surface free energy, decreasing as the nucleation radius increases due to a decline in surface free energy while the volume free energy retains constancy. This concept is visually represented by the formation of stable nuclei at a critical radius. Lastly, the same visualization features the calculated crystal structure of Niobium, a critical element in the electronics industry, based on its atomic radius, volume, and packing efficiency within a unit cell.
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