The mole percentage of a solute in a semi-infinite solid block is calculated as a function of distance from the surface. Carbon and copper are the diffusing species and their surface concentrations are fixed using a slider. Display the diffusing systems by checking the boxes for carbon into iron (C into Fe), copper into aluminum (Cu into Al) and copper into nickel (Cu into Ni). Use sliders to vary the temperature of the block and the diffusion time.
The concentration \(C_x\) is:
where \(C_0\) is the initial concentration of the diffusing molecule in the bulk solid, \(C_S\) is the external surface concentration of the diffusing molecule, \(x\) is the distance into the bulk solid, \(D\) is the diffusion coefficient characteristic of the diffusing molecule and the solid, \(E_a\) is activation energy for diffusion in the specific system, \(R\) is the gas constant, \(T\) is temperature and \(t\) is time.
\(C_0 = 0\) for this Demonstration. That is, at time zero, the concentration of the diffusing species is zero everywhere except at the surface.
The following parameters are used:
carbon diffusing into iron (C into Fe):
\(E_a = 80\) kJ/mol, \(D = 6.2\times10^{-7}\) mm\(^2\)/s
copper diffusing into aluminum (Cu into Al):
\(E_a = 136\) kJ/mol, \(D = 6.5\times10^{-5}\) mm\(^2\)/s
copper diffusing into nickel (Cu into Ni):
\(E_a = 256\) kJ/mol, \(D = 2.7\times10^{-5}\) mm\(^2\)/s.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Nathan S. Nelson. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.