Materials Science II

Diffusion, Nucleation and Growth

1. 1. A concrete dam has a base thickness of 50m and an upper thickness of 20m. The dam is used to retain water which is found to leak through it by diffusion. Calculate the flux of water through the base and top of the dam in litres/day/m2. Would you expect the leak rates to be higher in summer or in winter? [Assume D for water in concrete is 6x10-6m2/s]
2. The thickness of a carburised layer is 1.5mm after 6h processing at 950oC. How thick would the layer be if the processing time is raised to 20h?
3. Steel can be decarburised by holding in an oxidising atmosphere at elevated temperature as often occurs during annealing. Calculate the thickness of the decarburised layer if the steel is held at 900oC for 100h in a homogenising process. For C in g-iron D0=1.5x10-5m2s-1, Q=125kJ/mol, R=8.314J/mol/K.
4. A solution for non-steady state diffusion relevant to the carburising process is given by the following equation. For a 0.25%C steel calculate the time needed to raise the carbon concentration to 0.8% at a depth of 0.5mm in a carburising process where the surface carbon content is maintained at 1.2%. You may assume that the carburising process takes place at 950oC and the diffusion parameters are as in question 3.
5. The change in free work, W, during solidification as a function of precipitate radius, r, is given by the following equation.Derive expressions for the critical radius of the nucleus required for stable growth, r* and the critical nucleation energy DG*.

6. The driving force for solidification is given by the following equation.Calculate the critical nucleus size for aluminium (melting point 660oC) if solidification occurs at (a) 500oC and (b) 300oC. [The latent heat of melting for Al is 5x108Jm-3 and its solid surface energy is 0.5Jm-2].