# Physics: Thermodynamics Questions

## Transcribed Text

1) Consider interdiffusion between two thick (semi-infinite) layers of Fe, one side of which contains 0.5% C and the other 0.7% B at t = 0. Note that a table of erf(z) values can be found in Table 3.1 of the “Measuring diffusion coefficients” chapter uploaded to the course website in the supplemental reading folder. The time-dependent diffusion equation for this physical scenario is based on: ( )       = + Dt x c x t c c erf A A A 2 2 1 2 1 , * * , where erf is the error function, cA is the concentration of the species of interest, and cA* is the concentration at t = 0. Assume a diffusion coefficient of 8 x 10-8 cm2 /s for C and 1.2 x 10-7 cm2 /s for B. a) Plot the concentration profiles (similar to the graph above but with real calculations) at t = 1 s and 600 s from x = -2 mm to +2 mm. b) How thick would the B-containing Fe layer need to be to ensure less than 0.1% C content after 24 hours? In other words, at what thickness does the C content drop below 0.1% for this condition? 2) Read the attached paper [Paz y Puente et al., Acta Mater. 103, 534 (2016)] and answer the following questions: a) Why do the solid core/shell structures transform to hollow tubes over time? b) Which has more rapid diffusion, the core Ni80Cr20 material or the shell Ni2Al3 material? c) What is happening the initial heating time before the voids are formed? d) In the paper, two main techniques are used to study the void formation: x-ray tomography and optical microscopy. What is the relative advantage and disadvantage of each of these techniques compared to the other?

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