Calculating Diffusion Coefficient for TiAlN Alloy Coating

[mmoadi]

Homework Statement

Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is reduced by 19,000 times? In this attempt the steel had a thickness of
d(steal) = 0.5 mm, and the thickness of the alloys was d(alloy)= 10 nm.

Homework Equations

s²= 2Dt

The Attempt at a Solution

x= 19,000, D(steal) = 4 x 10^5 cm²/s, s(steal)= 0.5 mm, s(alloy)= 10 nm, D(alloy)= ?

s(steal)²= 2D(steal)t
s(steal)² + s(alloy)²= 2D(alloy)xt

s(steal)²/ [s(steal)² + s(alloy)²]= 2D(steal)t/ 2D(alloy)xt
s(steal)²/ [s(steal)² + s(alloy)²]= D(steal)/ D(alloy)x
D(alloy)= D(steal) [s(steal)² + s(alloy)²]/ s(steal)²x
D(alloy)= 21.1 cm²/s

Are my calculations correct?
Thank you for helping!

 

[anathema]

Yes, your calculations are correct. The diffusion coefficient of the TiAlN alloy coating would be 21.1 cm²/s, which is significantly lower than the diffusion coefficient of the steel tank (4 x 10^5 cm²/s). This means that the coating is effective in reducing the permeability of hydrogen through the steel tank, making it a promising solution for improving hydrogen storage.

 

[kerimek]

Yes, your calculations appear to be correct. However, it would be helpful to provide units for your final answer (in this case, cm²/s). Additionally, it would be beneficial to include a brief explanation of the steps you took to arrive at your solution, as this helps to show your understanding of the concept. Overall, your response is thorough and demonstrates a good understanding of diffusion coefficients and their application in this scenario.