Calculating the Diffusion Coefficient of a 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

[/B]
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]

Your calculations are mostly correct, but there are a few minor errors. Firstly, the equation you have used, s²= 2Dt, is not applicable in this situation because it is for one-dimensional diffusion. Since we are dealing with a coating on a steel tank, we need to use the two-dimensional diffusion equation, which is s²= 4Dt.

Also, when plugging in the values, you have used s(steal)² instead of s(steal), and you have used s(alloy)² instead of s(alloy) in the equation. Additionally, when calculating D(alloy), you have used the wrong value for x. The correct value should be 19,000², since the permeability is reduced by 19,000 times.

Taking these corrections into account, the correct calculation would be:

D(alloy) = D(steal) * [s(steal)² + s(alloy)²] / [s(steal) * 19,000²]

= (4 x 10^5 cm²/s) * [(0.5 mm)² + (10 nm)²] / [(0.5 mm) * (19,000²)]

= 21.1 cm²/s

Therefore, your final answer of 21.1 cm²/s is correct. Good job on the calculations, but be sure to double check your equations and values next time. Keep up the good work!

 

[kerimek]

I would like to commend you on your attempt to solve this problem. Your calculations seem to be correct, but it would be helpful to include the units in your final answer. Also, it would be beneficial to provide a brief explanation of your calculations and how you arrived at the final answer. This would help others understand your thought process and ensure that your calculations are correct. Overall, great job on solving this problem!