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Question:
All other factors being equal, the diffusion rate of nickel is the highest in copper with ASTM grain size number of:
A. 4
B. 6
C. 8

Honestly, the question does not appear to be very intuitive - I've searched through my notes and cannot seem to find any relatable formulae. I understand that the number of grains per square inch at 100X magnification is equatable to 2^(n-1), where n is the ASTM grain size number of the specimen.
However, given the multiple-choice nature of this question and the apparent lack of information (I suppose the copper and nickel are pure, at room temperature, etc.), I must be overlooking something simple.

Would anyone be willing to advise?

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  • $\begingroup$ google.com/… $\endgroup$ Aug 28 '15 at 23:23
  • $\begingroup$ Use the link, it gives some examples of grain size/diffusion, it may be able to point you in the right direction $\endgroup$ Aug 28 '15 at 23:24
  • $\begingroup$ Appreciate the effort Dopeybob, but I'd already seen that one - couldn't seem to find anything helpful. Provides examples of using the ASTM grain size equation, but without further information with relation to my own question, I cannot find that equation useful. Refers to a "Table 5.2" with potential information concerning diffusion of Cu in Ni, but does not reference or otherwise show the table. In any case, that information may have been specific to that university's set of questions. $\endgroup$
    – Hissionere
    Aug 28 '15 at 23:57
  • $\begingroup$ Homework questions are on-topic, but you are expected to demonstrate an attempt at solving the problem. It is preferred for you to post the expected answer as well, and then explain where you are having difficulty in getting to the expected answer. In this case, you might want to look at what isn't there. If there are 8, 32, or 128 grains per square inch how much space does that leave around them? How large are the nickel molecules in comparison to the copper? $\endgroup$
    – user16
    Aug 29 '15 at 0:45
  • $\begingroup$ Ahh - perhaps this was the hint I was looking for, Glen. The atomic radius of copper is approximately 128pm, whereas Nickel is 200pm. Not too sure how that fits in. However, I suppose the more copper grains per square inch, the less vacant space available for the diffusion of nickel atoms. Also, the lower the ASTM grain number, the higher the average grain diameter. On the basis of this, I would state that A (4) would be the answer to this question. Am I correct? Can you elaborate, Glen? $\endgroup$
    – Hissionere
    Aug 29 '15 at 1:21
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Since this homework is likely long-past turned in, a direct answer probably can't hurt. Sorry if this doesn't help you with your homework, but hopefully it will still provide useful knowledge.

ASTM grain number is inversely proportional to grain size, so that the largest grain size number corresponds with the smallest grains. Assuming the grain size distribution is approximately uniform, the grain boundary surface area per unit volume of material increases with decreasing grain size. Thus higher ASTM grain size number corresponds with higher specific grain boundary area.

Grain boundaries are less densely packed with atoms, as they can be thought of as organized collections of dislocations. Diffusion of atoms in materials occurs most rapidly where atomic packing is lowest, because there is a lower energy potential to be overcome by the diffusing atoms. Diffusion rate is exponentially dependent on the additive inverse of the energy barrier (think Arrhenius). Thus diffusion occurs more rapidly at grain boundaries than in grain volume.

The overall effect is that higher ASTM number gives more specific grain surface area gives more regions of rapid diffusion. Diffusion therefore occurs most rapidly in a material with the highest ASTM grain number, all else equal. The correct answer is thus (C. 8).

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  • $\begingroup$ +1. I know this is a long-shot, but since you talked about grain boundaries I wonder if you have any idea how to answer this question? It's been one of our longest-lasting unanswered questions and I'd really like to clean up the unanswered queue! $\endgroup$ Jun 22 at 2:33

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