Nanocrystalline Ni-Mo alloys of various sizes

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Nanocrystalline Ni-Mo alloys were prepared through electrodeposition, revealing varying hardness values based on grain size. The Hall-Petch relationship was referenced, suggesting that hardness can be plotted against d^-1/2 to derive constants Ho and k. Participants expressed confusion about how to interpret the graph and calculate these constants, with some suggesting that the y-intercept represents Ho and the slope represents k. There was a call for clearer articulation of the question to facilitate better assistance, as the initial inquiry seemed overly complex for a material science problem. Overall, the discussion highlighted the need for a straightforward approach to analyzing the relationship between grain size and hardness in nanocrystalline alloys.
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Homework Statement


Nanocrystalline Ni-Mo alloys of various grain sizes (d) were prepared by electrodeposition. They showed the following hardness values.
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Homework Equations


Ho=Hi + k/d^1/2

The Attempt at a Solution


1. Plot a hardness vs d^-1/2
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Graph
graph.JPG


3. Use best fit analysis and calculate the values for hall petch constants (Ho) and k for both sections of the graph.
I used a best fit line on the graph but a bit confused how this would help me. I don't know where to start at all. To find the hall-petch constants.
 

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You did not get a reply for more than 12 hours. I will give this a try. I know literally nothing about material science, after taking a look on wiki: grain boundary strengthening page, I don't think I understand the question properly!

If I would approach this problem like any other, I would say that the y-intercept in the graph is ##H_{o}##, while the slope is the strengthening coefficient ##k##.

Is this really your question? for someone taking material science this sounds like a very weird question. If this is not the what you are asking about, can you elaborate more and focus more on the exact issue rather than vaguely stating it? This will make it easier for people with no experience in materiel physics to help you.
 
Phylosopher said:
You did not get a reply for more than 12 hours. I will give this a try. I know literally nothing about material science, after taking a look on wiki: grain boundary strengthening page, I don't think I understand the question properly!

If I would approach this problem like any other, I would say that the y-intercept in the graph is ##H_{o}##, while the slope is the strengthening coefficient ##k##.

Is this really your question? for someone taking material science this sounds like a very weird question. If this is not the what you are asking about, can you elaborate more and focus more on the exact issue rather than vaguely stating it? This will make it easier for people with no experience in materiel physics to help you.
I think my professor wanted it to be a simple question and i am just over analyzing it. -,- I think you are right.
 
Side remark: I wouldn't trust that linear fit.
 
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