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I Factors that determine the coefficient of linear expansion

  1. Mar 5, 2017 #1
    ΔL=LαΔT

    The concept is interesting and applying its formula isn't even tedious, but what are the real factors that determine α here? I understand that thermal expansion is a direct consequence of the average separation between atoms. And that the coefficient can be found through different experiments. But I want to understand why different solids have different coefficients.

    I think my strongest insight is that α value must be somehow inversely proportional to a solid's density. So we have soft metals like aluminum with high values of α and epoxy with twice that of alumn. And then we have dense metals like steel that don't really expand that much. Titanium is one of the hardest metals I've worked with and its coefficient α is very low. Is there a strong relationship between these two? Or is there a factor more relevant?
     
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  3. Mar 6, 2017 #2
    I would probably guess that the strength of the molecular bonds is a better predictor of thermal expansion. Of course, stronger molecular bonds go somewhat hand in hand the more rigid the object is, and thus solids would have less expansion.
     
  4. Mar 6, 2017 #3

    Mapes

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    Agreed. Since thermal expansion in ceramics and metals is primarily dependent on the shape of the atomic pair potential and its depth, the coefficient of thermal expansion in these materials is generally inversely correlated with the density, the stiffness, and the melting temperature, all of which tend to increase with bond strength.
     
  5. Mar 6, 2017 #4

    Vanadium 50

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    I don't think it's simple. Here's the coefficient of thermal expansion for Fe/Ni alloys as the Ni composition varies. Note the sharp minimum at 36%.

    350px-Invar-Graph-CTE-composition.svg.png
     
  6. Mar 6, 2017 #5

    Mapes

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    Oh, definitely. My link shows only the trend for elements, and even then the correlation isn't absolute. With ferritic alloys, you're going to get some coupling with magnetism that could complicate things tremendously. (Or let you design a cool low-thermal-expansion material, depending on how you look at it!)
     
  7. Mar 7, 2017 #6
    Really good stuff, thanks a bunch. Just a very subtle follow-up question on this...
    how does thermal conductivity relate to this coefficient? Does it have to do with its density, stiffness, melting temp like Mapes noted or molecular bonds like Rumborak suggested?
    When i a build a chart, there doesn't seem to be any, proportional or not, relationship..
    metal / a / k
    iron / 12 / 0.163
    copper/ 16.6 / 0.99
    Alum / 22.2 / 0.50

    It's a very small sample, but it already prevents any kind of linear relationship.. When I manipulate the formulas "ΔL=LαΔT" and "k = (Q*L) / (A*ΔT*Δt)", there definitely is some kind of inverse proportionality inherent, but the could the other variables be weighted more resulting in my skewed chart?
     
  8. Mar 7, 2017 #7
    Is there a specific reason why you would think the two are related? I mean, two values not being related is probably more the norm than the exception.
     
  9. Mar 7, 2017 #8
    Only because I have a lab question that asks what the relationship between the two is.. But yeah, to digress more, when I had manipulated the two formulas "ΔL=LαΔT" and "k = (Q*L) / (A*ΔT*Δt)", I ended up with a single equation that was obnoxiously hairy where, while "k" was on one side and "1/α", there was just too many other variables that affected the relationship..
     
  10. Mar 7, 2017 #9

    DrClaude

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    Then such a question needs to be asked in the homework forum, with an attempt at a solution.

    Thread closed.
     
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