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Estimating Resistivity of Amorphous Metal - Condensed Matter

  1. Feb 20, 2015 #1
    1. The problem statement, all variables and given/known data
    Estimate the resistivity of an amorphous metal whose mean free path is of the order of an atomic spacing. Compare your answer to crystalline copper.


    2. Relevant equations
    VF = h(bar) KF / m
    VF = l / τ
    ρ = m / n e2 τ

    3. The attempt at a solution

    I think my real issue with this question is i'm not sure what are reasonable numbers to estimate with.

    We need to find τ to plug into ρ = m / n e2 τ

    Using VF = l / τ we can rearrange to get τ = l / VF


    for l:

    We are told the mean free path, l, is of the order of an atomic spacing but I am not sure what is a reasonable estimation of this is?

    for VF:

    VF = h(bar) KF / m

    KF3 = 3π2n where n = NAρ/atomic weight

    Again Im not sure what to use as my values for ρ and atomic weight. It seems as though I am missing something about amorphous metals. I understand that they have disordered structures but how can i make an estimation for KF with that little information.

    Thanks in advance to anyone that replies and apologies if this is a bit of a basic question.

     
  2. jcsd
  3. Feb 21, 2015 #2

    mfb

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    Staff: Mentor

    A factor of 2 does not matter here, so you can look up the size of atoms of your favorite metal and use this. Same for density and atomic weight.

    In general, the rough size of atoms (order of magnitude) is something you should know.
     
  4. Feb 22, 2015 #3
    Thank you for your reply. I think I am still getting a bit confused as, as I understand it amorphous metals are glasses and therefore, depending on their density, can have a much larger atomic spacing?

    Regardless i'll complete the question with a spacing of a few angstroms. Thank you
     
  5. Feb 22, 2015 #4

    mfb

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    2016 Award

    Staff: Mentor

    As I said, a factor of 2 does not matter here. A few angstrom is fine.
     
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