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Determine if BCC or FCC structure

  1. Aug 28, 2009 #1
    Hey guys ive got a question and im not sure how to go about answering it without looking up a table of characteristics of elements!

    Niobium has an atomic radius of 0.1430nm and a density of 8.57g/cm^3. Determine wheather it has an FCC or BCC crystal structure?

    Now i think you have to use the equation p=nA/VcNa
    n=number of atoms associated with each unit cell
    A=atomic weight
    Vc= volume of unit cell
    Na= Avogadro's number

    but to use the equation you need to know if it is an BCC or FCC structure so you know which n value to use then inturn how to get Vc.

    so my question is how do i go about this type of problem??

    Thanks :smile:!
  2. jcsd
  3. Aug 28, 2009 #2
    FCC or BCC isnt just determined by the radius or density. it is also determined by the direction of bonds that particular element prefers. if there is no preferred direction, all elements wud settle into either FCC or HCP (or a ramdom close packing). but on the other hand no preferred direction is usually a sign of chemical inertness, so they wud rather be gaseous.

    all in all ... it is impossible to predict the crystal structure based on unisotropic information about the element. however once you know the crystal structure then you can predict what changes will be in this structure if you add a dopant. and that change is many time just governed by ratio of radii of two elemnts.
  4. Aug 28, 2009 #3
    There are 4 parts to this problem.
    1. How many atoms per unit cell in BCC and FCC?
    2. What is the volume of a BCC or FCC unit cell given that the distance between nearest neighbor atoms is r*2?
    3. Given the atomic mass, the volume of the unit cell, and the number of atoms per unit cell, what is the density of FCC vs BCC?
    4. Of those two densities, which is closest to the measured value?
  5. Aug 28, 2009 #4
    so the problem doesnt ask you to determine whether it is BCC or FCC. you just assume it is FCC (or BCC) and compute the above four small problems. and then you compare your answer to the actual measured value and try to guess what is the actual structure.

    now do you need help in computing these simple things ? there are three ways out of it.

    1. just apply the formula after seeing any other such solved problem. there are scores of such problems in any entry level book. more so in scahum's series problem books.

    2. read how the formulae are derived and then apply it without consulting any solved problem.

    3. do the step 1 and then step 2 in succession. this is the way i would recommend.

    good luck
  6. Aug 28, 2009 #5

    thanks guys i solved it! i just wrote up two equations for the density one assuming FCC and one assuming BCC and the BCC answer is closest to the density given therefor it is correct :smile:
  7. Dec 2, 2010 #6
    Hey guys,

    I just saw your discussion about determining if BCC or FCC structure. I have another general question. What is the reason(s) to crystallize a mater in BCC, FCC or any other crystal structure? Is it just because crystallography concepts or there is any energy related reason? I just want to know whether it is possible to predict if an unknown matter crystallize in a specific crystal structure?

    Any comments is highly appreciated, please.
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