1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The number of ways of placing M atoms on the interstices of a lattice

  1. Dec 2, 2013 #1

    ppy

    User Avatar

    Hi,

    N atoms are arranged to lie on a simple cubic crystal lattice. Then
    M of these atoms are moved from their lattice sites to lie at the
    interstices of the lattice, that is points which lie centrally between the
    lattice sites. Assume that the atoms are placed in the interstices in a
    way which is completely independent of the positions of the vacancies.
    Show that the number of ways of taking M atoms from lattice sites
    and placing them on interstices is W = (N!/M!(N − M)!)2 if there
    are N interstitial sites where displaced atoms can sit.

    I literally do not know where to start with this question I know W is the number of ways of choosing M atoms from N atoms but I don't really know where to go with this.

    Help would be great.

    Thanks :)
     
  2. jcsd
  3. Dec 2, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    What does the 2 mean? W = (N!/M!(N − M)!)2?

    This can be expressed as (N choose M)2. And it does exactly what the name suggests: (N choose M) calculates the number of ways to choose M atoms out of N (to decide which atoms you move), and you get the same factor again for the choice of the interstitials.
     
  4. Dec 3, 2013 #3

    ppy

    User Avatar

    Hi yes the 2 should be a squared. This question is worth 6 marks. What would you have to do to get so many marks other than writing what you suggested?
     
  5. Dec 3, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I have no idea about the scale of the marks, but writing that down in a more ordered way should be sufficient.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: The number of ways of placing M atoms on the interstices of a lattice
Loading...