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Find the lattice type and base in 2D crystal

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Draw the position of the atoms in the two neighboring planes of the GaAs crystal perpendicular to vector [010].

    Find the type of the lattice and the basis of 2D crystal which is made by singling out those two neighboring layers from 3D lattice.

    2. Relevant equations

    GaAs is the same structure as ZnS. And I've drawn the 'top view' of the lattice, the one that can be found in Kittel, Solid State, on the page 17. The plane perpendiculat to [010] is (010) - one that goes on the side parallel with the x-axis and through point 1 on the y-axis, if the corner atoms are on the positions 0 and 1.

    The top view of the lattice looks like this:

    6TiwR.png

    And if I got it right the 2D lattice looks like this:

    LYdJf.png

    But what are the primitive vectors? And what kind of a latice is this?

    IS the 2D Bravais lattice oblique? With primitive vectors:

    [itex]\vec{a}_1=\frac{a}{4\sqrt{2}}(\hat{x}+\hat{y})[/itex]
    [itex]\vec{a}_2=a\hat{x}[/itex]

    Where a is the length of the side of a crystal?
     
    Last edited: Sep 5, 2012
  2. jcsd
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