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Crystal-Bravis Lattice Definitions

  1. Nov 2, 2010 #1
    There is such thing as a orthorhombic body centered crystal lattice. I am wondering why this is the case

    see the image bellow, we can find a repeating pattern which has a smaller area.

    Orthorombic.png

    A unit cell
    - must be selected such that it has the highest symmetry and the smallest area, however i do not see how the red unit cell has a higher symmetry. According to our lecture the red unit cell has a higher symmetry by 90 degrees, therefore a orthorhombic cubic has a body centered from

    The green shape can be reflected vertically and horizontally, however the point of reflection where the axis of symmetry passes through is not the same is this why there is a higher symmetry for the red ( default) unit cell?

    The blue atom is from a neighboring unit cell
     
    Last edited: Nov 2, 2010
  2. jcsd
  3. Nov 2, 2010 #2

    Borek

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    Staff: Mentor

    Are all atoms identical?
     
  4. Nov 3, 2010 #3
    yes all atoms are identical, the blue one is from a neighboring unit cell
     
  5. Nov 4, 2010 #4

    DrDu

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    Science Advisor

    As you observed correctly, even in centered lattices it is always possible to chose a unit cell which only contains one lattice point.
    The choice of the centered cells is mainly convention. I was astonished to find that it is quite involved to define mathematically in what sense the 14 Bravais lattices are different.
    See, e.g., S. Sternberg, Group theory and physics.

    I would only speak of lattice points and not of an atom as "crystal=lattice+cell". Hence the cell can be very complicated, e.g. a protein. Nevertheless the lattice is made up of simple points.
     
  6. Nov 4, 2010 #5

    Borek

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    Staff: Mentor

    Yes, atom was a wrong word. What I was asking about was whether all lattice points are equivalent. In ionic crystal nodes are occupied by different objects, so it can (?) be possible that the cell smallest in geometrical terms is not representative to whole crystal.
     
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