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Math Help - Bravais Lattice Type

  1. #1
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    Bravais Lattice Type

    I have been given the three coordinates a=(3,1,0) b=(5,0,0) and c=(5/2, 5/2, 1). I then have to find the Bravais Lattice type. Can someone explain how I go about this. I am not sure on the actual process on how to determine the Bravias Lattice Type.

    Hope someone can help me out.
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  2. #2
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    Quote Originally Posted by bex23 View Post
    I have been given the three coordinates a=(3,1,0) b=(5,0,0) and c=(5/2, 5/2, 1). I then have to find the Bravais Lattice type. Can someone explain how I go about this. I am not sure on the actual process on how to determine the Bravias Lattice Type.

    Hope someone can help me out.
    See this link here. You have been given the three vectors that determine the shape and size of the unit cell. What you need to do is find out how long each is and what the angles are between them. You can find the length by the Pythagorean theorem and the angles by using the dot product. (You could use the cross product as well, but the dot product is the typical way to do it.)

    If you need further help, just let us know.

    -Dan
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    Bravais Lattice

    Ok, I have found the length of each vector, and the ngle between each one using the dot product, but from the link to the wikipedia page I am not sure where to go from here. How do I know which crystal system to use. Could really do with some help on this one.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by bex23 View Post
    Ok, I have found the length of each vector, and the ngle between each one using the dot product, but from the link to the wikipedia page I am not sure where to go from here. How do I know which crystal system to use. Could really do with some help on this one.
    All three angles are unequal and none are equal to 90 degrees. Thus it has to be a triclinic lattice.

    -Dan
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  5. #5
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    Bravais Lattice

    Hi. Thanks for your help Dan, but I have one more question. How did you decide that the lattice was a triclinic one. As you said all the angles are different but according to the wikipedia page given, this could also mean that it could be a rhombohedral (trigonal) lattice. How did you decide between the two. Hope you can clear this up for me.

    Bex
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