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Lattice systems and group symmetries

by fyw
Tags: lattice, symmetries, systems
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Apr27-14, 09:19 PM
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Dear all,

In Marder's Condensed matter physics, it uses matrix operations to explain how to justify two different lattice systems as listed in attachment.
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However, I cannot understand why the two groups are equivalent if there exists a single matrix S satisfying S-1RS-1+S-1a=R'+a'.

Can someone help me to understand it? Thank you.
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Greg Bernhardt
May6-14, 11:48 PM
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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
May7-14, 12:44 AM
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PF Gold
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Marder is saying that if there is a linear map between the two lattice systems, then they are equivalent. The original system is defined by a Rotation (R) and a translation (a).

The matrix S and its inverse are performing a similarity transformation (coordinate system change) on R, and also apply it to the translation.

Marder then notes if there exists one such linear transform, then there exists a family of them.

Personally I found Marder too abstract for my taste, though the group theoretical approach to crystallography is very powerful. But most of the math is not very difficult - it just appears dense because of the writing style.

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