(xyz) (xyz) (xyz) (xyz)

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Presentation transcript:

(xyz) (xyz) (xyz) (xyz) Space groups I centering & 222 - start from P222 I222 (xyz) (xyz) (xyz) (xyz) a/2 + b/2 + c/2 translation to body centered lattice point

Space groups I centering & 222 - start from P222 (xyz) (xyz) (xyz) (xyz) (1/2 + x, 1/2 + y, 1/2 + z) ( 1/2 - x, 1/2 - y, 1/2 + z) (1/2 - x, 1/2 + y, 1/2 - z) (1/2 + x, 1/2 - y, 1/2 - z) a/2 + b/2 + c/2 translation to body centered lattice point 1/2+ 1/2-

What new symmetry elements arise from translation? Space groups I centering & 222 - start from P222 I222 What new symmetry elements arise from translation? a/2 + b/2 + c/2 translation to body centered lattice point 1/2+ 1/2-

Space groups I centering & 212121 - start from P212121 a/2 + b/2 + c/2 translation to body centered lattice point 1/4 1/2 - z 1/2 + z P212121

Space groups I centering & 212121 - start from P212121 a/2 + b/2 + c/2 translation to body centered lattice point 1/4 1/2 - z 1/2 + z z - z What's new?

4i (xyz) (xyz) (xyz) (xyz) Space groups Mirrors - start with mm2 Pmm2 4i (xyz) (xyz) (xyz) (xyz)

Space groups Glides - start with mm2 - substitute glide for mirror Pbm2 What's new? 4d (xyz) (xyz) (x,y+1/2,z) (x,1/2-y,z)

Space groups Glides & 21s - start with mm2 - add 21, remove mirrors, add glide 1/2+ ? 1/2+ Pna21

Space groups Glides & 21s - start with mm2 - add 21, remove mirrors, add glides Pna21 1/2+ na21 - ma (b/2+c/2) mb a/2 2 c/2 like 2 (a/2+b/2)