EMS162_2011_Lecture5

EMS162_2011_Lecture5 - EMS 162 - Winter 2010 48 Yayoi...

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1 1/20/2011 EMS 162 - Winter 2010 43 Yayoi Takamura 32 Point Groups in 3D 1/20/2011 EMS 162 - Winter 2010 44 Yayoi Takamura Glide Planes • a-glide plane: mirror plane perpendicular to b - axis or c - axis + translation along a -axis by ½ a Translation vector, a Shift = ½ Mirror b -axis Mirror c -axis (x,y,z) (x + ½,-y,z) (x,y,z) (x + ½,y,-z)
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2 1/20/2011 EMS 162 - Winter 2010 45 Yayoi Takamura c-Glide Plane Right handed Left handed (x,y,z) (y,x,z+1/2) 1/20/2011 EMS 162 - Winter 2010 46 Yayoi Takamura Glide Planes • n-glide plane: mirror plane perpendicular to a -, b - or c - axis + translation along diagonal by ½ d d=a+b, d=a-b, d=a+b+c, etc… e.g.: mirror plane c- axis + translate ½ ( a+b ) (x,y,z) (x + ½, y + ½, -z)
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3 1/20/2011 EMS 162 - Winter 2010 47 Yayoi Takamura n -Glide Planes Translation vector, b Shift = ½ ( b+c ) (x,y,z) (-x,y + ½,z + ½) Mirror plane to a -axis Mirror plane to b -axis Translation vector, a Shift = ½ ( a+c ) (x,y,z) (x + ½, -y, z + ½) 1/20/2011
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Unformatted text preview: EMS 162 - Winter 2010 48 Yayoi Takamura Glide Plane Notation 4 1/20/2011 EMS 162 - Winter 2010 49 Yayoi Takamura Screw Axis Combination of rotation + translation parallel to the rotation axis Rotation, =360/N where N=1, 2, 3, 4, 6 Translation, t = k/N where 1 < k < N-1 Side view Top view 2 1 screw axis 1/20/2011 EMS 162 - Winter 2010 50 Yayoi Takamura 3-Fold Screw Axis clockwise counter clockwise Translation vector, c Shift = 1/3 Shift = 2/3 5 1/20/2011 EMS 162 - Winter 2010 51 Yayoi Takamura 4-Fold Screw Axis Reduced representation Counter clockwise rotation Translation vector, c Shift = 1/4 1/20/2011 EMS 162 - Winter 2010 52 Yayoi Takamura 4-Fold Screw Axis Reduced representation Clockwise rotation 6 1/20/2011 EMS 162 - Winter 2010 53 Yayoi Takamura International Tables for Crystallography...
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EMS162_2011_Lecture5 - EMS 162 - Winter 2010 48 Yayoi...

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