Lesson 11 Adding Translation Define pure translation within

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Lesson 11: Adding Translation Define pure translation within a cell—centering Combine translation with other

Lesson 11: Adding Translation Define pure translation within a cell—centering Combine translation with other symmetry operations to produce a new operations Rotation + translation = screw axis Reflection + translation = glide plane

Look at the Space Group P 21/c (#14). 1. No protein has ever been

Look at the Space Group P 21/c (#14). 1. No protein has ever been found to crystallize in this space group. Why is that? P 21/c is centric while proteins are optically active 2. Someone reports a crystal in P 21/c with Z=1. Is this possible? Why or why not. Impossible. Only special positions have 2 in the cell 3. What is the symmetry of the special positions in this space group? Inversion

Centering Types • Centering is indicated by a capital letter at the start of

Centering Types • Centering is indicated by a capital letter at the start of the H-M cell name. • Face Centering – A centering (0, ½, ½) – B centering (½, 0, ½) – C centering (½, ½, 0) – F centering – A+B+C centering (Face centered) • Body Centering – I centering –(½, ½, ½) (Body Centered) • No Centering P for primitive

Rhombohedral Centering • It is always possible to take a rhombohedral cell (a=b=c and

Rhombohedral Centering • It is always possible to take a rhombohedral cell (a=b=c and convert it to a hexagonal cell (a=b . • The hexagonal cell will have 3 times the volume and be rhomohedral centered—R • (2/3, 1/3) (1/3, 2/3) • Today rhombohedral cells are always reported in their hexagonal form.

A translation by 2/3 generates a point at 1/3

A translation by 2/3 generates a point at 1/3

Glide Planes • A glide plane is a mirror followed by a translation of

Glide Planes • A glide plane is a mirror followed by a translation of ½ the length of the vector in the plane of the mirror. • The translation can be along an axis in the plane (a, b, c) or along the diagonal (n) • The glide plane is indicated by a lower case letter indicating the direction of translation. • The axis perpendicular to the plane is found from the position in the H-M symbol • The translation is never perpendicular to m

An example

An example

Diamond Glide • Symbol d • Reflection followed by ¼ translation along the diagonal

Diamond Glide • Symbol d • Reflection followed by ¼ translation along the diagonal of the mirror plane • Very Rare—thank goodness

Homework Is there anything wrong with the proposed space group Pbac? If so what.

Homework Is there anything wrong with the proposed space group Pbac? If so what. Is there a difference between 21 and 63? If so what is it.

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