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Translation & Symmetry Operations in Crystallography: P21/c Space Group

Explore the concept of pure translation and its combination with other symmetry operations in the P21/c space group. Understand the limitations for protein crystallization in this group and the significance of special positions. Learn about different centering types and their representation in the H-M cell name. Study glide planes and their characteristics in crystallography.

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Translation & Symmetry Operations in Crystallography: P21/c Space Group

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  1. 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

  2. Look at the Space Group P21/c (#14). 1. No protein has ever been found to crystallize in this space group. Why is that? P21/c is centric while proteins are optically active 2. Someone reports a crystal in P21/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

  3. 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 (Facecentered)‏ • Body Centering • I centering –(½, ½, ½) (Body Centered)‏ • No Centering P for primitive

  4. 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) (1/3, 2/3, 2/3)‏ • Today rhombohedral cells are always reported in their hexagonal form.

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

  6. 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

  7. An example

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

  9. 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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