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Consider the pattern below with White, Grey and Dark grey circles

Understand crystal lattice structures, lattice points calculation, motif identification, symmetry elements, space group determination, and Wyckoff positions assignment. Learn about information reduction in transitioning from lattice and motif to space group and Wyckoff positions.

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Consider the pattern below with White, Grey and Dark grey circles

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  1. Consider the pattern below with White, Grey and Dark grey circles (skip the concepts which you are not familiar with)

  2. 1) Draw the conventional UC, name the lattice and calculate the number of lattice points per cell Name: Simple square lattice Lattice Points per cell: 1

  3. 2) Draw alternate non-primitive cells

  4. 3) Identify the lattice points and the motif Alternately a set with this circle as lattice point could be chosen

  5. 4) Draw the fundamental (shortest) lattice translation vector and write its Miller Indices

  6. 5) Overlay various symmetry elements

  7. 6) Identify the space group (Hermann-Mauguin symbol) and the Asymmetric Unit Unit cell with symmetry operators and Asymmetric unit

  8. 7) Assign Wyckoff positions to the species Please also refer to: from_L+M_SG.ppt

  9. 8) What is the reduction in labour (information) in going from the Lattice + Motif picture to the Space Group + Wyckoff Positions picture? • Lattice + Motif pictureLattice = Square lattice, Motif = 2 Open circles, 4 light grey circles and 4 dark grey circles For each circle (x,y) coordinates have to be specified  10  2 = 20 pieces of information Specification of lattice is 1 more piece of information Total: “21” pieces of information • Space Group + (Asymmetric Unit) + Wyckoff Positions picture Space group = p4gm, 2a (Open circle), 4c (light grey circle) and 4c (dark grey circle) Specification of space group → 1 piece of information Specification of 3 Wyckoff positions → 3 pieces of information Specification of the value of ‘x’ for light and dark grey circles → 2 pieces of information  Total: “6” pieces of information Note the reduction in labour/information even for a simple crystal

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