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Crystal Systems

Bravais Lattices. Crystal Systems. Cubic. Primitive, FCC, BCC. Orthorhombic. Primitive, FC, BC, EC. Rhombohedral. Primitive. Tetragonal. Primitive, BC. Triclinic. Primitive. Hexagonal. Primitive. Monoclinic. Primitive, EC. Layer arrangement view. Layer A. Layer B. Layer C.

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Crystal Systems

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  1. Bravais Lattices Crystal Systems Cubic Primitive, FCC, BCC Orthorhombic Primitive, FC, BC, EC Rhombohedral Primitive Tetragonal Primitive, BC Triclinic Primitive Hexagonal Primitive Monoclinic Primitive, EC

  2. Layer arrangement view Layer A

  3. Layer B

  4. Layer C Cubic Close Packing (CCP) Layer A Layer B Layer C

  5. Layer arrangement view Layer A

  6. Layer B

  7. Layer A Hexagonal Close Packing Layer A Layer B Layer A

  8. Hexagonal Primitive Unit Cell shape view Unit Cell arrangement view

  9. Packing Fraction depends on: 1. Layout of each layer 2. Placement of one layer over the other

  10. Voids Two types of voids: Octahedral Tetrahedral Found only in FCC & Hexagonal primitive unit cells Octahedral void in FCC

  11. Each octahedral void located at the edge center is shared by 4 unit cells Total contribution of edge centre voids = No. of Octahedral voids per unit cell = Rank of unit cell Contribution of central void Total contribution of all octahedral voids per unit cell of FCC = 4 Voids

  12. Tetrahedral void in FCC x-axis (0,0,0) (a/2, a/2,0) y-axis (a/4, a/4,a/4) (0, a/2,a/2) (a/2, 0,a/2) z-axis Voids

  13. (0,0,0) (a/2, a/2,0) (a/4, a/4,a/4) Voids

  14. With each corner as origin there are 8 tetrahedral voids in FCC unit cell  No. of tetrahedral voids = 2  no. of Octahedral voids Voids

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