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UNIT CELL – The smallest repeating unit of a crystalline solid

Discover the smallest repeating unit of crystalline solids, including simple cubic and body-centered cubic structures. Learn about efficient ways to pack atoms and different unit cells for ionic crystals.

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UNIT CELL – The smallest repeating unit of a crystalline solid

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  1. UNIT CELLS UNIT CELL – The smallest repeating unit of a crystalline solid EXP11-1 (of 11)

  2. SIMPLE CUBIC UNIT CELL Length of 1 side of the unit cell: Full atoms in the unit cell: 2r (r = radius of one particle) 8 × ⅛ = 1 EXP11-2 (of 11)

  3. BODY-CENTERED CUBIC UNIT CELL 4r s d s s Length of 1 side of the unit cell: 4r ___ √3 (8 × ⅛) + 1 = 2 = 4r√3 ______ 3 s2+ d2 = (4r)2 s2 + s2 + s2 = (4r)2 3s2 = 16r2 s2 = 16r2 _____ 3 Full atoms in the unit cell: EXP11-3 (of 11)

  4. The most efficient ways to pack atoms: 1st layer EXP11-4 (of 11)

  5. The most efficient ways to pack atoms: 1st layer 2nd layer EXP11-5 (of 11)

  6. The most efficient ways to pack atoms: 1st layer 2nd layer 3rd layer This is hexagonal closest packing (hcp), and it makes hexagonal prism unit cells EXP11-6 (of 11)

  7. The most efficient ways to pack atoms: 1st layer 2nd layer 3rd layer EXP11-7 (of 11)

  8. The most efficient ways to pack atoms: 1st layer 2nd layer 3rd layer This is cubic closest packing (ccp), and it makes face-centered cubic unit cells EXP11-8 (of 11)

  9. FACE-CENTERED CUBIC UNIT CELL EXP11-9 (of 11)

  10. UNIT CELLS FOR IONIC CRYSTALS Zinc sulfide Zn = S = (8 x 1/8) (4 x 1) + (6 x 1/2) = 4 = 4  ZnS EXP11-10 (of 11)

  11. UNIT CELLS FOR IONIC CRYSTALS Sodium chloride (12 x 1/4) (8 x 1/8) + (1 x 1) + (6 x 1/2) Na = Cl = = 4 = 4  NaCl EXP11-11 (of 11)

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