Solid State

Crystal Lattices and Unit Cells


  • Crystal lattice(s): The regular three dimensional arrangement of constituent particles (also called as points) is called crystal lattice.
  • It expands infinitely along all the coordinate axis
  • A portion of crystal lattice can be shown as follows
  • Unit cell(s): Smallest repeating structural unit in crystal lattice is known as unit cell.
  • It can be shown as follows
  • There are mainly two types of unit cells (i) Primitive unit cell (ii) Centered unit cell
  • Primitive Unit Cell: If points occupy only at corner of unit cell is called primitive unit cell.
  • Centered Unit Cell: If points occupy in addition to corner either face centre (or) body centre or edge centre are called Centered Unit Cell.
  • Centered unit cells again of mainly three types.
    (i) Body centered cubic crystal
    (ii) Face centered cubic crystal (or) cubic close pack
    (iii) End centered cubic crystal.
  • Body centered cubic crystal (B.C.C): If points occupy in addition to corner at body centre of unit cell is called B.C.C lattice.
  • Face centered cubic lattice (F.C.C): If points occupy centre of all faces in addition to corner are called F.C.C.
  • End centered cubic lattice (E.C.C): If points occupy only at a pair of opposite face centres in addition to corner called end centre unit cell.

View the Topic in this Video from 0:08 to 8:55

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Density of unit cell = \tt \frac{mass \ of \ unit \ cell}{volume \ of \ unit \ cell}
d = \frac{Z.m}{a^{3}} = \frac{ZM}{a^{3} \times N_{A}} kg/cm^{3}
[Mass of an atom m = \frac{M}{N_{A}}]
(The density of the unit cell is same as the density of the substance.)
where,
d = density of unit cell, M = molecular weight
Z = number of atoms per unit cell, NA = Avogadro number
a = edge length of unit cell.