What is a unit cell? Explain Bravais lattices.

unit cell

i. A unit cell is the smallest repeating structural unit of a crystalline solid. A crystalline solid can be obtained by repeating the unit cells (of the same crystalline substance) in space in all directions.

ii. The lines connecting centres of the constituent particles are drawn to represent a unit cell. The constituent particle can be an ion or an atom or molecule of the crystalline solid.

iii. The points at the intersection of lines which represent constituent particles are called lattice points. These lattice points are arranged in a definite repeating pattern. Any one lattice point is identical to the number of other lattice points.

iv. Space lattice is the collection of all the points in the crystal having similar environment.

a portion of a three dimensional cubic lattice and its unit cell

Bravais Lattices:

i. The three dimensional arrangement of lattice points represents a crystal lattice. Thus, a crystal lattice is a regular arrangement of the constituent particles (atoms, ions or molecules) of a crystalline solid in three dimensional space.

ii. There are only 14 possible three dimensional lattices, as proved by the French mathematician, Bravais. These are called Bravais Lattices.

iii. Lattice points when joined by straight lines gives the geometry of the lattice. iv. Shape of any crystal lattice depends upon the shape of the unit cell which in turn depends upon following two factors,

a. The length of the three edges: a, b and c.

b. The angles between the edges: α (between edges b and c), β (between edges a and c) andγ (between edges a and b).

c. Thus, a unit cell is characterised by six parameters a, b, c,a, β and γ The complete crystal lattice can be obtained by extending the unit cell in all three directions.

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