Crystal Lattices and Unit Cell

Crystal Lattices

The main characteristic of crystalline solids is a regular and repeating pattern of constituent particles. If the three dimensional arrangement of constituent particles in a crystal is represented diagrammatically, in which each particle is depicted as a point, the arrangement is called crystal lattice. Thus, a regular three dimensional arrangement of points in space is called a crystal lattice.

 

There are only 14 possible three dimensional lattices. These are called Bravais Lattices. The following are the characteristics of a crystal lattice: (a) Each point in a lattice is called lattice point or lattice site. (b) Each point in a crystal lattice represents one constituent particle which may be an atom, a molecule (group of atoms) or an ion. (c) Lattice points are joined by straight lines to bring out the geometry of the lattice.

 

 

UNIT CELL

Unit cell is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice. A unit cell is characterised by: (i) Its dimensions along the three edges, a, b and c. These edges may or may not be mutually perpendicular. (ii) Angles between the edges, α(between b and c), β(between a and c) and g (between a and b). Thus, a unit cell is characterised by six parameters, a, b, c, and α, β, g.

 

 

Types of Unit Cells

Unit cells can be broadly divided into two categories, primitive and centred unit cells.

(a) Primitive Unit Cells When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell.
(b) Centred Unit Cells When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centred unit cells are of three types:
(i) Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners.
(ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.
(iii) End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

 

 

 

S.No.	CRYSTAL SYSTEM	UNIT CELL TYPE	EDGE LENGTH & ANGLES	EXAMPLE
1	CUBIC	Simple/Primitive	a=b=c α=β=g=90⁰	Polonium
2	CUBIC	Body Centred	a=b=c α=β=g=90⁰	Fe, Rb, Na, Ti, W, U, Zr
3	CUBIC	Face Centred	a=b=c α=β=g=90⁰	Cu, Al, Ni, Au, Ag, Pt
4	TETRAGONAL	Simple/Primitive	a=b≠c α=β=g=90⁰	SnO2
5	TETRAGONAL	Body Centred	a=b≠c α=β=g=90⁰	TiO2CaSO4
6	ORTHORHOMBIC	Simple/Primitive	a≠b≠c α=β=g=90⁰	Rhombic Sulphur
7	ORTHORHOMBIC	Body Centred	a≠b≠c α=β=g=90⁰	KNO3
8	ORTHORHOMBIC	Face Centred	a≠b≠c α=β=g=90⁰	BaSO4
9	ORTHORHOMBIC	End Centred	a≠b≠c α=β=g=90⁰	MgSO4.7H2O
10	MONOCLINC	Simple/Primitive	a≠b≠c α=β=90⁰ , g≠90⁰	Monoclinic Sulphur
11	MONOCLINC	End Centred	a≠b≠c α=β=90⁰ , g≠90⁰	Na2SO4.10H2O
12	TRICLINIC	Simple/Primitive	a≠b≠c α≠β≠g≠90⁰	K2Cr2O7 H3BO3
13	HEXAGONAL	Simple/Primitive	a=b≠c α=β=90⁰ , g=120⁰	ZnO BeO CoS SnS
14	RHOMBOHEDRAL	Simple/Primitive	a=b=c α=β=g≠90⁰	Calcite NaNO3 FeCO3