B TECH
COMPUTER SCIENCE ENGINEERING
PHYSICS (BTPH101-23)
ELEMENTS OF CRYSTALLOGRAPHY
Crystal Structure
The arrangement of atoms or ions or molecules in a crystal is known as Crystal Structure.
The crystal structure can be described with the help of simple concepts of lattice and unit
cell.
A unit cell is the convenient smallest block or geometrical figure of a crystal lattice which,
when repeated again and again symmetrically along three dimensions in space, generates the
complete lattice.
For a three-dimensional lattice, the unit cells are in the form of a parallelepiped. The choice of
unit is not unique. According to the requirement of the case, either a primitive or a
non-primitive unit cell or block can be selected as a unit cell.
The parallelepipe defined by the translational vectors a, b, c, which are the shortest possible
distances along three crystallographic axes x, y, z, is called a Primitive unit cell8. A primitive
unit cell is a minimum volume unit cell and has lattice points only at its corners.
Hence, a unit cell is described by 6 parameters: three primitive vectors a, b, c , and three
angles (α, β, γ) between the primitives.
A unit cell is the smallest volume of the crystal which characterizes the arrangement and
position of atoms, and it serves as a building block for the crystal12. The volume of a primitive
cell is given by:-v=∣a.b×c∣
Since a primitive unit cell has the smallest volume, points are only at its corners. In this
structure, each atom is surrounded by its nearest neighbors located at the corners of the
cube.
BRAGG'S LAW:-
It states that if the path difference (d) between two crystal planes is equal to a whole number
multiple of the incident wavelength of X-Rays, and the angle of incident and scattered X-Rays
is equal, then constructive interference will take place.
