Physics for Electronics Engineering: Unit I: Crystallography
Space Lattice (crystal Lattice)
Crystallography
A crystal is an array of atoms in three dimensions. As a matter of convenience, these atoms can be associated with a set of imaginary points in space.
SPACE
LATTICE (CRYSTAL LATTICE)
A crystal is an array of atoms in three
dimensions. As a matter of convenience, these atoms can be associated with a
set of imaginary points in space.
These points are arranged in such a way
that every point has an identical surrounding as any other point in three
dimensions and it is known as a space lattice or simply lattice.
Lattice is an imaginary geometrical
concept. It is a large assembly of points in which each point represents the
position and orientation of an atom in the crystal.
Note:
In 2 dimensions, the arrangement of points is only in 2D (X & Y).
Definition
- Space
lattice is an array of points in space to represent atoms in a crystal in which
the environment about each point is the same i.e., every point has identical
surroundings as that of every other point in the array.
Explanation
The collection of points in two
dimensions is shown in fig. 1.3 (a) and (b)
It is found that in fig 1.3 (a) the
environment (position of neighbouring points) about any two points is same.
Hence, it is a 2D lattice.
The mathematical representation of a 2D
lattice is T = la + mb where l and m
are integers, a and b are the translation vectors in X and Y
directions.
For example T = AB = 2a + 2b as shown in fig 1.3(a)
On the other hand, in fig. 1.3 (b) the
environment about any two points is not the same. So, it is not a proper
lattice.
A similar argument is extended to
three-dimensional space lattice. For 3D, T
= la + mb + nc such that a, b and
c are the translation vectors.
Lattice
points
The points in a space lattice are called points (Fig. 1.4).
Lattice
lines
The lattice points are joined with lines
as shown in fig. 1.4. These lines are known as lattice lines.
Lattice
plane
A plane containing lattice points is
known as lattice plane. (fig. 1.4)
Physics for Electronics Engineering: Unit I: Crystallography : Tag: : Crystallography - Space Lattice (crystal Lattice)
Physics for Electronics Engineering: Unit I: Crystallography
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Physics for Electronics Engineering
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