Fundamental types of crystal lattices and their symmetry operations.
a. Types and classes of crystals,
b. Symmetry operations in crystals
In this lecture we will follow through our basic knowledge gained in the last lecture. — lecture — I, II, and shed light on the most interesting properties of crystal lattices, viz. their symmetry properties. Based on their properties we will classify them into various types and classes.
ii. Lattices satisfy additional symmetry operations. But due to the constraint of translational symmetry the total number of symmetry operations that the lattices can satisfy is reduced to a minimum.
iii. This means in 2-dimensional lattice constructs we have only 5 types of lattices which satisfy additional symmetry operations. In 3-dimensional geometry there are a total of 14 classes of lattices.
iv. Thus in 3-dimensional lattices the 14 classes of Bravais lattices are categorized into 7 types or systems of fundamental lattices.
v. The extra symmetry operations are
inversion about a space point and
reflection about a plane passing through a lattice point or
their possible combinations.