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Question
How many space lattices (bravais lattices) are obtainable from the different crystal systems?
How many space lattices (bravais lattices) are obtainable from the different crystal systems?
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Solution
There are seven unique and basic unit cell shapes (primitive unit cells) with varying elements of symmetry in a three-dimensional space.
On combining the 7 crystal systems with the 4 possible unit cell types (SCC, BCC, FCC, EC) only 14 different 3-D lattices are possible.
These lattices are called Bravais lattices.
Cubic crystal has 3 bravais lattices. They are primitive, body centred and face centred.
Tetragonal crystal has 2 bravias lattices. They are primitive and body centred.
Orthorombic crystal has 4 bravias lattices. They are primitive, end centred, body centred and face centred.
Monoclinic crystal has 2 bravias lattices. They are primitive and end centred.
Hexagonal has only one bravias lattice. It is primitive.
Rhombohedral has one bravias lattice. It is primitive.
Triclinic has one bravias lattice. It is primitive.
Thus, we have totally 14 Bravias lattices.
On combining the 7 crystal systems with the 4 possible unit cell types (SCC, BCC, FCC, EC) only 14 different 3-D lattices are possible.
These lattices are called Bravais lattices.
Cubic crystal has 3 bravais lattices. They are primitive, body centred and face centred.
Tetragonal crystal has 2 bravias lattices. They are primitive and body centred.
Orthorombic crystal has 4 bravias lattices. They are primitive, end centred, body centred and face centred.
Monoclinic crystal has 2 bravias lattices. They are primitive and end centred.
Hexagonal has only one bravias lattice. It is primitive.
Rhombohedral has one bravias lattice. It is primitive.
Triclinic has one bravias lattice. It is primitive.
Thus, we have totally 14 Bravias lattices.
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