Crystallography- Lattices and Bravais Lattices

Question 1

What is a lattice?

Answer 1

A set of points in space such that the surroundings (and symmetry) of one point are identical with those of all the others

Question 2

Features of a lattice

Answer 2

Is homogeneous, infinite, of constant point density, has equal or higher symmetry than the full crystal structure

Question 3

What are lattice points?

Answer 3

Mathematical points in space which might coincide with atom positions or might not

Question 4

Unit cells and lattice points

Answer 4

Might contain one (primitive) or more (non-primitive) lattice points. Corners of unit cells are preferred lattice points. More lattice points might occur in the body or face centre of the unit cell.

Question 5

Condition for nearest neighbours for a lattice

Answer 5

Distance to nearest neighbours must be the same for every point. Number of nearest neighbours must be same for each point

Question 6

4 modes of lattice centering

Answer 6

No centre (P): primitive unit cell
Face centering (F): all faces of unit cell have an extra lattice point
Body centering (I): centre of unit cell volume has a lattice point
Single face centre (C): sides A, B or C only have a lattice point (base-centered)

Question 7

14 Bravais lattices

Answer 7

Triclinic P
Monoclinic P and C
Orthorhombic P, C, I, F
Hexagonal P
Rhombohedral P
Tetragonal P and I
Cubic P, I, F
These are in specific numbered order 1 to 14

Question 8

Why are there only 24 Bravais lattices?

Answer 8

The other 14 possible solutions are redundant because they are identical to some of the others