6.9: Crystals and periodic molecules
- Page ID
- 52340
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The particle in a box approximation is too crude for most problems. Tight binding, on the other hand, is often quite computationally intensive. But fortunately, we can make simplifications when the material is periodic. In this lecture, we are interested in first describing 1d, 2d and 3d periodic materials, and then calculating their wavefunctions. We‟ll begin with some definitions.
The Primitive Unit Cell
A primitive unit cell of a periodic material is the smallest possible arrangement of atoms that can be copied to construct the entire material.
Primitive Lattice Vectors
Given a primitive unit cell, we can construct the periodic material by translating the unit cell by multiples of the primitive lattice vectors.
Some examples may help