ABSTRACT
Because U(R0) is an arbitrary constant, it can be set to zero. Also, the derivative of the potential is zero at its minimum:
(6.2)
dU dR R0
0=
The lowest-order term that survives is the quadratic term:
(6.3)
U R d U dR
R R R
( ) ( )= −1 2
Letting
(6.4)
C d U dR R
≡ 2
we see that the potential is just that of a spring:
(6.5)
U R C R R( ) ( )= −1 2 0
where C is the force constant. Therefore, for small oscillations, we can model a crystal as a system of springs and masses.
