Many layers of atoms
Consider many layers of regularly spaced atoms, such as we
might encounter in a crystalline material. We already know that a diffracted beam from a
single layer of atoms has qOUT =
qIN. We need to know what spacing of the
layers of atoms will give rise to scattered waves being in phase, when
interacting with many layers
of atoms.
Consider two waves C and D, scattered from particles in adjacent planes
separated by a distance d. They are only in phase if the extra path length of
wave D over C (= x + y) equals a whole number of wavelengths.
The equation for this path difference gives the Bragg law:
-
x + y
= 2dsinq = nl
This condition which gives rise to diffracted beams
depends on the wavelength, l;
the spacing of the planes of atoms, d;
and the angle of incidence of the beam, q.
This condition is known as Bragg's law:
-
nl = 2dsinq
For a
particular pair of d and
l values there may be several values of q at which
diffraction occurs.