Bragg Law for X-ray Diffraction

Crystals contain arrays of atoms, and there are many planes defined by the atoms. Consider a set of horizontal planes in the sketch shown below. A beam of x-rays is directed at a crystal from the upper left. The beam has angle q from horizontal planes before scattering off the atoms. Consider two rays that bounce off in the same direction f as shown.

q……………f

(It looks like q + f = 90^o, this is accidental.) d is the hypotenuse of two right triangles: the slanted dotted lines are constructed ^ to the incoming and reflected beams, so you can see that the lower beam travels a total distance dsinq + dsinf farther than the upper one.

Hence dsinq +dsinf = ml is the condition for maxima. This is known as the Bragg law, and it is useful for experimental determination of crystal structure.

It turns out that when q = f , the maxima are greater, so another version of the equation is 2dsinq = ml .

Note that the angle is not with respect to the normal line; if you use that, replace sines with cosines.

Now scatter back to one of the main pages:

Mechanics
Fluids, heat, electricity and magnetism
Vibrations and waves
Quantum

F. Gram, Cuyahoga Community College West, Parma, OH 44130.
fredrick.gram @ tri-c.edu (remove spaces, copy and paste into email)