X-ray diffraction

Bragg diffraction. Waves 1 and 2, in phase with each other, glance off atoms A and B of a crystal that has a separation distance d between its atomic, or lattice, planes. The reflected (glancing) angle θ, as shown by experiment, is equal to the incident angle θ. The condition for the two waves to stay in phase after both are reflected is that the path length CBD be a whole number (n) of wavelengths (λ), or nλ. But, from geometry, CB and BD are equal to each other and to the distance d times the sine of the reflected angle θ, or d sin θ. Thus, nλ = 2d sin θ, which is the Bragg law. As may be seen from the diagram, when n = 2, there is only one wavelength along path CB; also, the reflected angle will be smaller than that for, say, n = 3. Waves reflected through an angle corresponding to n = 1 are said to be in the first order of reflection, the angle corresponding to n = 2 is the second order, and so on. For any other angle (corresponding to fractional n), the reflected waves will be out of phase and destructive interference will occur, annihilating them.

X-ray diffraction, phenomenon in which the atoms of a crystal, by virtue of their uniform spacing, cause an interference pattern of the waves present in an incident beam of X-rays. The atomic planes of the crystal act on the X-rays in exactly the same manner as does a uniformly ruled diffraction grating on a beam of light. A beam of X-rays contacts a crystal with an angle of incidence θ. It is reflected off the atoms of the crystal with the same angle θ. The X-rays reflect off atomic planes in the crystal that are a distance d apart. The X-rays reflecting off two different planes must interfere constructively to form an interference pattern; otherwise, the X-rays would interfere destructively and form no pattern. To interfere constructively, the difference in path length between the beams reflecting off two atomic planes must be a whole number (n) of wavelengths (λ), or nλ. This leads to the Bragg law nλ = 2d sin θ. By observing the interference pattern, the internal structure of the crystal can be deduced. See also Bragg law; Laue diffraction pattern.