Radiography in Modern Industry - Kodak

The position of the spots is determined by Bragg's Law, namely, nλ = 2d sin θ where n is theorder of the spectrum, λ the wavelength of the x-rays, d the distance between the atomic planesinvolved, and θ the angle between the diffracted x-ray and the atomic plane. Because a crystal isa regular arrangement of atoms in space, there are many planes at different angles, just as thereare many different rows of trees with different spacings in an orchard, depending on the angle atwhich the orchard is viewed. If the crystal is properly oriented and suitably rotated or oscillated(Bragg's method), and the x-rays used are monoenergetic, the information thus obtained isparticularly useful for the determination of the internal structures of crystals (See Figure 111).Figure 111: X-ray diffraction pattern of silver oxalate (Ag 2 C 2 O 4 ) made by the rotatingcrystal method, illustrated Figure 11A.Besides certain technical limitations of the Laue method, the necessity for always having a singlecrystal available is a handicap. The Debye-Scherrer-Hull method (See Figure 109B) commonlyutilizes a small amount of the sample in powdered form packed in a fine glass capillary, or stuckto a fiber or flat ribbon of material transparent to the x-rays. The resulting random distribution oftiny crystals permits Bragg's Law to be satisfied for many different lattice planes within the crystal.In this system, monoenergetic x-rays are used. Determination of crystal lattice constants can bemade by the Debye-Scherrer-Hull method (Figure 112).Radiography in Modern Industry 173