ABSTRACT
Most readers are probably familiar with the Bragg formula for x-ray diffraction (XRD), 2d sin u ¼ nl, and the selection rules that tell us that the sum of the Miller indices for bodycentered cubic (bcc) crystals must be even and the indices for face-centered cubic (fcc) crystals must be all even or all odd in order to produce a diffraction peak. The intent of this chapter is to give a more general derivation of the Laue conditions leading to Bragg reflections of electrons and phonons that take place in three-dimensional (3D) crystals. These reflections from lattice planes within the crystal are fundamental to the understanding of the thermal and electronic properties of materials. In the process, the reciprocal lattice will be introduced which will be widely used in subsequent chapters to describe how materials behave thermally, electronically, magnetically, and photonically.
