) making interceptsin the ration 1/h: 1/k: 1/l
10 CHAPTER 1. STRUCTURE FACTOR AND LATTICE Spacing of the hkl planes We know that e i G . r is also the equation of a plane wave, with wavevector G propagating in the direct lattice. The surfaces over which G . r is a constant are the wavefronts. The discussion in the preceeding section implies that the hkl planes are precisely such wavefronts. Therefore the spacing between two successive hkl planes, for which the constant n 0 in eqn 1.21 differs exactly by 1, must be the wavelength associated with G . We thus get a very important result -if d hkl denotes the distance between two successive planes, then d hkl = 2 π | G | (1.22) Density of points on an hkl plane The density of points (per unit area) in an hkl plane is n hkl = d hkl V (1.23) where V = a 1 . a 2 × a 3 is the volume of the primitive unit cell. The proof is left as an exercise. PROBLEM : Prove eqn. 1.23 These two results will come in very handy when we discuss diffraction from a lattice. Direction in a lattice If a vector points along r = n 1 a 1 + n 2 a 2 + n 3 a 3 then we denote this direction as [ n 1 ,n 2 ,n 3 ]. Note the use of different brackets to avoid confusion with Miller indices.
Chapter 2 Diffraction and basics of crystal structure Lecture notes for PH409 (Jul-Dec2013): K. Das Gupta References: 1. Chapter 5 Solid State Physics , N. W. Ashcroft and N.D. Mermin 2. Chapter 1 & 2 Introduction to Solid State Physics, C. Kittel 3. Useful (free) software for visualising crystal structures:•XCrysden : •POV-ray : •Crystosim : sangals/crystosim/finalsolution/startpage.htmlHow does oneknowabout the structure of a solid or a liquid or a glass? There is a generic answer to this
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