X-Ray Diffraction Simulation
Identification of Lattice and Determination of Lattice Constant by X-Ray DiffractionSimulation
IntroductionRegular arrangement of atoms in molecules and extended solids is very common. In crystalline solids theatoms are arranged in repeating three-dimensional arrays or lattices. Information regarding atomic bonddistances and angles is fundamental to understanding the chemical and physical properties of materials. Sinceatomic dimensions are of the order of angstroms (10 m), unraveling the relative atomic positions of a solidrequires a physical technique that operates on a similar spatial scale, Diffraction experiments involving X-ray,electron and neutron sources have therefore played a very crucial role in unraveling these structures. Thesignificance of these experiments in science and engineering courses has been recognized. However, the costof the equipment and the hazards associated with these experiments have made them very difficult to beintegrated and included in a teaching laboratory setting.The present set-up overcomes these limitations. An increase in scale by thousands from short wavelengths ofX-rays to the long wavelengths of visible light, and by hundreds of thousands from an array of atoms in acrystal or an extended solid to an array of dots, allows us to replicate the basic features of a structuraldetermination experiment in a teaching laboratory.In place of Bragg diffraction whose results are to be simulated, we use Fraunhofer diffraction. Visible laser lightpasses through an array of scattering centers (dots) on a 35 mm slide. The diffraction pattern is viewed atwhat is effectively infinite distance (a meter or so). This arrangement is capable of illustrating many of theessential features of the standard X-ray experiment. Mathematically, the equations for Fraunhofer and Braggdiffraction have a similar functional dependence on the interatomic distance, wavelength and the scatteringangle. The symmetry of the diffraction pattern is same as the symmetry of the lattice causing the diffraction.The central piece of the set-up is a slide (transparency) with eight (A-H) different arrangements of scatteringcenters (dots) on different portions of the slide (Figure 3). The examples presented here serve to illustratehow the spacings, symmetries, spot intensities and systematic absences in a diffraction pattern are related tothe lattice from which it is derived. Although these are two-dimensional lattices, they mimic what would beobserved for diffraction from particular three-dimensional structures that are viewed in projectionperpendicular to a face.
SetupA battery operated laser mounted on a stand is put at one end of anoptical bench. The slide is mounted on another stand (Figure 1)which is kept at about 10-20 cm away from the laser such that thelaser light falls normally on the slide. The slide on this stand can bemoved sideways and vertically so that the laser light falls ondifferent portions of the slide. The diffraction pattern is observed ona perspex screen (Figure 2) fixed normal to the laser light at theother end of the optical bench. The whole set-up is put in adarkened room where the experiment is performed.
AimThe basic aim of the experiment is to identify the lattice and to determine its lattice constant.