Presentation on theme: "Lecture 20 X-Ray Diffraction (XRD)"— Presentation transcript:
1Lecture 20 X-Ray Diffraction (XRD) Theory and Analytical Technique
2X-Ray Analysis X-rays discovered in 1895 Fundamental to understanding of crystal structure and symmetryPowder diffraction analyses are a simple and inexpensive method for identifying minerals, especially fine-grained minerals
3X-ray Crystallography X-ray wavelengths are on the same order of magnitude as atomic spacings.Crystals thus make excellent diffraction gratingsCan use the geometry of the x-ray spots to determine geometry of grating (i.e. the crystal)nλ = 2d sin θ
4Bragg DiffractionDiffraction from a three dimensional periodic structure such as atoms in a crystal is called Bragg Diffraction.Similar to diffraction though grating.Consequence of interference between waves reflecting from different crystal planes.Constructive interference is given by Bragg's law:Where λ is the wavelength, d is the distance between crystal planes, θ is the angle of the diffracted wave. and n is an integer known as the order of the diffracted beam.nλ = 2d sin θFollowing Bragg's law, each dot (or reflection), in this diffraction pattern forms from the constructive interference of X-rays passing through a crystal. The data can be used to determine the crystal's atomic structure.Following Bragg's law, each dot (or reflection), in this diffraction pattern forms from the constructive interference of X-rays passing through a crystal. The data can be used to determine the crystal's atomic structure.
5X-ray GenerationX-rays – High energy*, highly penetrative electromagnetic radiation*E = hc/λ λ(X-rays) = Å (avg. ~1 Å)λ(visible light) = ÅX-ray Vacuum TubeCathode (W)– electron generatorAnode (Mo, Cu, Fe, Co, Cr) – electron target,X-ray generatorOur instrument uses a copper target
6When light hits an electron, the electron jumps to a higher energy level, then drops back to its original, shell, emitting lightX-ray SpectraContinuous spectra (white radiation)– range of X-ray wavelengths generated by the absorption (stopping) of electrons by the targetCharacteristic X-rays – particular wavelengths created by dislodgement of inner shell electrons of the target metal; x-rays generated when outer shell electrons collapse into vacant inner shellsK peaks created by collapse from L to K shell;K peaks created by collapse from M to K shellKKX
7X-ray Crystallography Methods Single-Crystal: Laue MethodSeveral directions simultaneously fulfill Bragg equationsGood for symmetry, but poor for analysis because distortedFig 7.39 of Klein (2002) Manual of Mineral Science, John Wiley and Sons
8X-ray Diffraction (Bragg’s Law) nλ = 2d sinθDefines the spacing (d) of atomic planes and incident angle (θ) at which X-rays of a particular wavelength will reflect in phase (i.e., diffract)GE+EH = nλθ’≠ nλGE + EH is the path difference, waves add if equal to nλ
9X-ray Crystallography Methods: Single-Crystal: PrecessionUse motors to move crystal & sensor to satisfy Bragg equations for different planes without distortionsFig of Klein (2002) Manual of Mineral Science, John Wiley and Sons
10X-ray Crystallography Methods PowderEasiestInfinite orientations at once, so only need to vary q ,the angle of the incident beam of x-ray light.
11Powder Diffraction Method Requires random orientation of very fine crystalsIncident beam of a certain X-ray wavelength will diffract from atomic planes oriented at the appropriate θ angles for the characteristic d spacingRandom orientation of crystals will produce more intense diffraction peaks for particular angles that correspond to characteristic atomic planes