奈米量测技术(III)XRD(X-rayDiffraction)(部分).PDF

奈米量測技術 (III) XRD (X-ray Diffraction) (部分) 連興隆 X-ray Diffraction Miller indices 布拉格定律(Bragg’s Law) Scherrer’s Formula Data Analysis Examples Miller Indices Miller Indices are a symbolic vector representation for the orientation of an atomic plane in a crystal lattice and are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes. (hkl) = parenthesis designate a crystal face or a family of planes throughout a crystal lattice. XRD Energy source: X-Ray Cu K α8.04 keV, λ= 0.154 nm 當X-ray透過具晶格結構之材料時, 產生建設性干涉(constructive interference) Bragg’s Law n λ= 2 d sin θ Constructive interference only occurs for certain θ’s correlating to a (hkl) plane, specifically when the path difference is equal to n wavelengths. Summary of Bragg Laue When a diffraction condition is met there can be a reflected X-ray Extra atoms in the basis can suppress reflections Three variables λ, θ, and d λis known θis measured in the experiment (2 θ) d is calculated From the planes (hkl) a is calculated θ- 2 θScan The θ- 2 θscan maintains these angles with the The θ- 2 θscan maintains these angles with the sample, detector and X-ray source sample, detector and X-ray source Normal to surface Only planes of atoms that share this normal will be seen in the θ- 2 θScan Smaller Crystals Produce Broader XRD Peaks Scherrer’s Formula K ∗λ t B ∗cosθ B t = thickness of crystallite K = constant dependent on crystallite shape (1-0.89) λ= x-ray wavelength B = FWHM (full width at half max) or integral breadth θB = Bragg Angle Scherrer’s Formul