LECTURE 20 Miller indices

# LECTURE 20 Miller - SUMMARY FROM LAST CLASS X-ray diffraction • Each crystal structure has a specific set of planes and d-spacings and can be

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Dr. P. Lucas U of A MSE 110 X-ray diffraction: Each crystal structure has a specific set of planes and d-spacings and can be defined by this unique collection of d-spacings. XRD is used to determine crystal structures by measuring d-spacings. X-rays are energetic photons generated by atomic core electronic transitions made possible by the creation of an electron vacancy on the K level (n=1). Electron vacancies are created in X-ray tubes by knocking off K electrons with a high energy electron beam. The beam of X-rays is reflected by subsequent atomic layers in the crystalline sample if the path length difference between rays reflected by subsequent atomic layers is equal to a whole number of wavelength. All the rays are then in phase and interfere constructively. The conditions for refraction are expressed in Bragg’s law n λ =2d·sin θ The incident beam angle θ is scanned between 0 and 90º and a peak is recorded for the d-spacing of each atomic plane. SUMMARY FROM LAST CLASS

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Dr. P. Lucas U of A MSE 110 Bragg’s Law: reflection order n XRD The reflection order n is equal to the number of wavelength in the path difference between two rays reflected from subsequent atomic layers. However the size of λ is typically of the order of d (hence n<2) so that we usually only consider the first order reflection n=1 and Bragg’s Law reduces to: Ray 1 Ray 2 Ray 3 n λ =2d·sin θ From Bragg’s law therefore n λ <2d 1 sin 2 < = θ λ d n λ = 2d·sin θ
Dr. P. Lucas U of A MSE 110 X-Ray pattern: We can then calculate the set of d corresponding to the crystal structure. XRD

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## This note was uploaded on 10/06/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at University of Arizona- Tucson.

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LECTURE 20 Miller - SUMMARY FROM LAST CLASS X-ray diffraction • Each crystal structure has a specific set of planes and d-spacings and can be

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