ME362_F10-L6_Imperfect-I

ME362_F10-L6_Imperfect-I - Lecture 6 X-Ray Diffraction...

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1 X-Ray Diffraction Imperfection in Solids (I) Lecture 6

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2 Can we measure lattice parameters? Incoming X - rays diffract from crystal planes. Measurement of: Critical angles, θ c , for X - rays provide atomic spacing, d. Adapted from Fig. 3.2W, Callister 6e .
3 Bragg equation n λ = 2d sin θ where d is the spacing between adjacent crystal planes, and θ is the angle of scattering

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4 Interplanar spacing Direct function of the Miller indices for the plane For a cubic system, where a is the lattice parameter. For a hexagonal system, where a and c are lattice parameters d hkl = a h 2 + k 2 + l 2 d hkl = a 4 3 (h 2 + hk + k 2 ) + l 2 (a 2 /c 2 )
5 Reflection Rules Bragg law: necessary condition, but not sufficient condition for diffraction Non - primitive unit cells have atoms at additional lattice sites located along a unit cell edge, within a unit cell face, or interior of the unit cell extra scattering centers can cause out - of - phase scattering to occur at certain Bragg angles

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6 Cubic planes {hkl} Sum: h 2 +k 2 +l 2 BCC FCC {100} 1 {110} 2 110 {111}
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ME362_F10-L6_Imperfect-I - Lecture 6 X-Ray Diffraction...

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