Bragg angle, deviation from exact

Figure 3.11. The diffracted intensity /g as a function of the deviation from the exact Bragg angle calculated from the kinematical theory.

Figure 3.10. The Ewald sphere construction in reciprocal space when there is a slight deviation from the exact Bragg angle.

In practical electron microscopy, it is often important to be able to determine accurately the deviation A0 from the exact Bragg angle 0. We now consider in some detail how we can use Kikuchi lines for doing this. 

Figure 4.11. Diagram showing the form of the variation of (q A0, the deviation from the exact Bragg angle.

Equations (5.8) differ from those calculated for an undeformed crystal, Eqs. (4.89) and (4.90), in that s is now replaced by (s+da /dz). Physically this means that the deformation of the crystal in the neighborhood of the defect causes a local change of s, the deviation from the exact Bragg angle, as has already been discussed in Section 5.1 see Figure 5.3, for example. It is clear that if a = 0, then Eqs. (5.5) and (5.8) reduce to the equations for an undeformed crystal, and the defect will be out-of-contrast. 

Figure 8.41. DF images (g = 242) of the modulated structure in bytownite (An73). (a) Average deviation from the exact Bragg angle (b) s=0. Note how the contrast washes out in (b). (From McLaren 1974.)...

Section 5.7.2). Chadderton (1964) used this model in conjunction with the two-beam dynamical theory of electron diffraction, Eqs. (5.5a, b), to calculate contrast profiles for tracks at different positions in the crystal and for different values of the deviation s from the exact Bragg angle and the... 

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