Computer Simulation Tools for X-ray Analysis by Sérgio Luiz Morelhão

Author:Sérgio Luiz Morelhão
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Note 5.3: Integrated Intensity, Rotating Crystal Method (Zachariasen 1945).

Given

as the incident and diffracted wavevectors, respectively, described in spherical coordinates in relation to the rotation axis ϕ, Fig. 5.9. Following a procedure that is similar to that used in Exercise 5.2(b), the area under the intensity curve as a function of the rotation angle is

whose volume element is calculated by the Jacobian of the transformation: and

that is, , resulting in

Exercise 5.5.

Single crystal goniometers spatially orient the sample’s diffraction vectors starting from the orientation matrix. (a) With two crystallographic directions identified beforehand A = [A 1 A 2 A 3] and B = [B 1 B 2 B 3],9 find the orientation matrix and the crystalline lattice base vectors, i.e. edge vectors , , and , in an x y z coordinate system where the direction A coincides with the z-axis and direction B is within the x z-plane. (b) In a monoclinic lattice, and β ≠ 90∘, what is the orientation matrix for directions A = [100] and B = [010]? (c) With being the incident wavevector, which are the rotations necessary for reflection 002 to diffract on the x z incidence plane?

Answer (a): Directions A and B correspond to vectors and . Edge vectors, in matrix notation , , and , are defined arbitrarily since the unit cell geometry is maintained (see Exercise 4.​2). From the directions A and B, an orthonormal basis is created

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