Receiving slit plane

Equation of a Conic in the Receiving Slit Plane (Coordinate System CS)... 

Substituting this in Equation (10) and simplifying we obtain the equation of a conic in the receiving slit plane in implicit form ... 

The plane 90 determines, together with the equation of the receiving slit plane, the line of the intersection of these planes. In the coordinate system CSr the line of the intersection can be obtained easily from Equation (20) by setting the component z of the vector X to 0. Substituting coordinates of vector V and vector U in the coordinate system CS we obtain the equation of a straight line in the receiving slit plane ... 

As can be seen from the figure the conics produced by the diffraction cone with the different Bragg angles fill the receiving slit plane differently, being responsible for the asymmetry, apparent shift, and width of the diffraction peak (see also the Section 6.6.1.4). 

Figure 6.8 Intersections of the degenerated diffraction cone (20 = 90°) and receiving slit plane. Diffraction cones are produced by the incident ray from fixed point Ai = 0, 0) to points on the sample A2 having only an axial compo nent. The black rectangle represents the receiving slit. (Reprinted from Ref. 54. Permission of the International Union of Crystallography.)...

Absorption. An absorption correction is important for thick specimens with small absorption coefficient for X-rays. Consideration of absorption means that point A2 has a non-zero y component. As a consequence of this there is another conic that is important for considering the absorption. This conic is the intersection of the diffraction cone and the surface plane of the sample. Figure 6.16 shows schematically a part of the diffraction cone and a cross-section of the latter with the sample surface plane (plane in coordinate system CSl.). Points Dip (i= 1-4) are point projections of the receiving slit from point A2. Points Pap are projections of the intersection points P of the receiving slit and conic in the receiving slit plane. 

Figure 6.17 shows one example of the conic in the receiving slit plane (a) and corresponding conic in the sample surface plane (b). The conic in the sample plane can be considered also as a point projection (point A2) of the conic in the... 

Figure 6.17 Intersection of the diffraction cone with a) the receiving slit plane, and b) the sample plane. Case of absorption (the vertex of the diffraction cone is under the sample plane). D2D2D3D4 receiving slit. DjpD2pD3pD4p projection of the receiving slit from vertex of the diffraction cone into the sample plane.

Taking into account that for points on the receiving slit plane X = x,y,0 and expressing the scalar product by the sum of the eomponent products we can obtain the relation between v and y ... 

The shift of point A2 in the axial direction causes an equal axial shift of the middle point of the reflection conic in the receiving slit plane. In this sense the axial aberration is equivalent to using a narrow receiving slit with the width equal to that of the reflection region in the receiving slit plane. 

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