Divergence axial

The first two parameters, p and p2, account for the axial divergence of the incident beam and they can be expressed as... 

K is known as the shape factor or Scherrer constant which varies in the range 0.89 < XT < 1, and usually K = 0.9 [H.P. Klug and L.E. Alexander, X-ray diffraction procedures for polycrystalline and amorphous materials, Second edition, John Wiley, NY (1974) p. 656]. L.W. Finger, D.E. Cox, A.P. Jephcoat. A correction for powder diffraction peak asymmetry due to axial divergence, J. Appl. Cryst. 27, 892 (1994). 

R.W. Cheary and A. Coelho. A fundamental parameters approach to X-ray line-profile fitting, J. Appl. Cryst. 25, 109 (1992) R.W. Cheary and A.A. Coelho. Axial divergence in a conventional x-ray powder diffractometer. II. Realization and evaluation in a fundamental-parameter profile fitting procedure, J. Appl. Cryst. 31, 862 (1998). 

A proper configuration of the instrument and its alignment can substantially reduce peak asymmetry but unfortunately, they cannot eliminate it completely. The major asymmetry contribution, which is caused by the axial divergence of the beam, can be successfully controlled by Soller slits especially when they are used on both the incident and diffracted beam s sides. The length of the Soller slits is critical in handling both the axial divergence and asymmetry however, the reduction of the axial divergence is usually accomplished at a sizeable loss of intensity. 

There are 25 plates in a Softer slit. Axial size of the incident beam when it exits the slit is 12 mm. Calculate the length of the plates along the x-ray beam (/) if the slit results in the axial divergence of the beam, a = 2.5°. Neglect the thickness of the plates. 

Asymmetry was treated in the two-parameter approximation given by L.W. Finger, D.E. Cox, and A.P. Jephcoat, A correction for powder diffraction peak asymmetry due to axial divergence, J. Appl. Cryst. 27, 892 (1994). 

Figure 2.17 System aberrations of the X-ray diffractometer due to axial-divergence and flat-specimen errors. (Reproduced with permission from R. Jenkins and R.L. Snyder, Introduction to X-ray Powder Diffractometry, John Wiley Sons Inc., New York. 1996 John Wiley Sons Inc.)...

Least squares fit of the NAC reference sample synchrotron powder profiles obtained with the Ge(lll) analyzer crystal, (a) NAC (211) Bragg reflection (b) NAC (921) Bragg reflection. The flve other curves are, from left to right, the incident beam source profile, the transfer function of the monochromator, the pure sample profile, the reflection profile of the analyzer, and the axial divergence asymmetry function, respectively. (From Masson, Doryhee, Fitch, by courtesy of J. Appl. Crystallogrfi... 

There are two different approaches for calculation of the instrumental function. The first is the convolution approach. Proposed more than 50 years ago, initially to describe the observed profile as a convolution of the instrumental and physical profiles, it was extended for the description of the instrumental profile by itself According to this approach the total instrumental profile is assumed to be the convolution of the specific instrumental functions. Representation of the total instrumental function as a convolution is based on the supposition that specific instrumental functions are completely independent. The specific instrumental functions for equatorial aberrations (caused by finite width of the source, sample, deviation of the sample surface from the focusing circle, deviation of the sample surface from its ideal position), axial aberration (finite length of the source, sample, receiving slit, and restriction on the axial divergence due to the Soller slits), and absorption were introduced. For the main contributors to the asymmetry - axial aberration and effect of the sample transparency - the derived (half)-analytical functions for corresponding specific functions are based on approximations. These aberrations are being studied intensively (see reviews refs. 46 and 47). 

Figure 6.15 shows the instrumental profile caused by axial shift of the points Ai and A2 i.e. arbitrary axial divergence). 

The corrections should be made to take into account the change, first of all, in the axial divergence and, perhaps, in the equatorial divergence. It is easy to see from Figure 6.24 that the maximal axial divergence can be estimated as yAX = Axl R + < + b). Substituting the values 7 = 217.5 mm,... 

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