Theory of the calibrator.



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Theory of the calibrator.

The following short section is adopted from the original theory section of [93] and is included here for the sake of completeness.

The orientation of the calibrator crystal is described with respect to a laboratory frame coordinate system having in the direction of the incident X-rays, pointing vertically upwards and pointing horizontally to complete a right-handed system. The reference orientation is taken to be when is along and the reciprocal lattice vector points directly back along the incident beam vector . Rotations from this reference position about and are described by the angles and .

Assuming an arbitrary crystal orientation given by and , for any reciprocal lattice vector in the laboratory frame, the angle of incidence , of the beam to the diffracting plane may be expressed as

By combining this equation and the Bragg equation, taking the Bragg angle as , the following result is obtained.

 

where is a constant and equal to [114] for in Åand in . The orientation of may now be related back to its orientation in the reference position (denoted by a prime) by

and by substituting for in Eq. gif we arrive at

 

A final correction to in the above equation yields the true energy . The correction used is that proposed by Materlik and Kostroun [83] and takes the form

 

where b is an asymmetry parameter and , being the refractive index.



Gwyndaf Evans
Fri Oct 7 15:42:16 MET 1994