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. 
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.
