A detailed description of the curved crystal monochromator geometry and its characteristics has been given
by Lemonnier et al [75] and has been reviewed more recently by
Caciuffo et al [21].
The spectral bandpass of a curved crystal monochromator is dominated by three factors.
Firstly the intrinsic width, 
(given by Eq. 
) of the
particular crystal reflection being used is of importance. Secondly
the curvature of the crystal must be accounted for since this fact along with the horizontal angular
spread of the fan of radiation will in general combine to give a Bragg angle variation along the length
of the crystal. The change in Bragg angle due this effect is given by [21]
where L is the illuminated length of the crystal, 
is the Bragg angle, 
is
the angle of the Fankuchen cut and 
and 
are the source-crystal and crystal-focus distances respectively.
A special case known as Guinier condition is reached when
In this case 
.
The third contribution to broadening arises from the finite horizontal source size, 
. The angle
which the source subtends at the crystal is 
.
The overall spectral width is therefore given by [75]
The spectral bandwidth at the focus may however be narrower than that emerging from the monochromator
crystal because of the collimator slits 
which are positioned 
in front of the focus. These
slits trim down the beam in the horizontal and in doing so effectively make the length of monochromator
crystal seen from the focus smaller, i.e. reducing the value of 
. If the angular width of incoming
radiation accepted by is 
then the length of crystal contributing to
the focus is
and 
must be calculated using 
instead of in Eq. .
The typical settings for the horizontal collimator slits of 
, and the 
Fankuchen angle mean
however that the whole length of the crystal is visible from the focus and that the horizontal beam size at the
crystal will actually be the dominating factor.
For the X11 beam line, 
, 
, 
and 
.
Substituting these values into Eq. and we obtain a value
for 
of 
.
The shape of the distribution of energies was measured by recording the
the Bragg reflection profile from an oriented perfect silicon crystal. The crystal was
rotated around a horizontal axis perpendicular to the beam direction and a reflection
was measured using a scintillation detector placed so as to accept back diffracted X-rays.
Figure shows the diffraction profile obtained.
It is apparent from the shape of the reflection that the bending of the monochromator
crystal is not uniform along its length. This may be the result of thermal distortion of the
crystal. The FWHM of this reflection was found to be 
in
angle space.
Figure: Diffraction profile obtained from rocking over the 
reflection collected
in back diffraction mode from a perfect silicon crystal. The profile reflects the distribution
of energies in the monochromatic beam.
The flux delivered by the X11 beam line at the focus is > 10 times that for X31 due to
the 
focussing and the broader band of energies passed by the monochromator.
