X11 beam line characteristics.



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X11 beam line characteristics.

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. gif) 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. gif. 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. gif and gif 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 gif 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.



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