Logo Mode (1): Flat Plate with/without Analyser Crystal
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Mode (1): Flat Plate with/without Analyser Crystal

The diagram below illustrates this basic mode (without analyser crystal): a beam of near-parallel monochromatic X-rays strikes the surface of a flat "plate" sample at an angle θ. If the Bragg condition is satisfied and diffraction occurs, as illustrated, then the diffracted X-rays which reach the detector will also be travelling at an angle θ to the sample; this means that the total angle between the incident and diffracted beams is 2θ. This configuration can be retained for different θ provided we always rotate the detector twice as much (2θ) as the sample (θ). There are some advantages in using this so-called 2θ:θ motion, and you will come across it often during this course.

It is important to understand that higher density materials, including many inorganic compounds, are highly absorbent of x-rays at the wavelengths in common use for powder diffraction. As a result of this, where flat plate sample geometry is in use most of the diffraction occurs within a thin layer close to the sample surface. One consequence of this is that, on average X-ray photons travel a similar distance within the sample before and after they are diffracted (this will be explained more fully later in the course). It turns out that this gives rise to an advantageous "cancelling out" feature, making the effects of X-ray absorption much less of a problem. A disadvantage, however, of flat-plate holders is that they can give rise to preferred orientation.

The diagram is shown together with a typically good quality powder diffraction pattern from fluorescein diacetate, collected over 6 hours on Daresbury SRS-synchrotron station 9.1.


The useable intensity of an incident X-ray beam and its parallelism are often mutually opposed. Yet we need both: the intensity to provide statistically better data, and the parallelism to provide accuracy and resolution. Generally a synchrotron is able to deliver a much greater intensity for a given degree of parallelism, compared to a laboratory powder diffractometer. The illustration above represents a good typical synchrotron combination with regards to intensity and resolution. If however one wants to increase resolution without regard to intensity then the so-called "double crystal" arrangement as seen below can be used; the further improvement in resolution is a consequence of the second "analyser" crystal. This analyser crystal is set to diffract only X-ray photons of the same wavelength as those given by the monochromator (the "first crystal"), and will only diffract (i.e. "pass on" to the detector) a narrow angular range of X-rays scattered by the sample.
However the price paid for this double crystal arrangement is loss of intensity. To compensate for this, long collection times are required to obtain statistically good patterns. A novel way of reducing the counting time in this mode has been devised at the ESRF by Prof. Andrew Fitch in which 9 analyser crystals (each with a detector) are ganged up to work simultaneously in parallel.

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© Copyright 1997-2006.  Birkbeck College, University of London.
 
  		Author(s): Paul Barnes
Simon Jacques
Martin Vickers