5.5 X-ray absorption in Debye-Scherrer Geometry

While x-ray absorption is usually not a problem in Bragg-Brentano measurements, it is crucial that it be considered in the design of a Debye-Scherrer measurement and key to that is knowing the value of \(\mu R\), which is a unitless quantity that measures the amount of absorption.

GSAS-II provides a tool, program Absorb (see §19.1) that can be used to determine the linear absorption coefficient, \(\mu \), and where \(R\) is the radius of the sample capillary. Note that since \(\mu \) normally has units of \(\rm cm^{-1}\), \(R\) must be converted to the inner radius in cm, since normally capillary sizes are given as a diameter in mm, and often for the outer dimension. In addition to computing \(\mu \) and \(\mu R\), program Absorb plots the effect of changing the x-ray wavelength and the range for the correction as a function of \(2\theta \), which can be useful to consider potential changes to the measurement.

The effect of absorption on the experiment will depend on the magnitude of \(\mu R\), as follows:

• \(\mu R < 0.5\): in this range the effect of absorption is quite small and can be ignored. At \(\mu R = 0.5\), approximately 50% of the incident x-ray flux is lost to absorption, but the variation with angle is less than 5% over the likely range of the experiment and thus is negligible.
• \(0.5 < \mu R < 1.0\): In this range, absorption becomes significant, where at \(\mu R = 1.0\) as much as 80% of x-rays are absorbed and the absorption correction can be as large as 20-25%. However, a rule of thumb developed by Alan Hewat long ago for Debye-Scherrer geometry is that if \(\mu R\) is less than 1, the effect of absorption will be a minor perturbation on the ADPs, so unless having an accurate ADP determination is particularly important, an absorption correction can be omitted.
• \(1.0 < \mu R < 1.5\): In this range absorption will significantly degrade reflection intensities, with losses as high as 90% of x-rays lost to absorption, but the data can be corrected well. If it is possible to reduce the sample diameter to bring \(\mu R < 1\), this would improve the experiment. If not, an absorption correction is necessary to obtain accurate results as it can change the measurements by nearly a factor of 2.
• \(1.5 < \mu R < 2.5\): At this point absorption now is quite severe. Even at high angles (where losses are least desirable) the vast majority of the incident beam is lost. This can be successfully corrected, but this is less than ideal. Plan to increase counting times by as much as an order of magnitude over what would normally be required. Consider the options in the next section as alternatives.

• \(2.5 < \mu R\): Under normal circumstances, these measurements are not successful. Some people will consider making a measurement with \(\mu R < 5\) if the result is sufficiently valuable to afford the measurement time. There are a number of options that should be considered to reduce the sample absorption:

  • if near an element’s absorption edge, use a different wavelength, if not near an edge, decrease the x-ray wavelength;
  • consider using a smaller diameter capillary;
  • consider diluting the sample, either with a small unit cell crystalline material that will add only a small number of peaks (diamond powder?) or a low-density non-crystalline phase (amorphous boron?).

If you are performing an experiment with a highly absorbing sample, you are recommended to measure a good estimate for the packed density of the actual specimen you are using for the measurement. This can be done by weighing the capillary before filling it and again after filling it. This will require a balance with microgram sensitivity. In addition, estimate the length and inner diameter of the region filled with the sample to determine the volume. A microscope can be helpful for this.