173 ANALYSIS OF LOW MASS ABSORPTION MATERIALS USING GLANCING INCIDENCE X-RAY DIFFRACTION N. A. Raftery, L. K. Bekessy, and J. Bowpitt Faculty of Science, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland, Australia ABSTRACT This article shows that a mirror based glancing incidence (low ω) geometry may be suitable for analysis in cases of low mass absorption materials, particularly if there is only a limited quantity available. After conversion for the James relationship there is very little difference between the symmetric and asymmetric parallel beam data for 2θ > 2ω, however care must be taken to properly weight the data in the asymmetric case if it were to be used in a modelling approach such as Rietveld Analysis. The materials examined were paracetamol and low ash coal. There is evidence of a slight suppression of background in the low 2θ region (<2 2θ) for the converted glancing incidence data compared to the symmetric data. There is a systematic difference between the converted glancing incidence data and the symmetric data for 2θ < 2ω. INTRODUCTION Bragg-Brentano geometry offers many advantages due to its focussing nature. These advantages include good intensity and resolution. However there are restrictions due to its focussing nature as well as inherent aberrations [1]. One of the most important restrictions is that the sample surface must be on the theta rotation axis, otherwise there is a specimen height displacement error. The nature of a specimen displacement error is an angular dependant diffraction peak shift and slight peak broadening due to defocusing. Closely related is the error associated with the scattering that occurs from varying depths into the sample which is due to the low absorption by sample of the incident beam. The nature of this transparency error is an angular dependant diffraction peak shift and different type of peak broadening due to defocusing. Some success has been achieved in modelling these effects [2] in a Bragg-Brentano geometry. Another restriction, in the case of lowly absorbing materials, is that there must be sufficient sample thickness for the sample to be considered infinitely thick. If the sample is not infinitely thick then there will be systematic intensity loss at high 2θ which modelling cannot address. For paracetamol (C 8 H 9 NO 2 ), the CuKα radiation has a penetration depth of 3.5 mm at θ = 35 (for a packing density of.5). At some value of θ/2θ the beam length at the sample will exceed the sample length below this value there is systematic loss in scattering intensity. An alternative diffractometer geometry is an X-ray mirror based parallel beam. Mirror based parallel beam offers good intensity, moderate resolution and fewer aberrations [3]. Any symmetric geometry (θ/2θ) has similar absorption depth limitations and irradiation length limitations. If a shallow incidence angle (or glancing incidence) geometry is used then the nature and extent of these problems are changed. While there is no effect of the resolution of the powder X-ray diffraction data when the incidence angle is changed [3], there is an angular dependant variation in the diffraction intensity [3,4].
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174 This article shows that there may be some value in adopting a glancing incidence geometry in the case of a low absorption material. EXPERIMENTAL DETAILS The equipment used was a PANalytical X Pert Pro diffractometer with a PW35/6 theta/theta goniometer and a PW3373/ copper long fine focus X-ray tube. A PW1348/66 X-ray mirror was used to produce a parallel beam approximately 1.2 mm in height and 2 mm in width. The beam width was restricted to 1 mm by use of a mask. Soller slit packs of.4 rad was used in the pre-diffraction and post-diffraction optics. The post diffraction optic was a.9 parallel beam collimator with a large area (25 mm 2 mm) proportional detector. A low incidence angle (ω) of 4 was used. Comparison data was taken in symmetric geometry (θ/2θ). The samples were low ash coal (<2% mineral matter) and commercially available paracetamol. The samples were micronised in a McCrone mill. The samples were side drifted into 15 mm wide, 35 mm long by 2 mm deep sample holders. COMPARISON OF EXPERIMENTAL DATA A graphical comparison of data and differences between the glancing incidence and symmetric data for the low ash coal and paracetamol are plotted in Figures 1 and 2 respectively. The glancing incidence data was converted by the James formula [4] R = 2 [1 (sin ω sin(2θ ω))] Where R is the ratio of the glancing incidence (or asymmetric) measured intensity and the symmetric (ω = θ) measured intensity. Some general features are: at low 2θ (2θ < 2ω) the intensity of the converted glancing incidence data always exceeds that of the symmetric data; at high 2θ the intensity of the converted glancing incidence data approximates that of the symmetric data; at low 2θ (2θ > 2ω, 1 to 2 ) the intensity of the symmetric data always slightly exceeds that of the converted glancing incidence data. Phenomenon 1 is unexpected. While at some value of θ the beam length at the sample exceeds the sample length in the symmetric case. For the geometry specified, the irradiated beam length should not exceed the sample length at any angle used. Due to the conversion of the glancing incidence data, the estimated standard deviation of the two data sets differ [3].
175 2 15 counts 1 5-5 2 4 6 8 1 2θ Figure 1. Low ash coal plotted are the symmetric, the converted glancing incidence (ω =4 o ) data, and the difference between the two (symmetric converted). counts 45 4 35 3 25 2 15 1 5-5 2 4 6 8 1 2θ Figure 2. Paracetamol difference plotted are the symmetric, the converted glancing incidence (ω = 4 ) data, and the difference between the two (symmetric converted). Phenomenon 2 is expected. While at some value of 2θ the penetration depth normal to the surface will exceed the sample thickness for the symmetric geometry, the attenuation is exponential and most absorption occurs in the upper few layers. In Figure 3 the relationship of the expected diffracted intensity with depth for various incidence angles for the symmetric case is calculated for paracetamol. It is not expected that the penetration depth will exceed the sample thickness for either the low ash coal or the paracetamol. Phenomenon 3 is marginal and unexpected. It appears to be a difference in the background.
176 12 1 8 percent 6 4 2 1 2 3 depth (mm) Figure 3. Calculated expected diffraction intensity with depth normalised to infinite thickness intensity in the case of paracetamol θ = 35, θ = 7. CONCLUSIONS Glancing incidence analysis of low mass absorption materials holds some promise. It can avoid the low absorption related problems of peak shift (if a Bragg-Brentano geometry is used) and potential intensity loss at high 2θ (if a symmetric geometry is used). It remains to be shown that the James conversion is an exact representation of the relationship between the asymmetric and symmetric intensities, but it is a good first order approximation. The intensity differences which occur when ω < θ make it prudent to collect and use data for 2θ > 2ω. REFERENCES [1] H. P. Klug, L. E. Alexander. X-ray Diffraction Procedures. Wiley (1974). [2] R. W. Cheary, A. A. Coelho, J. P. Cline. Fundamental Parameters Line Profile Fitting in Laboratory Diffractometers, J. Res. Natl. Inst. Stand. Technol. 19, 1-25 (24). [3] N. A. Raftery, R. Vogel. Limitations of asymmetric parallel-beam geometry, J. Appl. Cryst. 37, 357-361 (24). [4] R. W. James. The Optical Principles of the Diffraction of X-rays. London: Bell (1967).