Possibilities and limitations of X-ray diffraction using high-energy X-rays on a laboratory system

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1 Z. Kristallogr. Suppl. 30 (2009) / DOI /zksu by Oldenbourg Wissenschaftsverlag, München Possibilities and limitations of X-ray diffraction using high-energy X-rays on a laboratory system J. te Nijenhuis *, M. Gateshki, M. J. Fransen PANalytical B.V., Lelyweg 1, 7602 EA Almelo, The Netherlands * hans.te.nijenhuis@panalytical.com Keywords: diffraction, pair distribution function, high-energy X-rays, nanocrystalline materials Abstract. Analyzing powder diffraction data of nanocrystalline and amorphous materials using the pair distribution function method provides useful information about long and short range ordering in the material investigated. We have developed the application of PDF analysis on a standard laboratory system employing an X-ray tube with a silver anode as X- ray source. Meaningful results have been achieved from a range of samples that allowed for comparison with previously reported data, obtained using synchrotron radiation. Introduction Recent years have shown an increased interest in nanomaterials due to their specific properties. Structural information about these materials can be derived from broad, not welldefined features in a diffractogram. Analysis of nanomaterials therefore needs a totalscattering approach, including both peaks and diffuse scattering, rather than relying on Bragg peaks only. One of the most promising analytical methods used is atomic pair distribution function (PDF) analysis. Originally, this method was developed to study amorphous and highly disordered materials. More recently, it has been used also for the analysis of nanostructured materials. Since the method requires short wavelengths, traditionally the measurements are performed at synchrotron facilities, making use of both the high photon energies and the high photon flux that these beam lines offer. On the other hand, in-house measurements with various X-ray wavelengths have been reported as well [1, 2]. We have investigated the possibility to study nanomaterials on a standard laboratory system, using Ag Kα radiation. In this paper we describe the first results on nanocrystals, liquids and amorphous materials. Pair distribution function analysis The pair distribution function G(r) describes the probability of finding two atoms separated by a distance r in the material under investigation. The PDF method extracts structure-related information from powder diffraction data [3]. Since the technique takes both Bragg and

2 164 European Powder Diffraction Conference, EPDIC 11 diffuse scattering into account, it provides information not only about the long-range (>10 nm) atomic ordering but also about the short-range ordering in materials. The method is performed in the following steps: (i) the diffraction pattern is corrected for background (using a separate diffraction measurement of an empty sample container), Compton scattering, detector dead-time, absorption, diffraction geometry and polarization; (ii) the corrected X-ray diffraction data is scaled into electron units and the reduced structure function [4] is calculated; (iii) the structure function is Fourier transformed into the atomic pair distribution function: G(r) = 4πr (ρ(r) - ρ 0 ) (1), in which ρ(r) is the local atom number density, and ρ 0 is the mean atom number density. Since the method does not presume a periodicity in the material, it is widely applied for the study of nanocrystalline and amorphous materials. The data can be used for full-profile fitting to refine structural models [5]. Experimental setup X-ray diffraction measurements were performed on a PANalytical X Pert PRO MPD system equipped with a programmable divergence slit, a capillary spinner, programmable antiscatter and receiving slits and a scintillation detector. An X-ray tube with a silver anode was used as X-ray source, delivering Ag Kα radiation with a wavelength of nm. Additional shielding was applied to the optical path in order to achieve a feature-free background. The samples have been prepared in glass capillaries with a diameter of 2 mm. Scans along the 2θ axis were made up to an angle of 160 degrees corresponding to a scattering vector Q of 22 Å -1. The scattering vector is given by Q = 4πsin(θ) /λ. Data acquisition times were typically in the order of 20 h. Initial data treatment, including background subtraction and optional Kα 2 stripping was done using X Pert HighScore [6]. For PDF analysis and fitting, we used the software RAD [7] and PDFgui [5]. Results and discussion Samples of different nature crystalline, nanocrystalline, amorphous solid and liquid were selected to test the applicability of PDF analysis on a standard XRD system. The results of these experiments are described below. 2theta deg. (Ag radiation) a) b) Figure 1. (a) XRD measurement and (b) reduced structure function of silicon carbide.

3 Z. Kristallogr. Suppl. 30 (2009) 165 Silicon carbide Figure 1a shows a diffraction pattern of silicon carbide powder in a capillary, together with a measurement of an empty capillary. The reduced structure function obtained from the corrected intensity data is shown in figure 1b. After Fourier transformation the PDF as shown in figure 2 was obtained. The maxima in this graph could be identified as the interatomic distances Si-C, Si-Si and C-C, derived from the sphalerite crystal structure of SiC [8]. G(r) (Å -2 ) Gdiff Gobs Gcalc Radial distance (Å) Figure 2. Experimental (circles) and calculated atomic PDF (red line) of SiC. Table 1. Interatomic distances of SiC calculated determined from the experimental PDF (fig.2). Atoms Orientation Interatomic distance (Å) Si C ¼ <111> 1.89 Si Si, C C ½ <110> 3.08 Si-C ¼ <311> 3.61 Si Si, C C <100> 4.36 Si C ¼ <331> 4.75 Si Si, C C ½ <211> 5.34 Anatase Measurements performed for PDF analysis typically require long-range scans up to high 2θ angles, where the diffracted intensities are low. Variable counting time (VCT) methods can be applied to spend longer counting times at the high-angle, low-intensity region of the diffractogram at the cost of time spent on the low-angle region. Schematically the redistribution of measurement times is shown in figure 3. The total measurement time is the same for both situations. In order to investigate the improvement of data quality at high Q-values, experiments of typically 20 h measurement time were performed on nanocrystalline anatase (TiO 2 ) with an average particle size of 15 nm using constant and variable measurement times according to the scheme given in figure 3. The resulting reduced structure functions are shown in figure 4.

4 166 European Powder Diffraction Conference, EPDIC 11 5 s/step θ 2θ 9 Figure 3. Constant counting time (left) and variable counting time (right) as a function of 2θ angle. F(Q) (Å -1 ) F(Q) (Å -1 ) Figure 4. Reduced structure functions of anatase, measured using variable and constant counting times. The noise level at high Q-values of the variable counting time measurement is improved in comparison with the constant counting time measurement allowing the observation of additional structure-related features. No reduction in data quality has been observed in the low Q- range. The PDF from the VCT experiment and the calculated PDF are in good agreement. G(r) (Å -2 ) Gdiff Gobs Gcalc Radial distance (Å) Figure 5. Experimental (circles) and calculated atomic PDF (red line) of nanocrystalline anatase. Vanadium oxide xerogel Vanadium oxide xerogel (V 2 O 5 nh 2 O) does not form crystals, that can be analysed with the use of traditional crystallographic methods. The diffraction pattern (see figure 6) only shows a combination of Bragg-like peaks and broad diffuse features.

5 Z. Kristallogr. Suppl. 30 (2009) 167 Figure 6. XRD measurement on vanadium oxide xerogel. The PDF, derived from the measurement was compared to the PDF obtained from a structure model described by Petkov et al. [9]. This model describes the crystallites consisting of bilayers of V 2 O 5, made of square pyramidal VO 5 units and separated by water molecules. PDF analysis in figure 7 shows a good fit at distances in the intralayer region (r < 1.15 nm) and a not so good fit in the interlayer region (r > 1.15 nm). The same observation was made by Petkov et al. [9] based on synchrotron measurements with a wavelength of nm. It was proposed that the bilayer slabs are not perfectly stacked, but are turbostratically disordered. G(r) (Å -2 ) X Pert PRO, Ag radiation ( = 0.56 Å) Gobs Gcalc Radial distance (Å) Figure 7. Atomic PDF of vanadium oxide xerogel. Amorphous solids Fumed silica powder has been used as an example of applying PDF analysis to amorphous materials. Traditional structure analysis does not give much information; only a few humps can be seen in the scan in figure 8a. After calculating the reduced structure function in figure 8b more structure can be observed. PDF analysis of these data helps to reveal the short range order by determining average distances between the nearest neighbouring atoms.

6 168 European Powder Diffraction Conference, EPDIC 11 Figure 8. XRD measurement (left) and reduced structure function (right) of silica. The PDF in figure 9 shows five clear peaks that could be determined as first and second order Si-Si, O-O or Si-O interatomic distances in silica as given by Mozzi and Warren [1]. 3 G(r) (Å -2 ) r (Å) Figure 9. Atomic PDF of fumed silica. Figure 10. Atomic PDF of water. Liquids As in amorphous materials, liquids do not have a periodic arrangement of the atoms, and therefore no sharp diffraction maxima in the diffractogram. However, with the use of PDF analysis average distances between the atoms can be observed. As an example we show here the results of tap water. The PDF in figure 10 shows a relatively narrow peak for the first O- O distance (ca. 2.8 Å). The maxima for the second and third coordination spheres are less sharp. These results are in accordance with the synchrotron data, employing photon energies of 10 kev (λ 0.12 nm) reported by Hura et al. [10]. Discussion The results achieved from a standard laboratory XRD system show a good agreement with data reported in literature, obtained from both in-house equipment and synchrotron beam lines, despite the different characteristics of synchrotron and tube radiation. The spectrum of the Ag radiation used contains the Kα 1 - Kα 2 doublet; numerical corrections had to be applied to remove the Kα 2 component. The spectrum of synchrotron radiation is monochromatic. To our knowledge the resolution of the measurements with open receiving slit are comparable to the resolution of synchrotron data recorded using an imaging plate. The long 2θ measurement range allowed for maximum scattering vectors up to 20 Å -1. The high-energy X-rays of a synchrotron facility give the possibility to obtain higher Q-vectors, although in practice values larger than 30 Å -1 are rarely used for PDF analysis.

7 Z. Kristallogr. Suppl. 30 (2009) 169 Signal-to-noise ratio of the data depends on the measurement time in both cases. The measurements reported here took 20 to 24 hours typically, compared to a few minutes or even seconds in a synchrotron. On the other hand, the flexibility and accessibility of an inhouse system make it the ideal tool for preparation and pre-screening for valuable beam time. Conclusions Results of PDF analysis on a range of samples measured on a standard laboratory XRD system, equipped with an X-ray tube with a silver anode, have been shown. Meaningful results have been achieved, that allowed for comparison with data reported in literature, even though the attainable Q-range is not as high as with synchrotron radiation. The current results encourage investigating the applicability of the PDF method on other materials with other optical configurations and detectors. References 1. Mozzi, R.L. & Warren, B.E., 1969, J. Appl. Cryst., 2, Brühne, S., Uhrig, E., Luther, K.-D., Assmus, W., Brunelli, M., Masadeh, A.S. & Billinge, S.J.L., 2005, Z. Kristallogr., 220, Egami, T. & Billinge, S.J.L., 2003, Underneath the Bragg peaks: Structural Analysis of Complex Materials (Amsterdam, The Netherlands: Elsevier Science B.V.). 4. Klug, H. P. & Alexander, L. E, 1974, X-ray Diffraction Procedures for Polycrystalline Materials (New York, NY, USA: Wiley). 5. Farrow, C.L., Juhas, P., Liu, J. W., Bryndin, D., Bozin, E. S., Bloch, J., Proffen, Th. & Billinge, S. J. L., 2007, J. Phys.: Condens. Matter, 19, X Pert HighScore, software program for phase identification, 7. Petkov, V., 1989, J. Appl. Cryst., 22, Braekken, H., 1930, Z. Kristallogr, 75, Petkov, V., Bozin, E., Billinge, S.J.L., Vogt, T., Trikalitis, P. & Kanatzidis, M., 2002, J. Am. Chem. Soc., 124, Hura, G., Sorenson, J., Glaeser, R.M. & Head-Gordon, T., 2000, J. Chem. Phys., 113, Acknowledgements. The authors gratefully acknowledge Prof. V. Petkov, Central Michigan University, Mt. Pleasant, MI, USA and Prof. B. Palosz, Institute of High Pressure Physics, Polish Academy of Sciences, Warsaw, Poland for providing respectively the vanadium oxide xerogel and silicon carbide samples described in this paper.

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