RIETVELD REFINEMENT OF POWDER DATA FROM MULTILAYER OPTICS

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1 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume RIETVELD REFINEMENT OF POWDER DATA FROM MULTILAYER OPTICS ABSTRACT Scott T. Misture NYS College of Ceramics at Alfred University, Alfred, NY An empirical evaluation of powder diffraction data collected using multilayer optics was performed by determining the peak shapes as a function of angle and performing Rietveld refinements. Data collected using a parabolic multilayer optic in the incident beam and either a long Soller collimator or a flat multilayer optic in the diffracted beam were evaluated. NIST Standard Reference Material SRM64OC (silicon) was used in the analysis. The results demonstrate that parallel beam data can be easily modeled using Pearson VII or pseudo-voigt profiles and the Rietveld refinements are reliable. The profile shapes obtained using two multilayer optics are unusual and warrant further investigation. INTRODUCTION Incorporating multilayer optics in laboratory x-ray instruments has revolutionized many diffraction and scattering measurements [l-9]. Parallel beam optics are particularly attractive for powder diffraction when compared to Bragg-Brentano geometry, because of the insensitivity to systematic specimen displacement errors [ 1,6]. The critical component in a parallel beam system is a parabolically curved graded multilayer optic that harnesses some -0.5 degree of divergence from a line source and creates a -1 x 10 mm parallel beam by Bragg diffraction. The efficiency of multilayer optics is generally much higher than traditional crystal optics, and the parallel beam has a divergence on the order of 110 arcsec (0.03 ). Multilayer optics, therefore, can be coupled with crystal optics on sealed tube systems and still provide reasonable count times. Although several investigations of the performance of multilayer optics have been performed, the literature is lacking a study of the applicability of the data for Rietveld refinement of powder diffraction data. EXPERIMENTAL PROCEDURE A Siemens D500 diffractometer with a Cu tube was modified to contain an Osmic Max-Flux@ G013-BA parabolic multilayer optic on the incident beam side. The Max-Flux@ optic was housed in a standard Huber monochromator housing after some minor modification. The Max- Flux@ optic was mounted antiparallel to the anode, or in other words, on the same side of the beam as the anode. This mounting configuration causes a lower angle of incidence on the small d-spacing side of the optic to balance the beam divergence across the optic.

2 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Osmic Parabolic Multilayer Optic GO-13A Axial Soller Parallel - Beam Soller Collimator 0.15 Divergence ( a > Adjustable Slits Side-Drifted Powder Specimen Soiler Collimator Scintillation Detector Incident Beam From Osmic Max-Flux@ M, Parabolic Mult Optic GO-13A Side-Drifted Powder -. Specimen.I Scintillation Osmic Max-Flux@ Detector Flat Multilayer Adjustable Ontic - I Slits Figure 1: Schematics of the optical configurations used in the experiments. (a) Incident beam parabolic multilayer Max-Flux@ optic and Soller collimator in the diffracted beam; (b) Flat multilayer optic in the diffracted beam. 1 Yhe diffracted-beam side was equipped with either standard optics or another multilayer. For the standard configuration, a long Soller collimator or parallel beam attachment was fitted. The divergence of the collimator used was 0.15, and scintillation detector was fitted directly behind the collimator. No monochromator crystal was used in this configuration because the Max-Flux@ optic reduces the Cu K/3 radiation. The multilayer optic used on the diffracted beam side is a flat non-graded multilayer manufactured by Osmic, Inc., with dimensions of -3 x 7 cm and a d-spacing of 0.38 nm. In addition to the multilayer optics, the instrument included 3 axial divergence collimators on the incident and diffracted beam sides, as well as multiple adjustable slits to limit the beam. All experiments were performed using the full 0.8 x 12 mm beam and coupled 0-28 geometry. Step I

3 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume > l 0 * l l 3 L - $j B q q (TI $ Two Theta (degrees) Figure 2: FWHM of the diffraction peaks for SRM64OC silicon vs. angle for two instrumental configurations. The data were fitted with split pseudo-voigt profiles and the error bars represent the estimated standard deviation of the value. Points without visible error bars have error bars smaller than the symbols. ns were performed using a step size of and count times of 10 sec. per step. The specimen used for the data reported here was NIST SRM64OC silicon that was side-drifted into a specimen holder with dimensions of 15 by 25 mm and a thickness of 1.5 mm. The peak profiles vs. angle were determined using Shadow [ 1 l] to tit each profile individually with split pseudo-voigt profiles. Rietveld analysis was performed using GSAS [ 121. RESULTS AND DISCUSSION Figure 1 contains schematics of the optical configurations. Figures 2 and 3 show the results of fitting pseudo-voigt profiles to the two diffraction patterns. As shown in Fig. 2, the full width at half maximum (FWHM) follows the familiar trend of increasing FWHM with diffraction angle. Note that the FWHM when using the Soller collimator is some 1.5 times greater than the data from the system with two multilayer optics in the low to mid-angle region. This is the expected result because the divergence of the flat optic is approximately three times smaller than that of the Soller collimator. The resolution of the measurement with two multilayer optics is

4 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume comparable to that obtained in Bragg-Brentano geometry when using an incident beam monochromator. [lo]. In contrast, the measurement with a Soller collimator in the diffracted beam provides data comparable to a typical Bragg-Brentano measurement incorporating 1 divergence slits and a graphite diffracted-beam monochromator. Figure 3 shows the pseudo-voigt mixing parameters as a function of angle corresponding to the fitted profiles. For the measurement using the Soller collimator, Fig. 3a, the mixing parameter increases monatonically with angle as the profiles become more Lorentzian. There is no significant difference in line shape between the low and high-angle sides. As shown in Fig. 3b, however, the low and high angle line shapes are different for the data collected with two multilayer optics. Figure 3b shows that the mixing parameters are different below and above The origin of this difference remains unclear, but it must be recognized when using symmetrical profiles to describe the line shapes. Additional analysis is underway to further quantify the profile shapes. The Rietveld refinements were approached using the strategy of fixing known values and 0.6 &. Mixing Parameter, Low Angle (a) l Mixing Parameter, Low Angie (b) a, 0.7 VJ Mixing Parameter, High Angle v Mixing Parameter, High Angle E E 1.2. s 0.6 a z? 0.5.x E ' ' 0.3 s!!a I F P 1 :sj 0.8 % i a l t tg a 8 s t g II p f if i Two Theta (degrees) Two Theta (degrees) a p pii Figure 3: Peak profile shapes resulting from fitting split pseudo Voigt profiles. (a) Mixing parameters for the data collected with a Max-Flux@ optic and a Soller collimator; (b) mixing parameters for data collected with two multilayer optics. r&ining only physically meaningful variables. This approach was adopted to ensure that the refinements could be used to evaluate the instrument without producing unphysical values of variables that tend to correlate. The lattice parameters were fixed to the NIST certified values, and the parameters refined were limited to: the Cagliotti profile width parameters, Lorentzian components of size/strain broadening, transparency of the specimen, a simple asymmetry correction, polarization, diffractometer zero shift, and isotropic thermal parameters. Note in particular that the specimen displacement correction in GSAS was not refined, and the only systematic error refined was the zero shift. Figure 4 and Table 1 show the results of the refinements. Although the weighted residuals are slightly high at 12 and 17%, the 2 values are reasonable. As indicated by the difference pattern in Fig. 4, there is clearly an inadequacy in the profile shapes for describing the data.

5 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Nonetheless, there are no significant problems with either refinement, and even the isotropic thermal parameters are reliable. Table 1 and Fig. 3b indicate that the profile shapes present a minor problem when refining data collected using two multilayer optics in the beam path. Additional work is underway to better characterize the peak shapes in this optical configuration. SUMMARY Powder diffraction data obtained using multilayer optics are similar enough to traditional optics that a common Rietveld analysis package can model the data with reasonable accuracy. No significant problems were encountered when refining NIST SRM64OC standard silicon powder data, which indicates that using multilayer optics does not introduce any problematic instrumental characteristics. The profile shapes used in the analysis do not model the observed profiles exactly, and further work is underway to quantify the profile shapes from systems incorporating two multilayers. I I I I I I I I I I I II II II II II II II II -j ^---_-- --& ~-- 1LILsI ~~-~.--,----~-----~-- I I I I I I Theta, deg XlOE 2 Figure 4: Rietveld refinement of SRM64OC Si powder for data collected using a Max-Flux@ optic and Soller collimator. Observed, calculated, and difference patterns are shown as well as line location markers.

6 Copyright (c)jcpds-international Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume Table1 : Rietveld refinement results for the two datasets. Rietveld Parameter GSAS Max-Flux@ & Soller Max-Flux@ & Flat Variable Multilayer Weighted Residual (%) WRP Chi Squared Cagliotti Parameters U 2 2 V -2-2 W (0.09) Lorentzian Broadening Lx 1.23(0.05) 1.1 S(O.05) LY 3.08(0.01) 4.24(0.11) Gaussian component GP 5.8(0.1) 0.09(0.24) Asymmetry ASP 4.43(0.08) 2.79(0.05) Zero Shift ( 28) Zero (0.001) 0.024(0.0001) Isotropic Thermal Parameter (A*) Uiso (0.0001) (0.0002) REFERENCES 1. M. Schuster and H. Gobel, Application of Graded Multilayer Optics in X-ray Diffraction, Adv. X-Ray Anal., Vol. 39, pp (1995). 2. B. Kanngieber and B. Beckhoff, EXCITATION OF LOW Z ELEMENTS BY MEANS OF A CYLINDRICAL GRADED MULTILAYER AS A HIGH ENERGY CUT-OFF IN EDXRF ANALYSIS, Adv. X-Ray Anal., Vol. 39 pp (1995). 3. C. Michaelsen, P. Ricardo, D. Anders, M. Schuster, J. Schilling and H. Goebel, IMPROVED GRADED MULTILAYER MIRRORS FOR XRD APPLICATIONS, Adv. X-Ray Anal., Vol. 42 (2000). 4. Boris Vex-man, Licai Jiang, Bonglea Kim, Rick Smith, Nick Grupido, CONFOCAL GRADED d-spacing MULTILAYER BEAM CONDITIONING OPTICS, Adv. X-Ray Anal., Vol. 42 (2000). 5. T. Holz, R. Die&h, H. Mai, and L. Brugemann, Application of Ni/C Gobel Mirrors, Materials Science Forum Vols , pp (Trans-Tech Publications, Switzerland) (2000). 6. T. Misunaga, M. Saigo, G. Fujinawa, Parallel-Beam Powder Diffractometers Using Laboratory X-Ray Sources, International Union of Crystallography Newsletter, No (2000). 7. Eberhard Spiller, X-RAY OPTICS, Adv. X-Ray Anal., Vol. 42 (2000). 8. R. Stammer, R. Hopler, M. Schuster and H. Gobel, X-RAY OPTICAL CONSIDERATIONS ON PARABOLIC GRADED MULTILAYERS ON THE DIFFRACTED BEAM SIDE IN X- RAY DIFFRACTION, Adv. X-Ray Anal. Vol41 (1999). 9. T. Holz, R. Dietsch, H. Mai, L. Briigemann, S. Hopfe, R. Scholz, R. Krawietz, B. Wehner, Pulsed Laser Deposition of laterally graded NE-multilayers and their application in parallel beam X-ray optics, Adv. X-Ray Anal., Vol41 (1999). 10. J.P. Cline, NIST Standard Reference Materials for Characterization of Instrument Performance, Industrial Applications of X-Ray Diffraction. F.H. Chung and D.K. Smith, Eds. (Marcel Dekker, Inc., 1999). 11. Materials Data, Inc., Livermore, CA. 12. A.C. Larson, R.B. Von Dreele, General Structure Analysis System GSAS, Los Alamos National Laboratory, Los Alamos, NM, June 2001.