CALIBRATION OF DIFFRACTOMETERS: A TEST METHOD TO MONITOR THE PERFORMANCE OF INSTRUMENTS. G. Berti, U. Bartoli, M. D Acunto and F.

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1 Materials Science Forum Online: ISSN: , Vols , pp 7-30 doi:10.408/ 004 Trans Tech Publications, Switzerland CALIBRATION OF DIFFRACTOMETERS: A TEST METHOD TO MONITOR THE PERFORMANCE OF INSTRUMENTS G. Berti, U. Bartoli, M. D Acunto and F. De Marco Department of Earth Science, University of Pisa, Via S. Maria 53, I Pisa, Italy Diffraction Measurement and Testing Centre (Centro Diffratometria) Consorzio Pisa Ricerche, P.zza A. D Ancona, 1 Pisa Italy Keywords: Calibration, calibration curves, systematic errors Abstract. Reproducibility of diffraction experiments provides an indication of data consistency with respect to different variables. The level of reproducibility and accuracy of the diffraction measurements is increased when using calibrated instruments. The paper presents most significant results of the Calibration Monitoring of Diffractometers, a project using a systematic approach to the Round Robin tests. At the present stage, the results suggest that instrumental performances and other related experimental effects in a diffraction the experiment can be summarised through characteristic curves. Introduction Diffraction measurements involve a set of operations, procedures and protocols for translating the collected data in physical meaning. Many round robin tests conducted over the past twenty-five years have given the common result of high internal consistency of data and unexpected low accuracy; thus resulting in some difficulties to reliably compare the data. The data comparison can be significantly dependent on aspects like specimen characteristics, performance of instruments and their variation in time. A good calibration procedure ought consider all these variables by evaluating the residual systematic effects still present after a good performed instrument alignment. Repeatability and/or reproducibility (i.e. intentionally repeated measurements according to specified invariant conditions) of X-ray diffraction measurements shall be controlled in relation to the deviations () from the expected diffraction angles [1-4]. Uncontrolled systematic effects lead to biased evaluation of these characteristic deviations ( characteristic curves), thus vanishing the comparison effectiveness of the diffraction data. It has been shown [5] that a curve can be dealt out for calibration procedure. This calibration curve represents the optimum alignment taking in account several nominal instrumental aspects. Nevertheless, it has been shown also that the experimental contribution is summarised by the correction curve [-3]. It has been found that the correction curves tend to have a time invariant shape, when the calibration process uses a traceable operative protocol (including sample preparation and mounting). When the correction curve is invariant with time, it shall be considered characteristic of that specific diffraction measurement (i.e. diffractometer and other experiment related factors). The Calibration Monitoring of Diffractometers (CMD) project was launched in 1997 in order to verify the reproducibility and repeatability of data collected from a number of different participating diffractometers; the obtained results provided the useful indication that the characteristic curves might become a good test for checking the repeatability and reproducibility of the diffraction measurements. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-08/04/16,:4:41)

2 8 European Powder Diffraction EPDIC 8 The aim of the present paper is to show how characteristic curve can support the effective goodness of diffraction experiments and measurements. The characteristic curve has been used as a guide to compare the experimental CMD results and to provide a method for obtaining meaningful values which enhance the data accuracy. Implementation of the test method Like the usual round robin tests, even the CMD project was proposed to collect data from a common sample. Portions of a certified commercial sample of Alumina (Al O 3 with 99% purity and crystallite size ranging around 5µ) was made available to the participants, who have cyclically collected data in the range of 0-90 (in ). The time interval between two distinct cycles was about six mounts. In this lap of six months, the participating laboratories used the diffractometers routinely according to the laboratory needs and uses. The protocol adopted for the CMD project was described by ref. [3], it uses the Diffraction Instrumental Monitoring Method (DIM). DIM is an option of a more general software package DISVAR [1], it translates the nominal values (provided by either the manufacturer or the user) of the parameters to the effective ones obtained under working conditions of the instrument and the whole experiment (zero-calibration, specimen surface displacement, axial and equatorial divergence, focal spot size, receiving slit size and setting, diffractometer radius etc.). DIM determines the effective values of parameters for Bragg-Brentano diffractometers with parafocusing configuration and it produces a curves (the correction curves) for each geometrical function used to calculate the effective values of the parameters. The invariance with time of the correction curve shape, guaranties the stability of the associated parameters (experimental invariance) and it is helpful for checking the reproducibility or repeatability of the measurements. Traditionally accuracy and precision account for the differences between the true diffraction angle, the Bragg angle, B, and the actually observed angle. The true angle is not knowable and then it substituted by the expected angle. The angle is expected according to a certain calculation (based on the Bragg law). Fact is that when this observed angles are affected by inherent aberrations; even the separations (i.e. accuracy ) from the observed are affected by similar aberrations. In order to remove this quandary, a more general diffraction angle of the Bragg angle shall be used. This new general angle offers a powerful tool for the accurate evaluation of the line position because it accounts for the difference between the true angle and the value of the physically observable diffraction angle (not the actually one). The new angle is hereafter referred as the Wilson angle W. It is obtained from the Bragg angle taking in account the experimental effects (geometric and wavelength dispersion) on the centroid displacements, and the mean square broadening of the peaks. The geometrical forms derived by the theory developed by A.J.C. Wilson [6-7] and associated to the various terms effecting the centroid and the variance. DIM requires a set of 14 parameters to characterise the correction. In addition to those, it is necessary to identify the crystalline class of the analysed material. This block of parameters (instrumental and lattice constants) constitute a part of the initial set of data. The other one is the set of values associated to each Bragg reflection. Bragg reflection data processing is carried out by four distinct controls of the internal consistency of data (peak position, FWHM, normalised intensity, peak shape). The diffraction pattern process is performed by using the pseudo-voigt function to represent the diffraction line profiles.

3 Materials Science Forum Vols The results presented here concern the cyclic calibration of three diffractometers of the group of participants. These diffractometers are labelled her by A, B, and C and considered in Fig. 1. When the evaluation of the Wilson angles have been accomplished satisfactorily by using DIM, the deviation () of the Wilson angles from the expected (Bragg) ones is plotted against. Each angular deviation is then compiled in curves that represent the overall correction required to bring the Wilson angle to straddle around the expected Bragg angles [1]. 0,0 1-0, ,013-0,0 1-0,0-0,0 3-0,018-0,03-0, , A B 0,04 0-0,04-0,08-0, C Figure 1. Characteristic curves for the diffractometers A, B and C. cycle and third cycle. first cycle, second Fig. 1 reports three cyclic calibrations on the three A,B and C diffractometers. For the diffractometers A and B, characteristic curves of both first and second cycle generally tend to overlap. Instead, the third cycle shows a relevant shift that translates to differences among the effective values of the parameters. In order to check the physical meaning of these differences, the diffractometer C has been used as the testing diffractometer to impose actions and operations related to the re-alignment process as suggested by DIM. The result is the gradual approach of correction curve to zero line.

4 30 European Powder Diffraction EPDIC 8 Discussion of results and conclusions The evaluation of instrument contribution of diffractometer C was helpful to give the correct interpretation to the curves shown by the independent diffractometers, A and B; it explains the time shift and constitute a confident base to assign the role of characteristic curve of the experiment. In fact, the overall uncertainty (the error bars) on the characteristic curve may be profitably estimated by adopting an approximation method [1] (i.e. similar to the Levenberg-Marquandt one) to run the effective value in a restrained space of parameters near the expected minimum. These curves demonstrate that, a part from certain (even significant) differences still remaining, among the curve representing the three cycles, cases exist where we can be confident of the invariance of the curves. This invariance reflects the values of the parameters which contribute to the diffraction line position after a good alignment. Many repeated cycles are required to confirm the reliability of this approach tending to define characteristic curve of diffractometer. When the statistics will be satisfactorily accomplished and the reliability of the approach confirmed over a number of different cycles, each diffractometer will be characterised by a well established characteristic curve in relation to the experiment and the level of sophistication required for that. Moreover, calibration operation will take great benefit from considering that the various effective parameters influence the position and the broadening of the diffraction line at different order of magnitude. The accuracy of the calculation of the effective parameters depends on how many parameters can be effectively used. This implies that efforts should be done for determining the uncertainty over each individual parameters. It would contribute to define possible features of instrumental characteristic curves. Because time-invariant characteristic curves give a control stage of quality measurement, time-invariant characteristic curves shall be reproduced as close as possible (within the experimental errors) every time a well defined experiment is repeated. References [1] G.Berti, S.Giubbilini, E.Rognoni: Powder Diffraction 10 (1995), p. 104 [] G.Berti: Powder Diffraction 16 (001a), p. 1 [3] G.Berti: Powder Diffraction 16 (001b), p. 6 [4] G.Berti, M.D Acunto: Advances in X-ray Analysis Vol.45 (001), in press [5] R.Jenkins, R.L.Snyder: Introduction to X-ray Powder Diffractometry (John Wiley & Sons, 1996). [6] A.C.J. Wilson: The mathematical theory of X-ray powder diffraction (Philips Technical Library, The Netherlands 1963). [7] A.C.J. Wilson: Accuracy in Methods of Lattice-Parameter Measurements in Accuracy in Powder Diffraction, National Bureau of Standards Special Publication 567 (1980), p. 35 Acknowledgment Authors thank all Institutions and private companies who are participating in the initiative of the activity of Calibration Monitoring o Diffractometer. We mention here University of Pisa (earth Science Department), CNR-Pisa (Centro Studi Geologia Strutturale Dinamica Appennino), Fiat Research Centre (Torino), Health&Safety local Agency of Verona, TiOxide Hunterman (Scarlino - Grosseto), Colorobbia Italia (Empoli- Firenze), Italian Aeronautic Ministry (Roma).

5 European Powder Diffraction EPDIC / Calibration of Diffractometers: A Test Method to Monitor the Performance of Instruments /