AUTOMATED RIETVELD-ANALYSIS OF LARGE NUMBERS OF DATASETS

Transcription

1 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol AUTOMATED RIETVELD-ANALYSIS OF LARGE NUMBERS OF DATASETS Sven Vogel, Hans-Georg Priesmeyer Institut für Experimentelle und Angewandte Physik der Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, Kiel, Germany Abstract During investigations of phase transformation kinetics by diffraction techniques, several hundreds or even thousands of diffraction patterns are collected. Automation of the data analysis process is mandatory to perform for example a long sequence of Rietveld refinements. The Bragg edge transmission (BET) technique, a neutron time-of-flight method, allows acquiring patterns of sufficient statistics to derive structural information on the sample within the order of 10 seconds. For data analysis of such BET patterns a Rietveld-type of software was developed. To allow efficient analysis of a large number of patterns collected during investigations of phase transitions by BET, the automation presented here was included in this software. It is based on a script language capable of loops and conditional fitting. A single result file containing the desired variables (volume fractions, lattice parameters etc.) is created. An application example and possible consistency checks for the results are also presented. Although the concepts were developed for BET data, they should be widely transferable to powder diffraction data analysis. Introduction The available intensities at modern synchrotron and neutron sources allow time-resolved diffraction [1]. Applications of time-resolved diffraction include investigations of kinetics of phase transformations and chemical reactions (e.g. [2]). During the course of such an experiment, hundreds or even thousands of datasets are created. The number of spectra to be analysed will still further increase, once BET imaging becomes possible. Manual analysis using the Rietveld method [3] of such huge numbers of datasets is impractical. Hence, an automation of the Rietveld procedure is required. Such automation is also convenient in the case of analysis of small numbers of similar patterns, e.g. a sample under different loads in a stress/strain measurement. A novel neutron technique, so-called Bragg-edge transmission (BET), allows time-resolved studies at pulsed neutron sources with time resolutions in the order of 10 seconds. For this technique, the neutron intensity transmitted through the sample rather than the intensity diffracted by the sample is used. As this intensity is much higher than the intensity typically detected in a diffraction setup, the temporal resolution is much better than in the case of a diffraction experiment. The crystallographic information is obtained from the so-called Braggedges that appear in the transmitted spectrum [4]. A Rietveld-type of software for the dataanalysis of such spectra named BETMAn (Bragg-Edge Transmission Measurement Analysis software) was developed [5]. Although the automation procedure described here so far works on Bragg-edge transmission data, the general principles and conclusions presented are transferable

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol to diffraction data analysis. Requirements The fundamental task of automated Rietveld analysis is the application of an appropriate variation scheme to a sequence of patterns. A variation scheme in this context is a parameter turn-on sequence [6], [7]. For instance, in a first step, an overall scale factor is fitted, in a second step, additionally background and scale factors of phases are variable while in a third step also lattice parameters are fit and so on. As they are the best guess, starting values for a given pattern are the final values of the previous pattern. For the first pattern, a manual refinement is required. Especially at a spallation source, beam failures may occur during the experiment resulting in datasets with lower or even no intensity. For automated analysis, such patterns must be excluded to avoid divergence. Without rejection, for later datasets with sufficient statistics no starting values would be available due to the diverged fit. For example in the case of phase transformations, the evolving phase has typically a very low initial volume fraction for the first patterns. Again to avoid divergence, parameters like the lattice parameters must not be refined if the volume fraction of such a phase is below a certain limit. This calls for conditional refinements. Consistency checks should be possible to increase the confidence in the results. BETMAn Script Language A script language included in BETMAn meets all the requirements mentioned above. The scripts are format-free ASCII-files consisting of command keywords, parameters and comments. A reverse analysis is possible, i.e. an analysis run from the chronologically last to first pattern leading to slightly different starting values for each pattern. In case of sub optimal overall starting values from a manual refinement, the resulting time series, e.g. volume fraction, lattice parameter etc. versus time, for the forward and backward analysis would not be overlaying within the margin of error. The reverse analysis is also very useful for evolving phases, which can be followed using starting values from patterns where this phase contributes a huge volume fraction. This makes the fit of early patterns, where the phase exhibits only a small volume fraction, much more robust. The criterion of overlaying time series is treated as a consistency check. It must hold also for an offline change of the time resolution by summing a certain number of patterns prior to the fit. The generated time series in that case is naturally based on data of better statistics and hence exhibits less scatter. Again, forward and backward analysis must produce the same curves, but also time series of different time resolution must overlay within their margins of error. For these two checks, only one or two lines of the script files need to be changed, allowing to readily perform these checks. As in the case of single powder pattern data analysis, consistent parameter values are not necessarily obtained in the first attempt and for example the limits for conditional refinements need to be fine-tuned (e.g. the minimum volume fraction required for a lattice parameter refinement). Again, the script language allows to easily vary these limits and restart the analysis. Commands exist that allow generation of a single overall result file containing only the parameters of interest for a given experiment. Plots of parameters versus time resulting from different analysis directions and time resolutions are quickly generated from these files and hence the above mentioned consistency checks are easily possible. During experiments, several external

4 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol variables might be observed. For example, the sample temperature could be measured with a thermocouple and recorded on a second computer. During the data analysis with BETMAn, such variables can be merged together with the structural information into the overall result file, allowing to obtain for instance the temperature dependence of the lattice parameter very quickly. Any quantity recorded with a timestamp can be related to the structural information by the timestamps of the measured BET patterns in this way. Manual assignment of temperatures etc. to hundreds of BET datasets would be time consuming and hence the efficiency of the data analysis is increased by this option. Example The following listing is an example of a BETMAn script file used to analyze data of an investigation of the isothermal decomposition of austenite (γ-fe) to bainite (a ferritic/α-fe phase, see [4] and [5] for a detailed description of this experiment). Keywords start with a # -character, any other line is treated as comment. Fit variables and phases are accessed via clear names assigned during initialization. The line numbers are inserted for reference in the explanations below and are not part of the script file. Define the start values for the very first pattern 1 #start k:\vax98\steel\samplee\startvalues Define the log file of XSYS DAQ, containing start/stop times of patterns 2 #xsyslog k:\vax98\alldata\xsort1998.log Define the accelerator log file providing beam current 3 #ccrlog k:\vax98\alldata\beamcurrent.txt Define file with temperature profile 4 #temperature k:\vax98\temperatures\steel7.txt Define minimum number of total counts of a pattern to filter no-beam runs 5 #min_counts 4e7 add 4 datasets (xsys data areas) before the fit 6 #xsys_areas 4 Define parameters to be included in the overall result file 7 #extract Lattice parameter a (Alpha Fe) 8 #extract Lattice parameter a (Gamma Fe) 9 #extract Number of scattering centers per unit area (Alpha Fe) 10 #extract Number of scattering centers per unit area (Gamma Fe) 11 #extract Edge profile parameter sigma1 (Alpha Fe) 12 #extract Edge profile parameter sigma1 (Gamma Fe) 13 #extract B_iso for atom Fe (Alpha Fe) 14 #extract B_iso for atom Fe (Gamma Fe) 15 #extract VOLFRACTIONS 16 #extract TOTALCOUNTS 17 #extract CHISQ 18 #extract GOF 19 #extract RVALUE

5 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Process file list 20 #fileloop k:\vax98\steel\samplee\files.txt From here on, the actual fit is controlled. All commands are executed for each data file in the file list. Refine overall scale-factor 21 #variable k:\vax98\steel\step1_adfconst.var 22 #cycles 1 23 #refine refine volume fractions and incident intensity 24 #variable k:\vax98\steel\step2_adfconst.var 25 #cycles 3 26 #refine conditional refinements: 27 #if VOLFRAC Alpha Fe < 10 refine N_scatt, B_iso, edge-width and a0 g-fe plus N_scatt a-fe 28 #variable k:\vax98\steel\step3_adfconst.var 29 #cycles 5 30 #refine 31 #endif 32 #if VOLFRAC Alpha Fe between 10 and 25 refine N_scatt, B_iso, edge-width and a0 g-fe plus N_scatt, B_iso a-fe 33 #variable k:\vax98\steel\step4_adfconst.var 34 #cycles 5 35 #refine refine N_scatt, B_iso, edge-width and a0 of g-fe plus edge width and a0 of a-fe with constant number of scattering centers of a-fe 36 #variable k:\vax98\steel\step5_adfconst.var 37 #cycles 5 38 #refine 39 #endif 40 #if VOLFRAC Alpha Fe between 25 and 75 refine N_scatt, B_iso, edge-width and a0 of both g-fe and a-fe 41 #variable k:\vax98\steel\step6_adfconst.var 42 #cycles 5 43 #refine 44 #endif append a line to the overall result file 45 #writeresult 46 #endfileloop

6 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol End of the script. Line 1 provides the file with the overall starting values. Lines 2 to 4 define files containing timestamps of the analyzed patterns, beam current and temperature information. In the following two lines, the minimum number of counts required for a pattern to include it in the analysis and the number of patterns to sum prior to the analysis are given. The section of lines 7 to 19 defines the variables that are to appear in the overall result file. For each fit parameter, a column with the desired parameter value and the e.s.d. value is added to the overall result file by the #writeresult-command in line 45. The #fileloop-command in line 20 both defines the ASCII-file with a list of filenames and the beginning of a section that is executed for each file in this list. The end of this loop is defined by the #endfileloop-command in line 46. Lines 21 to 26 are executed unconditionally for each dataset. The #variable-command loads a usereditable variation scheme, the #cycles-command defines the number of fit-cycles and #refine starts the fit. Between line 27 and 44, several blocks of conditional refinements are given that are executed depending on the volume fraction of the ferrite phase α-fe. If a condition evaluates to true, all commands between #if and #endif are executed. Conclusions Automation of the data analysis clearly is required to allow an efficient data analysis for experiments generating several hundreds or thousands of datasets. It is also convenient for smaller numbers of similar datasets as is for example the case for a sample under different loads in a stress/strain measurement. To react on beam fluctuations/failures and for example low volume fractions of phases that prevent the fit of certain structural parameters, conditional refinements are required. Consistency checks, like forward and backward analysis and variation of time resolution, that should produce overlaying time series, are strongly recommended. In conjunction with the generation of a single result file containing all desired structural parameters and merging of data from external sources, like sample temperature, the script language built into BETMAn has proven to be a powerful and robust tool during the analysis of about ten experiments with several ten thousand patterns analyzed. Although developed for the analysis of BET patterns, the concepts presented should be transferable to the Rietveld analysis of diffraction data. References [1] Helliwell, J. R., Rentzepis, P. M., Time-resolved Diffraction, Oxford Series on Synchrotron Radiation, Clarendon Press, Oxford, [2] Barnes, P., Colston, S., Craster, B., Hall, C., Jupe, A., Jacques, S., Cockcroft, J., Morgan, S., Johnson, M., O Connor, D., Bellotto, M., J. Synchr. Rad., 2000, 7, [3] Rietveld, H. M., J. Appl. Cryst., 1969, 2, [4] Vogel, S., Bourke, M. A. M., Hanan, J. C., Priesmeyer, H.-G., Üstündag, E., submitted to Advances in X-ray Analysis. [5] Vogel, S., 2000, PhD-thesis, Universität Kiel, available online at [6] Young, R. A., The Rietveld Method, Oxford University Press, Oxford, 1993, table 1.5. [7] McCusker, L. B., Von Dreele, R. B., Cox, D. E., Louer, D., Scardi, P., 1999, J. Appl. Cryst., 32,