- Email: [email protected]
Software development for studies of diffuse scattering using CCD-detectors and synchrotron radiation sources
Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
Software development for studies of diffuse scattering using CCD-detectors and synchrotron radiation sources C. Paulmann*, R. Kurtz, U. Bismayer . Hamburg, Grindelallee 48, D-20146 Hamburg, Germany Mineralogisch-Petrographisches Institut, Universitat
Abstract A graphical-user-interface based software system was developed to cover advanced data processing requirements which arise from studies of diffuse scattering in disordered minerals using synchrotron radiation sources and CCD-detectors. The software includes interfaces to standard applications, procedures for numerical processing of large data sets, corrections for sample external scattering and detector-specific distortions, different scaling options to correct the data set against the varying primary beam intensity as well as procedures to reconstruct arbitrary slices in reciprocal space on a regular grid. The software system was successfully applied in studies of diffuse scattering in disordered REE-doped germanates, phase-transition studies of synthetic titanite and studies of the thermal recrystallization behaviour of radiation-damaged (metamict) minerals. # 2001 Elsevier Science B.V. All rights reserved. PACS: 07.85.Qe; 61.10.Eq; 61.72.D; 07.05.Kf Keywords: Synchrotron; CCD; Diffuse scattering; Software
1. Introduction The combination of modern area detector systems and synchrotron radiation sources greatly facilitates studies of diffuse scattering in disordered crystals or time-resolved studies. Since summer 1997 the beamline F1 at HASYLAB/DESY (Kappa-diffractometer) is equipped with a commercial CCD-detector system including software for data collection and processing. However, the commercial software system is primarily optimimized for processing of Bragg *Corresponding author. Tel.: +49-40-428-3820-62; fax: +4940-428-3824-22. E-mail address: [email protected] (C. Paulmann).
intensities and average structure determinations, whereas studies of diffuse scattering in disordered minerals require a pixel-by-pixel processing of the CCD-data resulting in large temporary data-sets (>10 Gbyte). To cover advanced data-processing requirements beyond the standard applications, a software system was developed and tested during different studies of disordered minerals like REEdoped Ge-mullites, phase-transition studies of synthetic titanite (CaTiSiO5) [1] and kinetic studies of radiation-damaged (metamict) minerals [2].
2. Software features The software system was developed as graphical-user-interface application running under
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 6 0 7 - 6
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C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
Windows NT/98/95 with no special hardware requirements. Besides routines to read in the CCD-system specific raw data, the software provides several interfaces for conversion and reduction of the raw data to different target formats like bitmaps or standard spreadsheet applications. Algorithms for advanced numerical processing of complete data sets are also included (e.g. averaging, addition or low-pass filter for noise-reduction). Special attention was paid to background corrections for sample-external scattering (e.g. beam stop), corrections for detectorspecific distortions, scaling strategies for varying primary beam intensities and routines for the reconstruction of arbitrary slices in reciprocal space. Especially, the latter points are of great importance for qualitative and quantitative studies of diffuse scattering phenomena in disordered systems. In addition to the interactive graphical interface a built-in script-language provides a noninteractive access to every subroutine in order to run time-consuming tasks on large data sets obtained in diffuse scattering studies.
3. Raw data scaling Different off-line scaling strategies were implemented due to the following reasons. An on-line monitoring of the primary beam demands the implementation of an additional data-interface to the commercial software systems, a task which can give rise to severe problems with the system stability. Studies of diffuse scattering require long exposure times which may cause a blooming of strong Bragg reflections. Consequently, several identical data collections with shorter exposure times and subsequent summation are more favourable but require an exact scaling of the different data sets against the varying primary beam intensity. Several strategies and algorithms were developed to perform an external scaling of complete data sets without any on-line monitoring. These include (a) scaling against the storage ring current assuming a direct proportionality to the primary beam intensity, (b) scaling against standard frames across a certain region in reciprocal space, (c) computing scale factors from
equally spaced frames of the data set by analyzing a particular frame area. Each strategy provides a more or less coarse set of grid points representing the exponential decrease of the primary beam intensity during a synchrotron radiation run. By fitting an exponential decay function to these grid points individual scale factors for every data frame (and pixel) can be calculated. However, the scaling strategy must be chosen according to the actual experiment and sample under investigation. Scaling against the ring current is sensitive against the beam stability and may result in unexpected scale factors if any beamline components (e.g. monochromator stabilization) cause irregular variations of the primary beam intensity. The scaling with frame-internal scale factors demands the selection of a frame area with fixed 2y-range across the complete data set showing pure background scattering. Special care must be taken if the sample gives a broad and structured distribution of diffuse scattering throughout reciprocal space. Accurate scale factors can be determined from standard frames recorded in fixed time intervals (ca. 10 min). However, this strategy is the most time consuming and therefore does not appear to be applicable for time-resolved studies. Recently, the different scaling strategies were successfully applied in an in situ study of the thermal recrystallization behaviour of metamict titanite, which shows severe dose-dependent structural damages. Upon thermal annealing, the system displays time- and temperaturedependent recrystallization effects on different kinetic scales. Further details can be found in Ref. [2].
4. Detector distortion correction Another problem for studies of diffuse scattering with CCD-detectors arises from the detectorspecific spatial distortion caused by the fibre-optic between phosphor and CCD-chip which may result in differences of more than 20 pixel between observed and calculated positions. Internal procedures to correct these distortions are usually provided by the commercial software systems.
C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
The spatial resolution of the commercial corrections is sufficient for studies of average structure determinations but does not account for a 3D-mapping of diffuse scattering intensities. Furthermore, these software systems do not provide an optimal interface for processing extremely large data sets obtained during diffuse scattering studies. Hence, external procedures were developed which calculate spatial correction tables on a finer scale than the commercial procedures to achieve a higher accuracy. Correction tables for the x- and y-coordinates are computed on a 4 4 pixel grid with a bicubic spline interpolation and
Fig. 1. Calculated detector distortions for a 512 512 pixel CCD-frame. Top: x-coordinate corrections, bottom: y-coordinate corrections.
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stored as look-up-tables (LUT) in memory to provide a fast access. Between the grid-points of the LUT the pixel-individual corrections are calculated with a bilinear approximation. Fig. 1 shows the calculated distortion corrections of the x- and y-coordinates of a 512 512 pixel CCD-frame.
5. Reciprocal space reconstruction During small incremental rotations of the sample each pixel of the flat detector surface integrates over varying sizes of reciprocal volume elements which are swept through the Ewald sphere. The size of these volume elements depends on the rotational increment and the location in reciprocal space. Consequently, the diffuse scattering is sampled on an irregular grid in reciprocal space. The reconstruction of arbitrary slices and volumes in reciprocal space requires the mapping of these raw-data onto a regular grid in reciprocal space. Many aspects including the correction of experimental parameters (polarization, Lorentz factor) for an image-plate system with fixed rotation axis and detector were reported in Ref. [3]. However, the four-circle geometry at beamline F1 results in a more complex calculation. According
Fig. 2. Reconstructed hk1=4 layer of REE-doped Ge-mullite. 0.04h, k43.0; Dh, Dk=0.02.
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C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
to the beamline-specific scattering geometry the reciprocal coordinates h of every pixel *D in the detector coordinate system (xD, yD, zD) can be calculated according to
previously been observed in pure (Al, Si)-mullites (Al2[Al2+2xSi22x]O10x) [4,5]. The software can be obtained free by contacting the authors.
h ¼ U 1 R1 Rð2yÞ DK Dideal *D where Dideal is the ideal detector matrix at 2y=08, DK the detector misalignment matrix, R(2y) the detector swing matrix, R1 the inverse instrumen tal matrix, ½RðjÞ RðwÞ RðoÞ1 ; U1 the inverse orientation matrix. As an example, Fig. 2 shows the reconstructed hk1=4 layer of REE-doped Ge-mullite displaying a pattern of rhomb-shaped diffuse scattering. An almost similar pattern caused by a specific set of inter-defect correlation vectors has
References [1] T. Malcherek, C. Paulmann, M.C. Domeneghetti, U. Bismayer, J. Appl. Crystallogr. 34 (2001) 108. [2] C. Paulmann, U. Bismayer, L.A. Groat, Z. Kristallogr. 215 (2000) 678. [3] M.A. Estermann, W. Steurer, Phase Transitions 67 (1998) 165. [4] C. Paulmann, S.H. Rahman, S. Strothenk, Phys. Chem. Minerals 21 (1994) 546. [5] S.H. Rahman, S. Strothenk, C. Paulmann, J. Eur. Ceram. Soc. 16 (1996) 177.
Software development for studies of diffuse scattering using CCD-detectors and synchrotron radiation sources C. Paulmann*, R. Kurtz, U. Bismayer . Hamburg, Grindelallee 48, D-20146 Hamburg, Germany Mineralogisch-Petrographisches Institut, Universitat
Abstract A graphical-user-interface based software system was developed to cover advanced data processing requirements which arise from studies of diffuse scattering in disordered minerals using synchrotron radiation sources and CCD-detectors. The software includes interfaces to standard applications, procedures for numerical processing of large data sets, corrections for sample external scattering and detector-specific distortions, different scaling options to correct the data set against the varying primary beam intensity as well as procedures to reconstruct arbitrary slices in reciprocal space on a regular grid. The software system was successfully applied in studies of diffuse scattering in disordered REE-doped germanates, phase-transition studies of synthetic titanite and studies of the thermal recrystallization behaviour of radiation-damaged (metamict) minerals. # 2001 Elsevier Science B.V. All rights reserved. PACS: 07.85.Qe; 61.10.Eq; 61.72.D; 07.05.Kf Keywords: Synchrotron; CCD; Diffuse scattering; Software
1. Introduction The combination of modern area detector systems and synchrotron radiation sources greatly facilitates studies of diffuse scattering in disordered crystals or time-resolved studies. Since summer 1997 the beamline F1 at HASYLAB/DESY (Kappa-diffractometer) is equipped with a commercial CCD-detector system including software for data collection and processing. However, the commercial software system is primarily optimimized for processing of Bragg *Corresponding author. Tel.: +49-40-428-3820-62; fax: +4940-428-3824-22. E-mail address: [email protected] (C. Paulmann).
intensities and average structure determinations, whereas studies of diffuse scattering in disordered minerals require a pixel-by-pixel processing of the CCD-data resulting in large temporary data-sets (>10 Gbyte). To cover advanced data-processing requirements beyond the standard applications, a software system was developed and tested during different studies of disordered minerals like REEdoped Ge-mullites, phase-transition studies of synthetic titanite (CaTiSiO5) [1] and kinetic studies of radiation-damaged (metamict) minerals [2].
2. Software features The software system was developed as graphical-user-interface application running under
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 6 0 7 - 6
1114
C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
Windows NT/98/95 with no special hardware requirements. Besides routines to read in the CCD-system specific raw data, the software provides several interfaces for conversion and reduction of the raw data to different target formats like bitmaps or standard spreadsheet applications. Algorithms for advanced numerical processing of complete data sets are also included (e.g. averaging, addition or low-pass filter for noise-reduction). Special attention was paid to background corrections for sample-external scattering (e.g. beam stop), corrections for detectorspecific distortions, scaling strategies for varying primary beam intensities and routines for the reconstruction of arbitrary slices in reciprocal space. Especially, the latter points are of great importance for qualitative and quantitative studies of diffuse scattering phenomena in disordered systems. In addition to the interactive graphical interface a built-in script-language provides a noninteractive access to every subroutine in order to run time-consuming tasks on large data sets obtained in diffuse scattering studies.
3. Raw data scaling Different off-line scaling strategies were implemented due to the following reasons. An on-line monitoring of the primary beam demands the implementation of an additional data-interface to the commercial software systems, a task which can give rise to severe problems with the system stability. Studies of diffuse scattering require long exposure times which may cause a blooming of strong Bragg reflections. Consequently, several identical data collections with shorter exposure times and subsequent summation are more favourable but require an exact scaling of the different data sets against the varying primary beam intensity. Several strategies and algorithms were developed to perform an external scaling of complete data sets without any on-line monitoring. These include (a) scaling against the storage ring current assuming a direct proportionality to the primary beam intensity, (b) scaling against standard frames across a certain region in reciprocal space, (c) computing scale factors from
equally spaced frames of the data set by analyzing a particular frame area. Each strategy provides a more or less coarse set of grid points representing the exponential decrease of the primary beam intensity during a synchrotron radiation run. By fitting an exponential decay function to these grid points individual scale factors for every data frame (and pixel) can be calculated. However, the scaling strategy must be chosen according to the actual experiment and sample under investigation. Scaling against the ring current is sensitive against the beam stability and may result in unexpected scale factors if any beamline components (e.g. monochromator stabilization) cause irregular variations of the primary beam intensity. The scaling with frame-internal scale factors demands the selection of a frame area with fixed 2y-range across the complete data set showing pure background scattering. Special care must be taken if the sample gives a broad and structured distribution of diffuse scattering throughout reciprocal space. Accurate scale factors can be determined from standard frames recorded in fixed time intervals (ca. 10 min). However, this strategy is the most time consuming and therefore does not appear to be applicable for time-resolved studies. Recently, the different scaling strategies were successfully applied in an in situ study of the thermal recrystallization behaviour of metamict titanite, which shows severe dose-dependent structural damages. Upon thermal annealing, the system displays time- and temperaturedependent recrystallization effects on different kinetic scales. Further details can be found in Ref. [2].
4. Detector distortion correction Another problem for studies of diffuse scattering with CCD-detectors arises from the detectorspecific spatial distortion caused by the fibre-optic between phosphor and CCD-chip which may result in differences of more than 20 pixel between observed and calculated positions. Internal procedures to correct these distortions are usually provided by the commercial software systems.
C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
The spatial resolution of the commercial corrections is sufficient for studies of average structure determinations but does not account for a 3D-mapping of diffuse scattering intensities. Furthermore, these software systems do not provide an optimal interface for processing extremely large data sets obtained during diffuse scattering studies. Hence, external procedures were developed which calculate spatial correction tables on a finer scale than the commercial procedures to achieve a higher accuracy. Correction tables for the x- and y-coordinates are computed on a 4 4 pixel grid with a bicubic spline interpolation and
Fig. 1. Calculated detector distortions for a 512 512 pixel CCD-frame. Top: x-coordinate corrections, bottom: y-coordinate corrections.
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stored as look-up-tables (LUT) in memory to provide a fast access. Between the grid-points of the LUT the pixel-individual corrections are calculated with a bilinear approximation. Fig. 1 shows the calculated distortion corrections of the x- and y-coordinates of a 512 512 pixel CCD-frame.
5. Reciprocal space reconstruction During small incremental rotations of the sample each pixel of the flat detector surface integrates over varying sizes of reciprocal volume elements which are swept through the Ewald sphere. The size of these volume elements depends on the rotational increment and the location in reciprocal space. Consequently, the diffuse scattering is sampled on an irregular grid in reciprocal space. The reconstruction of arbitrary slices and volumes in reciprocal space requires the mapping of these raw-data onto a regular grid in reciprocal space. Many aspects including the correction of experimental parameters (polarization, Lorentz factor) for an image-plate system with fixed rotation axis and detector were reported in Ref. [3]. However, the four-circle geometry at beamline F1 results in a more complex calculation. According
Fig. 2. Reconstructed hk1=4 layer of REE-doped Ge-mullite. 0.04h, k43.0; Dh, Dk=0.02.
1116
C. Paulmann et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1113–1116
to the beamline-specific scattering geometry the reciprocal coordinates h of every pixel *D in the detector coordinate system (xD, yD, zD) can be calculated according to
previously been observed in pure (Al, Si)-mullites (Al2[Al2+2xSi22x]O10x) [4,5]. The software can be obtained free by contacting the authors.
h ¼ U 1 R1 Rð2yÞ DK Dideal *D where Dideal is the ideal detector matrix at 2y=08, DK the detector misalignment matrix, R(2y) the detector swing matrix, R1 the inverse instrumen tal matrix, ½RðjÞ RðwÞ RðoÞ1 ; U1 the inverse orientation matrix. As an example, Fig. 2 shows the reconstructed hk1=4 layer of REE-doped Ge-mullite displaying a pattern of rhomb-shaped diffuse scattering. An almost similar pattern caused by a specific set of inter-defect correlation vectors has
References [1] T. Malcherek, C. Paulmann, M.C. Domeneghetti, U. Bismayer, J. Appl. Crystallogr. 34 (2001) 108. [2] C. Paulmann, U. Bismayer, L.A. Groat, Z. Kristallogr. 215 (2000) 678. [3] M.A. Estermann, W. Steurer, Phase Transitions 67 (1998) 165. [4] C. Paulmann, S.H. Rahman, S. Strothenk, Phys. Chem. Minerals 21 (1994) 546. [5] S.H. Rahman, S. Strothenk, C. Paulmann, J. Eur. Ceram. Soc. 16 (1996) 177.