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Industrial Group of the BCA
Industrial Group
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| Laboratory No. | Rutile | Anatase |
| 1 | 98.90 | 1.10 |
| 2 | 99.15 | 0.85 |
| 3 | 99.30 | 1.50 |
| 4 | 99.16 | 0.84 |
| 5 | - | - |
| 6 | 99.20 | 0.80 |
| 7 | - | - |
| 8 | 99.55 | 0.45 |
| 9 | 98.80 | 1.20 |
| Standard Values | 99.16 | 0.84 |
In a close run thing the winner was laboratory number 4 whose results were spot on!
Pharmaceutical Compound
| Laboratory No. | Lactose | Paracetamol |
| 1 | - | - |
| 2 | 83.20 | 16.80 |
| 3 | - | - |
| 4 | 93.20 | 6.80 |
| 5 | 84.20 | 15.80 |
| 6 | 80.50 | 19.50 |
| 7 | 85.20 | 14.80 |
| 8 | - | - |
| 9 | - | - |
| 10 | 86.10 | 13.90 |
| Standard Values | 84.92 | 15.08 |
Laboratory 5 not quite good enough and was beaten by Laboratory 7
Many thanks to all who took part and hopefully the workshop in York provided the key to improvement for those who were wide of the mark.
UK Instrument Sensitivity (Intensity) Round Robin.
This report is available as a 224kb .PDF file to download and print. For further information please contact the author: [email protected]
Routines and spreadsheets are available to perform the Round Robin tests on your own equipment. Details and downloads are available in a selftest guide.
Dave Taylor
A Summary of a "Round-robin" exercise comparing the output of computer programs for lattice parameter refinement and calculation.
E H Kelly
Emeritus
The Electricity Council Research Centre
Capenhurst
Chester
CH1 6ES
Transcribed from Eric Kelly's original published in late
1980's by D J Taylor [email protected] in the year 2000.
(I apologise for any transcription errors I may have
introduced!)
NOTE: Address information quoted is that at the time of the
measurements please address any inquiries to Dave Taylor who will
attempt to put you in touch with any of the participants.
- Preface - careful how you use mathematics
- 1. The round-robin exercise
Examples used- Guinier focusing camera data
- Diffractometric data from "Specpure" rolled copper sheet
- Diffractometric data from "Puratronic" calcium tungstate
- Photographic data, as published
- 2. The responses
- 3. Some Observations
- 4. Acknowledgements
- 5. References
- 6. Participants
- 7. Programs
- Results
- Example 1 triclinic
- Example 2 cubic
- Example 3 tetragonal
- Example 4 monoclinic
- standard parameters d-spacings etc
- Example 1 triclinic
- Example 2 cubic
- Example 3 tetragonal
- Example 4 monoclinic
Preface
Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness: but, nevertheless, what you get out depends upon what you put in: and as the grandest mill in the world will not extract wheat-flour from peas-cod. so pages of formulae will not get a definite result out of loose data.
T H Huxley
Discourses.Biologica1 and Geological Essays 1909
The agreement among laboratories was about 1 part in 10,000: this includes random and systematic errors. This is much lower than the precision generally reported by the individual laboratories and often claimed in the literature.
W Parrish
Results of the I.U.Cr. precision
lattice-parameter project
Acta Cryst. 3. 838. (1960)
1. The round-robin exercise.
The Industrial Group of the British Crystallographic Association held a Specialist Interest Workshop on Computer Programs for Powder Diffraction Problems on October 9 1986. During the meeting, it became apparent that there were a number of computer programs being used for lattice parameter calculation and refinement. It was felt that it would be both useful and interesting to set up a "round robin" exercise to compare the output from some of these programs to see whether they all produced similar answers.
Four sets of data were circulated, in March 1987,to BCA members who had expressed their intention to participate. The four sets of data are reproduced at the end of this note. The data were obtained as follows:
Example 1. Guinier focusing camera data, as published (Reference 1, example 1 and Reference 2) and used with permission. The compound was a polynuclear uranyl nitrate of formula [(UO2)6(OH)12(H2O)](NO3)2.xH2O where x was about 6. This data was selected as being of high quality: further, it had already been used in the development of a program for the evaluation of X-ray powder measurements.
Example 2, Diffractometric data from "Specpure" rolled copper sheet, collected at ECRC. The material had strong preferred orientation.
Example 3. Diffractometric data from "Puratronic" calcium tungstate, CaWO4 , collected at ECRC.
Example 4. Photographic data, as published, (Reference 1, example 3) and used with permission.
This example was selected as typical of that which may be obtained in industrial research: it was a complex pattern, not of the highest quality. The compound was hafnia, HfO2The tables circulated were produced to conform with the suggestions of NBS Monograph 25, using the ECRC implementation of the computer program NBS*EXAIDS83 (Reference 3). Participants were left free to use as much, or as little, of the data as they wished, or their system required. No suggestions were offered on philosophical aspects, such as whether peak positions or d-spacings were to he treated as the raw data.
2. The responses.
For each example, a table of reported results is included with this note. Several participants supplied many more results than are included here: the results from up to fourteen computer runs coming from individual laboratories. Where the information was supplied, the tables of results include a note of the extrapolation function(s) employed and whether two-theta or d-spacing information was treated as raw data.
One participant used a suite of programs which, inter-alia, suggested an alternative unit-cell for Example 1. This alternative is not included in the results tabulated, but did lead to an interesting observation. (see later.)
3. Some observations.
The programs used by one participant resulted in refinement in terms of an alternative unit cell. The resultant parameters, when transposed to the reduced unit, agreed closely with the results of other participants. As an experiment, the alternative unit cell suggested for Example 1 was used as input data for the ECRC implementation of FIRESTAR and NBS*EXAIDS83: the former program failed to produce a result whilst the latter produced a solution for which the figures of merit (both de Wolff and Smith & Snyder) were closely similar to those obtained for the data circulated. One might conclude that the programs should not be treated in "black-box" fashion but should be supplied with appropriate data only.
One participant, using an integrated system supplied by a diffractometer manufacturer, reported that different results were obtained when the data were entered interactively at the terminal and when the data were read from stored disc files.
Where the user has such control, compiler options should be chosen with care. For example, the Prime computer system normally stores numbers with truncation, rather than rounding. A compiler option allows for rounding: with this option in force results obtained were identical with either single or double precision compilation. Of course, this may reflect good programming practice, where appropriate variables have been declared as double precision. Detailed checking of program code has not been undertaken. Since some of the programs under consideration involve subtraction of small numbers, where data processing is least accurate, use of inappropriate compilation may be a significant source of possible error.
Not all participants used the most appropriate extrapolation function for each example. The tables of results include a note of the function(s) employed, where the information was supplied.
Whilst this small survey cannot suggest a "best-buy", it is perhaps worth noting that, of the three programs used at ECRC during this survey, the program "FIRESTAR" is the most user-friendly. Data are input in free format and the program does not need an initial guess at the lattice parameters. However, the data must be fully indexed.
The program numbered 12 (or 11) is reasonably user-friendly, but requires fixed-format input, which must be fully indexed. Variations as large as 10% in the initial parameters given cause no significant changes in the refined cell parameters.
The program NBS*EXAIDS83 is the most comprehensive of these three: considerable study of the User Manual is necessary. The program will index an unknown pattern, provided that the symmetry is known. However, the final refined cell parameters are very dependent upon the initial estimates input: small changes in the estimates lead to rejection of reflections so that refinement occurs in terms of too small a proportion of the data input.
4. Acknowledgements.
Thanks are due to the participants in this survey, all of whom took much time and trouble in processing the data. Many wrote letters of explanation and observation and some have made source code of their programs available. My thanks to you all.
Dr J A C Marples kindly provided the identity of the compound used for the data in Example 1. (Reference 2) The pattern is not included in the JCPDS files, nor in Determinative Tables.
My thanks are due to a number of colleagues at Capenhurst, particularly in the Theoretical Section, for their help and patience.
Finally, it is inevitable that there will be transcription errors in so many tables of numbers. My apologies to any who feel maligned - the responsibility for errors is mine.
5. References.
1. FIRESTAR-2. A computer program for the evaluation of x-ray powder measurements and the derivation of crystal lattice parameters. I. F. Ferguson et al. United Kingdom Atomic Energy Authority Northern Division Report ND-R-909(S) H. M. Stationery Office, February 1987. 2. The preparation and properties of a polynuclear uranyl nitrate. J. L. Woodhead et al. J. inorg. nucl. Chem. 28. 21752185, (1966). 3. NBS*AIDS80 (Now NBS*EXAIDS83) A FORTRAN program for Crystallographic Data Evaluation. A. D. Mighell et al. National Bureau of Standards Technical Note 1141. April 1981. 4. Indexing and Least-Squares Refinement of Powder Diffraction Data. D. E. Appleman et al. NTIS PB-216 188/USGS-GD-73-003 February 1973. List of participants. Mr B A Bellamy Harwell Laboratory United Kingdom Atomic Energy Authority Oxford OX11 ORA. Dr J Chisholm Mineralogy Department British Museum (Natural History) London SW7 5BD. Mr J L C Daams Philips Research Laboratories PO Box 80000 5600 JA Eindhoven The Netherlands. Dr P Holdway Materials & Structures Department Royal Aircraft Establishment Farnborough. Mr E H Kelly The Electricity Council Research Centre Capenhurst Chester CH1 6ES. Dr J I Langford Department of Physics The University of Birmingham PO Box 363 Birmingham B15 2TT Dr R Nicholls Pye Unicam Ltd. York Street Cambridge CB1 2PX. Mr T Ruben Cookson Group plc Central Research 7 Wadsworth Road Perivale Greenford UB6 7JQ. Miss J Shackleton Springfields Nuclear Power Development Laboratories United Kingdom Atomic Energy Authority Springfields Salwick Preston PR4 ORR. List of programs used etc. 1. FIRESTAR -results as reported in Reference 1. FORTRAN77 2. FIRESTAR -running on ECRC Prime computer. -Compiled with single precision, normal truncation 2a. FIRESTAR -running on ECRC Prime computer. Compiled with single precision, with rounding 3. FIRESTAR -running on VAX 11/780. 4. NBS*EXAIDS83 -running on ECRC Prime computer. FORTRAN77. Compiled with double precision. 5. "In-house" program, in FORTRAN. Compiled with single precision. 6. "In-house" program in Hewlett-Packard BASIC. "Full precision" (12 significant figures.) 7. Philips' APD system. Written in PASCAL. running on PDP11/23 under RSX11. 8. Philips' proprietary program. Written in ALGOL 60. Running with double precision. 9 Philips' APD system. 9a Siemens' APPLE program: part of the DIFFRAC package. 10. Siemens' APPLE program: part of the DIFFRAC package. Running on a DEC Micro-PDP11/23. 11. "In-house", public domain program. Written in FORTRAN77. Compiled with double precision. IBM system 12. Same program as 11, running on ECRC Prime computer. Compiled with double precision. NOTE The Siemens' APPLE program was originally published by the U.S. Geological Survey (Reference 4.) Use of the same code in NBS*EXAIDS83 is acknowledged in the user manual supplied. Results reported for Example 1 - triclinic. Where reported, estimated standard deviations are given. a b c alpha beta gamma comment 1 11.2541 13.5573 8.0082 116.274 91.351 106.925 N/R d NB twice the s.d. 0.0086 0.0094 0.0057 0.045 0.035 0.036 2 11.2524 13.5554 8.0074 116.272 91.348 106.923 N/R d NB twice the s.d. 0.0092 0.0100 0.0059 0.047 0.036 0.037 2a 11.2520 13.5549 8.0072 116.273 91.348 106.923 N/R d 3 11.2574 13.5601 8.0091 116.263 91.357 106.923 N/R d NB twice the s.d. 0.0092 0.0103 0.0060 0.047 0.040 0.044 3a 11.2564 13.5599 8.0087 116.265 91.356 106.930 N/R d NB twice the s.d. 0.0085 0.0095 0.0056 0.044 0.037 0.041 4 11.2690 13.5732 8.0155 116.263 91.361 106.921 1.sq. d 0.0028 0.0022 0.0013 0.014 0.018 0.018 5 11.25688 13.56037 8.00903 116.264 91.356 106.932 N/R d 0.00464 0.00505 0.00299 0.025 0.020 0.022 5a 11.25686 13.56034 8.00902 116.264 91.356 106.932 Roberts d 0.00466 0.00507 0.00301 0.025 0.020 0.022 6 program does not accommodate triclinic case 7 11.26560 13.57650 8.01660 116.261 91.368 106.908 l.sq. 2th 8 11.2719 13.5806 8.0287 116.24 91.39 106.91 l.sq. 9 11.25468 13.55875 8.00778 116.265 91.365 106.916 l.sq. 2th 9a 11.26697 13.57337 8.01583 116.262 91.365 106.925 l.sq. 2th 0.00166 0.00203 0.00104 0.012 0.013 0.014 10 11.26874 13.57275 8.01623 116.262 91.385 106.901 l.sq. 2th 0.00191 0.00201 0.00119 0.016 0.016 0.021 10a 11.26788 13.57365 8.01721 116.271 91.385 106.907 1.sq. d 0.00222 0.00209 0.00128 0.013 0.016 0.016 11 11.2647 13.5703 8.0146 116.263 91.356 106.930 Roberts d 0.0012 0.0016 0.0008 0.009 0.009 0.010 12 11.2647 13.5703 8.0146 116.263 91.356 106.930 Roberts d 0.0012 0.0016 0.0008 0.009 0.009 0.010 Results reported for Example 2 - cubic Where reported, estimated standard deviations are given. 1 2 3.6116 0.0005 Roberts 2th twice the s.d. 2a 3.6116 0.0005 --do-- 3 3.6115 0.0008 N/R 2th twice the s.d. 3a 3.6145 0.0007 N/R d twice the s.d. 4 3.6145 0.00019 1. sq. 2th. 5 3.61150 0.00036 N/R 5a 3.61151 0.00036 Roberts 6 3.6116 0.0002 1.sq. 7 3.61408 1.sq. 8 3.6116 1.sq. 9 3.61160 1.sq. 2th 9a 3.61156 0.00021 1.sq. 2th 10 3.61431 0.00026 1.sq. 2th 10a 3.61431 0.00024 1.sq. d 11 3.61140 0.00026 Roberts 12 3.61140 0.00026 Roberts Results for Example 3 - tetragonal where reported, estimated standard deviations are given. a c 1 - - 2 5.2373 11.3829 Roberts 2th 0.0007 0.0034 NE twice the s.d. 2a 5.2473 11.3829 Roberts 2th 0.0007 0.0034 NE twice the s.d. 3 5.2374 11.3622 N/R 2th 0.0015 0.0036 NE twice the s.d.. 3a 5.2416 11.3716 N/R d 0.0015 0.0035 NE twice the s.d.. 4 5.2441 11.3750 l.sq 2th 0.00003 0.0016 5 5.23750 11.36228 N/R 0.00074 0.00177 5a 5.23742 11.36212 Roberts 0.00076 0.00181 6 5.2384 11.3651 l.sq 0.0005 0.0014 7 5.23650 11.36290 l.sq.(max. number of singly explained lines) 8 5.2369 11.3610 l.sq. 9 5.23641 11.36155 l.sq. 2th 9a 5.23860 11.36481 l.sq. 2th 0.00043 0.00138 10 5.23777 11.36656 l.sq. 2th 0.00019 0.00048 10a 5.24212 11.37605 l.sq. d 0.00020 0.00050 11 5.2382 11.3637 Roberts 2th 0.0003 0.0009 12 5.2381 11.3637 Roberts 2th 0.0003 0.0009 Results for Example 4 - monoclinic. Where reported, estimated standard deviations are given. a b c beta 1 5.1184 5.1823 5.2875 99.314 N/R film measurements 0.0037 0.0030 0.0032 0.045 NB twice the standard devn. 2 5.1150 5.1813 5.2895 99.286 N/R d NE twice the s.d. 0.0056 0.0049 0.0041 0.069 2a 5.1150 5.1813 5.2895 99.286 N/R d NS twice the s.d. 0.0056 0.0049 0.0041 0.069 3 5.1182 5.1803 5.2871 99.315 N/R 2th NE twice the s.d. 0.0036 0.0029 0.0032 0.043 3a 5.1168 5.1803 5.2871 99.313 N/R d NE twice the s.d. 0.0041 0.0034 0.0035 0.048 4 5.1068 5.1764 5.2819 99.248 l.sq. d 0.0036 0.0018 0.0020 0.037 5 5.11764 5.18300 5.29013 99.3078 N/R 0.00274 0.00217 0.00228 0.0330 5a 5.11801 5.18333 5.29048 99.3083 Roberts 0.00279 0.00221 0.00232 0.0329 6 5.1092 5.1778 5.2799 99.233 l.sq 0.0043 0.0019 0.0020 0.040 7 5.11898 5.17193 5.28205 99.358 1.sq 8 5.1217() 5.1816 5.2862(a)99.261 l.sq. a & c reported reversed 9 5.12014 5.18143 5.28555 99.247 l.sq. 2th 9a 5.11185 5.17722 5.28503 99.301 l.sq. 2th 10 5.11195 5.17722 5.27969 99.220 l.sq. 2th 0.00296 0.00181 0.00200 0.039 10a 5.10904 5.17374 5.28123 99.353 l.sq. d 0.00263 0.00159 0.00180 0.039 11 5.1130 5.1792 5.2857 99.30 N/R 0.0021 0.0017 0.0017 0.03 12 5.1130 5.1792 5.2857 99.295 N/R 0.0021 0.0017 0.0017 0.029 Example 1. Triclinic material, no intensities, wavelength 1.54056 Nominal cell constants: a 11.25 alpha 116.00 b 13.60 beta 91.50 c 8.00 gamma 107.00 d-spacing intensity h k l Observed 2-theta 11.45 0 0 1 0 7.712 10.62 0 1 0 0 8.320 9.550 0 -1 1 0 9.250 7.904 0 0 -1 1 11.184 7.078 0 0 0 1 12.495 6.740 0 1 1 0 13.125 6.443 0 1 -1 1 13.733 6.248 0 -1 -1 1 14.162 6.059 0 0 -2 0 14.607 5.955 0 -1 2 0 14.865 5.794 0 1 -2 1 15.281 5.732 0 0 2 0 15.445 5.581 0 -2 1 0 15.857 5.456 0 1 0 1 16.233 5.307 0 2 0 0 16.691 5.143 0 -1 1 1 17.227 5.055 0 0 1 1 17.529 4.855 0 -1 -2 1 18.259 4.777 0 -2 2 0 18.557 4.661 0 -2 0 1 19.025 4.464 0 2 -2 1 19.871 4.442 0 1 -3 0 19.971 4.293 0 2 1 0 20.671 4.139 0 1 1 1 21.453 4.055 0 -1 3 0 21.903 3.943 0 0 -1 2 22.533 3.920 0 2 0 1 22.663 3.906 0 2 -3 1 22.749 3.821 0 0 3 0 23.261 3.800 0 -1 -1 2 23.393 3.754 0 3 -1 0 23.683 3.744 0 1 -2 2 23.743 3.686 0 0 2 1 24.123 3.664 0 -1 -2 1 24.273 3.640 0 -2 -2 1 24.431 3.599 0 1 -1 2 24.717 3.590 0 -2 2 1 24.781 3.558 0 0 -3 2 25.003 3.549 0 -1 0 2 25.069 3.534 0 3 0 0 25.179 3.521 0 1 -3 2 25.275 3.391 0 1 -4 1 26.257 3.367 0 3 -2 1 26.453 3.295 0 -2 -1 2 27.041 3.268 0 3 -1 1 27.267 Example 2. Cubic material, with intensities, wavelength 1.54056 Diffractometer data. Nominal cell constant : a 3.60 d-spacing intensity h k l Observed 2-theta 2.088 16 1 1 1 43.34 1.808 100 2 0 0 50.47 1.2773 46 2 2 0 74.25 1.0896 29 3 1 1 90.07 1.0436 9 2 2 2 95.24 0.9035 12 4 0 0 117.14 0.8292 12 3 3 1 136.78 0.8083 14 4 2 0 145.01 Example 3. Tetragonal material, with intensities, wavelength 1.54056 Diffractometer data. Nominal cell constants: a 5.24 c 11.37 d-spacing intensity h k l Observed 2-theta 4.772 116 1 O 1 18.594 3.105 503 1 1 2 28.748 2.845 74 O 0 4 31.449 2.623 77 2 O O 34.180 2.383 3 2 O 2 37.755 2.296 66 2 1 1 39.238 2.257 12 1 1 4 39.953 2.087 20 1 O 5 43.352 1.995 43 2 1 3 45.464 1.9275 142 2 0 4 47.151 1.8536 53 2 2 0 49.152 1.7271 7 3 0 1 53.023 1.6879 71 1 1 6 54.353 1.6327 28 2 1 5 56.352 1.5913 88 3 1 2 57.954 1.5526 39 2 2 4 59.544 1.4421 11 3 2 1 64.633 1.4220 8 0 O 8 65.661 1.3856 6 3 O 5 67.614 1.3577 7 3 2 3 69.194 1.3356 6 2 1 7 70.508 1.3106 10 4 0 0 72.059 1.2640 5 4 1 1 75.162 1.2495 44 2 O 8 76.193 Example 4. Monoclinic material, no intensities, wavelength 2.28970 Original data is photographic: data is calculated from film measurements, with shrinkage corrections. Nominal cell constants: a 5.12 b 5.18 beta 99.3 c 5.29 d-spacing intensity h k l 2-theta 4.89 0 1 0 0 27.10 3.67 0 0 1 1 36.40 3.60 0 1 1 0 36.92 3.14 0 -1 1 1 42.78 2.815 0 1 1 1 48.00 2.601 0 0 0 2 52.22 2.583 0 0 2 0 52.62 2.519 0 2 0 0 54.07 2.481 0 -1 0 2 54.97 2.317 0 0 2 1 59.21 2.195 0 -2 1 1 62.86 2.174 0 1 0 2 63.56 2.008 0 1 1 2 69.51 1.980 0 -2 0 2 70.66 1.834 0 0 2 2 77.23 1.805 0 2 2 0 78.72 1.791 0 -1 2 2 79.45 1.771 0 -2 2 1 80.57 1.681 0 2 0 2 85.85 1.646 0 0 1 3 88.14 1.641 0 -1 1 3 88.44 1.632 0 1 3 0 89.12 1.599 0 -3 1 1 91.44 1.581 0 -1 3 1 92.79 1.573 0 -2 2 2 93.44 1.535 0 1 3 1 96.44 1.531 0 -3 0 2 96.78 1.499 0 1 1 3 99.58 1.487 0 -2 1 3 100.68 1.467 0 3 1 1 102.58 1.446 0 0 2 3 104.73 1.440 0 -1 2 3 105.28 1.426 0 2 3 0 105.83 1.417 0 -1 3 2 107.75 1.410 0 2 2 2 108.52 1.370 0 -2 3 1 113.36 1.353 0 1 3 2 115.55 1.342 0 1 2 3 117.16
Eric Kelly
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