Caveate: In powder diffraction, programs not using Maximum Entropy algorithms can result in noisy,
difficult to interpret Fourier Maps. Unless explicitely mentioned, below programs do not
use Max Ent as part of Fourier map generation. The only available Rietveld program
that links into Maximum Entropy at this time (September 2000) is RIETAN2000 as mentioned below.
Bayesian/Maximum Entropy methods for sharpening up Powder Diffraction derived Fourier electron density contour maps
- Web example of Bayesian/Maximum Entropy methods for powder diffraction Fourier Maps:
Some References (taken from "Maximum Entropy & Powder Diffraction", Lecture Notes,
Robert J. Papoular, papou@llb.saclay.cea.fr, Les Houches 2000 - recent Developments in NEutron Scattering - 2 -12 May 2000):
- Christopher J. Gilmore, "Maximum Entropy and Bayesian Statistics in Crystallography:
a Review of Practical Applications", Acta Crys. Section A. (1996). A 52, 561-589
"You should all it 'entropy' and for two reasons: first, the function is already in use in
thermodynamics under that name; second, and more importantly, most people don't know what
entropy is, and if you use the word 'entropy' you will win every time!
von Neumann's advice to Shannon as to what to call the function -"
- S.F. Gull and J. Skilling, "Maximum entropy method in image processing" IEE Proceedings, Vol. 131. Pt. F, No 6,
October 1984, pg 646-.
- J. Skilling and R.K. Bryan, "Maximum entropy inmage reconstruction: general algorithm"
Mon. Not. R. astr. Soc. 1984) 211, 111-124.
- Alastair Livesey and John Skilling, "Maximum Entropy Theory"
Acta Cryst. (1985). A41, 113-122.
- Shintaro Kumazawa, Yoshiki Kubota, Masaki Takata and Masoto Sakata,
"MEED: a program package for electron-distribution calculation by maximum-entropy"
J. Appl. Cryst. (1993). 26, 453-457
- W.I.F. David,
"Extending the power of powder diffraction for structure determination"
Nature, Vol 346, 23 August 1990, 731-
- D.S. Sivia and W.I.F. David,
"A Bayesian Approach to Extracting Structure-Factor Amplitudes from Powder Diffraction Data"
Acta Cryst (1994), A50, 703-714.
- Wei Dong and Christopher J. Gilmore,
"The Ab Initio Solution of Structures from Powder Diffraction Data: the Use of Maximum Entropy and Likelihood to Determine the Relative Amplitudes of Overlapped Reflections Using the Pseudophase Concept"
Acta Cryst (1998), A54, 438-446.
- M. Sakata, R. Mori, S. Kumazawa and M. Takata,
"Electron-Density Distribution from X-ray Powder Data by Use of Profile Fits and the Maximum-Entropy Method"
J. Appl. Cryst. (1990). 23, 526-534
- Tomohiro Ikeda, Makoto Sakata, Masaki Takata, Brendan j. Kennedy, David J. Cookson and Christopher J. Howard,
"Electron and Nuclear Densities of a Pyrochlore, Y2Sn2O7 Studied by the Maximum Entropy Method"
Proc. Int. Conf. SRMS-2, Jpn. J. Appl. Phys. Vol. 38 (1999) Suppl. 38-1, pp. 93-96.
- R. J. Papoular and D. E. Cox,
"Model-Free Search for Extra-Framework Cation in Zeolites Using Powder Diffraction"
Europhysics Letters, 32 (4), pp. 337-342 (1995).
- K. Knorr, F Madler and R. J. Papoular,
"Model-free density reconstruction of host/guest compounds from high-resolution diffraction data"
Microporous and Mesoporous Materials 21 (1998) 353-363.
- Masaki Takata, Eiji Nishibori, Buntaro Umeda, Makoto Sakata, Etsuji Yamamoto and Hisanori Shinohara,
"Structure of Endhedral Dimetallofullerene Sc2@C84"
Physical Review Letters, Volume 78, Number 17, 28 April 1997.
- Masaki Takata, Eiji Nishibori, Buntaro Umeda, Makoto Sakata, Etsuji Yamamoto and Hisanori Shinohara,
"Structure of Endhedral Dimetallofullerene Sc2@C84"
Physical Review Letters, Volume 78, Number 17, 28 April 1997.
- Masaki Takata, Eiji Nishibori, Buntaro Umeda, Makoto Sakata, Etsuji Yamamoto and Hisanori Shinohara,
"Conformation by X-ray diffraction of the endohedral nature of the metallofullerene Sc2@C84"
Nature, Vol. 377, No. 6544, pp. 46-49, 7th September 1995.
- B. Bagautdinov, J. Luedecke, M. Schneider and Sander van Smaalen,
"Disorder in the Crystal Structure of Cs2HgCl4 Studied by the Maximum Entropy Method"
Acta Cryst (1998), B54, 626-634.
- Robert E. Dinnebier, Martin Schneider, Sander van Smaalen, Falk Olbrich and Ulrich Behrens,
"Disorder determined by high-resoluton powder diffraction: structure of pentamethylcyclopentadienyllithium"
Acta Cryst (1999), B55, 35-44.
- K. Burger and W. Prandl,
"A new type of constraint in the maximum-entropy method using ambigous phase information from anomalous-scattering powder data"
Acta Cryst (1999), A55, 719-728.
- K. Burger, D. Cox, R. Papoular and W. Prandl,
"The Application of Resonant Scattering Techniques to Ab Initio Structure Soluiton from Powder Data using SrSO4 as a Test Case"
Acta Cryst (1998), 31, 789-797.
- Bo Brummerstedt, Jens Ledet Jensen and Jacob Danielsen,
"Errors in Maximum-Entropy Charge-Density Distributions Obtained from Diffraction Data"
Acta Cryst (1997), A53, 376-387.
- R. Y. de Vries, W. J. Briels and D. Feil,
"Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method"
Physical Review Letters, Volume 77, Number 9,26th August 1996.
Freely Available Maximum Entropy software for X-ray and Neutron Diffraction
- MEED/MEM/Fousyn/mevius/dsurf - Fortran (webpages in Japanese):
- MEED, MEEDCAB and MEND - Fortran:
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