Application of the maximum-entropy method to powder-diffraction data
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
ch. 4.8,
pp. 473-488
[ doi:10.1107/97809553602060000963 ]
; Palatinus &
van Smaalen, 2002 ;
van Smaalen et al., 2003 ; Buchter et al., 2011). The same condition holds for MaxEnt reconstruction of extended X-ray absorption fine structure (EXAFS) analysis (Gull & Skilling, 1984 ...
Cambridge algorithm (Bryan & Skilling, 1980, 1986; Burch et al., 1983; Skilling & Bryan, 1984; Gull & Skilling, 1987, 1999)
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.5.3,
pp. 477-477
[ doi:10.1107/97809553602060000963 ]
requirements of the MEM approach, for example leading to an MEM-optimized electron density that better obeys the criterion than the Sakata–Sato algorithm does (
van Smaalen et al., 2003). Nevertheless, the MEM-optimized electron-density map ...
[
more
results from section 4.8.5 in volume H]
Stopping criterion
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.8.2,
pp. 485-486
[ doi:10.1107/97809553602060000963 ]
the atoms. This procedure has worked well for several data sets. It could be shown that the optimal value of is related to the goodness of fit (GoF) of a multipole refinement using the same data by the relation = 0.68 × GoF (
van Smaalen & Netzel, 2009 ...
[
more
results from section 4.8.8 in volume H]
Accurate electron densities
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.7.6,
pp. 484-485
[ doi:10.1107/97809553602060000963 ]
[
more
results from section 4.8.7 in volume H]
Constraints in the MEM based on the measured intensities from powder-diffraction data
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.6,
pp. 477-480
[ doi:10.1107/97809553602060000963 ]
on calculated structure factors,, of the prior structure model (Palatinus &
van Smaalen, 2005): where the symbols have the same meaning as in equations (4.8.10) and (4.8.28), but and is the number of reflections included in the PDC ...
[
more
results from section 4.8.6 in volume H]
The principle of maximum entropy
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.2,
pp. 474-475
[ doi:10.1107/97809553602060000963 ]
Crystallographic MEM equations
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.4,
pp. 476-476
[ doi:10.1107/97809553602060000963 ]
Prior densities in MEM calculations
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.3,
pp. 475-476
[ doi:10.1107/97809553602060000963 ]
et al., 1995 ; Schotte et al., 1995 ; de Vries et al., 1996 ; Roversi et al., 1998 ; Papoular et al., 2002 ; Palatinus &
van Smaalen, 2002 ;
van Smaalen et al., 2003 ; Buchter et al., 2011). The same ...
Introduction
Magdysyuk, O.V.,
van Smaalen, S. and
Dinnebier, R.E.,
International Tables for Crystallography
(2019).
Vol. H,
Section 4.8.1,
pp. 473-474
[ doi:10.1107/97809553602060000963 ]
size 0.1 e Å −3 . [Reprinted with permission from de Vries et al.
(1996). Copyright (1996) American Physical Society.]
References
Dinnebier, R. E., Schneider, M.,
van Smaalen, S., Olbrich, F. & Behrens, U ...
