Extraction of the integrated intensities

Parent Previous Next

Extraction of the integrated intensities ('extraction' command)

       To calculate the integrated intensities, the program uses the Le Bail algorithm (Le Bail et al., 1988) and combines it with a least squares procedure minimizing the quantity:

(1)


The summation in (1) goes over all the data points,
wi = 1 /yi2
yoi = observed intensity at the i-th step
yci = calculated intensity at the i-th step

(2)

The summation over h includes neighbouring Bragg h reflections,

s

=

scale factor

LPh

=

Lorentz - polarization factor

mh

=

reflection multiplicity

Fh

=

structure factor

P

=

profile function

A

=

asymmetry function

ybi

=

background intensity at the i-th step.


The background in (2) is automatically estimated and is described by the polynomial function (Young, 1993)

N, the polynomial degree, is automatically defined by the program as the number which provides the best fit of the background interpolation points.

is the associated to the minimum intensity in the range in which the background is estimated.
From the pattern a standard peak is automatically selected. The standard peak fitting is performed to provide the starting values of the variables to refine in the least squares procedure.
The full pattern is automatically divided into intervals. The refined parameters derived by the fitting of each interval will be taken into account for the final full pattern fitting.
The following profile shape functions are available for user choice:

Pearson VII

Gaussian

Lorentzian

Pseudo-Voigt

where

The default is the Pearson VII function. In this case

otherwise

The peak shape, the asymmetry, the cell and the background parameters are all refined by the program. To overcome the tendency of the Le Bail algorithm to equipartition the intensities of strongly overlapping reflections, a new approach was introduced. It is based on the random variation of the reflection intensities belonging to a given cluster and on the subsequent selection of the good fit feasible trials.
After a first default run of EXTRA, it is possible to run it again starting from the refined variables in the previous run. In this case the preliminary standard peak procedure and the interval by interval extraction procedure are skipped. The related command is %RECYCLE.

Directives in extraction command

The following directives must be added after the command '%extraction' in the input file to activate some specific features of the procedure

ALL

To activate the procedure of selection of the profile function type (among Pearson VII, Gaussian, Lorentzian, Pseudo-Voigt) from the best fit of each interval.

DAMPING x

x is the damping factor used in the least squares routine (default value 0.1). (It is convenient to use a small x value).

FAST

This directive is used if the graphic interface has been requested by the "window" command. In this case, the user graphic interaction in a default run is avoided.

FIRST

To activate the procedure of selection of the profile function type (among Pearson VII, Gaussian, Lorentzian, Pseudo-Voigt) from the best fit of the first interval .

FRECYCLE filename.ext

If the "filename" is available from a previous run of EXPO2014 (or EXTRA), or from any source containing hkl and the corresponding F-squared values, Le Bail algorithm is started again for obtaining new estimates.

GAUSSIAN

To use only if the gaussian function is preferred.

INTERVAL n

n is the number of intervals in which the powder pattern is divided (max 8). n is only given if the user wants to change the automatic division of the pattern.

LORENTZIAN

To use only if the lorentzian function is preferred.

LOWB

To reduce the background by a constant factor equal to the minimum value observed count.

NCYCLE n

n is the number of cycles for each interval (default value is 60).

NOBA

To not refined the background

NOCELL

To skip the cell refinement.

NOSINGLE

This directive is used if the preliminary fitting of the standard peak (automatically selected by the program) is omitted. In this case a preliminary fitting of the first interval is carried out.

OPTI

To continue the refinement procedure for each interval.

POLYNOMIAL k

k is the background polynomial degree (max 10). k is given if the user wants to use a fixed degree in each interval and not the degree automatically selected by the program.

PVOIGT

To use only if the Pseudo-Voigt function is preferred.

RANDOM p

To activate the random procedure in the integrated intensity extraction step. p is the coefficient for the reflection overlapping definition. Default value = 0.5

SMOO

To activate the procedure for calculating the background by following (Brückner, 2000). In this case the background is not refined.

STANDARD

To activate the procedure of selection of the profile function type (among Pearson VII, Gaussian, Lorentzian, Pseudo-Voigt) from the best fit of the standard peak.

SLOW

This directive can be used if the graphic interface has been requested by the "window" command. In this case the program stands by after some relevant calculations and waits for the user graphic interaction to go on.

VERBOSE

This directive is used to have a more detailed print in the output file. In this case, the Rp and Rwp values and the values of the refined variables are printed interval by interval.

WIDTH x

x is the factor which, multiplied by the FWHM of each peak, gives the total peak width. (In this case the automatic calculation of x is not taken into account).

ZEROPROFILE x

x is the 2θ shift value supplied by the user (to be substracted from the 2θ observed positions). In this case the automatic calculation of the 2θ shift using the preliminary fitting of the standard peak is skipped by the program).

Examples

Example 1

A Pseudo-Voigt function will be used and the background in each interval will be described by a constant. The counts file format is not the default one and the graphic window is suppressed. 

%structure mes
%job MES - data from home diffractometer
%initialize
%data
  pattern mes.pow
  cell 8.588 9.931 11.105 90.0 93.754 90.0
  content C 24 N 4 O 20 S 4 H 52
  spacegroup p 21/c
  wavelength 1.5406
  filetype double
%extraction
  pvoigt
  polynomial 0
%end 


Example 2

The starting values of the integrated intensities in the extraction step are supplied by the user in the file "yono.ext" and the number of least-square cycles is set to 40. 

%structure yono
%job YONO - Synchrotron data
%initialize
%data
   pattern yono.pow
   cell 9.385 16.394 3.627 90.000 101.067 90.000
   content Y 8 O 26 N 2 H 18
   spacegroup p 21
   wavelength 1.2323
   synchrotron
%extraction
   fstarting yono.ext
   ncycle 40
%end


 Example 3

The preliminary fitting of the standard peak is skipped and the starting 2θ shift value is supplied by the user (the program refines it).

%window
%structure agpz
%job AGPZ - data from home diffractometer
%init
%data
   pattern agpz.pow
   cell 6.526 20.059 6.464 90.000 90.000 90.000
   spacegroup p b c a
   content Ag 8 N 16 C 24 H 24
   wavelength 1.54056
%extraction
   nosing
   zeroprof 0.02
%continue


Example 4

Neutron data and a deuterium atom in the cell content are used. Fast graphic interaction for the integrated intensities extraction process is activated.

%structure baco
%job BACO - Neutron data
%initialize
%data
   neutron
   isotope H 0.67
   pattern baco.pow
   cell 10.0632 7.9330 6.8487 90.0 122.3423 90.0
   spacegroup C 2/m
   content Ba 4 C 8 O 20 H 8
   wavelength 1.909
%extraction
   fast
%continue


References


Le Bail, A., Duroy, H., Fourquet, J.L. (1988). Ab-initio structure determination of LiSbWO6 by X-ray

powder diffraction. Math. Res. Bull. 23, 447-452.

Created with the Personal Edition of HelpNDoc: Easy CHM and documentation editor