

================================   MARE    =====================================


 MARE is an widget based graphical interface to calculate: 
  - Spaghetti plots (lambda versis Psi for multiple crystal reflection)
  - The Umweganregung peak location plot (the diffracted wavelength 
       lambda vs. Psi) for a given primary reflection,i.e., an 
       horizontal cut of the spaghetti plot.  
  - The Glitches spectrum (the negative intensity for versus the
        wavelength) or a vertical cut of the spaghetti plot. 

  Psi is the azimutal angle of totation, i.e., the totation around
    the H vector (main reflection)



 In other words, if a crystal is set with a particular Bragg angle to match 
 a given reflection (inputs: H,K,L) at a given wavelength (input: WaveLength), 
 many other (secondary) reflections are excited when the crystal is rotated 
 around the azimutal angle Psi, without changing the Bragg angle. 

 The plot (WaveLength,Psi) of the possible reflections is calculated and
 contain all possible reflection curves up to a maximum reflection 
 (input: H Max,  K Max, L Max). 

 Umweg plot: 
 The intersection of these curves with an horizontal line at the wavelength 
 of the primary reflection (input: WaveLength) gives the position of the 
 peaks in the unweg plot. The width of each peak depends on the pendent of 
 the curve at the intersection. For that, the Psi1 and Psi2 intersection 
 angles with a band of width (input: DeltaWaveLength) are calculated. With 
 this width and the intensity of the diffraction line, it is possible to 
 compute a Gaussian that "roughly" describe the peak.
 
 Glitches plot: 
 The intersection of these curves with a vertical line at a given Psi 
 gives the position of the peaks in the glitches plot. The width of each 
 peak is the difference between the wavelength values for Psi+/-DeltaPsi
 With this width and the intensity of the diffraction line, it is possible to 
 compute a Gaussian that "roughly" describe the peak.
 

 The program computes first all Miller indices hkl associated to the
 different crystal planes which meet the diffraction condition (multiple
 diffraction events) in the two-beam multiple diffraction approximation.

 The structure factor, independent of the energy (i.e., no anomalous
 scattering) is calculated for each reflection. 

 In the spaghetti plot all reflections, except all that have structure
 factor zero (i.e., forbidden reflections) are plotted. 

 The azimuthal angle Psi is calculated relative to an arbitrarily chosen 
 reference direction perpendicular to the scattering vector of the primary 
 reflection.  (See Ref). The considered reflection is displayed in the 
 header of the xop macro that produces the plot.  

 The theoretical frame of the program is essentially provided in:
     B.H. Cole et al, "Simultaneous Diffraction: Indexing Umweganregungen 
     Peaks in Simple Cases", Acta Cryst. (1962), 15, 138-144

 The peak intensity is calculated approximately, as Fh^2*L*P, 
 being L the lorentz factor, and P the polarization factor. The latter
  values are computed in the function bragg_lorentz(). 

 Note that this intensity is very approximated, because: 
       - The formula is not valid for perfect crystals, only for powders.
       - The total intensity must be the sum of the primary reflection
         plus the intensity of the so-called operative reflections plus the
         contribution of the cooperative ones. 
       - Anomalous scattering factors are not considered. 
       - The lorentz and polarization factor are not correctly used

 Therefore the resulting plots should be taken with care. 
 For a more detailed and accurate method, the following references may be used: 
       Rossmanith, Acta Cryst (1992) A48 596-610
       Rossmanith, Acta Cryst (2006) A62 174-177
       Rossmanith, J. Appl. Cryst. (2003) 36, 1467-1474  

 The program should deal with any crystal geometry, however, only the 
 cubic geometries have been tested. 


Description of the input parameters for MARE:
==============================================

Crystal:           crystal type

H main
K main
L main             (H,K,L) of the primary reflection [deg]

H max:             max H for calculated reflection curves.
K max:             max K
L max:             max L

Eliminate reflections with fh less than:
                   Numerical value for discarding low intensity reflections.
                   Default 1d-8, eliminates zero (i.e., forbidden) reflections.
                   Look at the outputs using "Edit buffer" button in the
                   output windows to see the used fh (real part of the
                   structure factor).

Display:           select the type of output

Wavelength [A]:        The wavelength (in A) for calculating the
                       unweg pattern (the line wavelength=constant
                       intersect the curves in the spaghetti plot).
Delta Wavelength [A]:  The band width around Wavelength.

Phi [deg] (for Glitches):   Phi value for the vertical cut of the
                            spaghetti plot.

Delta Phi [deg]:       the band width around Phi.


The program creates a script that must be run with "Run Script" to produce
the graphical output.