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******************   Documentation for LAPOD   ******************
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  PROGRAM AUTHOR - J. Ian Langford,
                   School of Physics & Space Research,
                   University of Birmingham,
                   Birmingham B15 2TT,
                   UK.
                   Tel. (44) 21 414 4662/4666;
                   FAX (44) 21 414 4719;
                   E-Mail:  J.I.LANGFORD@BHAM.AC.UK


  REFERENCE - Langford, J.I., J. Appl. Cryst. 4, 259-260 (1971)
              and 6, 190-196 (1973)




                            LAPOD
                          --------


 Least-Squares Refinement of Cell Dimensions from Powder Data by               
 Cohen's Method.

 13.ii.70: Original version
 17.i.84:  FORT77 Version
 12.v.94:  PC version (Ron Pflaumer)
 12.i.98:  Minor upgrade
 17 May 1999 - Put on CCP14 site: http://www.ccp14.ac.uk/ccp/web-mirrors/lapod-langford/



 INPUT/OUTPUT FILE FORMATS:

 Input:


 Input data via unit IR, set to 1 in program ("filename.lap" for UNIX and VMS,
 and "filename.LAP" for PC version).  For UNIX and VMS versions, only type
 the filename, since the extension is added by the program.  For the PC 
 version, type the full file designation, including the ".LAP" extension. 

 Line 1:     Title
 Line 2:     Wavelength (A), Diffractometer radius (mm)
 Line 3:     Crystal System Code: 1 Triclinic, 2 Monoclinic, 3 Orthorhombic,
             4 Hexagonal, 5 Rhombohedral, 6 Tetragonal, 7 Cubic
 Line 4:     Trial cell dimensions.  ALL SIX MUST BE INPUT.  Values are not
             critical, since least-squares regression is linear.          
             However, it is sometimes convenient to compare refined cell
             dimensions with those of a standard, e.g. the end member of an
             isomorphous series, etc.
 Line 5:     h k l      2Theta     weight
 et seq.
             h k l:
             Miller indices must be separated by at least one space.

             2Theta:
             Not all observed 2Theta values need to be input;  strong and/or
             well resolved lines can be selected, unlike pattern indexing,
             where the first 20 or so 2Theta values must be input.  As a rough
             guide, ideally the number of data input should be about 10 plus
             the number of parameters to be refined.
             If possible, 2Theta values should be pre-corrected for 
             systematic errors by means of an internal or external standard
             [control code 2].  Alternatively, raw data can be corrected
             for a known error in the 2Theta scale, specimen-surface
             displacement (SSD, mm) and sample transparency (linear absorption
             coefficient, 1/mm, 'thick' sample correction) [code 1].
             0.0 is input for the last, if no transparency correction is
             required. Additionally, there is provision for refining the zero
             error [code 3], the SSD [code 4] or both these quantities [code 5].  However, 
             the use of codes 3-5 is not recommended unless the data are of high 
             quality, i.e. good counting statistics and a precise determination
             of line position for all reflections.  If random errors are
             large, relative to systematic errors, unacceptably large
             standard deviations in the refined cell dimensions may result.
 
             Weight:
             Data can be weighted according to the intensity of a reflection,
             degree of overlap, etc., if desired.  However, the weight
             accorded reflections is normally set to 1.0.


 Output:

 Output is to Unit IW, set to 7 ("filename.out" for UNIX and VMS, and 
 "filename.OUT" for PC version).  For UNIX and VMS versions, only type
 the filename, since the ".OUT" extension is added by the program.
 For the PC version, type the full file designation, including the ".OUT"
 extension.

 The quantity refined is Vc = Q(Obs) - Q(Cal), where Q = 1/d*d.  The residuals
 Vc (x 1E5) are listed in the output table and the sum should be ~zero,
 if systematic errors have been removed.  Inspection of the table indicates
 whether a reflection has been incorrectly indexed or its position is
 inaccurate.  Also given are the sum of the differences between the obs.
 and calc. values of 2Theta and the standard deviation.  The latter should
 relate to the estimated precision with which line positions have been
 determined.  Other items in the output are self-explanatory.


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