




















[9;80s
(B[1m
	    P R O F I L E   R E F I N E M E N T   P R O G R A M

			U S E R 'S   G U I D E



[22m
		      Program version 3-JAN-1989

			     Martti Nurmela

			     Imatran Voima Oy

			     Helsinki, Finland



								1




[1m	 	PROFILE REFINEMENT PROGRAM, USER'S GUIDE[22m



Valid for version  3-JAN-1989 including Voigtian profile shape function,
texture corrections according to M. Jarvinen and x- ray data processing
capability.



[1m				General[22m



Input lines follow  the rules of  FORTRAN 77 free format  with following
restrictions and extensions:
1. Blanks are equivalent to zeros  if only blanks  and zeros are present
   on the rest of that line.
2. If a line or rest of it is blank,  search is not extended to the next
   line but all numbers that are required to be on that line will become
   zeros.
3. Character texts may not be included between apostrophes.
4. Real numbers may be given without a decimal point.
5. A real number  may be given  instead of an integer.  In that case the
   real number is rounded to nearest integer.

As a consequence of this,  all input values must  be given  on the lines
they are specified; the number of input lines is predefined.

The intention is to get rid of column-bound input.

In following sections  there are two kinds of input data -  single lines
and groups of lines.  These groups contain more than one lines belonging
tightly together.  In most cases the number of lines in a group is given
on some earlier line.

								2


[1m
I		   DESCRIPTION OF PREPARATION PROGRAM


I.a		Description of Input Lines and Line Groups[22m

________________________________________________________________________

Line  1 TITLE	Any alphanumeric character string at most 80 characters.
________________________________________________________________________

Line  2 CTHM	Correction for diffracted beam analyzer crystal.  Used
		only for x-rays.
	K	Polarization in parallel plane.  K = 0.5 for characte-
		ristic radiation,  K = 0.1  for synchrotron radiation.
		K = 0 for neutrons.
	CUT	Number of halfwidths  considered on  each side of peak
		position. Default value is CUT = 5.0.
________________________________________________________________________

Group 3 p1, b1	At most  99 lines  giving  background position  in  0.01
	p2, b2	degrees  2-theta and  background  height  at this angle.
	 . . .	These lines  must be in  ascending order of  2-theta and
	 . . .	the set is  terminated by a line with  -100 on its first
	pn, bn	field. Between given points background value is obtained
		with linear interpolation. The last line is required and
		it may be the 100th one.
________________________________________________________________________

Group 4 low,	At most  9 lines  giving lower  and higher bound in 0.01
	high	degrees  2-theta of an excluded region.  Note that these
		numbers  are given with negative sign.  Again the end of
		this group is signalled with -100 on the first field.
		That  line may be the tenth one  and it may  be  present
		only if excluded regions were given.
________________________________________________________________________

Line  5 N	Number of reflections listed in group 7.
________________________________________________________________________

Line  6 Nh, Nk, Denominators of the  Miller indices  h, k, l.  These are
	Nl	included to avoid using non-integer indices. The program
		interprets the Miller indices as h/Nh, k/Nk, l/Nl.
________________________________________________________________________

Group 7  	N  lines each having the following numbers:
	ICODE	= 1 means  this reflection is due to neutron nuclear
		    scattering.
		= 2 means this reflection is due to neutron magnetic
		    scattering.
		= 3 means  this reflection is due to neutron nuclear
		    and magnetic scattering.
		= 4 means this reflection is due to x-ray scattering.
	h,k,l	The Miller indices.  All reflections that contribute
		to any part of the pattern must be included.
	MULT	The multiplicity of reflection h,k,l.
________________________________________________________________________
								3


________________________________________________________________________

Line  8 ALPHA	Counter starting angle in 0.01 degrees 2-theta.
	DELTA	Counter step size in 0.01 degrees 2-theta.
	OMEGA	Counter finishing angle in 0.01 degrees 2-theta.
________________________________________________________________________

Group 9 -	(OMEGA-ALPHA)/10  lines each containing  profile pattern
		counts starting from angle ALPHA in steps of DELTA.
		There are 10 counts on each line.
________________________________________________________________________








[1mI.b	      Description of Output from Preparation Program[22m



The reflections are listed into unit 7 under the heading

	NO.	CODE	H  K  L    MULT    HW	POSN

HW  and POSN are in  0.01 degrees 2-theta.  Three successive reflections
appear on each output line.

The profile intensities are listed into unit 8 under the heading

	POSN	I+B	B     I    W	PEAKS	SHAPE

where I+B is  the raw pattern and  B is the background.  W is the weight
given to this channel.  Under PEAKS there is given  the range of reflec-
tions that contribute  to this channel  and under  SHAPE there are stars
the amount of which is equal to the number of contributing reflections.

								4


[1mII		    DESCRIPTION OF REFINEMENT PROGRAM


II.a		Description of input lines and line groups[22m


________________________________________________________________________

Line  1	 TITLE	Any alphanumeric character string at most 80 characters.
________________________________________________________________________

Line  2  GROUP	Space group number  of structure - an integer  from 1 to
		230.  If the structure is  orthorhombic,  however,  also
		the unique  axis choise must be given.  This is done  by
		including one of characters  a,b,c,A,B or C right  after
		space group number.  E. g.,  if space group is 27 and b-
		axis is  choosed to be the unique axis,  the information
		is given in form  27b  or  27B.

	 ANGLE  Incident  angle of measuring  geometry.  Three cases are
		available, angles are in degrees:

			Incident
		Case	 angle	  Alpha  Geometry
		______________________________________________________

		  1	       0      0  Symmetric reflection geometry

		  2	      90     90  Symmetric transmission or
                                         Debye-Scherrer geometry

		  3	0< |x| <90  B+x  Guinier reflection or
                                         Seeman-Bolhlin (x < 0) or
					 Guinier  transmission (x > 0)
					 geometry. B is Bragg angle.
		______________________________________________________

		According to  the table above  alpha is calculated  
                from incident angle.  Alpha is used to make texture  
                corrections independent of different measuring 
                geometries. 
                Alpha is the angle between polar axis (rotation or 
                fiber axis) and diffraction vector, x is the angle
                between the incident beam and the specimen surface.
		The  theory of texture  corrections was developed by 
		Dr. Matti Jarvinen,  
		Lappeenranta  University of Technology,	Finland.
		If incident angle is not known, 0 or 90 is suggested.

         RADIAT Character string starting with X or N indicating whether
                X-rays or neutrons were used,  respectively.  Lower case
		letters are also accepted.
________________________________________________________________________
								5

________________________________________________________________________

Line  3	 EPS	Forced termination of refinement is performed if for all
		parameters, calculated shift < EPS * estimated error.

	 CALC   = 0  when only  neutron nuclear  intensities  are to  be
		calculated, i.e. if CODE = 1 for all reflections.
		For x-rays  CALC has no meaning.  However,  CALC = 0  is
		recommended.
		= 1  when the magnetic  intensities are to be calculated
		according to the formula of Halpern and Johnson.
		= 2  when  the average  magnetic intensities  are to  be
		calculated in a uniaxial  configurational spin symmetry.
		= 3  when  the average  magnetic intensities  are to  be
		calculated in a cubic configurational spin symmetry.
	 LIM	The  limiting angle in  0.01 degrees 2-theta below which
		the diffraction peaks are to be corrected for the asymm-
		etrical vertical divergence effect.
________________________________________________________________________

Line  4	 CENTRE	= 1 for non centrosymmetric space groups.
		= 2 for centrosymmetric space groups.

	 EQUIV	Number of equivalent positions.

	 TYPE	Number of nuclear scattering lengths. Zero for X-rays.

	 FORM	Number  of normalized  magnetic scattering curves  for
                neutrons or number of scattering factors for X-rays.

	 ATOM	Number of atoms.

	 ROT	Number  of magnetic vector  rotation matrices for each
		equivalent positions (see Hewat).

	 LAMBDA	Radiation wavelength in Angstroms.
________________________________________________________________________

Line  5	 R,T	Matrix R and vector T describing an equivalent position.
		Twelve numbers in order R11,R12,R13,T1,R21,R22,R23,T2...
________________________________________________________________________

Group 6	 M	Matrix M  describing the rotation of the magnetic vector
		of the first type of magnetic vector transformations  in
		this  equivalent position relative to position  (x,y,z).
		Nine numbers in order M11,M12,M13,M21, ...
		There is  a total of  ROT (see line 5)  such lines after
		each (R,T)-line.

NOTE:		The group of lines 5 and 6 is repeated EQUIV times  (see
		line 4)  so that the total number of lines 5 and 6  will
		be EQUIV * (1 + ROT).
________________________________________________________________________

Line  7	 SCAT	Total of TYPE (see line 4) scattering lengths (10 fm).

NOTE:		This line exists only if neutron data is processed.
________________________________________________________________________
								6

________________________________________________________________________

Line  8  DISPRE Total of  FORM dispersion corrections for  X-rays,  real
		parts.
________________________________________________________________________

Line  9  DISPIM Total of FORM dispersion corrections for X-rays,  imagi-
		nary parts.

NOTE:		Lines 8 and 9 do not exist for neutron case.
________________________________________________________________________

Line  10 NAME	Name of atom. Two characters specifying the atom.
________________________________________________________________________

Group 11 CURVES List of sin(theta)/lambda and f-values describing the X-
		ray  scattering curves or normalized magnetic scattering
		curves. These are given in pairs

			sin(theta1)/lambda	f11
			sin(theta2)/lambda	f12
				.		 .
				.		 .
				.		 .

		At most 20 such pairs may be given and the set is termi-
		nated with a line having -100 in its first field.
		After that  a new name of an atom and a new set of pairs
		follows giving values to

			sin(theta1)/lambda	f21
			sin(theta2)/lambda	f22
				.		 .
				.		 .
				.		 .

NOTE:		The number of these sets is given by FORM  (see line 4).
		So line 10 and group 11 are repeated  FORM times coupled
		together in the order 10,11,10,11, ...
________________________________________________________________________

Line  12 CYCLE	Number of refinement cycles required.

	 RELAXC	Relaxation factor for coordinate shifts.

	 RELAXB	Relaxation factor for temperature factor  and for aniso-
		tropic temperature factors.

	 RELAX	Relaxation factor for scale,  occupation number and mag-
		netic vector components.

NOTE:		For rest of the parameters relaxation factors are set to
		0.8.

	 OUT	= 0  for reduced output.
		= 1 Program will print observed and calculated  profile
		     intensities on last refinement cycle.
								7

	 PUNCH	= 0  for reduced output.
		= 1  Program will write into a disk file calculated  and
		     separated observed structure factors on last cycle.

	 PUNCH	= 2  Program  will write  into a disk file  observed and
		     calculated profile intensities on last cycle.
		= 3  means both case 1 and case 2 are active.
	 MATRIX = 0  for reduced output.
		= 1  Program will print  the correlation matrix elements
		     multiplied by 100.
________________________________________________________________________

Line  13 c	Overall scale factor such that y(calc) = c x y(obs).

	 Q	Overall isotropic temperature parameter.
________________________________________________________________________

Line  14 LABEL	At most four characters to identify atoms.

	 NTYP	Ordinal number of relevant scattering length (neutrons).
		Ordinal number of X-ray scattering curve (X-rays).

	 MTYP	Ordinal number of magnetic scattering curve.

	 MROT	Ordinal number  of magnetic vector rotation matrix  with
		each equivalent position. For magnetic atoms MROT > 1.

	 x,y,z	Fractional atomic coordinates.

	 B	Isotropic atomic  temperature parameter.  This is effec-
		tively added to the overall temperature parameter Q.

	 n	Occupation number.

	 K(xyz) Magnetic vector components in the directions x,y,z.
		These are only needed when MROT > 1.
________________________________________________________________________

Line  15   -    Six numbers the meaning depending on DIR on line 17:
		If DIR is negative,  these numbers represent anisotropic
		beta-temperature  parameters in  order   beta(11), (22),
		(33), (12), (13), (23).
		If  DIR is zero  or positive,  these  numbers  represent
		anisotropic B(ij) parameters in the order given above.

NOTE 1:		Lines 14 and 15 are repeated  ATOM times,  once for each
		atom (see line 4).

NOTE 2:		For further details, see Hewat (1974), p. 20.
________________________________________________________________________

Line  16 T,U,V,W Gaussian halfwidth parameters according to expression

		2Wg=SQRT(T*cot(theta)**2+U*tan(theta)**2+V*tan(theta)+W).

	 X,Y	Lorentzian halfwidth parameters  according to expression

		2Wl = X * tan(theta) + Y / cos(theta).
								8


	 Z,S	Zeropoint position of counter  in units  0.01 degrees of
		of 2-theta so that

		2-theta(obs) = 2-theta(calc) + Z + S*cot(theta).
________________________________________________________________________

Line  17 DIR	Zero  or positive integer  value indicates  the  lattice
		cell constants on following line are given in form a, b,
		c, alpha, beta and gamma.
		Negative number  means that  lattice constants are given
		as A,B,C,D,E,F.  With these the distance between lattice
		planes is given in form

		1/d**2 = Ah*h + Bk*k + Cl*l + Dkl + Ehl + Fhk.
________________________________________________________________________

Line  18   -	Cell dimensions in form defined by DIR on line 17.
________________________________________________________________________

Line  19 P	Asymmetry parameter.
________________________________________________________________________

Line  20 TEX	Fifteen texture parameters;the coefficients of
		symmetrized harmonic functions.
________________________________________________________________________

Line  21 SIZE	Total number of least squares parameters =size of normal
		matrix.
________________________________________________________________________


Following lines define  which parameters will take part in least squares
fit.
________________________________________________________________________

Line  22 CxCyCz Codewords for fractional atomic coordinates.
	 CB,Cn	Codewords for the isotropic temperature parameter and
		for the occupation number.
	 CK	Codewords for the magnetic vector components if MROT>1.
________________________________________________________________________

Line  23  -	Codewords for the anisotropic beta(ij) temperature para-
		meters.

NOTE:		The pair of lines 22 and 23 is repated ATOM times,  once
		for each atom. See lines 14 and 15.
________________________________________________________________________

Line  24 Cc,CQ	Codewords for the overall scale factor and for the over-
		all isotropic temperature parameter.
________________________________________________________________________
								9

________________________________________________________________________

Line  25 CT,CU, Codewords  for the  Gaussian  (T,U,V,W)  and  Lorentzian
	 CV,CW, (X,Y) halfwidth parameters.
	 CX,CY
	 CZ,CS  Codewords for counter zeropoint parameters.
________________________________________________________________________

Line  26 CCELL	Codewords for cell constants A, B, C, D, E and F.
________________________________________________________________________

Line  27 CP	Codewords for the asymmetry parameter.
________________________________________________________________________

Line  28 CTEX	Codewords for the texture parameters.
________________________________________________________________________

Line  29 NLC,	Number of linear constraint functions.
	 NLQ	Number of quadratic constraint functions.
________________________________________________________________________

Group 30 a i j	Coefficients  and indices of the first linear constraint
	 b k l	function.  Last term,  d is given without indices and it
	 ...	is the last term of this constraint.  The maximum number
	 d	of coefficients is 10, including d. Next line starts the
		second constraint and so on up to NLC constraints.
________________________________________________________________________

Group 31 a ijkl Coefficients  and indices of the first  quadratic const-
	 b mnop raint function.  See group 31. Up to NQC groups of lines
	  ...	are given.
	 d

Note:		The indices given on groups 30 and 31 have the following
		meaning.
		1st index can have values 1, 2 or 3 depending on whether
		instrument, crystal or atom parameters are used, respec-
		tively.  The order and meaning of each parameter is des-
		cribed at the beginning of the program source file.
		2nd index gives the particular parameter in the category
		chosen by the first index.
		3rd and 4th index  are for the second term  of quadratic 
		constraint  following the same rules as do the first and
		second index, respectively.
		Constraints are now constructed by equations

		a * param(i,j) + b * param(k,l) + ... = d 	(linear)
		a * param(i,j) * param(k,l) + b * ... = d 	(quadr.)
________________________________________________________________________
								10


[1mII.b		Description of Output from Refinement Program[22m


The output of refinement program is well described in Hewat  (1974).  In
addition to that, texture correction coefficient is given among the ref-
lection  data  printed on last  refinement cycle.  The coefficient  is a
number with which the intensity of a particular reflection was cor-
rected.


________________________________________________________________________


References: A. W. Hewat: Profile refinement of Neutron Powder
	    Diffraction Patterns - Crystal and Magnetic Structures,
	    ILL 1974.

	    Ahtee, M., Unonius, L., Nurmela, M., Suortti P.:
	    A Voigtian as Profile Shape function in Rietveld Refinement
	    J. Appl. Cryst. (1984). 17, 352-357.

	    Ahtee, M., Nurmela, M., Suortti, P. and Jarvinen, M.:
	    Correction for Preferred Ortientation in Rietveld 
	    Refinement.  J. Appl. Cryst. (1989). 22, 261-268
 
	    Jarvinen, M. (1986).: A New Texture Correction Model for
	    Rietveld Method. Proc. XII Conf. Applied Crystallography,
	    10-14 August 1986, Cieszyn, Polland. Supplement, pp. 7-12.

	    Jarvinen, M. (1989).: Preferred Orientation in Powder
	    Diffraction. Research Report 14/1989. Lappeenranta
	    University of Technology. Lappeenranta, Finland.


________________________________________________________________________

