CHAPTER 7
		     THE INDEX AND RAFIN PROGRAMS






	  7.1  <index

	     The  program  indexes  reflections	 on  the   basis   of	observed
	     2Theta, Omega, Chi, Phi   angles	when   the  cell  constants  and
	     wavelength are known.
	     It does not take into account systematic extinctions.

	     The process, when successful, has three steps.

	     First, it calculates, for each set of  observations,  all	possible
	     HKL's   for   which   <theta(calc)	  lies	 within	 <theta(obs) +/-
	      <delta <theta.
	     <delta <theta is given - see below -.
	     For <delta <theta = 0, the value defaults to 0.05.

	     Second, it finds for all combinations of two sets of  observations,
	     the  angle	 between  the  indexed HKL's for which <angle(calc) lies
	     within <angle<(obs) +/- <delta.
	     <delta given  - see below -. Delta = 0 causes default to 0.2

	     Finally, it finds all sets of indexed HKL's that explain all angles








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	  INDEX AND RAFIN.


     between the observed sets of Omega, Chi and Phi.

	     The user will normally be presented with several possible	sets  of
	     HKL's which fit within the limits given.
	     - they are already tested for right-handedness -
	     and he must now choose which set he likes the most.

	     If he wishes he may now specify which set of reflections  he  likes
	     and  the  program	will  then set up the input file for the program
	     <rafin, - see next section -.
	     The program ensures that the first two reflections	 are  acceptable
	     to	 <rafin.   The	user  must  say	 whether he wants the <ub matrix
	     written directly into <lsd ( for instant use ) and	 which	file  he
	     wants his <rafin input to come from (usually <rafin.dat).
	     The program <rafin is then automatically started.


	     Input to <index can be done either from the terminal or from a file
	     <index.dat
	     The format is the same, an example is given here.

	     THIS IS A DUMMY EXAMPLE	      ( text )
		5.82 16.15 4.09 90 103.2 90 .84 .15
						 (cell constants, lambda,








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	  INDEX AND RAFIN.


	     <delta)
		16.18 9.01 34.71 14.74 0	 (2Th, Om, Ch, Ph, <delta
		<theta)
		13.21 7.8 .71 -56.13 0.1	 (2Th, Om, Ch, Ph, <delta
		<theta)
		etc. etc.
		0				 ( end list with 2Th = 0 )


		The program will only suggest  sets  of	 indexed  HKL's	 if  all
	     reflections  are  explained.   If	not,  the user must himself look
	     through the list of  observed  and	 calculated  angles  to	 find  a
	     partial list.



	  7.2  rafin

	     This program determines orientation matrix (<ub) from two	or  more
	     sets   of	 orientation   angles	for   reflections,  and	 refines
	     (optionally) wavelength; zeroes of 2Theta, Omega or Chi; a,  b,  c,
	     alpha, beta or gamma.










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	  INDEX AND RAFIN.


		To call the program, type :--
	     ><run <rafin
	     after having set up the input file :

	     The input data are on <rafin.<dat
	     (teletype input can be used, but is cumbersome)

	     Use <teco to make or correct the file.

	     An example of the input file ( comments in parentheses ) :--

	     0 1     (second no. 0/1 for <ub not transferred/transferred to
	       <lsd)
	       0       (always)
		0 -4 -2 28.01 13.75  81.59  42.05  (H K L 2Theta Omega Chi Phi)
		4 -6  7 50.84 25.37  34.04  18.41
	       -2 -6  0 41.55 20.53  66.93  59.99
		4  0  4 19.74  9.94 -16.92  -5.40
		1 -5 -3 35.59 17.70  82.32   1.40
		6  0  0 18.47  9.26  -2.32 -46.95
	       0 .8405		(0/1 do not/do refine lambda; and lambda)
	       0 0.0 1 0.0 1 0.0	(0/1 for do not/do refine, 2Theta zero,
					-0/1 for do not/do refine, Om zero,
					-0/1 for do not/do refine, Chi zero.)








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	  INDEX AND RAFIN.


	     0 15.9158 0 7.1939 0 14.277 0 90 0 98.72 0 90
					(ditto for <a, <b, <c, <alpha, <beta and
	       <gamma)
	       2 0 0			(H K L list for angles to be calculated)
	       0 2 0
	       0 0 2
	       0 0 0			(end of list)
	       -1			(end of input file)

	       Ensure that <lsd is not running	if  you	 wish  to  transfer  the
	     matrix   and   wavelength	directly  into	its  parameter	section,
	     otherwise it may not be successful.
	     <rafin will never modify the zeroes for you. This is for you to  do
	     by <adding them to the values in <zer of <par.  Remember that for a
	     well aligned diffractometer, they will never change by very much.

	     Note: the first two  reflections  should  be  far	away  enough  in
	     reciprocal	 space	to  define a plane. They must be at least 45 deg
	     apart in Phi and only one may have Chi greater than 45 deg.

	     Note also that higher angle  (Theta)  reflections	usually	 give  a
	     better fit.

	     You cannot, obviously, refine lambda and  your  cell  at  the  same








								     Page 7 - 6

	  INDEX AND RAFIN.


	       time.



	  7.3  <acknowledgements

	     The <index program was written by M.S.Lehmann,
	      and J.M.Savariault.

	     The <rafin program was implemented at  the	 <ill  by  A.Filhol  and
	     M.Thomas.
	     It was implemented on the <pdp 11 system by A.Barthelemy.





















					   CHAPTER 8
				    THE HKLGEN AND GENLIS PROGRAMS






	  8.4  <HKLGEN

	     THIS PROGRAM IS USED TO GENERATE A LIST OF HKL's which can be  used
	     for input to the measurement routines of <lsd.
	     Indices can be generated internally in <lsd, but  it  is  generally
	     considered easier to create a list, and measure from this.

	     <hklgen will generate HKL's according  to	min  and  max  specified
	     indices, and will write them into output file(s) if they are inside
	     the Theta limits.

	     If <chi and <phi limits are specified, the program will  also  look
	     to see if the <hkl is measurable inside these machine limits.

	     If not, it will see if the Friedel Pair is inside limits

	     If this is also outside limits, it will see if the	 reflection  can
	     be measured for <hkl <psi=180








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		  <HKLGEN <AND <GENLIS


	     - <note this option means <chi = 90 -> 180 i.e. <up-side-down.

	     If measurement is not possible for any  of	 these	conditions,  the
	     <hkl is declared <blind.

	     Comments like <fr.pr <hichi <blind indicate these on <tty output.

	     To run the program do :--

	     ><run <hklgen
	     Input to the program is either from the terminal or   from	 a  file
	     <hklgen.dat, already created by the user.



	  8.4.1	 input from the terminal.

	     The first question asked  under  this  option  is	whether	 a  file
	     <hklgen.dat should be created.
	     If subsequent runs are envisaged, this might be a	good  idea.   In
	     this  case <teco can be used to make small changes to the input and
	     the program can be quickly re-run.
	     <hklgen then asks for the following parameters :--









								     Page 8 - 3

		  <HKLGEN <AND <GENLIS


	     1.	  Title. Up to 80 characters to be displayed at the top	 of  the
		  output.

	     2.	  Wavelength and the 9 'rules limiting possible	 reflections'  -
		  see  appendix C -- If you give wavelength = 0, the wavelength,
		  extinction rules, and orientation matrix will	 be  taken  from
		  <lsd's parameter files.
		  <chi	and  <phi  software  limits  are  also	taken	but   an
		  opportunity is given to over-write them.
		  -- If the wavelength	is given explictly, followed by up to  9
		  numbers  for the extinction rules, the orientation matrix must
		  then be given line by line.

	     3.	  Theta limits. ( Note <not 2-Theta limits ).
		  <chi and <phi limits ( if required ) must  also  be  given  in
		  this line.
		  -- If zeroes are given, no limits  will  be  included	 in  the
		  calculations.
		  -- If nothing is given, LSD's limits will be used  if data was
		  taken	 from  the parameter files, or it will default to zeroes
		  if the data above was given by the user.











								     Page 8 - 4

		  <HKLGEN <AND <GENLIS


	     4.	  Three numbers indicating the relative speed  of  variation  of
		  <h, <k and <l.
		  First number is the slowest changing index,  third  number  is
		  the fastest changing index.
		  1/2/3 is used to represent <h/k/l.
		  e.g. 3 2 1 means L changes slowest, then K,  with  H	changing
		  fastest.

	     5.	  Minimum and maximum indices in <hkl are now requested.
		  You must give <hmin <hmax <kmin <kmax <lmin <lmax.
		  Note however that before starting  the  calculations,	 <hklgen
		  calculates itself what is the maximum value for each index for
		  the specified Theta range and if this is inside these	 values,
		  they will be modified.
		  Therfore, if, for example 0 999 0 999 -999 999 is given,
		  <hklgen will calculate the maximum values and give HKL's for
		  positive H, positive K, positive and negative L.

	     6.	  Four numbers concerning various outputs from the program.
		  a) The first <npunch concerns the <hkl output file.
	  0 = no file for output
	  1 = file for output containing <hkl only in 3I4 format.
	  2 = file for <d15-ren ( not for <d8-d9 )
	  3 = file for output containing <hkl and setting angles.








								     Page 8 - 5

		  <HKLGEN <AND <GENLIS


	     b) The second <ipara concerns machine geometry.
	  0 = Bissecting geometry - (normal for <d8-d9 ).
	  1 = Normal beam geometry - ( rarely used on <d8-d9 )
	  3 = <d15 lifting counter mode ( used with <npunch = 2 )

		  c) The third number <nbites concerns <hkl output.
	  1 = write <hkl for each case in four separate files.
	  0 = write all HKL's in one single file FOR00x.<dat
	       ( x specified below ).

		  d) The fourth number <nlist concerns terminal output.
	  0 =  write each <hkl with angles and comment on terminal.
	       ( can take time and consume paper ).
	  1 = suppress most of the output on <tty.

	     7.	  If in previous line FOR00x.<dat was specified for <hkl output,
		  X must be given.
		  This is  the	last  line  in	the  input  but	 is  not  always
		  necessary.

		  The program then generates as specified, creating  file(s)  if
	     required. It gives a resume at the end and exits.










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		  <HKLGEN <AND <GENLIS





	  8.4.2	 input from file hklgen.dat

	     Input is given in exactly the same order as above, so  for	 a  more
	     detailed description of each parameter see previous section.

	     Two possible examples are given below.

		  KNUDDERKRYSTAL LAVET AF AARKVARD, 120K      (Text, 80
	     characters)
	     0.8405 0 0 0 0 0 0 0 0 0		  (Wavelength and the 9
							      Extinction rules.
	     )
	     0.043361 -.04190  .5399	     ( <ub given in three separate lines
	     -.046409 -.032053 .03721	     - as wavelength is given explicitly
	     -.00256  -.12861 -.02687
	     0 36 -20 95		      ( Theta limits and Chi limits -
						   - note - no limits on Phi. )
	     2 1 3			      ( relative speeds of <hkl.
						  - K slowest - L fastest. )
	     -99 -1 0 5 -99 99		      ( Hmin,Hmax,Kmin, etc.
						   - note all L's with all neg








								     Page 8 - 7

		  <HKLGEN <AND <GENLIS


		  H.
						   - K is only to 5. )
	     1 0 0 1			      ( a) Output file of <hkl.
						b) Bisecting geom - usual.
						c) All HKL's in <for00x.dat.
						d) Suppress most <tty output. )
	     3				      ( <hkl file on <for003.dat )


	     Second example - probably more normal :--

	     <sample <b <shell 30-35 <deg     ( Title )
	     0				      ( Lambda <ub, Extinction rules,
					 - <phi and <chi limits taken from <lsd
	     )
	     30 35			      ( Theta limits; note LSD's <chi
					      - and <phi limits are taken.
	     1 2 3			      ( <h slowest - <l fastest )
	     -99 0 -99 99 0 99		      ( all neg H - all K - all pos L )
	     1 0 1 0			      ( output file of <hkl only.
						Bisecting - usual.
						Four files of <normal.hkl.
							      <frprs.hkl.
							      <hichi.hkl.








								     Page 8 - 8

		  <HKLGEN <AND <GENLIS


								   <blind.hkl.
						List all on <tty.  )




		  The program is found on <dk2: under  <uic> [200,200].


	     <hklgen is a program which has evolved in the hands of :
	     A.Filhol, S.Mason. A.Barthelemy and J.Allibon.



	  8.5  genlis


	     the program generates a list of hkl  from	a  list	 of  reflections
	     produced  by coll5n or hklgen. the indices can be permuted, and for
	     coll5n lists limits can be applied to theta and sigma(fsq)/fsq.
	     up to 50 different reflections can be excluded from the list.

	     to produce the list do









								     Page 8 - 9

		  <HKLGEN <AND <GENLIS


		  >run genlis

	     and answer questions.
	     input file is punch-file produced by coll5n or hklgen. if old  data
	     is needed, mount the relevant disk on dk3:
	      for the exercise. the program will accept a series of input files,
	     if needed. output file name is chosen by the user.

	     the permutation of hkl is given by a combination of indices.
	     example:

	     h=-h-k
	     k=H
	     l=-l

	     in addition reflections can be rejected using  expressions	 of  the
	     kind  k-h>n,  where  n is an integer. this rejection is done before
	     the permutation.

	     repeated tests of sigma limits without stopping  the  program  will
	     produce  a	 series	 of  files  with  increasing  extension	 numbers
	     (assuming coll5n data is input, and that all input is on  a  single
	     file).









								    Page 8 - 10

		  <HKLGEN <AND <GENLIS


		  the program is largely self-explanitary and should be	 obvious
	     when it is used (or after a few attempts). have faith.

	     genlis was written by m. s. lehmann.


























					    APPENDIX C
					    RULES LIMITING POSSIBLE REFLECTIONS






        17.0 HKL
                	 0 : NO CONDITIONS
			 1 : H + K + L = 2n
			 2 : H, K, L all even or all odd
			 3 : -H + K + L = 3n
			 4 : H = K + L = 3n
			 5 : H + K = 2n
			 6 : K + L = 2n
			 7 : H + L = 2n
			 8 : H + K + L = 6n
			 9 : H, K, L all even
			 10 : H, K, L all odd
    			 11 : If H - K = 3n, then L = 6n












								      Page C - 2

				   RULES LIMITING POSSIBLE REFLECTIONS


	18.0  H K 0

	     0 : No conditions
			 1 : H = 2n
			 2 : K = 2n
			 3 : H + K = 2n
			 4 : H + K = 4n



	19.0  0 K L

	     0 : No conditions
			 1 : K = 2n
			 2 : K + L = 2n
			 3 : K + L = 3n
			 4 : K + L = 4n
			 5 : L = 2n



	20.0  H 0 L

	               0 : No conditions








								      Page C - 3

				   RULES LIMITING POSSIBLE REFLECTIONS


	                 1 : L = 2n
			 2 : H = 2n
			 3 : L + H = 2n
			 4 : L + H = 4n



	21.0  H H L

	                 0 : No conditions
			 1 : L = 2n
			 2 : H = 2n
			 3 : 2H + L = 4n