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DDDDDDD IIII CCCCCC VV VV OOOOOO LL 0000 66
DD DD II CC CC VV VV OO OO LL 00 00 66
DD DD II CC VV VV OO OO LL 00 00 66
DD DD II CC VV VV OO OO LL 00 00 66 66
DD DD II CC VV VV OO OO LL 00 00 66 66
DD DD II CC CC VVVV OO OO LL LL 00 00 66 66
DDDDDDD IIII CCCCCC VV OOOOOO LLLLLLLL 0000 66666
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TWO OPTIONS ARE AVAILABLE WITH DICVOL06
---------------------------------------
>> OPTION 0 IS DICVOL04 (OPTIMISED SEARCH TO BE USED WITH NORMAL QUALITY
DATA)
>> OPTION 1 OFFERS AN EXTENDED (EXHAUSTIVE) SEARCH (FOR DIFFICULT CASES)
[COMPARED TO DICVOL04 (2004) ONLY ONE ADDITIONAL INPUT PARAMETER IS ADDED
IN DICVOL06, i.e. OPTION IN CARD 5 (SEE BELOW)]
--------------------------------------------------------------
--------------------------------------------------------------
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| TO EXECUTE THE PROGRAM, ENTER : DICVOL06 |
| |
| THEN, ENTER THE INPUT FILE NAME and OUTPUT FILE NAME |
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PROGRAM FOR THE AUTOMATIC INDEXING OF POWDER DIFFRACTION PATTERNS BY
THE SUCCESSIVE DICHOTOMY METHOD.
------------------------------------------------------------------
>>>> THE REFERENCE FOR THIS PROGRAM, TO REPORT IN PUBLICATIONS, IS:
>>>> (1): A. Boultif & D. Louer, J. Appl. Cryst. 37, 724-731, 2004
------------------------------------------------------------------
THE FOLLOWING CRYSTAL SYSTEMS CAN BE ANALYZED: CUBIC, TETRAGONAL,
HEXAGONAL, ORTHORHOMBIC, MONOCLINIC AND TRICLINIC.
PRECURSOR PROGRAMS:
P1 & P2 (REF. 2), DICVOL (REF. 3), DICVOL91 (REF. 4), DICVOL04 (REF. 1)
=======================
FOR FURTHER INFORMATION CONTACT
D. LOUER
E-MAIL Daniel.Louer@free.fr
OR
A. BOULTIF
LABORATOIRE DE CRISTALLOGRAPHIE
DEPARTEMENT DE PHYSIQUE
FACULTE DES SCIENCES EXACTES
UNIVERSITE MENTOURI - CONSTANTINE
25000 CONSTANTINE - ALGERIE
TEL./FAX (213) 31 61 47 47
E-MAIL ABoultif@ifrance.com
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| G E N E R A L I N S T R U C T I O N S |
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DICVOL PROPOSES SOLUTIONS; THE USER DISPOSES OF THEM.
THE AUTHORS DISCLAIM RESPONSABILITY FOR ALL USE OF THIS PROGRAM
---------------------------------------------------------------
===> BEFORE USING DICVOL06, PLEASE READ REFERENCE 1, AS WELL AS THE
===> INSTRUCTIONS AND RECOMMENDATIONS BELOW.
_______________
INPUT DATA FILE
---------------
CARD 1 TITLE FREE FORMAT
CARD 2 N,ITYPE,JC,JT,JH,JO,JM,JTR FREE FORMAT
N NUMBER OF LINES USED FOR SEARCHING SOLUTIONS.
(This number is, generally, lower than the
number N_TOTAL of input lines). e.g. N = 20.
ITYPE SPACING DATA TYPE.
=1 THETA BRAGG ANGLE IN DEGREES.
=2 2-THETA ANGLE IN DEGREES.
=3 D-SPACING IN ANGSTROM UNIT.
=4 Q SPECIFIED IN Q-UNITS AS E+04/D**2.
JC =0 CUBIC SYSTEM IS NOT TESTED.
=1 CUBIC SYSTEM IS TESTED.
JT =0 TETRAGONAL SYSTEM IS NOT TESTED.
=1 TETRAGONAL SYSTEM IS TESTED.
JH =0 HEXAGONAL SYSTEM IS NOT TESTED.
=1 HEXAGONAL SYSTEM IS TESTED.
JO =0 ORTHORHOMBIC SYSTEM IS NOT TESTED.
=1 ORTHORHOMBIC SYSTEM IS TESTED.
JM =0 MONOCLINIC SYSTEM IS NOT TESTED.
=1 MONOCLINIC SYSTEM IS TESTED.
JTR =0 TRICLINIC SYSTEM IS NOT TESTED.
=1 TRICLINIC SYSTEM IS TESTED.
CARD 3 AMAX,BMAX,CMAX,VOLMIN,VOLMAX,BEMIN,BEMAX FREE FORMAT
AMAX MAXIMUM VALUE OF UNIT CELL DIMENSION A, IN ANGSTROMS.
(IF AMAX= 0.0 DEFAULT= 25. ANGSTROMS)
BMAX MAXIMUM VALUE OF UNIT CELL DIMENSION B, IN ANGSTROMS.
(IF BMAX= 0.0 DEFAULT= 25. ANGSTROMS)
CMAX MAXIMUM VALUE OF UNIT CELL DIMENSION C, IN ANGSTROMS.
(IF CMAX= 0.0 DEFAULT= 25. ANGSTROMS)
VOLMIN MINIMUM VOLUME FOR UNIT CELLS IN ANGSTROMS**3.
VOLMAX MAXIMUM VOLUME FOR UNIT CELLS IN ANGSTROMS**3.
(IF VOLMAX= 0.0 DEFAULT= 2500. ANGSTROMS**3)
BEMIN MINIMUM BETA ANGLE FOR MONOCLINIC CELLS IN DEGREES
(IF BEMIN= 0.0 DEFAULT= 90. DEGREES).
BEMAX MAXIMUM BETA ANGLE FOR MONOCLINIC CELLS IN DEGREES
(IF BEMAX= 0.0 DEFAULT= 125. DEGREES).
CARD 4 WAVE,POIMOL,DENS,DELDEN FREE FORMAT
WAVE WAVELENGTH IN ANGSTROMS (DEFAULT=0.0 IF CU K ALPHA1).
POIMOL MOLECULAR WEIGHT OF ONE FORMULA UNIT IN A.M.U.
(DEFAULT =0.0 IF FORMULA WEIGHT NOT KNOWN).
DENS MEASURED DENSITY IN G CM(**-3)
(DEFAULT =0.0 IF DENSITY NOT KNOWN).
DELDEN ABSOLUTE ERROR IN MEASURED DENSITY.
(DEFAULT =0.0 IF DENSITY NOT KNOWN).
CARD 5 EPS,FOM,N_IMP,ZERO_S,ZERO_REF,OPTION FREE FORMAT
EPS =0.0 THE ABSOLUTE ERROR ON EACH OBSERVED LINE
IS TAKEN TO 0.03 DEG. 2THETA (DEFAULT VALUE)
WHATEVER THE SPACING DATA TYPE (ITYPE IN CARD 2).
=1.0 THE ABSOLUTE ERROR ON EACH OBSERVED LINE IS
INPUT INDIVIDUALLY FROM CARD 6, AFTER THE
OBSERVED 'D(I)' ON THE SAME LINE, ACCORDING
TO THE SPACING DATA UNIT (e.g. 18.678 0.018 in
deg. 2theta)
EPS NE 0.0 AND 1.0
THE ABSOLUTE ERROR IS TAKEN AS A CONSTANT
(= EPS),IN DEG. 2THETA, WHATEVER THE SPACING
DATA TYPE (ITYPE IN CARD 2) (e.g. 0.02, which will
apply to all input lines).
FOM LOWER FIGURE OF MERIT M(N) REQUIRED FOR PRINTED
SOLUTION(S) (DEFAULT=0.0 M(N)=10.0).
N_IMP MAXIMUM NUMBER OF IMPURITY/SPURIOUS LINES ACCEPTED AMONG
THE FIRST N LINES [N_IMP takes into account both
impurity lines and peak positions out of the input
absolute angular error EPS].
IF N_IMP <0 THE SEARCH STARTS WITH ZERO IMPURITY LINES,
THEN, IT CONTINUES WITH ONE IMPURITY LINE, AND
SO ON UNTIL 'N_IMP' IMPURITY LINES IS REACHED.
ZERO_S A PRIORI SEARCH FOR A ZERO-POINT ERROR IN INPUT DATA.
=0 NO SEARCH
=1 SEARCH
IF ZERO_S NE 0 OR 1, THEN ZERO_S REPRESENTS A KNOWN
ZERO CORRECTION (e.g. -0.10) IN DEG. 2THETA.
ZERO_REF =0 NO 'ZERO-POINT' LEAST-SQUARES REFINEMENT.
=1 'ZERO-POINT' LEAST-SQUARES REFINEMENT.
OPTION =0 DICVOL04 OPTION (OPTIMIZED STRATEGY SEARCH WITH
DECREASING CELL VOLUMES).
=1 OPTION WITH EXTENDED (EXHAUSTIVE) SEARCH IN VOLUME
DOMAINS CONTAINING MATHEMATICAL SOLUTION(S)
(LONGER CPU TIMES).
IF OPTION IS OMITTED, DEFAULT IS DICVOL04.
CARDS 6 to 6+N_TOTAL D(I) [,EPSIL(I)] FREE FORMAT
(ONE FOR EACH INPUT LINE, FOR ALL N_TOTAL LINES)
D(I) VALUE DESCRIBING THE OBSERVED POSITION OF LINE 'I'
ACCORDING TO SPACING UNIT 'ITYPE'.
EPSIL(I) ONLY IF EPS=1.0 (CARD 5): ABSOLUTE ERROR FOR 'D(I)',
ACCORDING TO 'ITYPE',
[IF EPS= 0.0 OR EPS IS A CONSTANT NOT EQUAL TO 1.0 (e.g.
0.02)(SEE CARD 5), ONLY 'D(I)' ARE REQUIRED].
NOTE:
IF ITYPE=1,2,4 THE VALUES OF 'D(I)' AND 'EPSIL(I)' MUST
BE PREFERABLY (THOUGH IT IS NOT MANDATORY) LISTED IN INCREASING
ORDER.
IF ITYPE=3 THEY MUST BE PREFERABLY LISTED IN DECREASING ORDER.
___________
OUPUT FILES
-----------
DICVOL06 GENERATES TWO OUTPUT FILES:
- A FILE CONTAINING THE SOLUTIONS AS FOUND BY THE PROGRAM (ALSO
SEEN ON THE DISPLAY WHEN DICVOL06 IS RUNNING).
- A SECOND FILE WITH THE SAME NAME AND THE EXTENSION '.ord', IN
WHICH ALL (MATHEMATICAL) SOLUTIONS ARE RANKED ACCORDING TO THEIR
de WOLFF FOM.
*****************************************************
* *
* THE USE OF DICVOL06 *
* *
*****************************************************
USE AS INPUT DATA ALL AVAILABLE DIFFRACTION LINES (N_TOTAL). ONLY THE
FIRST N (eg 20, SEE CARD 2) LINES WILL BE USED FOR THE SEARCH OF
SOLUTIONS. THESE SOLUTIONS ARE SUBSEQUENTLY USED AUTOMATICALLY FOR
REVIEWING ALL N_TOTAL INPUT DATA. THE IMPURITY TOLERANCE 'N_IMP' IS
RELATED ONLY TO THE N LINES USED FOR SEARCHING SOLUTION(S) (OF COURSE,
OTHER UNINDEXED LINES CAN BE FOUND AMONG THE EXTRA INPUT LINES IN THE
REVIEWING PROCESS). BE CAREFUL IN USING THE IMPURITY TOLERANCE:
SPURIOUS LINES INCREASES THE RISK TO MISS THE CORRECT SOLUTION!
==> WITH GOOD QUALITY DATA, OPTION = 0 (i.e. DICVOL04) IS RECOMMENDED.
==>THE OPTION 'EXTENDED (EXHAUSTIVE) SEARCH' (OPTION =1 IN CARD 5),
CAN BE USEFUL IN CASES OF
(i) UNSTABLE CASES, i.e. MANY SOLUTIONS ARE FOUND IN A SMALL RANGE OF
CELL VOLUMES,
(ii) EXPECTED DIFFRACTION LINES ARE MISSING AMONG THE FIRST INPUT
LINES,
(iii) LOW QUALITY DATA,
(iv) SIGNIFICANT NUMBER OF IMPURITY LINES, ETC.
IF A SOLUTION IS FOUND IN A VOLUME SHELL, THE SEARCH IS EXHAUSTIVE
WITHIN THIS SHELL. THUS, THE SEARCH IS NOT EXTENDED TO THE NEXT VOLUME
SHELL (FOR THE SYMMETRY BEING ANALYSED). IF NEEDED, THE USER CAN RUN
AGAIN DICVOL06, FOR SELECTED LATTICE SYSTEMS, TAKING THE HIGHER VOLUME
VALUE OF THE ALREADY ANALYSED VOLUME SHELL AS 'VOLMIN' IN THE NEW INPUT
PARAMETERS SET (CARD 3).
GENERALLY, RUNS WITH OPTION =1 TAKE LONGER CPU TIMES AND THE NUMBER OF
MATHEMATICAL SOLUTIONS IS GREATER (IT HAS BEEN LIMITED TO THE FIRST 100
FOUND SOLUTIONS IN THE DICVOL06 OUTPUT FILE). BY ACTING ON THE INPUT
FOM (GREATER FOM IN CARD 5) SOLUTIONS WITH LOWEST FOMs CAN BE REJECTED).
BE CAREFUL: AS SOON AS 100 SOLUTIONS ARE FOUND THE CALCULATION STOPS.
DICVOL06 OFFERS THE POSSIBILITY TO ANALYSE YOUR INPUT DATA FOR THE
PRESENCE OF A ZERO-POINT ERROR. THE METHOD EMPLOYED CAN SUGGEST MORE
THAN ONE OR TWO SOLUTIONS (DUE TO UNCERTAINTY IN SEARCHING HARMONIC
DIFFRACTION LINES). THIS OPTION IS TO BE USED PRIOR THE INDEXING
PROCESS. PLEASE, AS FAR AS POSSIBLE AVOID THE USE OF THIS FACILITY BY
ENSURING THE QUALITY OF YOUR COLLECTED DATA!
USUAL 'ZERO-POINT' ERRORS (IF NOT TOO BIG) ARE GENERALLY CORRECTED BY
THE LEAST-SQUARES REFINEMENT OF THE 'ZERO-POINT' PARAMETER (ZERO_REF IN
CARD 5), TOGETHER WITH THE REFINEMENT OF CELL PARAMETERS. ZERO_REF IN
CARD 5 IS, IN FACT, AN EXTRA DEGREE OF FREEDOM IN THE REFINEMENT. IT
INCLUDES ALL SYSTEMATIC MEASUREMENT ERRORS FROM DIFFRERENT ORIGIN,
E.G. ZERO-POINT SHIFT, SAMPLE-SURFACE DISPLACEMENT, UMBRELLA EFFECT,
TRANSPARENCY, CAPILLARY DISPLACEMENT, ..
SUGGESTED STRATEGY:
------------------
IT IS RECOMMENDED TO USE A TWO- [1 & 2] OR THREE-STAGES PROCEDURE
(i.e. TRICLINIC LATTICES SHOULD PREFERABLY BE STUDIED SEPARATELY), e.g.:
1- SEARCH IN HIGH SYMMETRIES DOWN TO ORTHORHOMBIC.
CARD 2 : N,ITYPE,1,1,1,1,0,0
2- SEARCH IN MONOCLINIC SYMMETRY.
CARD 2 : N,ITYPE,0,0,0,0,1,0
3- IF NECESSARY, SEARCH IN TRICLINIC SYMMETRY.
CARD 2 : N,ITYPE,0,0,0,0,0,1
NOTE THAT FOR SOLUTIONS WITH MONOCLINIC AND TRICLINIC SYMMETRIES
THE PROGRAM PROVIDES THE REDUCED CELL. IF VARIOUS EQUIVALENT SOLUTIONS
ARE FOUND, ONLY ONE OF THEM IS LISTED IN THE OUTPUT FILE.
TRIGONAL SYMMETRY CASE WITH RHOMBOHEDRAL LATTICE: THE PATTERN IS
INDEXED WITH AN HEXAGONAL LATTICE, HAVING A UNIT CELL VOLUME THREE
TIMES GREATER.
RECOMMENDATIONS
---------------
READ CAREFULLY REFERENCES 1 AND 6 (AND 9), AS WELL AS THIS USER'S
GUIDE. PLEASE, SPEND TIME TO ENSURE THE QUALITY OF YOUR COLLECTED DATA
(SEE REF. 5). WITH ACCURATE DATA, THE SUCCESS RATE OF DICVOL06 IS VERY
HIGH. PEAK POSITIONS SHOULD BE EXTRACTED WITH A PROFILE FITTING
SOFTWARE. AN INTERACTIVE PROGRAM SHOULD BE PREFERRED, SINCE AUTOMATIC
EXTRACTIONS CAN MISS LINES (LOW INTENSITY, SHOULDER, ..).
WITH BAD DATA, THE CHANCE TO OBTAIN THE CORRECT SOLUTION IS SMALL AND
THE CALCULATION CAN BE TIME-CONSUMING.
WITH MODERN X-RAY POWDER DIFFRACTOMETERS (THE USE OF MONOCHROMATIC
RADIATION IS RECOMMENDED), ABSOLUTE ERRORS ON PEAK POSITIONS LOWER
THAN 0.02 DEGREES 2-THETA CAN BE ROUTINELY OBTAINED. FOR INDEXING
PURPOSES, ERRORS SHOULD NOT (IDEALLY) EXCEED 0.03 DEG. 2-THETA.
[IN EXCEPTIONAL CASES, A FEW LINES WITH GREATER INDIVIDUAL ESTIMATED
ERROR CAN BE INTRODUCED IN THE INPUT DATA. IN THIS CASE, USE THE
PARAMETER EPS= 1. IN CARD 5, AND ENTER INDIVIDUAL ERRORS AFTER D(I) FOR
EACH LINE].
WITH HIGH RESOLUTION POWDER DIFFRACTION DATA (CONVENTIONAL OR,
PARTICULARLY, SYNCHROTRON X-RAY SOURCES), THE ABSOLUTE ERROR IS
USUALLY LESS THAN 0.02 (OR EVEN 0.01 WITH ULTRA-HIGH RESOLUTION) DEG.
2-THETA; CONSEQUENTLY, EPS=0.02 (OR EVEN EPS=0.01) IS RECOMMENDED; THE
CONVERGENCE OF THE DICHOTOMY PROCEDURE WILL BE IMPROVED. HOWEVER, BE
SURE THAT THIS CONDITION IS TRUE FOR ALL LINES USED AS INPUT DATA.
(REMEMBER THAT ALL MATHEMATICAL SOLUTIONS WITHIN THE INPUT LIMITS AND
ERROR BOUNDS ARE FOUND, THE GREATER THEY ARE THE GREATER IS THE NUMBER
OF MATHEMATICAL SOLUTIONS).
===> N_IMP PARAMETER: N_IMP CAN BE USED IN CASE OF EXPECTED SPURIOUS
LINES (i.e. IMPURITY LINES, AS WELL AS OBSERVED LINES OUT OF THE INPUT
ERROR). N_IMP ACTS AT ALL SUCCESSIVE LEVELS OF THE DICHOTOMY ALGORITHM.
AS SOON AS AN INDEXING SOLUTION IS RETAINED, A LEAST-SQUARES REFINEMENT
OF LATTICE PARAMETERS IS CARRIED OUT. FOR THIS REFINEMENT A LARGER
ERROR ON OBSERVED LINES IS CONSIDERED. THEN, A LINE REJECTED AT THE
LAST DICHOTOMY LEVEL CAN, BY CHANCE, BE ACCEPTED WITH THE REFINED
LATTICE PARAMETERS. [EXAMPLE OF POSSIBLE CASE: N_IMP = 0 NO SOLUTION;
N_IMP = 1 ONE SOLUTION; HOWEVER, AFTER L-S REFINEMENT OF THE LATTICE
PARAMETERS ALL N LINES USED FOR SEARCHING SOLUTIONS ARE INDEXED WITH
THE REFINED PARAMETERS.]
NOTE THAT THE PROGRAM DICVOL06 IS EXECUTABLE FROM 7 LINES- 8 LINES IF
THE 'ZERO-SHIFT' IS REFINED - (THOUGH IT IS NOT RECOMMENDABLE SINCE L-S
REFINEMENT UNSTABILITIES CAN BE EXPECTED).
LONG AND SHORT AXIS CASES (DOMINANT ZONE CASES): IF SUCH CASES ARE
EXPECTED, THE NUMBER 'N' OF LINES (CARD 2) USED FOR SEARCHING THE
SOLUTION SHOULD, GENERALLY, BE GREATER THAN 20.
THE MINIMUM VALUE FOR A LINEAR LATTICE PARAMETER HAS BEEN FIXED TO 2.5
ANGSTROMS.
RELIABILITY OF INDEXING SOLUTIONS: READ PARAGRAPH 8 OF REF. 5 AND
REFS 7 AND 8.
THE BEHAVIOUR OF THE DICHOTOMY ALGORITHM WITH RESPECT TO THE NUMBER OF
LINES REQUIRED FOR INDEXING AND THE CASE OF BIPHASIC MIXTURE IS
DISCUSSED IN REF. 6.
THE LOGICAL FILTERS USED IN DICVOL06 FOR THE SELECTION OF SOLUTIONS
ARE DESCRIBED IN REF. 9.
NOTE THAT WITH THE OPTION DICVOL04 (OPTION =0), AS SOON AS A SOLUTION
IS FOUND, ONLY SOLUTIONS WITH SMALLEST VOLUMES WILL BE SUBSEQUENTLY
RETAINED. IF (FOR SOME REASONS!) YOU ARE NOT SATISFIED BY THE SOLUTION,
YOU CAN RUN AGAIN THE PROGRAM WITH AN INPUT LOWER VOLUME LIMIT SLIGHTLY
GREATER THAN THAT OF THE FOUND SOLUTION (THE EXHAUSTIVE SEARCH IS THEN
EXTENDED TO A HIGHER VOLUME).
NOTE THAT THE SEARCH IS EXHAUSTIVE WITHIN THE LIMITS ON THE INPUT DATA.
IN PARTICULAR, THE SEARCH IS CONSTRAINED BY THE HIGHER AND SMALLER
BOUNDS ON PARAMETERS, VOLUMES, SELECTED FOM AND ABSOLUTE ERRORS ON PEAK
POSITIONS. PLEASE ACT ON THESE PARAMETERS WHEN USING DICVOL06.
A LATTICE METRIC SINGULARITY OCCURS WHEN UNIT CELLS DEFINING TWO
LATTICES HAVE AN IDENTICAL SET OF CALCULATED d-SPACINGS. THIS CAN
BE OBSERVED WITH HIGH SYMMETRY LATTICES (READ REF.5, SECT. 4.2, AND
REFS THEREIN). SIMPLE RELATIONS EXIST BETWEEN THE PARAMETERS OF THE TWO
CELLS, AS WELL AS PARTICULAR CELL-VOLUME RATIOS. A TYPICAL CASE IS: AN
HEXAGONAL CELL [a, c, VOLUME V] CAN BE INDEXED WITH AN ORTHORHOMBIC
CELL [PARAMETERS: a/2, a SQRT(3), c, VOLUME V/2]. DUE TO THE STRATEGY
USED IN DICVOL, BASED ON AN ANALYSIS THROUGH DECREASING SYMMETRY, ALL
CELLS SHOULD BE, IN PRINCIPLE, DISPLAYED IN THE OUTPUT FILE (EXCEPT IF
A SOLUTION IS REJECTED BY THE INPUT MAXIMUM VOLUME).
CHECK ON VALIDITY OF AN INDEXING RESULT: PLEASE READ REF. 5 (SECT. 8)
POSSIBLE SPACE GROUPS: LOOK AT THE HKL CONDITIONS IN THE OUTPUT
LIST OF THE REVIEWING OF THE COMPLETE INPUT DATA PROVIDED AFTER A
SOLUTION IS FOUND FROM THE FIRST N LINES.
ADDITIONAL INFORMATION ON DICVOL06 SHOULD APPEARED IN REF. 9.
REFERENCES
1.- BOULTIF, A. AND LOUER, D., POWDER PATTERN INDEXING WITH THE
SUCCESSIVE DICHOTOMY METHOD.
J. APPL. CRYST. 37, 724-731 (2004).
2.- LOUER, D. AND LOUER, M., METHODE D'ESSAIS ET ERREURS POUR
L'INDEXATION AUTOMATIQUE DES DIAGRAMMES DE POUDRE,
J. APPL. CRYST. 5, 271-275 (1972).
3.- LOUER, D. AND VARGAS, R., INDEXATION AUTOMATIQUE DES
DIAGRAMMES DE POUDRE PAR DICHOTOMIES SUCCESSIVES,
J. APPL. CRYST. 15, 542-545, (1982).
4.- BOULTIF, A. AND LOUER, D., INDEXING OF POWDER DIFFRACTION
PATTERNS FOR LOW SYMMETRY LATTICES BY THE SUCCESSIVE
DICHOTOMY METHOD, J. APPL. CRYST. 24, 987-993 (1991).
5.- LOUER, D., AUTOMATIC INDEXING: PROCEDURES AND APPLICATIONS, IN
'ACCURACY IN POWDER DIFFRACTION II', NIST, SPEC. PUBL. No. 846,
GAITHERSBURG, MD, USA, pp. 92-104, 1992.
6.- LOUER, D. AND BOULTIF, A., INDEXING WITH THE SUCCESSIVE DICHOTOMY
METHOD, DICVOL04, Z. KRISTALLOGR. 23, 225-230 (2006).
7.- DE WOLFF, P.M., A SIMPLIFIED CRITERION FOR THE RELIABILITY
OF A POWDER PATTERN INDEXING, J. APPL. CRYST. 5, 108-113 (1968).
8.- SMITH, G. S. AND SNYDER, R. L., F(N): A CRITERION FOR RATING
POWDER DIFFRACTION PATTERNS AND EVALUATING THE RELIABILITY
OF POWDER-PATTERN INDEXING, J. APPL. CRYST. 12, 60-65 (1979).
9.- LOUER, D. AND BOULTIF, A., POWDER PATTERN INDEXING AND THE
DICHOTOMY ALGORITHM, Z. KRISTALLOGR., IN PRESS (2007).