Program N_TREOR
This is a Stand-alone version of N-TREOR (Version November 2001).
REFERENCE:
New techniques for indexing: N-TREOR in EXPO
J.Appl.Cryst. (2000) 33, 1180-1186
by Angela Altomare, Carmelo Giacovazzo, Antonietta Guagliardi,
Anna Grazia Giuseppina Moliterni, Rosanna Rizzi and Per-Erik
Werner
In EXPO N-TREOR is combined with a peak search procedure and a
a program set for structure determination.
If you are only interested in the description of how to run the
stand-alone version of the program go to the headline:
N_TREOR the stand-alone version of N-TREOR
N-TREOR is an updated version of TREOR90 described below.
The main changes characterizing N-TREOR with respect to TREOR90
are:
1) Several decisions normally made by the user of TREOR90 when
a default run fails or when a plausible solution is found
are automatically made by N-TREOR
a) If a plausible solution is found, the program will look for
a better solution in a new trial. This may be achieved by
requiring a higher M20 value or all the first 20 peaks to be
indexed.
b) If N-TREOR does not give satisfactory results in a default
run it repeats the unit cell search with wider error limits.
c) If still no solution is found, with increased error limits,
the maximum (h,k,l) Miller indices of the orthorhombic and
monoclinic base lines are increased and the error limits are
narrowed to 50 per cent of the default values. ( The reason
for narrowing the error limits is that a large number of big
erroneous unit cells may otherwise be generated in the trial
phase, and correct solutions may be eliminated before
refinement. There is always a need for more accurate data if
the unit cell is big. The figure-of-merit tests will
otherwise fail.)
2) The maximum cell volume and the maximum axis values
investigated by N-TREOR are preset to 4000 A**3 and 35 A,
respectively, if the maximum observed d value is greater
than 10 A. If the maximum observed d value is less than 10 A
the default values are (as shown in the key-word list below)
2000 A**3 and 25 A, respectively.
3) The dominant-zone tests in TREOR90 are improved, and if more
than the first 6 peaks can be indexed by a two-dimensional
rectangular cell,but no three-dimensional solution is found,
the first non-indexed peak is reported as a possible
impurity line that may be deleted in a second test.
4) Wavelength dependence of D1 and D2 ( error tolerances, see
the key-word list below) has been introduced.
DX = DXCU*(WAVE/1.560598)**2 where
DXCU = D1 and D2, respectively for CuK-alpha1 radiation
5) Monoclinic solutions are checked for possible rhombohedral
symmetry. If the symmetry is likely to be rhombohedral,
N-TREOR calculates the possible hexagonal axes. In general,
however, the user has to check for geometrical ambiguities.
In N_TREOR version November 2001, the rhombohedral cell is
also calculated and refined by PIRUM.
6) Possible zero shifts in the 2theta Bragg angles are tested.
This is probably the most serious systematic error in powder
diffractometry. Although well known internal as well as
external standard techniques exist, that can be used to
completely (or almost completely) eliminate such errors, the
experience from a large number of indexing problems shows
that zero point errors are frequently present in data sets
used for powder indexing. ( Suprisingly enough even modern
synchrotron data, with exceptionally high RELATIVE accuracy,
have sometimes been found to have large zero point errors.)
7) N-TREOR can suggest more candidate cells. In order to select
the best one, a modified de Wolff figure of merit M'20 has
been introduced, with
M'20 = (7-N-par)*M20 where
N-par is the number of cell parameters to be determined ( 6
for triclinic system, 4 for monoclinic,....), and M20 is the
original de Wolff figure of merit. Even if M20 is effective
as a tool for assessing the reliability of the cell, the
heuristic relation (M'20=.....) allows the program to prefer
a higher symmetry solution. E.g., of two possible unit cells
with similar M20 values, one monoclinic and the other
triclinic, the monoclinic is preferred by M'20.
8) The program PIRUM, originally an interactive program, has
been suitably modified in order to automatically refine the
unit cell parameters, without any user intervention. N-TREOR
performs a statistical study of index parity of the assigned
reflections in order to detect the presence of doubled axes
or of additional lattice points (A, B, C, I, R or F centered
cell). In these cases the reflection conditions are suitably
modified and the unit cell parameters are again refined.
It may be necessary, however, to check the analysis of
systematic extinctions in the condensed output file. The
reason is that mutiple indexed reflections are not analysed.
Additional refinement cycles are performed by PIRUM after
applying two supplementary origin shifts of +- one quarter
of the shift value selected by N-TREOR according to point 6
above. See also the keyword LIMIT.
9) It is not possible to interrupt the calculations by pressing
the key...I....This option is not available any more.
10) It is still possible to use the key-word system as described
below. Normally, however, only WAVE, LIMIT, CHOICE and END*
are needed.
11) Last corrections: September 2004
N_TREOR the stand-alone version of N-TREOR
Data input file:
LINE ONE. TITLE Any text in col.2-80
LINE SET TWO. One d-value and optionally INTENSITY on each
line. (Free format)
It is also possible to use other types of
input data. See keyword CHOICE in the key-
word list below. Note that the default value
of CHOICE is 4 in N_TREOR (i.e. d-values).
The data must be given in order, starting
with the low order lines.Generally the first
20-25 lines should be used. Remaining lines
(if any) may be used in later final refine-
ments. (The dialogue version of PIRUM).
INTENSITY data is optional. It is never used
by the program. If present, it will only be
transferred to the output lists as (max.) 4
digits integers.
STOP LINE FOR LINE SET TWO IS A BLANK LINE
The program will ask for file names and Theta-shift.
The normal Theta-shift is the step used in the data collection;
(Usually =0.01 for Wave=1.5406 A) i.e. 0.02 deg. in 2theta.
LINE SET THREE.(See general description of this line set below)
Below 4 examples of line set three for N_TREOR are given:
Example 1.
end*
Comment:This is the only key-word needed for a normal N_TREOR
run if CuK-alpha1 radiation has been used and d-values are
given.
Example 2.
wave=1.529, end*
Comment: Error limits are wave-length dependent. It is therefore
important to give the wave-lenght, although the d-values are not
wave-lenght dependent. Do not forget the , before next key-word.
Example 3.
limit=1, end*
Comment: LIMIT is a new key-word, not present earlier in TREOR.
LIMIT can be any integer between 1 and 10 (default value is 10).
The parameter LIMIT can be given a value less than 10 in order
to reduce the maximum number of zero shifts tested. ( The number
of zero shifts applied will be dependent on the result of the
the calculations and is therefore usually less than 10).
If you have good reason to belive that the zero point error is
negligible, you may save a lot of computer time by limit=1
Example 4.
choice=0, limit=1, end*
Comment: Input data are sine square theta values derived from
an instrument with strictly monochromatic CuK-alpha1 radiation.
About limit=1, see example 3 above.
WARNINGS:
A) In the present version of the program the automatic tests of
index parity are NOT complete. See comments about VISUAL
INSPECTION in the condensed output list. ( May be improved in a
later program version.)
B) On a PC the calculations may be very time consuming. It can
be recommended to use LIMIT=1 ( see Example 3 above) in a first
test run, at least if you have good reason to believe that the
zero point error is negligible.
C) OBS ! The best solution may be found ANYWHERE in the condesed
output file. The reason is that the automatic Pirum run may fail
and give more unindexed lines. It is recommended to always use
a separate Pirum run to check the possible solution/s.
END OF INSTRUCTIONS FOR THE STAND-ALONE VERSION OF N-TREOR
TTTTTTT RRRR EEEEEE OOOOO RRRR 9999 0000
T R R E O O R R 9 9 0 0
T R R E O O R R 9 9 0 0
T RRRR EEEEEE O O RRRR 99999 0 0
T R R E O O R R 9 0 0
T R R E O O R R 9 0 0
T R R EEEEEE OOOOO R R 9 0000
This is an autoindexing program and should be used to find a
physically plausible solution to an indexing problem.
It is not a program for final refinement of the unit cell
dimensions. (c.f. PIRUM or NBS*AIDS83)
Information for the programmer:
The TREOR99 version is written in Microsoft Fortran for PC.
The interrupt function (..press the letter i) is generally
not needed and if you want to use other compilers and/or
computers whithout any possibility to sense keyboard oper-
ations during the calculations, you may skip this in the
following way
Skip the include 'flib.fi' and 'flib.fd'
Replace the original subroutine chkkey by the following
dummy routine:
Subroutine chkkey(code)
integer*2 code
code=0
return
end
End of programmers information
FEBRUARY 1999
Two new keywords, ZEROSET and KREDUCT, are introduced. See
keyword list below. KREDUCT may be used in order to save
only the best trial solutions.It is presupposed then, that
input data is very accurate and a cell axis is expected to
be very long (>20 A)
In order to avoid run time errors, a large number of small
changes have been made.
The earlier program versions were somewhat dependent on
the wave-length used. The parameters: D1, D2 and SSQTL are
now automatically ( i.e. if SELECT=-1 ,the default value)
adjusted for WAVE. As in earlier program versions one can
forget about WAVE if CHOICE=4, i.e. if input data are
d-values.
If correct WAVE is given, also the correct diffraction
angles are reported in the output lists.
Monoclinic solutions are checked for possible rhombohedral
symmetry. If several high symmetry solutions are found, it
is recommended to decrease the parameter VOL in order to
find the smallest monoclinic cell (1/6 of the 'true' hexa-
gonal cell). Then treor will check if the true symmetry is
likely to be rhombohedral and calculate the possible
hexagonal axes.
SEPTEMBER 1997
(Below 1997 is changed to 1999 (changed february 1999)
Keywords (see below) may be written in upper or lower case.
The program will run in 1999 mode if the keyword
SELECT has the value -1 (default value)
The normal TREOR99 run is:
Title line: Any text in col. 2-80
Data lines: Less than 99 lines (Normally 20-25 lines).
Free format.
Only one value on each line is necessary.
Optionally an intensity may be given as a
second data on the line. Intensity data is
not used by the program and only transferred
to the output as max. 4 digits integers
A blank line:
choice=4, (if D-values were used on the data lines)
Do not forget the , before next key-word
Key-words may be given in arbitrary order
end* and on arbitrary lines but the end* must
be the last one.
Usually no other key-words than CHOICE need to be changed
from the default values.
If a solution is found the program will automatically
decrease NIX or increase MERIT and rerun the problem in
order to check if a better solution can be found. However,
triclinic tests will only be made if the first solution
was triclinic.
If no solution is found the program will automatically
change the parameters IDIV and the error limits D1 and D2
i.e. add 0.0001*(Wave/1.5405981)**2)and rerun the problem.
Of course the TREOR99 mode may take a minute more on a
Pentium but it is a strongly recommended, simple, safe and
powerful procedure.
Powder indexing depends to 95 per cent on the data quality
If you are using a Pentium processor the CPU time will
probably never exceed 3 minutes. ( A PC 486 may be almost
ten times slower.)
It is possible to run the program in TREOR4, TREOR90 or
TREOR99 mode
TREOR4 mode if VOL=positive value and SELECT is zero (or
more.)
TREOR90 mode if VOL=negative value and SELECT is zero (or
more)
TREOR99 mode if SELECT=-1 (Default) (Normally preferred
mode)
If the TREOR99 mode is used, you normally only need to
choose the correct CHOICE parameter.
In all modes most of the key-word parameters may be
changed from the default values ( c.f. the key-word list
below).
Do not change default values without good reasons. For
example do not change VOL from the default value, unless
you have reason to believe that the unit cell volume is
more than 2000 A**3 ( You will not reduce CPU time much if
you are using a VOL that is less than 2000 A**3)
If TREOR99 finds a plausible solution ( according to the
NIX and MERIT parameters) this will be announced on the
display and the user may ( although not recommended )
interrupt the calculations and look at the condensed
output list.
Interrupt...Press the letter i on the keyboard.
If the program is running on a Pentium there is no reason
for doing so.
(The interrupt function is at present only available in the
PC version.)
Problem notes:
A solution that is very close to a higher symmetry may be
lost in the condensed output list, although an acceptable
lower symmetry solution may be reported in the long output
list. This may happen if two cell dimensions are almost
equal.
JUNE 1995
Within this section JUNE 1995 to JUNE 1992 a very short
description for the lazy user of TREOR90 (who does not want
to read the complete documentation file) is given.
The normal TREOR90 run is:
Title line
Data lines (20-25 lines, only one d-value, col.1-16, on each
line)
A blank line
CHOICE=4, (if D-values were used on the data lines)
SELECT=0, (to avoid the TREOR99 mode)
VOL=-2000, (note the minus sign. --- a treor90 run)
END* (stop card)
It is now possible to interrupt the calculations. This can
be done by the letter i on the keyboard. Then the program
will stop soon. The reason for this option is that one
should never hesitate to give VOL eq. a negative value i.e.
the most efficient test of all symmetries. One can always
stop for example triclinic tests from the keyboard. (This
option is only available on the PC version of the program)
If no solution is found rerun the problem, but include the
following keyword line:
D1=0.0003, D2=0.0005,
(note the , after each keyword value)
Another test is to set
IDIV=0,
which means that the first seven lines will not be changed
by ( what treor may erronously judge as ) higher order lines
The parameters MERIT and NIX may also be changed. ( See
below.) The first accepted solution may not be the best one.
Therefore, follow the instructions on the condensed output
file.
Do not print the long output file. Use your editor and look
for the most promising M-TEST lines.
This program should be used to find a physical plausible
solution of the indexing problem. The refinement is only
preliminar ( not Hess weighted). Especially lines at high
diffraction angles may be unindexed by treor.
In final refinements all lines, all extinction conditions,
Hess weights ( i.e. all diffraction angles should be given
equal weights)and all knowledge about intensity distribution
between overlaps ( if available) should be used.
From this department a flexible dialouge program,(version
930101 of PIRUM) may be distributed.
Program NBS*AIDS83 is (probably ?) recommended by ICDD.
JUNE 1992
It is strongly recommended to run TREOR90 on a PC/AT using a
486 CPU. Otherwise the VAX version TREOR90V may be used.
AUGUST 1990
OBS. In the PC/AT and VAX versions the subroutines ORTAL, MAEG
and COUNT are not vectorized. Vectorized versions of these
subroutines are available for CONVEX computers.
The original TREOR90 has been written for a CONVEX vector
processor. This should be kept in mind when the comments
below are read. The program may be very time-consuming on a
PC (unless a 486 processor is used).
1) Dominant zone test is added for the orthorhombic symmetry.
2) Dominant zone test is added for the triclinic symmetry.
3) Higher order lines among the first seven lines ( used in the
base line sets) are automatically excluded from the trial
phase of the calculations.
4) If a monoclinic or triclinic solution is found, the program
will end with a unit cell reduction followed by a conversion
of the reduced cell to a conventional cell according to the
metric symmetry. The reduction should be valid unless syste-
matic extinctions are found in the trial cell.
5) If a satisfactory solution is found, only the condensed out-
put file is needed. It contains all relevant information and
only one indexed list.
6) The general output list (that is normally not needed, cf. 5)
will only list trials where M20 ( or Mxx if less lines are
available) is 6 or more and not more than 3 lines among the
first 20 (or xx) lines are unindexed.
7) If the parameter VOL is given with a negative sign all symme-
tries are tested until a final solution is found- if possible.
OBS. This is the normal procedure for TREOR90
8) An algoritm for successive reduction of trial-cell volumes is
used in monoclinic and triclinic tests if a negative VOL
parameter is given. It is based on the input cell volume
limit and the number of trial cells found with IQ ( See
keyword IQ) or more than IQ indexable lines.
9) It is strongly recommended to give only the first ( well
checked and accurately measured ) 25 lines in the diffraction
data list (See LINE SET TWO).
10) It is expected that more than 95 per cent of monoclinic and
higher symmetry patterns and probably more than 50 per cent
of triclinic patterns will be indexed PRESUPPOSED the DATA
QUALITY is high ( i.e. average differences between calculated
and observed diffraction angles less than 0.02 deg. and also
the weak lines included in the data). The experience of tri-
clinic patterns is limited, however.
11) Obs. It is important to check cubic, tetragonal and hexagonal
solutions by a second run with KS=0 and THS=0 ( See key-word
list.) Do not trust cubic, tetragonal or hexagonal solutions
without an orthorhombic test.
12) The reason for testing the symmetries in correct order ( from
cubic to triclinic) and to START the orthrhombic, monoclinic
and triclinic tests with dominant zone tests is that by this
procedure false solutions are avoided.
13) For a normal TREOR90 run only the keywords
CHOICE=X, (see key-word list)
VOL=-2000, (OBS. The negative sign.)
END*
should be given after the diffraction data list. Computing
times of more than 1 minute is rare for monoclinic or higher
symmetries on a CONVEX computer. Computing times of more than
5 minutes (on a CONVEX) for a triclinic pattern has not yet
been found. For a VAX (Micro VAX II) computing times may be
more than 50 times longer. The PC/AT 486 is faster than the
Micro Vax II (but slower than CONVEX. The source code for VAX
is not exactly the same as for CONVEX. There are very small
differences between the PC/AT and the VAX versions, however.
The input of file names and OPEN statements must be changed
if you want to run this program on a VAX. Furthermore, the
VAX version uses a subroutine to measure the CPU-time.
14) The input format for LINE SET TWO ( See below) is changed in
agreement with the output format of the diffraction data file
from the Guinier-H{gg film scanner system ( at Stockholm
University). The change is mainly of interest for output of
intensities.
15) The original key-word instructions given below are relevant
as long as a positive VOL parameter is given.
16) If VOL is given a negative value (see 13 above) the following
key-words are fixed: MONO=135 and MONOSET=7. Other key-words
may be used as in the description below.
17) On the output lists
M-TEST= xx UNINDEXED IN THE TEST= y
usually means that xx is identical with M(20) and y is the
number of unindexed lines whithin the first 20 lines ( i.e.
used for the MERIT test). If less than 20 lines are available
xx and y refer to the number of lines used.
November 1988
29 11 88
Trial-and-error program for indexing of unknown powder patterns.
Cubic, Tetragonal, Hexagonal, Orthorhombic, Monoclinic and
Triclinic symmetries.
Version 2 1/9-75 = Version 26/4 plus
DENS,EDENS and MOLW. See Keyword list below.
Version 3 8/5-80 New output form
Version 4 2/10-84 = Version 3 plus
The following new options....
1. IDIV. See keyword IDIV below.
2. Monoclinic (020)-test
Ref: Smith,G.S. and Kahara,E J.Appl.Cryst.
8 (1975) 681
3. SHORT. See keyword SHORT below.
Short axis test. (Indexing of dominant zones.)
4. TRIC. See keyword TRIC below.
Indexing of triclinic patterns.
The source code was modified in order to decrease the CPU-times
in September 1988. The changes have no influence on input or out-
put from the program, but CPU-time reductions of 20-50 per cent
have been observed.
Version 5. (=Version November 1988) 29/11 1988
Dominant zone test introduced also for orthorhombic symmetry.
In version 4 high symmetry short axis solutions were only found
indirectly from the monoclinic tests.
Condensed output file.
A complete list of observed and calculated lines is only given
for the solution (if it is found) i.e. for an indexing where the
stop limits ( See keywords MERIT and NIX ) are fullfilled.
Normally only the condensed output file is needed.
If the stop limits are fullfilled the unit cell is refined three
cycles more. OBS. Final least-squares refinement should be made
by a separate program (for example by PIRUM). The TREOR program
is written in order to FIND a plausible cell, not to produce the
ultimate refinement.
Only the first part of the difference analysis table is printed
if no solution is found. (Usually it is not needed as you should
rerun the problem after modifications of the input data.)
If you have any questions, write to....
P.-E.Werner
Dept. of Structural Chemistry
Arrhenius Laboratory
Stockholm University
S-106 91 Stockholm,
SWEDEN
TEL: 08 / 16 23 93
FAX: 46-8-15 21 87
EMAIL: PEW@STRUC.SU.SE
It is believed, however, that the following documentation should
be sufficient for all careful readers.
GOOD LUCK!
R E F E R E N C E S
Basic principles. Werner,P.-E., Z.Kristallogr. 120 (1964) 375-387
TREOR, a semi-exhaustive trial-and-error powder indexing program
for all symmetries. Werner,P.-E., Eriksson,L. and Westdahl,M.,
J. Appl. Crystallogr. 18 (1985) 367-370
Refinement of unit cell. Werner,P.-E.,Arkiv Kemi 31(1969) 513-516
Figure of merit. De Wolff,P.M.,J.Appl.Crystallogr. 1(1968)108-113
Geometrical ambiguities. Mighell, A.D. and Santoro, A., J. Appl.
Crystallogr. 8 (1975) 372
G E N E R A L C O M M E N T S
This is a general trial-and-error indexing program for X-ray
diffraction powder patterns (i.e. all symmetries included).
Historical information ---- In order to reduce computing times on
computers without hardware floating point processers, parts of
the program have been written for integer calculations.
The parameters given as normal values in the keyword list below
should be regarded as an important part of the program. They are
based on experience from many successful runs on structures con-
firmed by single crystal data.
The parameters VOL and CEM, however, may be selected for the
actual data set and the symmetry tried.
...For a monoclinic trial the parameter MONO must be non-zero.
...For a triclinic trial the parameter TRIC must be 1.
A TREOR99 run (i.e. SELECT=-1) or a TREOR90 run (i.e. VOL= a nega-
tive number) will automatically check all symmetries.
Most of the powder patterns used to check the program have been
obtained by focusing Guinier-Hagg cameras. The photographs have
been measured by....
1. The method described by Hagg,G., Rev.Sci.Instr.18 (1947) 371
and Westman,S. and Magneli,A., Acta Chem. Scand. 11 (1957) 1587
2. The method described by Malmros, G. and Werner, P.-E., Acta
Chem. Scand. 27 (1973) 493
3. The film scanner system SCANPI ( written for the Guinier
film scanners LS18 and LS20)
The program has also been tested on a large number of NBS-data
sets. (JCPDS data sets.)
The accurate data obtained by NBS,National Bureau of Standards,
is clearly sufficient for successful indexing (in spite of the
fact that they are now usually obtained by powder diffracto-
meters. Unfortunately, however, many diffractometer data sets
found in the litterature show parabolic deviations between
observed and calculated diffraction angles.)
The following citations, however, should be emphasized....
'The paramount importance of resolution for indexing work
explains the high success rate for focussing camera data,
especially from Guinier-Hagg instruments, whose resolution can
omly be described as superb. It is rather less common ( and
considerably more expensive) to obtain as good resolution with
diffractometer data.'
'Powder indexing is not like structure analysis, which works
well on good data, and will usually get by on poor data given
a little more time and attention. Powder indexing works
beautifully on good data, but with poor data it will usually
not work at all'
Ref: Data accuracy for powder indexing.Shirley,R.NBS Spec. Publ.
567 (1980) P.370 and P.362 respectively.
WARNING!
A zero point error is much more serious than statistical errors
of the same magnitude.
Sigma(Two theta) should be less than 0.02 deg.
*******************************************
* DO NOT WASTE COMPUTER TIME ON BAD DATA. *
*******************************************
An indexing algorithm cannot be statet rigorously because of
the unpredictable distribution of unobserved lines and the
errors of measurements. One (or two) impurity lines may cause
severe problems.More impurity lines may rule out the possibility
to index the pattern. Therefore, it is expected that various
methods may be useful for various powder patterns. For example,
a multitude of non-systematic extinctions may not appreciably
affect the power of trial-and-error methods.
The least-squares refinement of the unit cell dimensions should
normally not be considered as the ultimate refinement. The main
purpose of this program is to FIND the unit cell. The program
PIRUM (version 930101) may be used for ultimate refinements.
PIRUM (version 930101) is a dialouge version of the old PIRUM
( cf. ref. /Refinement of unit cell/ given above. ) Extinction
conditions, Hess weights and max. accepted deviations between
observed and calculated 2theta in degrees are normally used in
version 930101 of PIRUM. In old PIRUM versions, parameters like
D1, D2, and SSQTL (See keyword list below) were used.
(cf. also the NBS*AIDS83 program. PIRUM is designed to be more
user-friendly, however.)
A limited number of nonsense cells may be printed on the output
file. You should look for max. De Wolff figure of merit ( not F-
index) and min. number of unindexed lines.
WARNING. You should not accept unindexed lines unless you are
able to explain them. On the other hand, you should not put in
uncertain (doubtful) lines in this program. They may be tested
later by a refinement program (ex. PIRUM).
I N P U T D A T A
LINE ONE. TITLE Any text in col.2-80
LINE SET TWO. One SQ and optionally INTENSITY on each line.
(Free format)
SQ (=Sine square theta). It is also possible
to use other types of input data. See keyword
CHOICE
The SQ data must be given in order, starting
with the low order lines.Generally the first
20-25 lines should be used. Remainging lines
(if any) may be used in later final refine-
ments. (Program PIRUM).
INTENSITY data is optional. It is never used
by the program. If present, it will only be
transferred to the output lists as (max.) 4
digits integers.
STOP LINE FOR LINE SET TWO IS A BLANK LINE (OR A NEGATIVE SQ)
LINE SET THREE. GENERAL INSTRUCTIONS.
All parameters in line set three have preset values.
A preset value is denoted 'NORMAL VALUE 'below.
Any 'NORMAL VALUE' may be changed in the following way:
KEYWORD1=VALUE1, KEYWORD2 = VALUE2,
KEYWORD3=VALUE3, ......., END*
1. The keywords are listed below
2. You must not forget =
3. The value may be given in free format ( integer or real ).
4. You must not forget ,
You may use arbitrary positions on the lines.
All blanks are irrelevant.
The number of lines is arbitrary. You may give one or more
key-word(s) on each line.
Line set three must end with the keyword END* (OBS. asterisk)
S T R A T E G Y
Unless SELECT=-1 (i.e. TREOR99 mode) or VOL=(a negative value)
(i.e. TREOR90 mode), the program will not differ much from
earlier program versions. See the comments on the top of this
list. Then (if VOL=negative value) only parameters such as NIX,
MERIT, IDIV and in exeptional cases D1, SSQTL and/or D2 may be
changed if indexing is not successful. Usually the main problem,
however, is the quality of your diffraction data.
Therefore, if the first run does not give a satisfactory
solution, it may be recommended to increse D1 and D2 to 0.0003
and 0.0005, respectively.
If the TREOR99 mode is used (i.e. SELECT=-1) the program will,
regardless a plausible solution is found or not, rerun the
problem and automatically adjust some parameters. Therefore it
is generally not necessary for the user to change the default
values in MERIT, NIX, D1 and/or D2.
If you are not using the normal TREOR99 procedure (i.e. SELECT=
-1) or the TREOR90 procedure(i.e. negative VOL) the standard
procedure is to start with the higher symmetries:
cubic, tetragonal, hexagonal and orthorhombic ( in one run).
Next the monoclinic symmetry may be tried. More than one job
may be needed..successively increasing the number of base line
sets, and cell volume (See keywords: VOL, CEM and MONOSET)
If formula weight and density are known, they may be used. (See
keywords: DENS, EDENS and MOLW). The CPU-time needed will then
usually be strongly reduced. (Unfortunately they are usually
not known and therefore they have not been used very much.)
LINE SET THREE EXAMPLES: (TREOR4, not normal TREOR99 or TREOR90
examples.)
EXAMPLE 1.Next line (except C in col.1) represents a line set 3
END*
Cubic, tetragonal, hexagonal and orthorhombic symmetries are
tried. It may be recommended to try a smaller VOL limit even if
a solution with acceptable figure of merit has been obtained.
Sometimes it is difficult to find the necessary transformations
between a high symmetry unit cell of too large dimensions and
the primitive one.
EXAMPLE 2. Next two line is a line set 3.
KS=0,THS=0,OS1=0,
CEM=20, V O L = 1000 , MONO=130,END*
This is an example of a first monoclinic trial. ( See keyword
MONO). Note that it is irrelevant if you give 'CEM=20.0' or
'CEM=20' etc.
EXAMPLE 3. Next.....etc.
KS=0,THS=0,OS1=0,
CEM=20, VOL=1500, MONO=130, END*
If example 2 is unsuccessful you may increase the VOL parameter
to 500
EXAMPLE 4. Next.....etc.
KS=0,THS=0,OS1=0,CEM=20,
MONOSET=7,LIST=1,
DENS=3.123,EDENS=0.2,MOLW=234,
END*
If you have any possibility to put in density and formula
weight, the CPU-time will be much reduced. This may also be
tried if you expect that the lattice contains a dominant zone
i.e. if in a test run you get a large number of trial cells
when using the keyword SHORT=1.
EXAMPLE 5. Next....etc.
CEM=20,VOL=700,TRIC=1,MERIT=20,END*
This is a triclinic test ( OBS. time-consuming) ( See. keyword
TRIC). A de Wolff figure merit of 20 may (sometimes) be needed
for a triclinic cell
The examples given above illustrate a step-wise strategy for
indexing. However, the VOL parameter may be estimated from the
D-value of the 20th line. (cf. keyword TRIC)
WARNING. If the unit cell has a small volume, for example
250 A**3 and VOL=2000 is used, the correct solution
may be lost in the trial process. The reason is that a
large number of large trial cells may erroneously
index more lines than the correct cell.
The problem is less severe in TREOR90 as a negative
VOL parameter will cause the program to test ( for all
but the triclinic symmetry) half the maximum volume in
a first step.
WARNING. Estimation of the unit cell volume from the relations
VOL(monoclinic cell)= 20*D(20)**3 where D(20)= the D-
value for line number 20, and VOL(orthorhombic) =
31*D(20)**3 are much less reliable than the correspon-
ding relation for the triclinic symmetry.
VOL(triclinic)=13.39*D(20)**3
Triclinic structures have no systematic extinctions!
For structures containing atoms with large differences
in scattering factors ( eg. metal-organic structures)
the general rule may fail also in a triclinic case.
Ref: Smith,G.S. J Appl. Crystallogr. 10 (1977) 252
It is usually easy to put in a known ( or expected ) cell edge
into the program. Example: A monoclinic trial with the restric-
tion that one cell axis is X.XX A. Add this D-value in line set
two. Suppose it will be line number 2. Then set MH2=1, MK2=1,
ML2=0 and MS2=1. Then the line will be used as A-axis or ( the
unique) B-axis in the monoclinic test.
Conclusion: It is usually easy to put in prior knowledge and
constraints -for example density- into the program. ( This
statement is made because of some misunderstandings in the
literature.)
H O W T O I N T E R P R E T T H E O U T P U T.
As in all good detective stories, the solution of the problem
will usually be given on the last page.....
i.e. the output list will be interrupted as soon as a unit
cell that will satisfy the criteria set by the keywords NIX
and MERIT are fullfilled. The main rule is that if all the
first 20 lines are indexed and the De Wolff figure of merit
M(20) is greater than 9, then the indexing problem is in
principle solved. This does not mean that the cell is reduced,
that a cell axis may not be double etc.,
UNIT CELLS OBTAINED BY THE PROGRAM SHOULD BE CAREFULLY CHECKED
A. If M(20) is less than 10 or more than one line is unindexed
within the 20 first observed lines the solution is probably
meaningless. Is any low-order line wrong ?
B. Check for common factors in the quadratic forms.
Example: A teragonal pattern may have H*H + K*K = 5*N
i.e. the A-axis is 2.3607 ( square root of 5) times shorter
than given on the output list.
Example: If all H, K or L are even, the corresponding cell
axis should be divided by 2.
C. If the unit cell obtained is centered, derive a primitive
cell. ( Run program MODCELL or a corresponding NBS program)
D. Reduce the primitive cell and derive the conventional cell.
(Run program REDUCT or a corresponding NBS program)
E. Hexagonal and tetragonal cells are sometimes indexed as
orthorhombic. Example: A=B*1.7321 i.e. a possible hexagonal
cell.
F. Check for geometrical ambiguities. See reference above. It
is also strongly recommended to chech cubic, tetragonal and
hexagonal solutions by an orthorhombic test. Put KS=0 and
THS=0 and re-run the problem.
There are two reasons for this procedure....
1. It may help you to identify geometrical ambiguities.
2. It has been found that sometimes very small orthorhombic
unit cells can be indexed in an acceptable way ( i.e.
fullfill the De Wolff criteria) by a larger unit cell of
higher symmetry. Although the unit cells are sometimes
related to each other, the relations are often difficult
to detect, and therefore it is often convenient to let
the program derive both solutions.
G. The De Wolff figure of merits are derived from the assump-
tion that no systematic extinctions are present and that
all lines are indexed. A high figure of merit has no meaning
unless all lines are indexed. The De Wolff figure of merit
will increase in the final refinement made with program
PIRUM, where the systematic extinctions can be taken into
account.
H. If possible, use the density and formula weight to check
that the unit cell contains an integral number of formula
units.
I. If a cell axis is more than 20 A....be suspicious!
It has been found that the De Wolff figure of merit may
fail in such cases. (Require M(20) > 20)
J. If one cell edge is much shorter than the others..........be
suspicious! It may be a dominant zone problem and the De
Wolff test may fail. (This problem is usually not severe in
TREOR90, where short axis tests are made prior to the
general tests.)
K. If a table starts with...NOT REFINED UNIT CELL...
two parameters are probably almost identical ( the symmetry
may be higher) and the trial cell parameters are used to
print the list.
L. If no satisfactory solution is found ( See the keywords NIX
and MERIT), the program may end with a small table con-
taining a difference analysis. The program is described in
Z. Kristallogr.120 (1964) p.381-382 (Werner,P.-E.) where it
is named I1. The most interesting differences are those
that have high multiplicities (on the top of the list) and
are not too small (to the right of the list). In the present
state of the program, the difference table is usually not
needed.
M. Why not solve the crystal structure from your powder data ?
This is the ultimate way to prove the unit cell!
K E Y W O R D L I S T
KEYWORD. NORMAL COMMENT.
VALUE.
KH =4 Max H for cubic base line.
KK =4 Max K for cubic base line.
KL =4 Max L for cubic base line.
OBS. The program will only generate
H greater than or equal to K and
K greater than or equal to L for
this line.
KS =6 Max H+K+L for this line.
OBS. If KS=0 cubic test omitted.
OBS. The cubic base lines are (1) and (2).
* * * * * * * * * * * * * * * * * * * * * * * * * * *
THH =4 Max H for tetragonal and hexagonal base lines.
THK =4 Max K for tetragonal and hexagonal base lines.
THL =4 Max L for tetragonal and hexagonal base lines.
OBS. The program will only generate
H greater than or equal to K for these lines.
THS =4 Max H+K+L for these lines.
OBS. If THS=0 tetragonal and hexagonal tests
omitted.
OBS. The tetragonal and hexagonal base lines
are (1,2),(1,3) and (2,3)
* * * * * * * * * * * * * * * * * * * * * * * * * * *
OH1 =2 Max H for the first orthorhombic base line.
OK1 =2 Max K for the first orthorhombic base line.
OL1 =2 Max L for the first orthorhombic base line.
OBS. The program will only generate
H greater than or equal to K, and
K greater than or equal to L for this line.
This is also valid if the SELECT parameter
is used. (See below).
OS1 =3 Max H+K+L for this line.
OBS. If OS1=0 orthorhombic test omitted.
OH2 =2 Max H for the second orthorhombic base line.
OK2 =2 Max K for the second orthorhombic base line.
OL2 =2 Max L for the second orthorhombic base line.
OS2 =4 Max H+K+L for this line.
OH3 =2 Max H for the third orthorhombic base line.
OK3 =2 Max K for the third orthorhombic base line.
OL3 =2 Max L for the third orthorhombic base line.
OS3 =4 Max H+K+L for this line.
OBS. The orthorhombic base lines are
(1,2,3) (1,2,4) (1,2,5) (1,3,4) (2,3,4) and (1,2,6)
if SELECT0=0 (See SELECT below)
* * * * * * * * * * * * * * * * * * * * * * * * * * *
MH1 =2 Max Abs(H) for the first monoclinic base line.
MK1 =2 Max K for the first monoclinic base line.
ML1 =2 Max L for the first monoclinic base line.
OBS. The program will only generate
H greater than or equal to L for this line.
EQ. TO L FOR THIS LINE.
This is also valid if SELECT is used.
(See SELECT below)
MS1 =2 Max Abs(H)+K+L for this line
The normal (and fast) way to test an expected cell
axis is to put it in as SQ number one (in card set
two) and set MH1=1, MK1=1, ML1=0 and MS1=1
MH2 =2 Max Abs(H) for the second monoclinic base line.
MK2 =2 Max K for the second monoclinic base line.
ML2 =2 Max L for the second monoclinic base line.
MS2 =3 Max Abs(H)+K+L for this line.
MH3 =2 Max Abs(H) for the third monoclinic base line.
MK3 =2 Max K for the third monoclinic base line.
ML3 =2 Max L for the third monoclinic base line.
MS3 =3 Max Abs(H)+K+L for this line.
MH4 =2 Max Abs(H) for the fourth monoclinic base line.
MK4 =2 Max K for the fourth monoclinic base line.
ML4 =2 Max L for the fourth monoclinic base line.
MS4 =4 Max Abs(H)+K+L for this line.
OBS. The monoclinic base lines are
(1,2,3,4) (1,2,3,5) and (1,2,4,5)
If SELECT is less than 6. (See SELECT below)
MONOSET =0 This parameter makes it possible to use more than 3
base line sets in the monoclinic trials.
If MONOSET is:
Greater than 3, base line set (1,3,4,5) will be used
Greater than 4, base line set (1,2,3,6) will be used
Greater than 5, base line set (2,3,4,5) will be used
Greater than 6, base line set (1,2,3,7) will be used
Thus max 7 base line sets can be used.
In N-TREOR (=STREOR), TREOR99 and TREOR90 modes
MONOSET is fixed = 7
MONOGAM=1 The best 5 (in N-TREOR 10) trial parameter sets
stored (See IQ) for each base line set will be
refined before next base line set is tested.
If MONOGAM=0 all base line sets are tried before
any refinement is made.
MONOGAM is only used in monoclinic tests.
It is recommended to use MONOGAM=1 because a refined
cell parameter set is always tested for the stop
limits NIX and MERIT. Thus CPU-time may be saved.
MONO =0 Max beta angle allowed in a cell.
OBS. No monoclinic test if MONO=0
(See also SHORT)
In N-TREOR (=STREOR), TREOR99 and TREOR90 modes
MONO is fixed = 135
SHORT =1 Short axis test.
The parameter is only used for monoclinic tests.
The first six lines are tested for the occurrence
of a common zero index in the six first lines.
If SHORT=0 no short axis test.
If you want to make this test without repeating
other monoclinic tests, you may give MONO a
negative sign.
* * * * * * * * * * * * * * * * * * * * * * * * * * *
USE =19 -or equal to the number of input lines if there are
less than 19 lines,
-or equal to the number of lines with sine square
thetas less than 0.327
-USE is the number of lines used in the trial-indexing
part of the calculations.
OBS. Max USE=20
OBS. If you want to change USE, you should also
change IQ. (See IQ).
IQ =USE-3 The number of indexable lines required in the trial-
indexing procedure if the cell should be stored for
ev. least-squares refinement.
These reciprocal cell parameters are printed if
LIST=1
LIST =0 See IQ above.
SELECT =-1 In N-TREOR (=STREOR) and TREOR99 SELECT must be -1
If you want to avoid the TREOR99 mode (but why ?..)
set SELECT=0 or...
if SELECT is positive the orthorhombic base lines
are (SELECT,1,2) (SELECT,1,3) and (SELECT,2,3) or..
if SELECT is greater than 5 the monoclinic base lines
are (SELECT,1,2,3) (SELECT,1,2,4) and (SELECT,1,3,4)
(Positive SELECT can not be used in TREOR99 mode.)
MERIT =10 The De Wolff figure of merit required as stop limit.
Ref: De Wolff,P.M. J. Appl. Crystallogr.
1 (1968) 108-113
( For cubic, tetragonal and hexagonal symmetries
are the different quadratic forms as given in
Int. Tabl. of X-Ray Crystallogr. (1968) Vol.2
p.109-145 used in the calculation of the number of
theoretical lines.)
OBS. The figure of merit calculations are not
strictly valid unless all 20 first lines are indexed.
NIX =1 If a cell after least squares refinemnet has a figure
of merit equal to or greater than MERIT and the
number of not indexable lines among the USE first
lines is less than or equal to NIX, the calculations
are stopped.
OBS. Otherwise he calculations will end with a
difference analysis (Program I1. Werner,P.-E.
Z.Kristallogr. 120 (1964) 375-378)
(Now not very useful list. --'historical')
IDIV =1 The 7 first lines are adjusted by (eventually
occurring) higher order lines.
If IDIV=0 no corrections.
Usually the default value 1 is o.k. There are
exeptions, however. If indexing is not
successful, you may try IDIV=0
WAVE =1.5405981 Wave length. (in Angstroem)
As a rule one should not change WAVE
If D-values are used in the input data file (See
CHOICE=4) one can always pretend that WAVE was
1.5405981 A. WAVE is then a formal parameter only
related to D1, SSQTL and D2 (See below).
VOL =2000 Max cell volume (in Angstroem**3)
A new option available in TREOR90 is to give a
negative value of VOL, ex. VOL=-2000.
See comments number 16 on the top of this list.
CEM =25 Max cell edge (in Angstroem)
The CPU-time depends on VOL and CEM
D1 =0.0002 (if WAVE=1.5405981) See D2 below.
SSQTL =0.05 (if WAVE=1.5405981) See D2 below.
D2 =0.0004 (if WAVE=1.5405981)
A line is regarded as indexed if..
sine square theta is less than SSQTL and
Abs(sine square theta observed minus sine square
theta calculated) is less than D1 or...
if sine square theta is greater than SSQTL and
the corresponding difference is less than D2.
D1, SSQTL and D2 are used in the trial indexing
part as well as in the least squares refinements
If SELECT=-1 are D1, SSQTL and D2 automatically
multiplied by the factor (WAVE/1.5405981)**2
(i.e. D1, SSQTL and D2 depend on WAVE)
CHOICE =4 Indicator defining SQ on card set two..
CHOICE=0 SQ=Sine square theta
=1 SQ=1/(D*D) (D-spaceing in Angstroem)
=2 SQ=Theta (Theta=Bragg angle in deg.)
=3 SQ=2*Theta
=4 SQ=D
OBS next line...
Default value in earlier TREOR-versions was 0
DENS =0 Density. (DENS=0 density not used.)
If only an integral number of molecules in the unit
cell is accepted DENS, EDENS and MOLW may be used.
(On your own responsibility)
DENS = density in gram per cm**3
EDENS =0 Not used unless DENS equals non zero.
EDENS= Max deviation in DENS.
OBS. DENS and EDENS are used in trial calculations
i.e. they are used on non refined unit cells.
Therefore, do not use too small EDENS
MOLW =0 Not used unless DENS ( and EDENS ) are non zero.
Mol. weight in A.U. (OBS. Crystal water included.)
It is not recommended to use DENS, EDENS and MOLW
TRIC =0 No triclinic test.
If TRIC=1 all higher symmetry tests are omitted and
a triclinic test is made.
It is presupposed that all higher symmetries have
been tried in earlier runs.
Although it is in principle possible to index any
pattern as triclinic, the indexing algorithm used
here is not effective for higher symmetries.
OBS. See comment 7 on the top of this list.
TRIC is not used in N-TREOR (=STREOR), TREOR99 and
TREOR90 modes.
ZEROSET =0 This keyword may be given as an integer.
ZEROSET*0.005 degrees are added to all theta-
values (i.e. ZEROSET*0.01 deg. to all 2theta).
Example: If 2theta-zero at 0.05 deg., then set
ZEROSET=-5
In N-TREOR different zero point positions are
automatically tested as explained under the
key-word LIMIT
KREDUCT =0 If KREDUCT is given, only trial solutions with
IQ=USE-(KREDUCT-1) number of lines indexed may
be saved for trial-refinements.
OBS. If KREDUCT=0 (or is not given) IQ=USE-3
(See keyword IQ above)
These reciprocal cell parameters are printed if
LIST=1
Thus, if KREDUCT=1 only trial-solutions where all
lines are indexed will be saved for further tests.
LIMIT =10 New key-word for program versions STREOR and NTREOR.
Max. number of origin shifts.
The program will ask for the theta-shift.
Normal theta-shift is 0.01 deg. if wave=1.5406 A
(i.e. 0.02 deg. in 2 theta)
Tests will be made for origin theta-shifts until
(LIMIT-1)*(theta-shift)
Thus, if LIMIT=1, no origin shift will be tested.
If you can expect that zero shift is negligible
you may save a lot of computing time if LIMIT=1
is used.
END* This keyword denotes the end of the parameter list.
(i.e. end of card set three)
C O M M E N T S F O R T H E P R O G R A M M E R
THE FILES ARE OPENED IN THE MAIN PROGRAM (THE FIRST PROG).
THE LOGICAL UNITS ARE..
NUIT=9 THE CONDENSED OUTPUT FILE.
IIN=8 THE DATA INPUT FILE.
IOUT=7 THE OUTPUT FILE.
NDISP=6 OUTPUT (ON DISPLAY) OF TRIAL PARAMETERS IF KEYWORD LIST=1
(SEE KEYWORDS IQ AND LIST)
LKEY=5 KEY-BOARD.
THE LOGICAL UNIT NUMBERS 5,6,7,8 AND 9 ARE GIVEN IN THE MAIN PROGRAM
AND MAY BE CHANGED FOR YOUR COMPUTER. THEY NEED NOT BE CHANGED IN
ANY OTHER PLACE OF THE PROGRAM, HOWEVER.
THE PROGRAM IS MAINLY WRITTEN IN FORTRAN (II) AND (IV), BUT
FORTRAN 77 HAS BEEN USED TO SOME EXTENT. (SEE FOR EXAMPLE SUBROUTINE
TWODIM.)-IT IS THE INTENTION, HOWEVER, THAT IT SHOULD NOT BE
DIFFICULT TO REWRITE THE FORTRAN 77 STATEMENTS IF ONLY FORTRAN(IV)
IS AVAILABLE.
It may be recommended to use the WATCOM FORTRAN 77 compiler.
VERSION 4 OF THE PROGRAM HAS BEEN DEVELOPED AT
STOCKHOLM UNIVERSITY USING A VAX 11/750 COMPUTER.
VERSION 5 WAS DEVELOPED FOR CONVEX 210, VAX 11/750 AND IBM PC/AT.
VERSION TREOR90 IS WRITTEN FOR CONVEX 210. A NON-VECTORIZED
VERSION IS ALSO AVAILABLE. TRICLINIC TESTS
MAY BE VERY TIMECONSUMING ON A VAX, HOWEVER.
CALLS FROM THE MAIN PROGRAM ARE TO...
PWINL.....THE DATA INPUT ROUTINE.
TREOB.....THE TRIAL MODULE (THE MOST TIME-CONSUMING PART).
TREOC.....PROG. FOR DIFFERENCE ANALYSIS AND ORGANISATION FOR TREOD.
TREOD.....LEAST SQUARES REFINEMENTS OF THE BEST TRIAL CELLS.