INPUT FOR LEAST SQUARES REFINEMENT OF UNIT CELL DIMENSIONS FROM
POWDER DIFFRACTION DATA
7094
IBSYS
There must be a title, parameter, and system extinction card
submitted with each problem. One or more observed reflection cards
may be submitted followed by an end of problem card. If no observed
reflections are given, the output will consist of theoretical reflections
only. The last end of problem card should be followed by an end of run
card.
The layout for a title card is as follows :
Column(s)
--------1- 4
Description
----------The word TITLE
)
)
)
Format A 4
5- 6
Must be blank
7-72
Any alphanumeric information
desired in heading
73-80
Not used
For the cards described below, blanks in numeric fields are interpreted as zeros by the program. If information is not entered in certain
fields, the program may enter "default" values. This is explained in
detail below.
The layout for a parameter card is as follows :
Column(s)
Description
------------------1- 4
The word PARA
)
)
5- 6
Must be blank
)
Format A 4
7-15
The unit cell length a. Format is F 9.6
16-24
The unit cell length b. Format is F 9.6
25-33
The unit cell length c. Format is F 9.6
34-36
The number of degrees in the interaxial angle alpha.
Format is I 3.
37-41
The number of minutes in the interaxial angle alpha.
Format is F 5.3.
42-44
The number of degrees in the interaxial angle beta.
Format is I 3.
45-49
The number of minutes in the interaxial angle beta.
Format is F 5.3.
50-52
The number of degrees in the interaxial angle gamma.
Format is I 3.
53-57
The number of minutes in the interaxial angle gamma.
Format is F 5.3.
58
ITHT - an integer indicating whether given values
of reflection angles Theta are multiplied by 2. If
ITHT is even 2Theta angles are given; if ITHT is odd
(e.g. 1) Theta angles are given directly. Thus, if
this field is blank 2Theta angles are implied.
Format is I 1.
59-61
THTMX, the maximum value of a reflection angle (in
terms of 2Theta or Theta according as ITHT is even or
odd),
to be considered in indexing observations during
the first NCYC cycles (see below). This does
not apply to fixed reflections, i.e. where at least
one of h, k, l is given as nonzero. If THTMX is
given as non-positive, it is reset to 20.0 degree (in
terms of the Bragg angle Theta - all calculations
being performed in terms of Theta; 2Theta values are
shown
for output if given as input).
Format for THTMX is F 3.0.
62
NCYC, the number of
indexed reflections
are not accepted in
Format is I 1.
If NCYC is given as
of 2 is assigned by
cycles during which nonwith angles exceeding THTMX
least-squares solutions.
zero (or blank), a default value
the program.
63-67
TOLMN, the minimum tolerance allowed (in terms of
2Theta or Theta according as ITHT is even or odd).
Format is F 5.4.
If TOLMN is given as non-positive, it is reset to
0.02 degree by the program.
68-72
The maximum allowable tolerance TOLMX in terms of
2-Theta or Theta according as ITHT is even or odd. If
TOLMX is given as no greater than TOLMN it is reset
to 5 times the value of TOLMN. Thus if columns
63 through 72 are left blank, TOLMX is assigned a
value of 0.1 = 5 x 0.02 degree.
(in terms of Theta for computations).
Format is F 5.4.
73-80
Not used.
As indicated above, certain fields such as for ITHT, THTMX, NCYC,
TOLMN and TOLMX may be left blank to obtain fairly typical values for
these parameters. In the same manner, except for triclinic systems, not
all of a, b, c, alpha, beta, gamma need be given explicitly - this will
be explained after describing the system extinction card. The layout
for such a card follows.
Column(s)
Description
------------------1- 4
The letters SYSE. Format is A4.
7-10
Must be one of the following eight names.
Format is A4.
1. CUBI for cubic crystal systems
2. TETR for tetragonal systems
3. ORTH for orthorhombic systems
4. MONO for monoclinic systems
5. RHOM for rhombohedral or trigonal systems
6. TRIC for triclinic systems
7. HXAG for hexagonal systems
8. HXAR for hexagonal-rhombohedral systems
12-14
HEMX, the value of 2Theta or Theta (according to ITHT
in column 58 of the preceding parameter card is even
or odd) to be used in determining the minimum
interplanar spacing for generated reflections.
This value may be superceded by given reflections
having greater Bragg angles. If this field is left
blank and there are no observed reflections THEMX
will be set to 90 degree in terms of Theta.
The format for THEMX is F 3.0.
15-20
PWL, the wavelength to be used in computing
minimum distance for generated reflections. If
given as non-positive a value of 1.5405 Angstrom
is assumed.
Format is F 6.5.
The following 27 columns indicate conditions for non-extinction for
certain classes of reflection. Format for each of these columns is I 1.
To be effective the integer n entered must be 2, 3, 4, or 6 in the
appropriate column; x, y, z are any integers. Note that if the crystal
type is HEXAR, column 26 will be considered as having a 3 whether entered
or not, the condition -h + k + l = 3.x holding for such crystals.
Column
-----21
22
Class of Reflection
------------------h k l
h k l
Condition(s) for Non-extinction
------------------------------h + k = x.n
h + l = x.n
23
24
h k l
h k l
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
h
h
h
h
h
h
0
0
0
h
h
h
h
h
h
h
h
0
0
h
h
h
h
k
k
h
h
h
h
k
k
k
0
0
0
k
k
k
h
0
k
0
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
0
0
0
0
0
0
l
l
l
l
l
k
h
h
k
h + k
-h + k
+
+
+
+
+
+
l
k
l
l
l
l
h
l
h + l
2h + l
k
l
k + l
h
l
h + l
h
k
h + k
h
h
k
l
h
l
h + l
h + 2l
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
x.n
x.n
y.n
z.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
x.n
Columns 48 through 70 are not used. Columns 71-72 contain SEMULT,
the
format being F 2.1; if this field is given as non-positive a value of 2.0
is set by the program.
According to the crystal system entered in columns 7-11, some information on the previous parameter card need not be entered. In particular
for CUBIC, only a (columns 7-15) need be entered; for TETRA only a
(columns
7-15) and c (columns 23-33) need be entered; for ORTHO only a, b, and c
(columns 7-33) need be entered on the parameter card; for MONOC a, b, c
and
beta (columns 42-49) must be entered; for RHOMB, a (columns 7-15) and
alpha
(columns 34-41) must be entered; for TRICL all lengths and angles must be
entered in columns 7-57; for HEXAG or for HEXAR only a and c must be
entered.
Following the system extinction card there usually will be a number
of reflection cards. The last of these should be followed by an end of
problem card which must have END in columns 1-3 and columns 4-6 blank.
Consequently none of the reflection cards should have these characters
in columns 1-6. The layout for a reflection card is as follows:
Column(s)
Description
------------------1- 4
Anything but the letters END followed by 3 blanks;
usually will be left blank; format is A 4.
5- 6
blank
7-11
h, the first
reflection index. Format is I 5.
12-16
k, the second reflection index. Format is I 5.
17-21
l, the third
22-30
D, the interplanar spacing as computed from the Bragg
relation using the observed Bragg angle Theta.
D need not be given if Theta (or 2Theta) is given.
Format is F 9.6.
31-38
The wave length (in Angstrom) associated with the current
reflection. If not given as positive, it is assumed to be
the same as the wavelength for the previous reflection.
(If a wavelength for the first reflection of a data set
reflection index. Format is I 5.
is
not given, the value given, or implied, on the previous
SYSEXT card is used.
Format is F 8.6.
39-47
The Bragg angle Theta (or 2Theta if ITHT - column 58 on
the
parameter card - is even). Format is F 9.5 and Theta
should
be given in degrees and a decimal fraction thereof. Theta
(or 2Theta) need not be given if D is given. If both
Theta
and D are given, D will be recomputed as the observed
d-spacing from Theta and the given or implied wavelength.
48-56
The weight WT to be associated with the value of Theta
for
the current reflection. Format is F 9.5. If WT is given
as non-positive, it is reset to 1.0 by the program.
57-80
Not used.
Note that for reflections that are to be indexed by the program by
comparing corresponding distances and angles with those of theoretical
reflections, lack of h, k, and l must be given as zero - thus for such
reflections columns 7 through 21 may be left blank. If one or more of
these reflection indices is given as non-zero, the indices read from the
reflection card will be maintained throughout the computer run.
The last END card of the deck should be followed by a card with
FINISH in columns 1 through 6.
The input data deck should be arranged as follows (following
a $ DATA card):
TITLE card
PARAM card
SYSEXT card
reflection cards (usually, but not necessarily)
END card (always, even if no reflection cards)
TITLE card (if more than one problem)
PARAM card
SYSEXT card
END card (end of last problem)
FINISH card