FullProf
Rietveld, Profile Matching & Integrated Intensities
HELP FULLPROF
1.- INTRODUCTION AND GENERAL INFORMATION
SHORT REFERENCE GUIDE OF THE PROGRAM
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* Program : FullProf *
***************************************
(Version 3.5d Oct98-LLB-JRC)
Juan Rodriguez-Carvajal
Laboratoire Leon Brillouin (CEA-CNRS)
Tel: (33) 1 6908 3343, Fax: (33) 1 6908 8261
Disclaimer:
The author is not responsible for erroneous results obtained
with FullProf. This guide cannot substitute the lack of
knowledge of users on crystallography, magnetism, diffraction
physics and data analysis. This short guide is merely a description
of the input files with minor explanations on how to proceed.
Powder diffraction is becoming more and more powerful but
FullProf is not an "automatic" (black-box) program, as is usually
found in single crystal structure determination.
No attempt has been made in order to predict the behaviour of
the program against bad input data. The user must check his(her)
data before claiming a misfunction of the program.
The author acknowledges all suggestions and notification of
possible bugs found in the program.
The most recent version of FullProf is either in "pub/divers/fullp"
or in
"pub/divers/fullp"
of the anonymous ftp-area of the LLB unix-cluster.
Users interested in create their own subroutines to link with FULLP-library
are asked to read the file "fpreadme" in the above mentioned disk-area.
To access this area from Internet, one has to type in the local host the
following commands:
LocalPrompt> ftp charybde.saclay.cea.fr
Answer with the word: anonymous , to the Login request and password.
Within the ftp prompt, do:
From a UNIX host:
ftp>cd pub/divers/fullp -> Go to FullProf area
ftp>get fpreadme -> Obtain the document
ftp>bye -> Return to host
From some VMS-VAX hosts:
ftp>set def "pub/divers/fullp" -> Go to FullProf area
ftp>get "fpreadme" -> Obtain the document
ftp>ex -> Return to host
----------------------------------------------------
1.1
FullProf is a program for Rietveld analysis (structure profile refinement) of
neutron (CW, TOF, nuclear and magnetic scattering) or X-ray powder diffraction
data collected as a function of the scattering variable T (2theta or TOF).
The program can be also used as a Profile Matching tool, without the
knowlegde of the
structure.
Single Crystal refinements can also be performed alone or in combination
with powder data.
FullProf has been developed starting from the program of
Wiles & Young, J. Applied Cryst.14,149(1981), (DBW3.2S, Versions 8711 and
8804).
The modifications of the code are mainly related with the re-organization of
the central routines performing the calculation of profile functions,
derivatives,
structure factors, and the introduction of many other things. The total source
is more than 1 Megabyte (more than 28.000 fortran lines).
The format of the main control input file (e.g. a control file created for use
with DBW-8711 can be used by FullProf with minor modifications). The input
file
is accepted as "interpreted free format".
The source is written in standard FORTRAN 77 language, and is organized
as to be easily adapted to different computers. The actual version can be
run on VAX, Alpha and Unix computers, MacIntoshes and on PCs (Lahey Computer
Systems Inc. FORTRAN-compiler, minimum 386/4Mb with co-processor required).
The migration towards genuine Fortran 90 is in progress.
---------------------------
1.2 1.3: Running the program, input and output
files. Input files CODFIL.PCR : Input control file
It must be in the current directory to run the program.
This file contains the title and crystallographic
data and must be prepared by user with a file editor.
There are two different formats for this file: the first
one is free format and closely related to that of
the Young & Wiles's program. The second is based on keywords
and commands.
(this last format is not available at present)
Warning : this file is normally up-dated every time you run the program
(see parameter NXT on line 3). In the first stages of a refinement,
it is wise to save a copy of this file with a different name.
The following files are optional.
FILE.DAT : Intensity data file (unit 4) : format depends on
instrument. If you do not specify the name FILE, the program
takes FILE=CODFIL. Not necessary for pattern calculation modes.
FILE.BAC : Background file (unit 12). The format of this file
is the following (as that of FILE.DAT for INSTRM =0):
first line : 2theta(initial) step 2theta(final)
following lines: list of intensities in free format.
CODFILn.HKL : Set of files with the reflections corresponding to
phase "n" (n is the ordinal number of a phase). These files are
optional and depend on the value of the parameter IRF(n) (see below)
If sequential refinements have to be done, this file is called HKLn.HKL
MYRESOL.INSTRU : File describing the instrumental resolution
function. Any name can be used and its content depend on the
value of the paramenter IRESO (see below).
GLOBAL.SHP : File providing a numerical table for calculating the
or peak shape and its derivative. The peak shape should
CODFIL.SHP : be given in a normalized form P(x) where the variable x is
chosen to give a FWHM=1 and the area is equal to 1 => Integ{x1,x2}[P(x).dx]=1.
That allows the use of the conventional U,V,W parameters for
defining the FWHM as a function of angle.
The format of this file is the following:
Line1: Any comment
Line2: Np8 , nupr , (anpr(j) ,j=1,nupr )
Np8 = Number of points
nupr = Number of different profiles
anpr(j) = Angle to which profile "j" is best adapted
The rest of the lines are columns with
X, P(X,1), PP(X,1),P(X,2), PP(X,2),...P(X,nupr), PP(X,nupr) in free format.
PP(X,j) is the derivative of P(X,j) with respect to X.
The profile of a reflection situated between anpr(j) and anpr(j+1)
is linearly interpolated between the profiles P(X,j) and P(X,j+1)
CODFIL.COR : File with corrections for integrated intensities of profile
intensities depending on the value of the variable ICORR . See below.
Output files *.OUT and *.SUM , their creation depends on the value of a flag
which is quoted in parenthesis. The ordinal number on the flag list is given
in brackets.
CODFIL.OUT : This is the main output file (unit 7) which contains
all control variables and structure parameters.
CODFIL.PRF : Observed and calculated profile (unit 1) : to be fed
into PLOTPOW, PLOTR , ...(if IPL2 different from zero)
In the case of ICRYG =1 (Integrated intensity mode) a list
of sin(theta)/lambda, Gobs, Gcalc is output after two
lines of comments.
CODFIL.RPA : Summary of refined parameters (unit 2) : short
version of CODFIL.SUM (if JCIL =1)
If the file exist the new data are APPENDED at the end.
CODFIL.SYM : List of symmetry operators (unit 3)
(if IPL1 =JSY =1)
(The last two files are necessary to run DISTAN or
BONDSTR)
CODFIL.SUM : Parameter list after last cycle (unit 8) : the
summary of the last parameters, their standard
deviations and reliability factors. An analysis
of the goodness of the refinement is included
at the end.
CODFIL.FOU : If JFOU =1
H,K,L, Structure Factors in Cambridge format (unit 9) :
to be fed into FOURTK (FOURPL) to produce Fourier maps.
It corresponds to the file usually called HKLFF.DAT but
you must prepare the second file CRYST.cry
If JFOU =2
(List of 'observed' structure factors in SHELXS format)
H,K,L, Fo, sigma(Fo) (3I4,2F8.2)
JFOU =-1 or -2, as above but they are calculated in
another way. The Fcalc in JFOU >0 may depend on the
peak shape and the integration interval, because they
are obtained by integration of the calculated profile in
the same way as the 'Fobs' are obtained from 'Iobs'.
If JFOU is negative, Fcalc are really the structure
factors of the conventional cell in absolute units.
JFOU =3 Format suitable for the program FOURIER
(3I4,2F10.4,f8.5,f10.4)
H,K,L,Freal,Fimag,sintheta/lambda,fobs
JFOU =4 Format (3I4,2F10.4,i8)
H,K,L,Fobs,Fcalc,nint(10000.* Phrd)
For JFOU = 3,4:
Phrd is the phase in radians and the observed and calculated
structure factors of the conventional cell are in absolute
units
CODFILn.SHX :If JFOU =2,-2, template of SHELXS *.IN file.
CODFILn.INP :If JFOU =3,-3, template of FOURIER *.INP file.
CODFILn.HKL :Files that can be input or output files. Depending
on the value of IRF(n)
CODFIL.INT :Single integrated intensity file when the program is
used for refining with ICRYG =1,2 (see below).
CODFIL.HKL : (if JLKH <>0, unit 10). Complete list of reflections
of each phase.
JLKH =1
--> If JOBTYP less than 2
reflection code, h, k,l, multiplicity, dspacing,twotheta,
FWHM, Iobs, Icalc, Iobs-Icalc.
--> If JOBTYP >1
h, k, l, multiplicity, Icalc, twotheta, dspacing
JLKH =2
--> Output for SIRPOW92
h,k,l,mul,sint/l,2t,Fwhm,F2,sF2
JLKH =-2
--> Output for EXPO
h,k,l,Fwhm,F2
JLKH =3,-3
--> Output of real and imaginary part of
structure factors (only for crystal structures)
h, k, l, mul, Freal, Fimag, 2theta, Intensity
If JLKH <0 the structure factors are given for the
conventional cell. Otherwise the structure factor
corresponds to the non-centrosymmetric part of the
primitive cell.
(the obtained file can be used as a CODFILn.HKL files for new runs)
JLKH =4
--> Output of: h, k, l, F2, sigmaF2. Where F2 is the "observed"
structure factor squared. The file could be used as input
for a "pseudo-single" crystal integrated intensity file
using ICRYG =1 and IRF=4
JLKH =5
--> Output of: h, k, l, mult, Fcalc, T, D-spacing, Q.
Where Fcalc is the module of the calculated structure factor.
This file can be used as input for JBT=-3 and IRF=2 in order
to perform quantitative analysis without re-calcultating
the structure factors for each cycle. The Fcalc are in
absolute units for the conventionnel call.
CODFIL.SAV : (if JCIL =2)
List of reflections between two selected angles
h, k, l, multiplicity, Iobs, twotheta, dspacing
For build-in sequential refinements (version 3.2 and higher) the user
must prepare the data files using names of the form CODnnn.dat .
COD stands for the code of these files and can be formed by whatever
number of characters (compatible with the actual operating system).
nnn stands for a sequence of integers. All CODnnn.dat files must
be in the same directory and the numbers nnn should be in between
a minimun number (first) and a maximun number (last) that are asked
by program. Holes are allowed between first and last.
The file CODFIL.PCR can have a different code (CODFIL could be different
of COD) and it will be used for refining the whole set of CODnnn.dat
files. The final results are contained in the CODFIL.RPA file.
For VaX-users using a command file to execute FullProf in cyclic mode:
For sequential refinements, *.DAT files will normally
be prepared by SEPFIL. In this case CODFIL must have
three letters (e.g.XXX) as code followed by a number.
The *.PCR file must be named XXXIN.PCR
XXXCYC.RES : In the case of sequential refinements, all the above
files would rapidly yield a quota exceeded error message. Thus only
condensed results are saved in files XXXCYC.RES (similar to CODFIL.RPA )
and XXXSUM.RES (similar to CODFIL.SUM ).
XXXHKL.RES : List of reflections of a selected zone of the
diffraction patern (useful with Profile Matching mode)
The final version of the file XXX**.PCR (where ** corresponds to the last
data set is also saved.
2.- DETAILED DESCRIPTION OF INPUT FILES - - -CODFIL.PCR CODFIL.PCR file with the left-ajusted capital "COMM", the new
CODFIL.PCR file has comments with mnemonics for each variable. If the user
introduce his(her) own comments, they are not saved in the new version of
the file. The unexperienced user can create a template by answering
"starting" (without quotes) to the prompt asking for the name of the file.
Note that a star after a line number (or a variable)
indicates that the line's (or variable) existence depends on the value of
a control variable.
============================================================================
LINE 1 : LINE 2 : JOBTYP , NPROF , NPHASE , NBCKGD , NEXCRG , NSCAT , NORI , IDUM , IWGT ,
ILOR , IASG , IRESO , ISTEP , NRELL , ICRYG , IXUNIT , ICORR
(15 integers)
(It is understood that they are separated by a space)
--------------Comment line :
!Job Npr Nph Nba Nex Nsc Nor Dum Iwg Ilo Ias Res Ste Nre Cry Uni Cor
----------------------------
JOBTYP = 0JOBTYP )>1 and IDUM =1 (see below) a calculated pattern is
created with the name CODFIL.SIM in format corresponding to
INSTRM =0. This pattern corresponds to an "ideal observed"
pattern and can be use for simulation purposes in order to
investigate the effect of systematic errors on the structural
parameters and on the reliability factors.
NPROF CODFIL.SHP
or in GLOBAL.SHP
9 T.O.F. Convolution pseudo-Voigt x Double Exponential
10 Not yet used
11 Split pseudo-Voigt function
12 Pseudo-Voigt function convoluted with axial divergence asymmetry
function (Finger, Cox & Jephcoat, J. Appl. Cryst. 27, 892, 1994)
NPHASE NPHASE <0 the number of phases is
(Nph) abs(NPHASE ) and the asymmetry correction is applied following the approximation of
C.J.Howard, J.Appl.Cryst.15 615-620 (1982) with the Simpson formula for five points)
NBCKGD NBCKGD <0 but IABS(NBCKGD )>4 the interpolation
is performed using cubic splines
-1 refine background with Debye-like + polynomial
function.
-2 Background treated iteratively by using a Fourier
filtering technique. An extra parameter is read
below. The starting backgroung is read from
file FILE.BAC as for NBCKGD =1.
-3 Read 6 additional polynomial background coefficients
NEXCRG NSCAT NSCAT >0, the program performs an internal
fit if a table is given in order to get coefficients
for the exponential expansion (see below).
If NSCAT <0, a linear interpolation is made.
NORI IDUM JOBTYP greater than 1 and IDUM is different than zero
a file CODFIL.SIM is generated
IWGT ILOR SENT0 in line 5)
=1 Flat plate PSD geometry
=2 Transmission geometry. Flat plate with the scattering
vector within the plate (Stoe geometry for X-rays)
=3 Polarization correction is applied even if the format of
the DATFIL.DAT file does not correspond to one of the
synchrotron explicitely given formats (see below).
This must be used for synchrotron data given in a
X,Y,Sigma format (INSTRM =10).
IASG IASG must be =1)
IRESO IRESO is not zero, the next line contains the name of the
file where the instrumental resolution function is given.
The profile is assumed to be a Voigt function (NPROF =7).
12 parameters or a table determine the resolution function.
Ui ,Vi ,Wi ,Xi ,Yi ,Zi (i=1,2 for lambda1 and lambda2 )
The different types of functions are:
=1 HG**2= (Ui*tan(q)+Vi)*tan(q)+Wi
HL= Xi*tan(q)+Zi
=2 HG**2= (Ui*tan(q)+Vi)*tan(q)+Wi
HL= (Xi*(2q)+Yi)*(2q)+Zi
=3 HG**2= (Ui*(2q)+Vi)*(2q)+Wi
HL= (Xi*(2q)+Yi)*(2q)+Zi
=4 List of values 2q, HG(2q), HL(2q)
(a linear interpolation is applied for intermediate 2q)
ISTEP ISTEP >1 the number of data points is reduced by
(Ste) a factor of ISTEP . Only those points corresponding to the
new step size ISTEP *STEP (see Line #3 below) are taken
into account in the refinement. Useful for speed-up
preliminary refinements.
NRELL NRELL lines specifying the number and the limit
of each parameter.
ICRYG ICRYG =2 no least-squares algorithm is applied.
Instead a Montecarlo search of the starting configuration
is performed. A selected number of parameters NRELL
are moved within a box defined by the NRELL relations
fixing the allowed values of the parameters. The best
(lowest R-factor) NSOLU solutions are printed and the
CODFIL.PCR file is updated with the best solution.
(See NRELL variable in this line and Line )
IXUNIT ICORR ITYCORR = 1 corrections are applied to the integrated
intensities. Standard deviations must not be given.
ITYCORR = 2 corrections are applied to the observed
profile. The corrected observed profile
and their variance are obtained as:
y(corr) = y(obs)/cor
Sigma2(y(corr)) = sigma2(y(obs))/cor^2 + sigma2(cor)/y(obs)^2
NPCORR : Number of coefficients of the empirical function.
ITYFUNC =1 Polynomial function:
cor = Sum{i=1,npcorr}{coeff(i)* T**(i-1))}
ITYFUNC =2 Exponential + Maxwellian for TOF raw data
cor = Coeff(1)+ Coeff(2)*Exp(-Coeff(3)/T^2)/T^5+
+ Sum{i=4,NPCORR,2}{Coeff(i)*Exp(-Coeff(i+1)*T^2)}
Line 2-1*: FILERES IRESO <>0.
The items in FILERES are read in free format.
The first line is considered as a title
For IRESO =1,2,3 the 12 parameters Ui , Vi , Wi , Xi , Yi , and Zi
are read from lines 2 and 3 (see the above line for the
available instrumental functions).
Example:
Line1: Resolution function of MyXrayDiffractometer
Line2: 0.00802 -0.00936 0.01024 0.0029 0.0 0.0 ! U1,V1...
Line3: 0.00774 -0.00552 0.00814 0.0000 0.0 0.0 ! U2,V2...
For IRESO =4, the file FILERES starts with a line whith the
title followed by a line with the number of points (NPOINS)
where the instrumental Gaussian and Lorentzian FWHM are given.
NPOINS lines follow containing the three items: 2thet, HG and
HL. The Bragg peaks of the diffraction pattern must be between
2thet(1) and 2thet(NPOINS). For this case the same resolution
function is applied to both wavelengths.
The maximum number of NPOINS is 30.
============================================================================
LINE 3 : IOT , IPL , IPC , MAT , NXT , LST1 , LST2 , LST3 , IPL1 , IPL2 , INSTRM ,
JCIL , JSY , JLKH , JFOU , ISHOR , IANALY
(17 integers)
--------------Comment line :
!Ipr Ppl Ioc Mat Pcr Ls1 Ls2 Ls3 Syo Prf Ins Rpa Sym Hkl Fou Sho Ana
----------------------------
List of output control flags : normally 0 = off / any value = on
IOT CODFIL.OUT (0)
(Ipr) 2 The files CODFILn.SUB with the calculated profile of
each phase are generated.
3 As 2 but the background is added to each profile.
IPL CODFIL.OUT
(Ppl) 2 Generates the background-file FILE.BAC
3 Puts difference pattern in file FILE.BAC
IPC CODFIL.OUT
(Ioc) = 2 The reflections corresponding to the second wavelength
are also writen if different from the first one.
MAT CODFIL.OUT
(Mat) If MAT =2, the diagonal of LSQ matrix is printed
before inversion at every cycle.
NXT CODFIL.PCR is re-written with updated parameters
(Pcr) 2 new input file --> CODFIL.NEW
LST1 CODFIL.OUT (usually 0)
(Ls1)
LST2 CODFIL.OUT (usually 0)
(Ls2) 4 In some versions of FullProf a plot of the diffraction
pattern is diplayed on the screen at each cycle of refinement.
LST3 CODFIL.OUT (usually 0)
(Ls3)
IPL1 CODFIL.OUT (+ CODFIL.SYM if JSY =1)
(Syo)
IPL2 CODFIL.PRF
(Prf) = 1 Format suitable for PLOTPOW, BENSTRAP,PLOTR , etc..
= 2 " " " IGOR (MacIntosh software)
= 3 " " " KaleidaGraph (MacIntosh software)
& PLOTR (Pc software)
= 4 " " " Picsure, Xvgr(Sun-Unix Software)
INSTRM INSTRM .
1 D1A/D2B format (original Rietveld-Hewat format :
the first line must be 2Thetai, step, 2Thetaf, i.e. the first
four lines of the POWDER file must be removed. Note
however that angles are given in degrees 2Theta, not
in hundredths of degree ! ).
2 D1B old format (DEC-10)
3 new format for D1B & D20 (Vax DataBase)
+/-4 Brookhaven synchrotron.
4: First line: 2thetamin, step, 2thetamax (free format)
Rest of file: pairs of lines with 10 items like
Y1 Y2 ......... Y10 -- (10F8) intensities
S1 S2 ......... S10 -- " sigmas
-4: Format given by DBWS program for synchrotron data.
(Version DBW3.2S-8711)
5 Data from GENERAL FORMAT for TWO AXIS instrument
3 lines of text followed by two lines with the items:
-> NPTS, TSample, Tregul, Ivari, Rmon1, Rmon2
-> Ti, step, Tf
Set of lines containing 10 items corresponding to
the Intensities in format 10F8.1, up to NPTS points
(NPTS=(Tf-Ti)/step+1), followed by the corresponding
sigmas in format (10f8.2) if Ivari=1. If Ivari=0
the sigmas are calculated as SQRT(Yi*Rmon1/Rmon2).
6 D1A/D2B standard format for files MYFILE.SUM
prepared by D1A(D2B)SUM or equivalent programs.
The extension of the data file must be 'dat'.
7 Files from D4 or D20L
8 Data from DMC at Wurenlingen (Paul Scherrer Institut)
9 Data of file CODFIL.UXD generated by the Socabim
software on X-Rays diffractometer.
10 X,Y,Sigma format with header lines.
In all cases the first 6 lines are considered
as comments.
If in the first line (left ajusted) appears the
keyword XYDATA, then the following 5 lines are
considered as the heading of the file. Among
these 5 lines the following keywords and values
have a meaning to the program:
-> INTER fac_x fac_y Interpol Stepin
-> TEMP tsamp
fac_x internal multiplier of X-values
fac_y internal multiplier of Y and Sigma-values
Interpol=0 Variable step is used in the program
=1 The variable step data are interpolated
internally to the constant step Stepin.
=2 Data are supplied directly at constant step
If no sigma values are provided the program assumes
that sigma(Y)=sqrt(Y).
You can add comments to the data file if they
start with the character ! in the first position
of the line. These lines are ignored by the program.
11 Data from variable time X-ray data collection
The first four lines are considered as comments
The following lines are:
-> 2Thetai, step, 2Thetaf Comment
-> (Time, Intensity) in format 5(F6, I10)
The program uses the information contained in Time
to normalize the observed intensities to the average
time and to calculate the variance of the
normalized values.
12 The input data file conforms to GSAS standard
data file. BINTYP = LOG6, TIME_MAP and LPSD are not
yet available
JCIL CODFIL.RPA
(Rpa) If the file exists before running the program
the new data are APPENDED.
2 prepares file CODFIL.SAV (sequential refinements)
JSY CODFIL.SYM (if 1, IPL1 must be set to 1)
(Sym)
JLKH CODFIL.HKL
(Hkl) = 1 as explained above
= 2 Output for SIRPOW.92
=-2 Output for EXPO
= 3 Output of Real & Imaginary
parts of Structure Factors
= 4 Output of h, k, l, F2, sF2 (to be re-used with IRF=4)
= 5 Output of h, k, l, mult, Fcalc, T, D-spacing, Q.
(to be re-used with JBT=-3 and IRF=2)
JFOU CODFIL.FOU
(Fou) = 1 Cambridge format
= 2 Shelxs format
(Prepares also the file CODFILn.SHX )
= 3 FOURIER format
(Prepares also the file CODFILn.INP )
ISHOR IANALY CODFIL.SUM .
=2 Prints also the actual dimension of arrays.
============================================================================
LINE 4* : LAMDA1 , LANDA2 , RATIO , BKPOS , WDT , CTHM , TMR , RLIM , K
(9 reals) (not needed if ICRYG is not 0)
--------------Comment line :
! lambda1 Lambda2 Ratio BKPOS Wdt Cthm muR AsyLim Rpolarz
----------------------------
OR (for T.O.F. data)
BKPOS , WDT , IABSCOR
(2 real + 1 integer)
--------------Comment line :
! BKPOS Wdt Iabscor
----------------------------
LAMDA1 LAMDA2 ABS(RATIO ) =Intensity ratio I(l2)/I(l1)
If RATIO <0 the parameters U , V , W (see below) for the
second wavelength are read separately.
BKPOS WDT CTHM TMR RLIM K IABSCOR LINE 5 : MCYCLE , EPS ,RELAX1 ,RELAX2 ,RELAX3 ,RELAX4 ,
THMIN , STEP ,THMAX (required for pattern calculation mode only),
ALPSD (required for flat plate PSD geometry only)
SENT0 (required for Bragg-Brentano X-ray ILOR =0,
when the cross section of the sample is
lower than the beam dimensions at low angles)
(1 integer and 10 reals)
--------------Comment line :
!NCY Eps R_at R_an R_pr R_gl Thmin Step Thmax PSD Sent0
----------------------------
MCYCLE EPS EPS *e.s.d.
RELAX 1 -> Atomic parameters:
coordinates, magnetic moments, site occupancies
& isotropic displacement (temperature) factors
2 -> anisotropic displacement (temperature) factors
3 -> profile parameters, asymmetry, overall displacement
(temperature), cell constants, preferred orientation
parameters, strains, size, propagation vectors & user-supplied parameters.
4 -> global parameters, zero-shift T0, background,
displacement and transparency.
THMIN STEP = step size in degrees T
THMAX ALPSD SENT0 SENT0 part of the beam doesn't
touch the sample and the intensity of reflections
below SENT0 have to be multiplied by the factor:
sclow=sin(theta)/sin(SENT0 )
============================================================================
LINE 6* : ICRYG is not 0)
--------------Comment line :
! 2Theta/TOF Background
----------------------------
if NBCKGD > 2 or NBCKGD less than -3, there are iabs(NBCKGD ) lines with
Pos = position in degrees T
Bck = background counts at this position
If NBCKGD is positive: linear interpolation
If NBCKGD is negative: cubic splines interpolation
============================================================================
- LINE 7* : ICRYG is not 0)
--------------Comment line :
! Excluded regions (LowT HighT)
----------------------------
if NEXCRG > 0, enter limits of excluded regions :
ALOW = low scattering variable bound in degrees or microsecs
AHIGH = high scattering variable bound in degrees or microsecs
============================================================================
LINE 8* : NSCAT sets of lines (needed only if you wish to enter your
own scattering length or form factor instead of using the
values stored in internal table; scattering factors and
anomalous dispersion corrections incorporated in the program.
--------------Comment line :
! Additional scattering factors
----------------------------
Line 8-1 : NAM , DFP , DFPP ,ITYM
(A4, 2 reals and 1 integer)
NAM = symbol identifying this set (left justified)
This symbol is converted to lower case for X-ray
diffraction global data.
DFP = Df' or neutron scattering length b
DFPP = Df" (ignored in the neutron case)
ITYM =1 Indicates that you are giving a magnetic form factor
If ITY =0 and and JOBTYP =1 or 3 (neutron case) the
next line must not be given. You are just giving the
Fermi length of the species NAM in DFP .
=2 Indicates that you are giving just Df' and Df"
and the program will use tabulated coefficients
for the sin(Theta)/l dependent part of f (X-rays).
The name NAM must correspond in this case to a
valid tabulated name (See Notes(1, 2) below).
At variance with the name used for determining the
scattering factor in the description of atoms, the
chemical symbol used in NAM must be LOWER CASE.
This is the most simple way of giving anomalous
dispersion parameters for synchrotron data.
Line 8-2 :
JHO3: magnetic form factor of Ho+3 as +c2
where c2 has been calculated using the dipolar
approximation. Seven coefficients A,a,B,b,C,c,D are
used for approximating +c2.
Note(2): If a table is supplied and NSCAT >0 the program performs an
internal fit to NINE coefficients and this could fails. If you
want a linear interpolation NSCAT must be negative and the
list is given as: 1000.0*2sin(Theta)/L- f
============================================================================
LINE 9 : LINE 10* : ICRYG is not 0)
Line 10-1 : ZER , FLGZER , SYCOS , FLCOS , SYSIN , FLSYN , LAMBDA , FLAMBDA , IGLMORE
(8 reals and 1 integer)
--------------Comment line :
! Zero Code Sycos Code Sysin Code Lambda Code MORE
----------------------------
ZER ZER
Note that the shift convention is opposite to that used
in Pawley's program.
FLGZER SYCOS FLCOS SYCOS
SYSIN FLSIN SYSIN
LAMBDA FLAMBDA LAMBDA . Cell parameters should be fixed if
wavelength is to be refined.
IGLMORE Line 10-1-1 : PO ,
CPO , Cp , CCp , Tau , CTau
(6 reals)
--------------Comment line :
! Microabsorption coefficients
! P0 Cod_P0 Cp Cod_Cp Tau Cod_Tau
----------------------------
Microabsorption coefficients and codes. See mathematical section.
(only used if ILOR =0 and JOBTYP =0 or 2)
Line 10-1 (bis)* ZERO , FZERO , DTT1 , FDTT1 , DTT2 , FDTT2 , TOFTET
(Replaces Line 10-1 for T.O.F. data)
--------------Comment line :
! Zero Code Dtt1 Code Dtt2 Code 2sinTh
-------------------------------------------------------------------
ZERO : Zero point for T (in microseconds) : Ttrue = Texp.-ZER
FZERO : Codeword for zeroshift
DTT1,DTT2 DTT1 + DTT2 * d) * d
FDTT1,FDTT2 : Codewords for DTT1,DTT2
TOFTET : value of 2sin(Theta) for the detector bank
Used for obtaining the wavelengths and for Lorentz factor.
Line 10-2* NBCKGD =-3, two lines more with coefficients:
BACK7, BACK8, BACK9, BACK10, BACK11, BACK12
FBACK7,FBACK8,FBACK9,FBACK10,FBACK11,FBACK12
--------------Comment line :
! Background coefficients/codes
----------------------------
BACK = background coefficients (see Mathematical section)
FBACK = codewords for background coefficients
If NBCKGD =1 (background read from file), BACK1 cannot be zero
Only four coefficients are needed if such a case. The comment
line in this case is:
--------------Comment line :
! Background Tranf_coefficients/codes
----------------------------
Line 10-3* : BACKs,FBACKs (Only if NBCKGD = -1)
(6 reals / 6 reals / 6 reals / 6 reals)
--------------Comment line :
! Additional background coefficients/codes
----------------------------
Four lines (see Mathematical section):
Bc1, Bc2, Bc3, Bc4, Bc5, Bc6
CBc1, CBc2, CBc3, CBc4, CBc5, CBc6
d1, d2, d3, d4, d5, d6
Cd1, Cd2, Cd3, Cd4, Cd5, Cd6
Line 10-4* : NBCKGD = -2)
--------------Comment line :
Window for Fourier filtering (appears in the same line as FWINDOW)
----------------------------
Window for Fourier filtering. The value of FWINDOW must be
much greater than the number of points subtended by the
base of a single Bragg reflections in the widest region
(a factor greater than five, at least!).
The starting background is read from file FILE.BAC
as in the case NBCKGD =1. But, at variance with the case
NBCKGD =1, the file FILE.BAC is re-written at the end of
the session.
============================================================================
LINE 11 : NPHASE sets of lines
----------------------------------------------------------------------------
Line 11-1 PHSNM = name of phase
(A70)
--------------Comment line :
! Data for PHASE number: n ==> Current R_Bragg: Rb
----------------------------
----------------------------------------------------------------------------
Line 11-2 : N , NDIST , NMAGC , PREF(1) , PREF(2) , PREF(3) , JBT , IRF , ISYM ,
ISTR , IFURT , ATZ , NVK , NPRO , IMORE
(3 integers, 3 reals, 5 integers, 1 real and 3 integers)
--------------Comment line :
!Nat Dis Mom Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More
----------------------------
N = number of atoms in asymmetric unit
The total number of atoms for all phases cannot be
greater than NATS (defined in PARAMETER statement
of FUL0.INC)
NDIST NMAGC PREF(1,2,3) JBT CODFILn.HKL file. This structure factor is
given for the non-centrosymetric part of the primitive
cell, so for a centrosymmetric space group with a centred
lattice the structure factor to be read is:
Freduced = Fconventional / (Nlat*Icen)
where Nlat is the multiplicity of the conventional cell and
Icen=1 for non-centrosymmetric space groups and Icen=2 for
centrosymmetric space groups.
= 4 The intensities of nuclear reflections are calculated from
a routine, supplied by the user, called STRMOD.
The default subroutine handles Rigid body groups.
= 5 The intensities of magnetic reflections are calculated from
a routine, supplied by the user, called MAGMOD.
=+10/-10 The phase can contain nuclear and magnetic contributions
STFAC is called for reflections with no propagation vector
associated and CALMAG is called for satellite reflections.
CALMAG is also called for fundamental reflections if there
is no propagation vector given but the number of magnetic
symmetry matrices is greater than 0.
The negative value indicates spherical components for
magnetic parameters.
For this case the atom parameters are input in a slightly
different way.
IRF CODFILn.HKL (where n
is the ordinal number of the current phase)
= 2 The list h,k,l,Mult,Intensity (or Structure Factor if JBT =-3)
is read from file CODFILn.HKL
=-1 The satellite reflections are generated automatically from
the given space group symbol
= 3 The list h,k,l,Mult,Freal,Fimag is read from file CODFILn.HKL
In this case, the structure factor read is added to that
calculated from the supplied atoms. This is useful for
simplifying the calculation of structure factors for
intercalated compounds (rigid host).
=4,-4 A list of integrated intensities is given as observations
for the current phase (In the case of ICRYG <>0 this is
mandatory)
The file CODFILn.HKL can also be named as HKLn.HKL , or CODFIL.INT
in the case ICRYG <>0.
The format of CODFILn.HKL files is the following:
For abs(IRF )<4:
The first two lines are read as titles (characters)
The rest of the lines consist on:
1) No propagation vectors
h k l m (IRF =1) (free format)
h k l m Coeff (IRF =1+JSOL =1) ( " )
h k l m Intensity (or F) (IRF =2) ( " )
h k l m Freal Fimag (IRF =3) ( " )
2) NVK propagation vectors
In the third line you have to give the number of propagation
vectors in format (32x,i2), then you give
NVK lines with: Nv K1 K2 K3 , where Nv is the ordinal number
of K and Ki are the components of K in free
format.
h k l nv m (IRF =1) (free format)
h k l nv m Coeff (IRF =1+JSOL =1) ( " )
h k l nv m Intensity (or F) (IRF =2) ( " )
h k l nv m Freal Fimag (IRF =3) ( " )
Note:
The generated files when JBT =2,3 may content additional items
that are not used by Fullprof. These items (sigma,angle,FWHM)
can be used by other programs.
The case IRF =1+JSOL=1 is to be used when shifts of Bragg
reflections are observed and a model for it is known. The
user must provide the value of the coefficient COEFF for
each reflection.
For abs(IRF )=4:
- The first line is considered as a TITLE
- In the second line the format of the intensity data to be
read below is given.
Example: (3i4,2f10.2,i4,3f8.4) (don't forget parentheses)
- R_lambda(n),Itypdata,ipow(n) (free format)
R_lambda(n) :wavelength for phase n
Itypdata = 0 Square of structure factors (F2) and
sigma(F2) are input.
= 1 Structure factors (F) and Sigma(F) are
input. These quantities are transformed
internally to case Itypdata=0.
Ipow(n) = 0 Single crystal observations.
= 1 Twinned single crystal observations.
Up to 6 hkl's can contribute to a
single observation.
= 2 Powder integrated intensities. In this
case cluster of peaks can be given.
For this case Itypdata is irrelevant.
-* cmono, rkks (to be given only for X-rays and Ipow=2)
Correspond to variables CTHM and K for
monochromator polarization correction.
1) No propagation vectors
h k l Gobs Sigma(Gobs) Icode c1 c2 c3
2) Propagation vectors
-Nok (number of propagation vectors: must be equal to NVK)
NVK lines with: Nv K1 K2 K3 , where Nv is the ordinal number
of K and Ki are the components of K in free
format.
h k l nv Gobs Sigma(Gobs) Icod c1 c2 c3
The format of the data corresponds to that given explicitely
in line 2 of the CODFILn.HKL file.
No data reduction is performed. The program expects
to be provided with an independent set of reflections.
nv is the ordinal number of the propagation vector
corresponding to the current observation (hkl).
Gobs and Sigma(Gobs) have different meanings depending on
the value of Itypdata and Ipow.
Ipow =0 Itypdata= 0 Gobs=F2
= 1 Gobs=F
Ipow =1 As above but is Gobs<0 the reflection
contributes to the next positive observation.
Ipow =2 Gobs= Sums of {jLpF2}
Icod: code for reflections indicating the scale factor
number to be applied (for twinned crystals or
inhomogeneous data).
If Ipow=2 and NVK><0 Icod is the multiplicity.
If Ipow=2 and NVK=0 the multiplicity is automatically
calculated from the symbol of the space group.
For IRF =4
c1,c2,c3: Not yet used
(coefficients for extinction corrections)
For IRF =-4
c1,c2: Real and Imaginary part of the partial calculated structure
factor or the reflection. The program will add this
contribution to the structure factor calculated with the
given atoms -> Ftot= F + Fp= (A+iB) + (c1+ic2). See comments
for IRF =3.
Examples:
Twinned Orthorhombic crystal with two domains
(a,b,c) (b,a,c)
h k l Gobs Sigma Icod
.............................
2 0 0 -1.0 0.0 2
0 2 0 3221.0 12.1 1
3 1 1 -1.0 0.0 2
1 3 1 1221.0 8.2 1
Powder cluster of peaks
1 1 1 23.2 0.4 1 Isolated peak
.............................
5 3 1 -1.0 0.0 1 Cluster of peaks: four
3 4 2 -1.0 0.0 1 independent reflections
4 4 1 -1.0 0.0 1 contribute to
5 0 3 832.1 9.4 1 <- this observation
ISYM =0 The symmetry operators are generated automatically from
the space group symbol.
=+/-1 The symmetry operators are read below. In the case
of a pure magnetic phase ISYM must be always equal to 1.
For JBT =10 with magnetic contribution ISYM could be 0
but a comment starting with "Mag" should be given after
the space group symbol (see below)
Note: For Profile Matching mode 2, IRF can be 0 in the
first run. In that case, a CODFILn.HKL file is
generated and IRF is set to 2 in the new CODFIL.PCR
file. The file is updated at each run in the
case of JBT =2. Of course ISYM must be 0.
If for a phase IRF .LE.0 and ISYM =1, the reflections
are generated from the symbol given in the place
reserved for the space group.
In that case, a file CODFILn.HKL is generated with
the relevant (non-zero) reflections and proper
multiplicities for the particular model described
by user-given symmetry operators. In addition the
calculated intensities are given in F2 (corrected
for multiplicity, scale and LP-factor) in absolute
units. The program doesn't use the intensities in
new runs reading this generated file.
The contain of this generated file, apart from the
features described above, is:
No k-vectors -> h k l m F2(calc) F2(obs)
k-vectors -> h k l nv m F2(calc) F2(obs) hr kr lr
with obvious meaning.
ISTR =0 If strain or/and size parameters are used, they are
those corresponding to selected models (see below)
=1 The generalized formulation of strains parameters will
be used for this phase. See below
=2 The generalized formulation of size parameters will
be used for this phase. See below
=3 The generalized formulation of strain+size parameters will
be used for this phase. See below
IFURT Number of further parameters defined by user, to be used
with user supplied subroutines.
AZT = Z.Mw.f^2/t
(useful to calculate the weight percentage of the phase)
Z: Number of formula units per cell, Mw=molecular wheight
f: Used to transform the site multiplicities used on line
11-41 to their true values. For a stoichiometric phase f=1
if these multiplicities are calculated by dividing the Wyckoff
multiplicity m of the site by the general multiplicity M.
Otherwise f=Occ.M/m, where Occ. is the occupation number
given in line 11-4-1.
t: Is the Brindley coefficient that accounts for microabsorption
effects. It is required for quantitative phase analysis only.
When phases have like absorption (in most neutron uses), this
factor is nearly 1. If IMORE=1 (see below) the Brindley-coeff.
is directly read in the next line (in such case ATZ=Z.Mw.f^2).
NVK = Number of propagation vectors. If NVK<0 the vector -K
is added to the list.
NPRO = Integer indicating the peak shape for the present phase
(see line 2). If NPRO =0, the default value NPROF is taken.
IMORE = If different from 0 a new line is read
----------------------------------------------------------------------------
Line 11-2-1* : JVIEW , JDIST , JHELIX , JSOL , JMOM , JTER , BRIND ,
RM1 , RM2 , RM3 , JTYP
(6 integers, 4 reals and 1 integer) (Read only if IMORE=1)
--------------Comment line :
!Jvi Jdi Hel Sol Mom Ter Brind RMua RMub RMuc Jtyp
----------------------------
JVIEW = 1 a file suitable for SCHAKAL is generated
= 2 a file suitable for STRUPLO is generated
(The extension of the file is in both cases ".sch")
=11 If JBT =2 a file CODFILn.INT with a list of
overlaped peak clusters is output.
JDIST = 1 Creates a file called CODFILn.ATM with all atoms
within a primitive unit cell for a magnetic phase. The number
"n" corresponds to the number of the current phase.If JBT =10 only
the list of magnetic atoms is generated.
-1 For a magnetic phase creates a file called
CODFILn.ATM with a format suitable for further
processing with the program MOMENT.
2 As 1 but for a crystal structure, all atoms
inside the conventional cell are generated.
JHELIX = 1 The real and imaginary components of the
Fourier coefficient of a magnetic atom are constrained
to be orthogonal. The factor 1/2 is also included
(see mathematical section).
JSOL = 1 Additional hkl-dependent asymmetry and shifts parameters
are read.
JMOM - unused at present
JTER - unused at present
BRIND - Brindley coefficient (see line 11-2)
RM1 - Used when IRF =4 and IMORE=1. If RM1=0.0 the program
makes RM1=1.0 internally. The meaning RM1 correponds to
the global weight of the integrated intensity observations
with respect to the global profile. The contribution
to the normal equations of the integrated intensity part
is multiplied by RM1.
RM2 - If IRF =4, RM2 is a factor for excluding reflections
only the reflections with Gobs>= RM2*Sigma(Gobs) are
considered in the refinement.
If JVIEW=11 and JBT =2 and IRF <>4 see note below.
RM3 - If RM3>0.9 the weights are divided by the Chi2 of the
precedent cycle (not tested!) for integrated intensity
refinements (IRF =4).
If JVIEW=11 and JBT =2 and IRF <>4 see note below.
JTYP - Job type for the phase. Allows the refinement of hetero
geneous data (Same values as the global variable JOBTYP
in line 2). For the moment is only useful for IRF =4.
Note:If JVIEW=11 and JBT =2 the parameters RM2 and RM3 are used to control
whether two consecutive reflections belongs to a same cluster.
This is only for IRF different from 4/-4.
The rule is the following:
The reflections i and i+1 belong to the same cluster if
a) TwTh(i+1)-TwTh(i) < (Fwhm(i)+Fwhm(i+1))*RM2/2
OR
b) TwTh(i+1)-TwTh(i) < (Fwhm(i)+Fwhm(i+1))/2 and I(i+1)<Isum*RM3
Isum being the cumulated integrated intensity of the current cluster.
If the RM2 and RM3 are given as zeroes, the program uses the values
RM2=1.0 and RM3=0.2.
----------------------------------------------------------------------------
Line 11-3 JBT =+10/-10 (See below)
--------------Comment line :
<-- Space group symbol (appears as default Comment)
----------------------------
Note that rhombohedral space groups must be given in
the hexagonal description.
Warning: don't forget blanks between symmetry operators;
it is advisable to check the Laue symmetry and
symmetry operators in the output file especially for
those space groups for which alternative origins are
shown (i.e. use the setting with -1 at the origin).
Upper and/or lower case characters can be used.
Some space groups are not correctly generated, for those
cases you have to change the setting or give your own
symmetry operators (see above ISYM ).
For cubic space group use the old notation, e.g. F d 3 m
instead of F d -3 m.
The space group symbol must be given even in the case that
you are giving your own symmetry operators. The reflections
(if they are not read from file) will be generated according
to the space group symbol.
A comment can be put after column 20. If this comment starts
with the keyword "Mag" (without quotes) then the following
line is read if JBT =10
----------------------------------------------------------------------------
Line 11-3-0* JBT =+10/-10 and Comment=Mag)
(up to 25 integers)
--------------Comment line :
! Time Reversal Operations on Crystal Space Group
----------------------------
NS is the number of independent symmetry operators given
in file CODFIL.OUT for the crystallographic space group.
Time_rev(i)=-1 if time reversal is associated to operator
"i" for magnetic symmetry, otherwise is equal to 1.
The order of operators is the same as in CODFIL.OUT , so
a first run is needed for knowing the list of
crystallographic symmetry operators.
For centrosymmetric groups Time_rev(NS+1) tells the program
if time reversal is associated (-1) or not (1) to the
inversion operator. This last item should be given only
for centrosymmetric space groups.
This approach assumes that the magnetic symmetry belongs
to the family of the crystallographic space group. However
the user can treat the problem using subgroups of the space
group (making the appropriate constraints in the atomic
positions) when needed.
Ex of lines 11-3/11-3-0*:
P 6/m m m Magnetic symmetry below
! Time Reversal Operations on Crystal Space Group
1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1
----------------------------------------------------------------------------
Line 11-3-1*: MULT , ICENT , NLAUE , NMAGR (Only if ISYM ><0)
(4 integers)
--------------Comment line :
!Nsym Cen Laue MagMat
----------------------------
MULT = Number or symmetry operators given below.
ICENT = 1 Non centrosymmetric structure
2 Centrosymmetric structure
NLAUE = Integer corresponding to the following laue classes:
1:(-1), 2:(2/m), 3:(mmm), 4:(4/m), 5:(4/mmm), 6:(-3,R), 7:(-3m,R),
8:(-3), 9:(-3m1), 10:(-31m), 11:(6/m), 12:(6/mmm), 13:(m3), 14:(m3m)
This number is only used for checking the symmetry operators
given by users. For a phase described in a hexagonal basis
one should put NLAUE =6,7...12, even if the space group symbol
used for generating the reflections is of different symmetry.
NMAGR= Number of magnetic rotation matrices for each
symmetry operator.
--------------------------------------------------------------------------
Line 11-3-2* MULT (1+NMAGR ) lines of the form:
=> If ISYM =1 the symmetry operators are given in numeric form:
--------------Comment line :
!S11 S12 S13 T1 S21 S22 S23 T2 S31 S32 S33 T3
!M11 M12 M13 M21 M22 M23 M31 M32 M33 Ph
----------------------------
. S11 S12 S13 T1 S21 S22 S23 T2 S31 S32 S33 T3 (3(3Int,1real))
. R11 R12 R13 R21 R22 R23 R31 R32 R33 .Phase (9Int,1real)
MULT .
.NMAGR lines
blocks . .
.
=> If ISYM =-1 the symmetry operators are given in alpha-numeric form:
e.g.
!
SYMM X,Y,Z
MSYM U,V,W, 0.0
!
SYMM X+1/2,-y, Z
MSYM -U, V,-W, 0.0
!
SYMM -x,-y,-Z
MSYM U, V, W, 0.0
The symbols U,V,W are used for the Fourier components of the
magnetic moments along X,Y,Z. The numerical value following
the MSYM operator is the magnetic phase in units of 2pi.
----------------------------------------------------------------------------
Line 11-4 : 4 or 2 lines for each of the N atoms
For X-ray or nuclear Neutron scattering: ---------->
----------------------------------------------------------------------
Line 11-4-1 LABEL , NTYP , X, Y, Z, B, N, IOPIN,IOPFIN,N_Type
(2A4, 5 reals and 3 integers)
--------------Comment line :
!Atom Typ X Y Z Biso Occ In Fin N_t /Codes
----------------------------
If JBT =4,-4 (structural model supplied by user): -->
Line 11-4-1 LABEL , NTYP , P1, P2, P3, P4, P5, P6, P7, P8
(2A4, 8 reals) {parameters defined by user in STRMOD}
--------------Comment line :
!Atom Typ p1 p2 p3 p4 p5 p6 p7 p8
! p9 p10 p11 p12 p13 p14 p15 p16
----------------------------
----------------------------------------------------------------------
For magnetic Neutron scattering: ------------------>
----------------------------------------------------------------------
Line 11-4-1 LABEL , NTYP , IMAGR, IK, X, Y, Z, B, N, Mx, My, Mz
(2A4, 2 integers and 8 reals)
--------------Comment line :
!Atom Typ Mag Vek X Y Z Biso Occ Rx Ry Rz
! Ix Iy Iz beta11 beta22 beta33 MagPh
----------------------------
If JBT =5,-5 (magnetic model supplied by user): -->
Line 11-4-1 LABEL , NTYP , IMAGR, IK, P1, P2, P3, P4, P5, P6, P7, P8
(2A4,2 integers and 8 reals) {parameters defined by user in MAGMOD}
--------------Comment line : (default JBT =5)
!Atom Typ Mag Vek X Y Z Biso Occ Mom beta Phase
! Phi & Theta of Cone-axis + unused params
----------------------------
----------------------------------------------------------------------
The variables defined either for nuclear or magnetic scattering have
the following meaning:
LABEL = Identification characters for atom or object.
NTYP = Link to scattering data for atom : either NAM from 8.1
or chemical symbol and valence to access internal
table (use only upper case letters). See note above
in line 8.
Also a series of special form factors (under test!) are
available with refinable parameters. For using this
option NTYP should be equal to one of the following
words: SPHS (available), SPHE, ELLI, DISK, TORE
SASH (not available yet), FUD1,FUD2,FUD3,FUD4 (to be
supplied by user in Fdum1.for (see Form_Factor subroutine).
See mathematical section for details.
IMAGR= Ordinal number of the magnetic rotation matrices
applied to the magnetic moment of the atom. To be
given only in the case of a magnetic phase
IK= Number of the propagation vector to which the atom
contributes. If IK=0 the atom is used for all the
propagation vectors in the calculation of structure factor.
If IK<0 the atom contributes to VK(abs(IK)) and to the
vector VK(abs(IK)+NVK/2)
X, Y, Z =fractional atomic coordinates
B = isotropic displacement (temperature) parameter in
angstroms**2
N = occupation number i.e. chemical occupancy x site
multiplicity (can be normalized to the multiplicity
of the general position of the group).
IOPIN,IOPFIN= Ordinal number of first and last symmetry operator
applied to the atom, apart from the identity which must
always be the first one.
Useful to describe pseudosymmetries.
This option is normally used when the user supply their
own list of symmetry operators (ISYM =1).Be careful with
multiplicity of reflections!. It is suggested that the
users supply also their list of reflections.
If IOPIN=IOPFIN=0 all the symmetry operators are applied.
Only used for crystallographic structures.
N_Type = 0 -> Isotropic atom
(no anisotropic temperature factors are given)
2 -> Anisotropic atom. The temperature factors should
be given below.
4 -> The form-factor of this atom is calculated using
a special subroutine and refinable parameters
should be given below (under test!)
Mx,My,Mz =Components along the crystallographic axis of the
magnetic moments (Bohr magnetons), if JBT =1.
In the case JBT =-1 these three parameters correspond to the
spherical components of the magnetic moment, in the following
order: M, Phi and Theta. M: magnitude of the magnetic moment
Phi and Theta are spherical angles of vector M (see note on
JBT =-1)
If the magnetic phase is incommensurate or described in the
crystallographic cell with the help of a propagation vector,
these component are actually the real part of the Fourier
components of the magnetic moment of the atom.
----------------------------------------------------------------------------
Line 11-4-2 : CX, CY, CZ, CB, CN, CMx , CMy , CMz
(8 reals)
CX, CY, CZ =codewords for fractional atomic coordinates
(see below)
CB = codeword for isotropic displacement (temperature)
parameter
CN = codeword for occupation number
CMx,CMy,CMz =codewords for magnetic moment components
If JBT =4,-4/5,-5 CP1, CP2, CP3, CP4, CP5, CP6, CP7, CP8
For X-ray or nuclear Neutron scattering: ---------->
----------------------------------------------------------------------------
STANDARD :
Line 11-4-3 : b11, b22, b33, b12, b13, b23 (For N_typ=2)
(7 reals)
--------------Comment line :
! beta11 beta22 beta33 beta12 beta13 beta23 /Codes
----------------------------
bij = anisotropic displacement (temperature) parameters (betas)
OR (For N_typ=4) (AND if N_typ=5, but not available)
--------------Comment line :
! Form-factor refinable parameters
----------------------------
Line 11-4-3 : f1 f2 f3 f4 f5 f6 f7
(7 reals)
Line 11-4-4 : Cf1 Cf2 Cf3 Cf4 Cf5 Cf6 Cf7
Line 11-4-5 : f8 f9 f10 f11 f12 f13 f14
(7 reals)
Line 11-4-6 : Cf8 Cf9 Cf10 Cf11 Cf12 Cf13 Cf14
(7 reals)
The parameters f1 to f14 are used for describing the form-factor
of the current object
RIGID BODY OR NON-STANDARD:
If JBT =4,-4 ---> P9, P10, P11, P12, P13, P14, P15
{parameters defined by user in STRMOD}
----------------------------------------------------------------------
For magnetic Neutron scattering: ------------------>
----------------------------------------------------------------------------
Line 11-4-3 : Mxi, Myi, Mzi, b11, b22, b33, MPhas
(7 reals)
If JBT =5,-5 ---> P9, P10, P11, P13, P14, P15, P12
{parameters defined by user in MAGMOD}
----------------------------------------------------------------------
Mxi,..= Imaginary components of the Fourier coefficient in
Bohr magnetons (If JBT <0, spherical components as
for real components Mx,My,Mz, see line 11-4-1)
bii = diagonal part of anisotropic temperature factors
MPhas = Magnetic phase of the atom (see mathematical section)
If JHELIX=1 (see line 11-2-1) the third component Mz is
calculated by the program in order to have an imaginary
vector orthogonal to the real vector.
If JBT <0, then the phi-angle of the imaginary part
is calculated by the program for keeping the orthogonal
constraint.
----------------------------------------------------------------------------
Line 11-4-4 : CB11, CB22, CB33, CB12, CB13, CB23, CMPhas
(7 reals)
CBIJ = codeword for anisotropic displacement (temperature)
parameters, or for imaginary components of the magnetic
Fourier coefficient.
CMPhas= codeword for magnetic phase.
If JBT =4,-4 CP9, CP10, CP11, CP12, CP13, CP14, CP15
************************************************************************
New input format for atom parameters
The lines 11-4-1 to 11-4-4 should be changed for the case JBT =10,-10
************************************************************************
For Xrays or nuclear+magnetic Neutron scattering: ---------->
----------------------------------------------------------------------
Line 11-4-1 : LABEL, NTYP, IMAGR, IK, X, Y, Z, B, N N_type (a)
(2a4,2int,5real,1int)
Line 11-4-2 : CX, CY, CZ, CB, CN (b)
(5 reals)
Line 11-4-3 : Mx My Mz Mxi Myi Mzi MPhas (c)
(7 reals)
Line 11-4-4 : CMx CMy CMz CMxi CMyi CMzi CMPhas (d)
(7 reals)
Line 11-4-5 : b11 b22 b33 b12 b13 b23 (e)
(6 reals)
Line 11-4-6 : Cb11 Cb22 Cb33 Cb12 Cb13 Cb23 (f)
(6 reals)
Line 11-4-7 : f1 f2 f3 f4 f5 f6 f7 (g)
(7 reals)
Line 11-4-8 : Cf1 Cf2 Cf3 Cf4 Cf5 Cf6 Cf7 (h)
(7 reals)
Line 11-4-9 : f8 f9 f10 f11 f12 f13 f14 (i)
(7 reals)
Line 11-4-10 : Cf8 Cf9 Cf10 Cf11 Cf12 Cf13 Cf14 (j)
(7 reals)
If N_type = 0 Only lines (a) and (b) need to be given
If N_type = 1 give the lines (a), (b), (c) and (d)
If N_type = 2 give the lines (a), (b), (e) and (f)
If N_type = 3 give the lines (a) -> (f)
if N_type = 4 give the lines (a), (b) and (g)->(j) (special form-factor)
--------------Comment lines :
!Atom Typ Mag Vek X Y Z Biso Occ N_type
!Line below:Codes
! Rx Ry Rz Ix Iy Iz MagPh
!Line below:Codes or...
! beta11 beta22 beta33 beta12 beta13 beta23 /Line below:Codes
----------------------------
This input could be also used for Xrays, in such case IMAGR and
IK should be zero for all the atoms and Jobtyp or Jtyp(n)=0. In
such case the space group symbol can be used for generation of
reflections and symmetry operators.
For a phase with magnetic contributions NTYP should be equal to
the magnetic form factor symbol. The program extracts internally the
fermi length symbol from NTYP. If there are magnetic contributions
the symmetry should be controlled by the user (ISYM =1) and the
magnetic part should be described with the formalism of propagation
vectors, the magnetic contribution is calculated only for the satellite
reflections. If fundamental reflections have magnetic contribution
the propagation vector k=(0,0,0) must be included explicitely if
there are other propagation vectors. If the magnetic cell is the
same as the chemical cell propagation vectors are not needed.
For the moment, the symmetry operators must belong to the group
of the propagation vector Gk, so some atoms need,in general, to be
repeated for the rest of positions not generated by Gk.
----------------------------------------------------------------------
----------------------------------------------------------------------------
====> For iabs(IRF )<>4 (no integrated intensity data) and ConstWavelength
----------------------------------------------------------------------------
Line 11-5-1 S , GAM1 , Bov , STR1 , STR2 , STR3 , IstrainModel
(6 reals and 1 integer)
--------------Comment line :
! Scale Shape1 Bov Str1 Str2 Str3 Strain-Model
----------------------------
S = scale factor
GAM1 = profile shape parameter , e.g. :
eta0 for NPROF =4,5 but not for NPROF =7 (see line 11-6-1)
m0 for NPROF =6
Bov = overall isotropic displacement (temperature) factor
in angstroms**2
STR1 ,STR2 ,STR3 = strain parameters, defined through the subroutine
STRAIN (see additional information)
If ISTR=1 set these values to 0.0
IstrainModel = Integer to select a particular model for strains
in subroutine STRAIN.
--------------------------------------------------------------------------
----------------------------------------------------------------------------
Line 11-5-2 : CS , FLGAM1 , CBov , CSTR1 ,CSTR2 ,CSTR3
(6 reals)
CS = codeword for scale factor
FLGAM1 = codeword for GAM1
CBov = codeword for overall isotropic displacement
(temperature) factor
CSTR1 ,CSTR2 ,CSTR3 = codeword for strain parameters
If ISTR=1 set these values to 0.0
---------------------------------------------------------------------------
----------------------------------------------------------------------------
====> For iabs(IRF )=4 (integrated intensity data)
----------------------------------------------------------------------------
Line 11-5-1 Line 11-5-2 : CSc1, CSc2, CSc3, CSc4, CSc5, CSc6
(6 reals)
Sci = scale factor for domain (i)
CSci = code of the scale factor for domain (i)
For powder data only the first scale factor is used
--------------------------------------------------------------------------
===> End iabs(IRF )=4
----------------------------------------------------------------------------
====> For iabs(IRF )<>4 (no integrated intensity data) and ConstWavelength
----------------------------------------------------------------------------
Line 11-6-1 NPRO =11 (split pseudo-Voigt)
! Ul Vl Wl Xl Y GauSiz LorSiz Size-Model
----------------------------
(7 reals and 1 integer)
For profiles 0 to 6 and 12:
FWHM^2 = (U+DST^2)*Tan^2(Theta) + V*Tan(Theta) + W + IG/cos^2(Theta)
=====> For NPROF = 4 (tripled pseudo-Voigt), the three
components are assumed to have the same eta0 and FWHM,
so the effective total width depends on the additional
shape parameter Shp1 (see line 11-8-3).
The profile function is given by the formula:
p4(x) = X*pV(x-D) + (1-X-Y)*pV(x) + Y*pV(x+D)
where
D = Shp1 /d.costheta
pV(x) = Eta0*L(x)+(1-Eta0)*G(x)
So, apart from the FWHM that is calculated from U,V,W
DST and IG parameters for a single component, the profile
function has FOUR shape parameters Eta0 , X, Y and Shp1 .
This function is adapted for medium resolution neutron
powder diffractomers having defects on the monochromator
and/or the guide spacial spectral distribution giving
rise to a non-gaussian distribution of wavelengths.
=====> For NPROF = 5 and 12 (pseudo-Voigt) the eta parameter
can be dependent on X through the formula:
pV(x) = Eta*L(x)+(1-Eta)*G(x)
Eta = Eta0 + X * 2Theta
=====> For NPROF = 11 (split pseudo-Voigt) DST and IG are common
to the left and right parts of the profile. Moreover additional
FWHM parameters are used as new shape parameters, so the
expression of the left FWHM(L) for NPROF =11 is
FWHM^2(L) = (Ul+DST^2)*Tan^2(Theta) + Vl*Tan(Theta)
+ Wl+IG/cos^2(Theta)+ Shp1/tan^2(2Theta)
Shp1 is applied only for 2Theta<=90. The value of ETA for the left
part is given by: Etal = Etal0 + Xl * 2Theta
The expression of the right part is:
FWHM^2(R) = (Ur+DST^2)*Tan^2(Theta) + Vr*Tan(Theta)
+ Wr+IG/cos^2(Theta) + Shp2/tan^2(2Theta)
Shp2 is applied only for 2Theta >90. The value of ETA for the right
part is given by: Etar = Etar0 + Xr * 2Theta
The FWHM and shape parameters for the right part are read in next lines
=====> For NPROF = 6 (Pearson-VII) the m parameter
can be dependent on X and Y through the formula:
m = m0 + 100* X / 2Theta + 10000* Y / (2Theta)**2
=====> For NPROF = 7, the FWHM of the two components is calculated as
FWHM^2(gaussian) = (U+DST^2)*Tan^2(Theta) + V*Tan(Theta) + W + IG/cos^2(Theta)
FWHM(lorentzian) = X tan(Theta) + (Y+ F(SZ))/cos(Theta)
All expressions are in (degrees 2Theta)^2
U,V,W = Half-width parameters (normally characterizing the instrumental
resolution function).
X = Lorentzian isotropic strain parameter.
DST(STR) = Anisotropic gaussian contribution of microstrain. It is
calculated in subroutine STRAIN as a function of IstrainModel
or ISTR. If IstrainModel <>0 then ISTR must be zero. DST depends
on STR1,STR2,...parameters and hkl.
IG= Isotropic size parameter of gaussian character
F(SZ)= anisotropic lorentzian contribution of particle size. It is
calculated in subroutine SIZE and depend on parameter SZ and hkl.
IsizeModel= Integer to select a particular model for F(SZ)
in subroutine SIZE.
----------------------------------------------------------------------------
Line 11-6-2 : CU, CV, CW, CX, CY CIG CSZ : codewords for the FWHM
(or shape) parameters
(7 reals)
----------------------------------------------------------------------------
Line 11-6-3 NPROF =5 but the left (x<0) and
right (x>0) parts of the profile have different U,V,W,eta0 and X
parameters. Additional shape parameters are also read.
Line 11-6-4* : CUr, CVr, CWr, CEtar0, CXr: codewords for the FWHM
and shape parameters
(5 reals) Read only if NPRO=11
----------------------------------------------------------------------------
===> End iabs(IRF )<>4
----------------------------------------------------------------------------
====> For iabs(IRF )=4 (integrated intensity data)
----------------------------------------------------------------------------
Line 11-6-1 Line 11-6-2 : CExt1, CExt2, CExt3, CExt4, CExt5, CExt6, CExt7
(7 reals)
Exti = Extinction parameter (i)
CExti = Code of the extinction parameter (i)
At present only the first extinction parameter is used.
===> End iabs(IRF )=4
----------------------------------------------------------------------------
Line 11-7-1 Line 11-7-2 : CA, CB, CC, CD, CE, CF :
(6 reals)
codewords for cell constants A, B, C, D, E & F defined
by :
1/d2 = Ah2 + Bk2 + Cl2 + Dkl + Ehl + Fhk
Note that these codewords do not refer directly to
the cell parameters; for instance, in the hexagonal
system, the last codeword CF must be the same as CA
and CB.
----------------------------------------------------------------------------
Line 11-8-1 NORI = 0, G1 = 0 means no preferred orientation
when NORI = 1, G1 = 1 means no preferred orientation
Pa1,..Pas4 =asymmetry parameters applied to angles below RLIM
(given on line 4 : see Mathematical section)
If NPHASE is negative only the first parameter is relevant.
----------------------------------------------------------------------------
Line 11-8-2 : CG1, CG2, CPas1, CPas2, CPas3, CPas4
(6 reals)
CG1, CG2 = codewords for preferred orientation parameters
CPas1,...CPas4 = codewords for asymmetry parameters
----------------------------------------------------------------------------
Line 11-8-3 RLIM .
----------------------------------------------------------------------------
Line 11-8-4* RATIO is negative.
--------------Comment line :
!Additional U,V,W parameters for Lambda2
----------------------------
----------------------------------------------------------------------------
Line 11-8-5* : CU2, CV2, CW2
(3 reals) Codewords of the additional U,V,W parameters
Read only if RATIO is negative.
----------------------------------------------------------------------------
TIME OF FLIGHT DATA ====> LINES 11-5-1 to 11-8-5 are substituted by the following lines for
TIME OF FLIGHT DATA
===============================================================================
Line 11-5-1: IstrainModel
(6 reals + 1 integer)
--------------Comment line :
! Scale Extinc Bov Str1 Str2 Str3 Strain-Model
---------------------------------------------------------------------------
Same parameters as in 11-5-1 for CW, except that GAM1 is replaced
by the extinction parameter EXT.
Line 11-5-2 : CS, FLEXT, CBov, CSTR1, CSTR2, CSTR3
(6 reals)
Codewords of the above parameters
----------------------------------------------------------------------------
Line 11-6-1: Line 11-6-2 CSig2, CSig1, CSig0, CXt, CYt, CZ1, CZ0
(7 reals)
Codewords of the above parameters
----------------------------------------------------------------------------
Line 11-6-3: Line 11-6-4 CGam2, CGam1, CGam0, CLStr, CLSiz
(5 reals)
Codewords of the above parameters
----------------------------------------------------------------------------
Line 11-7-1: Line 11-7-2 : CA, CB, CC, CD, CE, CF :
(6 reals)
Cell parameters and codewords as above.
----------------------------------------------------------------------------
Line 11-8-1: Line 11-8-2 : CG1, CG2, Calph0, Cbeta0, Calph1, Cbeta1
(6 reals)
Codewords of the above parameters
----------------------------------------------------------------------------
Line 11-8-3 : Abs1, CAbs1, Abs2, CAbs2
(4 reals)
--------------Comment line :
!Absorption correction parameters
----------------------------------
Abs1, Abs2 : Absorption correction parameters
CAbs1, CAbs2 : Codewords
The physical meaning of these parameters depend on
the function selected by IABSCOR (see Line 4)
----------------------------------------------------------------------------
=====================END=OF=SPECIFIC=INPUT=FOR=T.O.F.===========================
Line 11-8-6 Line 11-8-7* : CAhkl, CShf1, CShf2
Read only if JSOL=1
(3 reals)
CAhkl = codeword for hkl-dependent asymmetry parameter
CShf1, CShf2 = codewords for hkl-dependent shift parameters.
----------------------------------------------------------------------------
Line 11-8-8* : Sh1,Sh2,Sh3
--------------Comment line :
'Shift-cos(1) or Shift-sin(-1) axis' in the same line as the numbers
----------------------------
(3 reals) If Ishift= +/- 1, [Sh1,Sh2,Sh3] is the vector defining
the axial "shift-platelets".
----------------------------------------------------------------------------
Line 11-9* : Sz1,Sz2,Sz3
(3 reals) If IsizeModel= +/- 1, [Sz1,Sz2,Sz3] is the vector defining the
platelets.
----------------------------------------------------------------------------
Line 11-10-1* : St1,St2,St3
(3 reals) If IstrainModel =7, [St1,St2,St3] is the vector defining the
axial microstrain.
----------------------------------------------------------------------------
Line 11-10-2 IstrainModel > 8, 5 additional strain parameters
and codes.
--------------Comment line :
! 5 additional strain parameters (IstrainModel >8)
----------------------------
----------------------------------------------------------------------------
Line 11-11 Line 11-12 IFURT lines with further parameters introduced by
users, each line contains:
(A4,2 reals): NAMEPAR VALUEPAR CODEPAR
--------------Comment line :
! Further parameters:
----------------------------
----------------------------------------------------------------------------
Line 11-13 Line 11-14 Line 11-15 Line 11-16 LINE 12 NRELL lines containing the following items
(1 integer and 2 reals)
--------------Comment line :
! Hard limits for selected parameters:
----------------------------
NUMPAR, LowLIMIT, HighLIMIT
Where NUMPAR is the "number" of the parameter (as given
by the parameter code) to be constrained within the limits
specified by the interval [LowLIMIT, HighLIMIT]
For a proper use of this option one has to put limits
to the variable appearing for the first time with the
wished parameter code. This should have a positive sign
and a unit multiplier.
----------------------------------------------------------------------------
Line 12-1 ICRYG =2. The program tries NCONFG configurations
and select the best NSOLU solutions (lower R-factors) using
the first NREFLEX reflections of the file CODFILn.HKL.
If NSCALEF is different from zero, then the scale factor used
in the program is obtained from the relation:
Sum{Iobs}= Scale*Sum{Icalc}
A configuration means a set of NRELL values of the selected
parameters within the box defined in LINE 12.
The constraints established with the coding of parameters
have no the same meaning as with least-squares(LS). In LS
refinement for two variables having codes xx1.00 and xx0.5
the shift applied to the second variable is half the shift
applied to the first one irrespective of their initial values.
In Montecarlo search, the value of the second variable is
just half the value of the first variable. Only one parameter,
numbered here as "xx", controls the value of the two variables
either in LS or in Montecarlo searh.
----------------------------------------------------------------------------
LINE 13 IPL .ne.0 (line 3)
(2 integers)
--------------Comment line :
! Iscale Idif
----------------------------
ISCALE =counts per character position for observed and
calculated curves on line print plot
IDIF = counts per character for difference curve
----------------------------------------------------------------------------
LINE 14
3.- MATHEMATICAL INFORMATION 3.1: Calculated profile. Structure factors.
---------------------------------------------
Calculated counts yci at the ith step are determined by
summing the contribution from neighbouring Bragg reflections
plus the background :
yci = S SUM(Lh.Fh^2 .Omeg(Ti - Th).Ah.Th. Ph + ybi
where S is the scale factor
Lh contains the Lorentz, polarization and
multiplicity factors
Fh is the structure factor. The ratio of the
intensities for the two wavelengths is absorbed
in the calculation of Fh^2, so that only a
single scale factor is required.
Ah is the asymmetry function
Th is the transmission factor (line 4)
Ph describes the preferred orientation of the
sample
Omeg is the reflection profile function which
approximates the effects of both instrumental
and, possibly, specimen parameters.
ybi is the background intensity
------------------------------------------
Form-factor calculations and Refinements Magnetic scattering calculations 3.2: Background BKPOS - 1)^m) + SUM(Bcj sin[Qidj]/Qidj)
with 0<=m<=5 for NBCKGD =0, or 0<=m<=11 for NBCKGD =-3.
The origin of the background polynomial is given by a selectable
input parameter BKPOS (line 4) and should be supplied by the user.
The second sum (six terms) is used only if NBCKGR =-1. The parameter
to be refined are:
Bo,B1,...B5, Bc1,...Bc6, d1,...d6
Qi is given by Qi=4pi.sin(Thetai)/Lambda(1)
The parameters dj are distances in Angstroms.
The background can be also read from a supplied file FILE.BAC.
The actual background is calculated from the read background applying
the following formula:
Backg(2theta) = a * BackgRead [ (1+c) 2theta + d ] + b
The background parameters and codes, given in line 10-2*, correspond to
the coefficients of the above formula in the following order: a,b,c,d.
If a is given as zero, the program puts a=1. Limits against divergence
are fixed by program. The parameter c is allowed to vary up to a
maximum value abs(c)=0.1 and abs(d) is kept below 3 degrees (2theta).
The user can chek the excursion of those parameters out of the
allowed range when they are strictly zero and their standard
deviation is (fixed arbitrarily to) 0.99999.
This option is useful when complicated background shapes are present
due to sample environment.
A new procedure for treating the background has been introduced.
The background is ajusted iteratively at each cycle by using a
Fourier filtering technique. The starting background is read from
a file. At cycle "n" the new background is calculated from the old
one, cycle "n-1", with the formula:
Back(n) = Back(n-1) + Filtered[yobs-ycal](n-1)
where Filtered[yobs-ycal] is a strongly smoothed version
of yobs-ycal. The parameter controlling the smoothing is FWINDOW
which is equivalent to PST described in subroutine SMOOFT described
in Numerical Recipes (see ref 19). The implementation of SMOOFT in
FullProf is not the same as in ref 19.
When using this method it is wise to draw the final background
to see if it is really a smooth curve. This option is only
justifiable in cases of a very wavy background. The starting
background should be close to the real one.
----------------------------
3.3: Peak-shape functions NPROF (line 2).
The currently available functions are given above and their particular
definitions can be found in the literature.
---------------------------------------------------------
3.4: Monochromator, Lorentz and geometrical corrections CTHM and K in line 4);
the Lorentz polarization factor LP is calculated as :
LP = [1 - K + K .CTHM .cos(2Theta)^2]/2(sinTheta)^2.cosTheta
with CTHM = cos(2Thetam)^2. For instance with a Graphite
monochromator, CTHM = 0.8351 and 0.7998 for CuKb and CuKa
respectively.
Note that K is used only for synchrotron data (INSTRM =4,
or ILOR =3)and does not have to be input for other kind of
data:
- for neutrons, LP = 1/ 2sin2Theta.cosTheta i.e. K is ignored
- for characteristic X-Ray radiation (unpolarized beam)
the formula used is:
LP = [1 + CTHM .cos(2Theta)^2]/2(sinTheta)^2.cosTheta
that corresponds to the general formula above for K =0.5
multiplied by 2.
- for synchrotron radiation : K must be given (K ~ 0.1)
In the transmission geometry, flat plate with the scattering vector
within the plate (Stoe geometry for X-rays,ILOR =2)
the lorentz factor is:
L = 1/sin2Theta
and the polarization correction is given by:
P = K (1+ c1 cos2Theta^2)/(1+c1) + (1-K ) (1+ c2 cos2Theta^2)/(1+c2)
where c1= sqrt(CTHM ) = abs(cos(2Thetam))
c2= CTHM = (cos(2Thetam))**2
K = fraction of perfect crystal contribution
Note that the program, internally, calculates the Lorentz factor combined
with the absortion correction. A non-zero absorption coefficient (mt)
must be given to get correct results (see section 3.7 to know the total
correction for this case).
-----------------
3.5: Asymmetry RLIM in line 4) : the shape of the
peaks below RLIM is corrected using the semi-empirical function :
A = 1 - P.sign(2Thetai-2Thetah). (2Thetai-2Thetah)2 /tan2Thetak
where P is a refinable parameter.
The above formula for asymmetry correction has been removed from
the program. It was really very bad!. The expression given by
Berar & Baldinozzi (J.Appl.Cryst, 26, 128 (1993)) has been introduced
The asymmetry correction adopts now the form:
A = 1 + {P1 Fa(z)+ P2 Fb(z)}/tan Theta + {P3 Fa(z)+ P4 Fb(z)}/tan 2Theta
Where z = (2Thetai-2Theta-shift)/FWHM,
(Shift includes the zero-point and other shifting terms)
Fa(z)=2z exp(-z^2) , Fb(z) = 2(2z^2-3)Fa(z)
and has four independent parameters, which are read at the same
place as before.
If NPHASE <0 the method proposed by C.J.Howard, in J.Appl.Cryst.15
615-620 (1982), is used. The approximation of the convolution
integral is performed using the Bode's rule (Simpson formula for
five points). The profile is calculated as a superposition of five
profile functions (only pseudo-Voigt #5 and #7 are implemented for
this correction) calculated at displaced points:
Omega(x)={7g(x) + 32g(x+c2.P) + 12g(x+c3.P) + 32 g(x+c4.P) + 7 g(x+c5.P)}/90
Where x= 2Thetai-2Theta-shift, P is the asymmetry parameter and
cotan(2Theta) = 16.c2 = 4.c3 = 16/9.c4 = c5
----------------------------
3.6: Preferred orientation NORI = 0 --> The usual Rietveld function :
Ph = (G2+(1-G2)*exp(G1*a^2) )
where G1 and G2 are refinable parameters and
a is the acute angle between the scattering
vector and the normal to the crystallites
(platey habit).
Note that setting G1 to any number > 99.0 for
a phase causes the program to generate for
that phase only those reflections for which
d* is parallel to the preferred orientation
vector PREF specified in line 11.2.
NORI = 1 --> March's function
Ph = G2 + (1-G2) * ((G1cosa)^2 + (sina)^2/G1)^-1.5
where G1 is a refinable parameter. This expression is
adapted both to fiber and platey habits :
G1 < 1 platey habit ( a is the acute angle between
the scattering vector and the normal to the
crystallites)
G1 = 1 no preferred orientation
G1 > 1 needle-like habit (a is the acute angle between
the scattering vector and the fiber axis
direction)
Note that these values of G1 correspond to the
Bragg geometry of usual X-ray powder
diffractometer, for the Debye-Scherrer geometry
of most neutron powder diffractometers the
opposite holds.
The parameter G2 represents the fraction of the sample that
is not textured. The program put its value between 0 and 1
in case of divergence.
----------------------------------------
3.7: Absorption (and microabsoprtion) ILOR =2)
the absorption correction is implemented as:
Th = exp(-mt/cosTheta)/cosTheta
where t is the "effective" thickness of the sample. The product mt
is given in the same place as mR.
For Bragg-Brentano geometry in X-rays an angular-dependent
microabsorption correction has been introduced following reference 20.
The factor Th becomes:
Th ---> Th Sr = Th (1-P)
where Sr is given by the formula 6 of the first reference 20 (or
P is given by formula 17 of the second reference 20).
P = P0 * Cp * (Tau/sinTheta) * (1-Tau/sinTheta)
The limitations and degree of applicability of the above formula are
explained in reference 20.
-----------------------------
3.8: Systematic line shifts Bragg-Brentano parafocusing arrangement : the two largest systematic
aberrations of Theta-2Theta powder diffractometers operating in this geometry
arise from specimen displacement and transparency; the sample
displacement error is one of the largest systematic error affecting
line positions in this geometry. It is given by:
D2Theta = -2s/R cosTheta [in radians]
where s is the displacement of the sample surface with respect to the
axis of the goniometer and R the radius of the goniometer circle.
The negative sign means that a displacement away from the center of
the focusing circle moves the diffraction lines to lower 2Theta angle.
The refinable parameter is SYCOS = -2s/R. This is by far the largest
systematic aberration in this geometry. As the angles are expressed
in degrees in FullProf, the sample offset can be calculated as:
s = pi.R.SYCOS/180
The transparency correction is given by the relation:
D2Theta = 1/(2mR) sin2Theta [in radians]
where m is the linear absorption coefficient of the sample.
This relation holds in the case of thick absorbing samples and the
refinable parameter is SYSIN = 1/(2mR). For thin transparent samples,
the correction would write:
D2Theta = t/R cosTheta [in radians]
where t is the sample thickness; this (less usual) correction is not
explicitly included in the code but can be accounted for by the
displacement correction which turns out to show the same 2Theta dependency.
Note however that samples requiring that kind of correction would also
give biased integrated intensities; correction for this effect is not
implemented in FullProf. For further details on systematic aberrations
in Bragg-Brentano geometry, see [13].
b) Debye-Scherrer : the largest shifts of Debye-Scherrer rings result from
sample off-centering and absorption. Eccentricity perpendicular to the
incident beam direction is normally a second order effect if both sides
of the Debye-Scherrer ring are measured.
If only one side of the cone is measured, the line shift takes the form:
D2Theta = e/R cosTheta [in radians]
where e denotes the eccentricity, that is the refined parameter is
SYCOS = e/R.
Eccentricity in the incident beam direction is observed in both cases
and takes the form:
D2Theta = e/R sin2Theta [in radians]
i.e., the refined parameter is SYSIN = e/R. The correction is negative
for a shift along the beam direction towards the detector.
For highly absorbing specimen with radius r, diffraction is limited to
a cylindrical surface layer resulting in a maximum peak shift:
D2Theta = r/R cosTheta [in radians]
i.e., in this case, SYCOS = r/R. The latter effect also leads to
disymmetrical line profiles.
c) Curved position sensitive detector with flat plate sample : for the
asymmetric geometry of diffractometers using a curved position sensitive
detector (CPSD) with a flat-plate sample, the displacement correction
takes the form:
D2Theta = -s/(R.sina) sin2Theta [in radians]
where R is the radius of the CPS and a the incident beam angle
(in degrees) at sample surface. Thus, the parameter refined by FullProf
is SYSIN = -s/(R.sina). The negative sign means, as in the case of
Bragg-Brentano geometry, that a displacement away from the center of
the focusing circle moves the diffraction lines to lower 2Theta angle; the
value of the sample offset is given by:
s = pi.R.SYSIN.sina/180
------------------
3.9: Codewords 3.10: Standard deviations 3.11: Method of refinement 3.12: Agreement factors 3.13: Analysis of the refinement
4.- ADDITIONAL NOTES 4.1: Magnetic Refinements
---------------------------
For a conmensurate structure two descriptions of the magnetic
structure are possible: the general formalism using fourier
components of magnetic moments through the propagation vectors or
a crystallographic-like description using the magnetic unit cell.
The most simple one, for a non-expert user, is to describe the
magnetic structure in the magnetic unit cell. In that case two
important points must be taken into account:
a) For magnetic structures described in a magnetic unit cell larger
than the crystallographic cell, the coordinates of atoms must be
changed consequently, as well as the unit cell parameters.
The codes for common (or related) parameter with the crystallographic
counterpart, must be changed applying a the correct multiplicative
factor. It is worth stressing that codes for cell parameters are
actually applied to the "cell constants" defined by:
1/d2 = Ah2 + Bk2 + Cl2 + Dkl + Ehl + Fhk
Therefore, if you are dealing with an orthorhombic structure
which has a magnetic structure with propagation vector k=[1/2 0 0]
you have to use the magnetic unit cell 2xa, b, c and if the codes
of the crystallographic unit cell a,b,c are for example:
Cell a b c 90 90 90
CodeCell 81.00 91.00 101.00 0 0 0
the corresponding values for the magnetic counterpart are:
Cell 2a b c 90 90 90
CodeCell 80.25 91.00 101.00 0 0 0
the reason is that the crystallographic cell constant A is
in this case: Ac=1/a**2 and the magnetic cell constant is
Am=1/(2a)**2= 0.25*Ac. As explained above, the multiplicative
factor is applied to shifts of parameters.
b) The scale factors of the crystallographic and magnetic parts
have to be related in some way in order to get good values
of magnetic moments. This relation depends on the way the
users describes the magnetic structure, however several rules
can be useful to avoid bulk errors:
i) Use the correct occupation numbers in the crystallographic
part (=multiplicity of special position/general multiplicity)
ii) The number of magnetic atoms in the chemical unit cell must
coincide with the description above, therefore the occupation
numbers in the magnetic part are related to the number of
symmetry operators given, the centrosymmetry (or not) of the
magnetic structure.
If these requirements are satisfied and the magnetic unit cell
is the same as the chemical one, the scale factors are strictly
the same numbers; and, therefore represents the same parameter
with a shift equal to unity.
If the magnetic unit cell is a multiple one, and the above
requirements are satisfied, the relation between the scale
factors is a multiplicative factor given by:
Sc: crystallographic scale factor
Sm: magnetic scale factor
Sm = 1.0/(Volm/Volc)**2 Sc
In the case of large magnetic cells it can be more convenient to modify
the occupation numbers of magnetic atoms in such a way that the two scale
factors coincide.
For incommensurate magnetic structures the general formalism must be applied.
When the magnetic structure is described using the formalism of propagation
vectors, the components Mx,My,Mz no longer represent true magnetic moments.
The user should be cautious in interpreting the output files. The modulus of
the "magnetic moment" represent the Fourier component modulus of an atomic
magnetic moment which have to be calculated externally. The calculation of
the intensity is based on the expression of magnetic structure factor given
in mathematical section, therefore the user knows how to play with his input
items in order to obtain physically sound results.
For spherical description of the magnetic moments the following must be
taken into account:
The orthonormal system with respect to which are defined the
spherical angles verifies:
X axis coincides with the crystallographic A
Y axis belongs to the plane A,B
Z axis is perpendicular to the plane A,B
The particular implementation of spherical components in magnetic
structure refinements is that Z axis must coincide with C. That
works in all crystallographic systems except for triclinic. The
monoclinic setting must be changed to -> 1 1 2/m to satisfy the
above prescription.
--------------------------
4.2: Propagation vectors 4.3: Microstrains NPROF =7 must
be used. Only in that case can be performed a correct convolution of the
instrumental function with the intrinsic profile function (considered both
as Voigtians). In the case NPROF =7, isotropic lorentzian and gaussian contri-
butions of size and microstrains are represented by the following parameters:
Gaussian component Lorentzian component
Size: sqrt(IG) Y
Strain sqrt( U) X
The FWHM of the gaussian and lorentzian components of the Voigt function
for NPROF =7 is calculated using the expressions:
FWHM^2(gaussian) = [U + c.DST(STR)^2] * Tan^2(Theta) + V * Tan(Theta)
+ W + IG/cos^2(Theta)
FWHM(lorentzian) = X tan(Theta) + (Y + F(SZ))/cos(Theta)
The isotropic particle size broadening Y provides a size value given by:
size(lorentzian) = 180 K Lambda /(pi.Y) (Lambda & size in A)
K = FWHM/Integral-Breadth = 2/pi for a lorentzian
(with such value for K, size represent the volume averaged diameter
of crystallites in all directions)
For anisotropic contributions {DST(STR) and F(SZ)} the actual version of
FullProf has the following set of microstructural models:
Size effect:{only lorentzian component is taken into account for anisotropic
broadening of size origin through F(SZ)}
ISTR=0 and IsizeModel /= 0 {Integer to select a particular model for F(SZ)
in subroutine SIZE}
IsizeModel = 1 Platelet coherent domains. F(SZ) is assumed to
be of the form F(SZ)=SZ*cos(phi), where SZ is the refined
parameter and phi is the acute angle between the scattering
vector (h,k,l) and the vector defining the platelet
shape of domains {[Sz1,Sz2,Sz3] in line 11-9*}
IsizeModel =-1 Needle-like coherent domains. F(SZ) is assumed to
be of the form F(SZ)=SZ*sin(phi), where SZ is the refined
parameter and phi is the acute angle between the scattering
vector (h,k,l) and the vector defining the needle
shape of domains {[Sz1,Sz2,Sz3] in line 11-9*}
IsizeModel = 2 to 7, in these cases the broadening is considered only
for reflections of the form: (00l),(0k0),(h00), (hk0),
(h0l) and (0kl). The function is: F(SZ)=SZ.
IsizeModel =8 Only satellites reflections are considered to be broadened.
In this case also F(SZ)=SZ.
IsizeModel =9 Reflections (HKL) with H=2n+1 and K=2m+1 are broadened.
In this case also F(SZ)=SZ.
IsizeModel =10 Reflections (H0L) with H+L=2n are broadened.
In this case also F(SZ)=SZ.
IsizeModel =11 Reflections (HKL) except (HHL) are broadened.
In this case also F(SZ)=SZ.
IsizeModel =12 Reflections (HKL) with H=2n+1 are broadened.
In this case also F(SZ)=SZ.
IsizeModel =13 Reflections (HKL) with H=2n and K=2m+1 are broadened.
In this case also F(SZ)=SZ.
ISTR > 1 : A generalized formulation of the size effect is applied and the
size parameters (up to six) are given in line 11-14*.
In that case the F(SZ) function is given by:
F(p1...p6) = 180 Lambda/(pi^2) * d(hkl)^2* Quad(p1...p6)
Quad = p1 h^2 + p2 k^2 + p3 l^2 + 2 (p4 hk + p5 hl +p6 kl)
where the size parameters are p1,p2,...p6.
This formulation assumes that the average diameter can be
expressed as an ellipsoid of refinable parameters p1..p6. Therefore
= d(hkl) * Quad
Strain effects:{only gaussian component is taken into account for anisotropic
broadening due to strains through DST(STR)}
ISTR=0 and IstrainModel /=0 {Integer to select a particular model for DST(STR)
in subroutine STRAIN}
FWHM(strain) = DST tanTheta = c Sigma(1/d^2)/(1/d^2) tanTheta
the constant c is equal to 2 sqrt(Ln2) (180/pi). In the program the
effective value used is c*10e-3, therefore it is necessary to divide
the refined strain parameters by 1000. The user can consult the modules
FDUM's.FOR for details and reference 17.
IstrainModel = 1 Orthorhombic strain in a tetragonal lattice.
Refined parameter STR1.
IstrainModel = 2 Strain along "a" in an orthorhombic lattice.
Refined parameter STR1.
IstrainModel = 3 Strain along a diagonal of the ab plane in an orthorhombic
lattice for which an equivalent monoclinic double cell has been used.
Refined parameter STR1.
IstrainModel = 4 Same as 3 but strains along the two diagonals.
Refined parameters STR1, STR2.
IstrainModel = 5 Strain in an orthorhombic lattice with fluctuations along
"a" and "b" and correlation between "a" and "b".
Refined parameters STR1, STR2, STR3.
IstrainModel = 6 Strain in an orthorhombic lattice with fluctuations along
"a", "b" and "c" and corr(a,b)=-1, corr(a,c)=1, and
corr(b,c)=0.
Refined parameters STR1, STR2, STR3.
IstrainModel = 7 Uniaxial microstrain. DST(STR) is assumed to be of the
form DST(STR)=STR1*cos(phi), where STR1 is the refined
parameter and phi is the angle between the scattering
vector (h,k,l) and the vector defining the axial direction
of strains {[St1,St2,St3] in line 11-10*}
IstrainModel = 8 General anisotropic strain of hexagonal symmetry.
(See ref. 17)
STR1= Saa=Sigma(A), STR2= Scc=Sigma(C) STR3= Cac=Correl(A,C)
1/d^2 = SQ = A (h^2+k^2+hk) + C l^2 = A m^2 + C l^2
Var(SQ)= Saa^2 m^2 + Scc^2 l^4 + 2 Saa Scc Cac m l^2
FWHM^2 (strain)= Var(SQ) (P/SQ)^2
{P=180/pi*sqrt(8Ln2) 1.E-03 tan(theta)}
IstrainModel = 9 Strain adapted for compounds LaNi5-like. Formula by:
P.Thompson et al, J.Less Comm Met 129, 105-114 (1987)
Four param.: Gaussian FWHM=Sqrt(Sumj[S(j)]) tan(theta)
STR1 -> S(1) = x Par(1)
STR2 -> S(2) = l^4 /(h^2+k^2+l^2) x Par(2)
STR3 -> S(3) = (h^2 k^2+k^2 l^2)/(h^2+k^2+l^2) x Par(3)
STR4 -> S(4) = h^2 k^2 /(h^2+k^2+l^2) x Par(4)
IstrainModel =10 General anisotropic strain for orthorhombic symmetry.
(See ref. 17)
6 strain parameters corresponding to :
STR1=Saa=Sigma(A), STR2=Sbb=Sigma(B), STR3=Scc=Sigma(C),
STR4=Cab=Corr(A,B), STR5=Cac=Corr(A,C), STR6=Cbc=Corr(B,C)
Where:
SQ = A h^2+ B k^2 + C l^2
Var(SQ)= Saa^2 h^4 + Sbb^2 k^4 + Scc^2 l^4 +
2 Saa Sbb Cab h^2 k^2 +
2 Saa Scc Cac h^2 l^2 +
2 Sbb Scc Cbc k^2 l^2
FWHM^2= Var(SQ)(P/SQ)^2
{P=180/pi*sqrt(8Ln2) 1.E-03 tan(theta)}
IstrainModel =11 General anisotropic strain for monoclinic symmetry being
the setting gamma/=0 (2-fold axis along 001)
(See ref. 17)
{limited to 8 parameter by putting arbitrarily zero
two correlation values (Cad=Cbd=0)}
8 strain parameters corresponding to :
STR1=Saa=Sigma(A), STR2=Sbb=Sigma(B), STR3=Scc=Sigma(C), STR4=Sdd=Sigma(D),
STR5=Cab=Corr(A,B), STR6=Cac=Corr(A,C) ,STR7=Cbc=Corr(B,C), STR8=Ccd=Corr(C,D)
Where:
SQ = A h^2+ B k^2 + C l^2 + D hk
{ Saa^2 SaaSbbCab SaaSccCac 0 } (h^2)
{ SaaSbbCab Sbb^2 SbbSccCbc 0 } (k^2)
Var(SQ)=( h^2, k^2,l^2,hk){ }
{ SaaSccCac SbbSccCbc Scc^2 SccSddCcd} (l^2)
{ 0 0 SccSddCcd Sdd^2} (hk)
FWHM^2= Var(SQ)(P/SQ)^2
{P=180/pi*sqrt(8Ln2) 1.E-03 tan(theta)}
ISTR=1,3 The generalized formulation of the strain broadening is used
and 10 parameter are read in line 11-13*. The formalism is
that described in reference 17. The strain parameters correspond
to the fluctuations and correlations of direct cell parameters.
The lower symmetry is monoclinic with the conventional setting.
The hexagonal lattice is treated as a special case.
Strain parameters: Px = sigma(x), x,y = a,b,c, beta
corr(x,y) = sin(Pxy)
The parameter Pxy is an angle in degrees. This particular description
is for taking into account that corr(x,y)=covar(x,y)/(sigma(x).sigma(y))
and must belong to the interval [-1,1]. The strain parameters are read
in the following order:
Pa, Pb, Pc, Pbeta, Pab
Pac, Pabeta, Pbc, Pbbeta, Pcbeta
Note:
-----
In some cases the use of size-strain options of the program, the computing
time is greatly increased. This is related to the fact that the number
of reflections contributing to each particular point of the diagram
increases because the broadening is quite important. An excessive
computing time may indicate a divergence of the refinement that has
attributed a too much large FWHM to some reflections.
------------------------------------
HKL-dependent shifts and asymmetry. JFOU is set to zero y the program.
------------------------------------
4.4: Quantitative phase analysis 4.5: User-supplied parameters NPHASE
The index J represents different atom parameters
J=1,2,3 : (x,y,z) fractional coordinates
J=4 : B isotropic temperature factor
J=5 : Occ. Occupation factor.
J=6....8: (Mx,My,Mz) Magnetic moment components
9...11: (Mxi,Myi,Mzi) Imaginary Magnetic moment components
J=12 : MPhas Magnetic phase of the atom
J=13..18: (betas11,22..) Anisotropic thermal factors
J=19..32: Coefficients of generalized form-factors
These atomic parameters can be used by the subroutines STRMOD and MAGMOD
for other purposes.
Moreover, there are other non-atomic parameters which can be used also for
defining generalized coordinates. They are internally stored in the array
PAR(K,J) where the index K run over the phases and J represents different
parameters:
PAR(K,J):K=1,2,....NPHASE
J=1 : S Scale factor
J=2 : Bov Overall temperature factor
J=3,4,5 : U,V,W Halfwidth parameters
J=6,..11 : A,B,C,D,E,F Cell constants
J=12,13 : G1,G2 Preferred orientation parameters
J=14 : As1 First Asymmetry parameter
J=15,16 : X,Y Shape parameters (depend on NPROF )
J=17 : eta(m) Shape parameter of p-Voigt(Pearson)
J=18..27 : Str1...Str10 Strain parameters
J=28 : IG Isotropic gaussian size parameter
J=29..34 : Siz1...Siz6 Anisotropic size parameters
J=35,36,37 : As2,As3,As4 Additional asymmetry parameters
J=38 : Asymhkl HKL-dependent asymmetry parameter
J=39,40 : Shf1,Shf2 HKL-dependent shift parameters
J=41,42 : Shap1,Shap2 Additional shape parameters
J=43,44,45 : U2,V2,W2.. U,V,W parameters for lambda(2)
J=46,47,48 : Ud,Vd,Wd U,V,W for right part of SpV(x)
J=49,50 : Eta0d, Xd Eta and X for right part of SpV(x)
J=51,..59 : CYi Coeffs. of Spherical Harmonics (size broad.)
J=60..MPAR : P1,P2,.... User-supplied parameters
LASTMPAR=59 Number of the Last parameter used
internally. To be used as offset
for user-supplied subroutines.
----------------------------------------------------------------------------
4.6: Examples of user-supplied CRYSTAL STRUCTURE REFINEMENTS
In FullProf the default JBT =4 option is an updated subroutine written
by V.Rodriguez which handles rigid body objects.
Guide for the
General Rigid-Body-Constraints/TLS Subroutine
for Rietveld Refinements
**********************
V1.4 (January 1997)
Dr V.Rodriguez
Laboratoire de Spectroscopie Moleculaire et cristalline *
(U.A.124 CNRS)
Universite de Bordeaux I, 351 cours de la Liberation
F-33405 TALENCE Cedex
Tel : (33) 56.84.63.61
Fax : (33) 56.84.84.02
* UMR Physico-Chimie Moleculaire since January 1st 1997
For further details see
"A routine for crystal-structure refinements based on rigid-body
model with constrained generalized coordinates and mean thermal
displacements"
Rodriguez V. and Rodriguez-Carvajal J.,
J. Applied Cryst., (to be published)
*********************
In the present version of Fullprof the default JBT =4 option refers to a
subroutine which handles rigid body objects. Here we give a short guide in
order to facilitate the use of this subroutine. This routine should be used
with caution and the user should be familiar enough with "conventional"
Rietveld refinements. The subroutine is still under improvement. At this
time, all the options have been well tested except option Nr 4 (see below).
I acknowledge all suggestions and notifications of possible bugs found in
the program.
It should be pointed out that option JBT =4 is not restricted to
"perfect" rigid-body-groups. In the standard definition of Rietveld atomic
positions, reduced coordinates are used. Within this subroutine, molecules
or atomic groups are defined by spherical internal coordinates and six
additionnal parameters, which define the groups position and orientation
in the crystal.
In addition, this extended version of Rietveld refinement allows to distort
groups in a final refinement step if required.
Note: Each parameter refering to the orthonormal crystal system is
recognized by the appended "c".
Each parameter refering to the orthonormal molecular system is
recognized by the appended "m".
A-Description of the parameters
*******************************
- Any kind of rigid body groups built from atoms can be generated.
- All parameters described below are refinable except optional
parameters P6 (always true) and P16 (specific to "satellite" rigid body
groups).
- Each group of atoms (rigid body group, RBG) is identified by 1 or 2
letters and a number from 1 to 99 (both compatible with the standard DBWS
format and the free format of Fullprof). The number indicates that a RBG is
defined. The label(two letters max.) and the number of the atom must not be
separated.
- Representation of RBG is performed as follow :
1) Definition of the isolated group in an orthonormal molecular
system. Each atomic position (xm,ym,zm) is defined through
spherical coordinates (dm=distance, thetam, phim). The centre
of this molecular system may or may not coincide with an atom.
2) Definition of the absolute position (Xc,Yc,Zc) and orientation
(angles THETAc, PHIc and CHIc) of the molecular orthonormal
system in the crystallographic orthonormal system. These are
standard EULER angles definitions.
In this way, each group is entirely defined within a crystal.
- Anti-clockwise rotations are always applied to spherical angles.
These standard spherical angles are defined as follow :
THETAc / thetam : inclination with respect to the Zc/zm axis of the
corresponding orthonormal system [-Pi, Pi].
PHIc / CHIc and phim: rotation around the Zc/zm axis of the corresponding
orthonormal system [0, 2*Pi].
- The orthonormal crystallographic system, with respect to which the
spherical angles THETAc, PHIc and CHIc of any RBG are defined, fulfills
the following conditions:
Xc axis coincides with the crystallographic direction a
Yc axis belongs to the plane (a, b)
Zc axis is perpendicular to the plane (a, b) (parallel to c*)
One can imagine how to place a rigid molecule in the correct position in the
unit cell by making the following operations:
- The RBG has been completely defined by the spherical coordinates
(dm,thetam,phim) of each atom in the internal orthogonal system, that
coincides at the beginning with the orthogonal crystallographic system.
- Perform a rotation CHIc of the whole RBG around the zm axis of matrix:
( COS(CHIc) -SIN(CHIc) 0 )
M1= ( SIN(CHIc) COS(CHIc) 0 )
( 0 0 1 )
- Perform a rotation of the wole RBG inclining their z-axis to
the angles THETAc and PHIc of matrix:
( COS(THETAc)*COS(PHIc) -SIN(PHIc) SIN(THETAc)*COS(PHIc) )
M2= ( COS(THETAc)*SIN(PHIc) COS(PHIc) SIN(THETAc)*SIN(PHIc) )
( -SIN(THETAc) 0 COS(THETAc) )
- Translate the origin of the RBG to the position (Xc,Yc,Zc) which are
transformed in reduced coordinates (xo, yo, zo) with xo=Xc/a, yo=Yc/b,
zo=Zc/c
- "Free atoms" (unconstrained or isolated) can be added with number 0
or without number. Each isolated atom has the same definition of
parameters as described in the Fullprof manual (see lines 11.4.1 and
11.4.3 of the Fullprof guide). Current information about "free atoms"
is printed to the screen when parameter P6 (see below) is set to any
negative value. Note that the following parameters: P6, P7, P8, P15
and P16, are obsolete in this case.
- Rigid body satellite groups (RBSG) can be also included in this
version, for example a methyl group within a rigid group such as
[N(CH3)4]+(tetramethyl ammonium). The definition and the structure
of the parameters are almost the same as those for a main RBG. The
coordinates of the centre of the satellite group should not be specified
since they are specified through the knowledge of its absolute position
in the input file "x.pcr". The orientation THETAc,PHIc of satellites
groups is also defined following the value of parameter P16 of the 1st
satellite atom (see below, option abs(P6)=2).
One easy external degree of freedom of the RBSG is the rotation around
the z-molecular axis i.e. the N-C bond. This degree of freedom is
accesible through the EULER angle PHIc that can be refined.
- All output is identical for isolated and/or constrained atoms.
- Every atom has 16 items stored in (X(Iphase,j),j=1,16) and each
parameter is denoted here as P1, P2, ...P16. The reading of these
parameters is described in lines 11-4-1 and 11-4-3 of the Fullprof
guide.
Example:
P1 P2 P3 P4 P5 P6 P7-THETAc
P8-PHIc
TD1 N .38900 .54090 .28796 4.00000 0.16667 1.000 -.290 .142
.00 .00 .00 .00 .00 .00 71.00 61.00
1.49300 1.57080 -.95532 .33333 .66667 .25000 1.04100 0
.00 .00 .00 .00 .00 .00 51.00
P9-dm P10-thetam P11-phim P12-xo P13-yo P14-zo P15-CHIc P16
x y z
TD2 C .47744 .84054 .28796 4.00000 0.16667 .000 .000 .000
.00 .00 .00 .00 .00 .00 .00 .00
.75000 1.57080 1.57080 .00000 .00000 .00000 .00000
.00 .00 .00 .00 .00 .00 .00
P9-dm P10-thetam P11-phim
x y z
O O .28146 -.04125 .41456 .00000 1.00000 -1.000 .000 .000
.00 .00 .00 .00 .00 .00 .00 .00
.03957 .07078 .09069 .00314 .01571 -.01501 0
.00 .00 .00 .00 .00 .00
beta11 beta22 beta33 beta12 beta13 beta23
-> In a RBG (here, the generic name is TD) each atom (TD1 and TD2)
has its internal coordinates stored in the following items:
distance to the centre dm : P9
Spherical angle thetam : P10
Spherical angle phim : P11
The atomic reduced cordinates are only for information with option 1
(RBG), see below for details.
Reduced coordinate x : P1
Reduced coordinate y : P2
Reduced coordinate z : P3
The parameters P4 and P5 have their usual meaning for each atom:
Isotropic temperature factor: P4
Ocupation number : P5
-> The first atom of each RBG (atom No 1, here TD1) contains the fractional
coordinates (xo, yo, zo) of the centre of the RBG (P12, P13, P14) and
the three EULER orientation angles THETAc, PHIc and CHIc (in radians,
respectively P7=-.290, P8=.142 and P15=1.041) of the whole group.
Here, the centre of the RBG does not coincide with an atom (N or C in
this example) since the first atom has a non zero value dm=P9=1.493.
Of course, it is possible to build a RBG with an atom coinciding with
the centre of the RBG.
-> The third atom (oxygen, Number 0 (or none which is equivalent to 0)) is
unconstrained ("free atom") and its items are the standard ones : here,
reduced coordinates (x, y, z) + atomic temperature parameters (betaij).
-> No terminal output is required for the whole RBG TD (P6>0).
Terminal output at each cycle is required for "free atom" oxygen
(P6<0).
B-Practical details
*******************
1- The item abs(P6) of the first atom indicates the option selected.
If P6<0, the current information is printed on the screen
and in the file CODFIL.OUT.
(file x.out). If the value of P6 is 0 for a RBG, the parameter
defaults to "1", corresponding to the standard RBG option.
2- The distance are expressed in the same unit as wavelength and cell
parameters (usually in angstroms) and the angles are always
expressed in radians:
3- The listing of the different options is a function of the main
optional parameter P6. In the following, the temperature parameters
are exclusively Boveral or Biso (isotropic Debye-Waller factors)
except for TLS option with abs(P6)=5.
abs(P6)= 1.0x : Normal rigid body option.
If x=1 the fractional coordinates of the center
of mass is output. That supposes that every atom
of the Molecule has been given explicitely in the
asymmetric unit.
2.xx : Satellite group (RBSG) option (Int(abs(P6))=2).
The integer value xx=100*(int(abs(P6))-2) gives the
absolute number of the reference group (as they
appear following the writing order, whatever the
number of phase).
--> The parameter P15 is assigned to the rotation CHIc
of RBSG as for RBG.
--> The parameter P16 of the first atom of the RBSG is
defined as follows: P16 = N1.N2 with
N1= Int(P16) : Nr of the first reference atom
of the reference RBG.
N2=100*(P16-Int(P16)): Nr of the second reference atom
of the reference RBG.
N1: Centre of the RBSG
N2: Optional (if N2 is given then N1-N2 defines
the internal z-axis)
Example: 3.02 1st reference atom = Nr 3
2nd reference atom = Nr 2
Atom Nr 3 is the centre of the RBSG and the
z axis of the RBSG is oriented in the
direction: atom Nr 2-> atom Nr 3.
Of course, the (xo, yo, zo) fractional coordinates of the
RBSG are not needed. The program calculates automatically
the corresponding values.
a) If the second atom is defined (N2#0), the
spherical angles of the RBSG are calculated from
these two reference atoms.
b) If the second atom is not defined (N2=0), the
centre of the main RBG is taken as the second
reference atom of the RBSG.
c) If N2=N1, the spherical orientation angles of the
RBSG are those of the main reference RBG.
Apart from these constraints, a RBSG is treated as
a normal RBG with as many atoms as desired. The
refinement of the centre of the RBSG as well as the
orientation angles THETAc and PHIc are performed in
the main RBG.
3.0x : The spherical coordinates (parameters P9, P10 and
P11) are generated from the reduced coordinates (P1,
P2 and P3) at the first cycle. Then the parameter
P6 is automatically set to 1 and the sign of the
option is kept i.e. the next option is RBG.
For selecting the internal orthogonal system the
user has to give in the parameters (P12,P13,P14)
the origin of the intenal orthogonal frame and in
(P9,P10,P11) the coordinates of an atom (that may
be fictitious) for defining the plane "xz".
The (P1,P2,P3) coordinates of the first atom defines
the z-axis of the internal frame, which is in the
direction V3=(P1-P12,P2-P13,P3-P14) in the
conventional crystal frame (fractional components).
the "y" axis in perpendicular to the plane "xz"
defined by the vectors:
V3=(P1,P2,P3)-(P12,P13,P14) -> z-axis
V1=(P9,P10,P11)-(P12,P13,P14) -> within the xz plane
y-axis is in the direction V3 x V1
This option is very usefull as it facilitates
the use of standard input file with JBT #4, the
conversion of published structures into spherical
internal coordinate systems, etc...
If x=1 the fractional coordinates of the center of
mass is output as in option 1.
4.xx : Option to generate an idealized molecule like
aliphatic chains, planar or helicoidal molecules...,
where xx is the number of atomic planes along the
RBG Zc axis which is the reference axis.
The spherical coordinates are calculated from three
parameters P9,P10 and P11. These parameters are
lost after processing. They are defined as:
P9 - distance of one atom to the center of the axis
P10 - angle between two atoms lying in consecutive
planes and the corresponding mid-point lying
along the Zc-axis.
P11 - order of the generating axis (integer)
Examples: 1-For an aliphatic chain Cn along Zc in the
(Xc, Zc) plane (conformation all trans).
distance = 1.54/2. (angstroms)
angle = 114.*pi/180. (radians)
axis order = 2
2-For benzene lying in the plane (Xc, Yc)
distance # 1.40*2. (angstroms)
angle = 0.*pi/180. (radians)
axis order = 6
The parameter P15 is assigned to CHIz as in the RBG
option and the parameter abs(P6) is set to 1 in the
1st cycle, the sign of the option is kept.
Therefore, the generated group is treated as a
normal RBG in the next cycles.
Remark : Further improvements are schedduled for this
option which is not very trustly at the present
time.
5.0x : TLS option for RBG including satellite groups, if
any. This TLS version is based on the formalism
of V.Schomaker and K.N.Trueblood, Acta Cryst.(1968),
B24, p-63. In this case, the refinement is performed
with the so called one step process i.e. atomic
positions and temperature factors TLS are refined
together.
The origin of the main RBG MUST be the centre of
mass of the entire group concerned !!! The
subroutine calculates the centre of mass of the
molecule if x=1. This option MUST be set when the
centre of the group does not coincide with the
centre of mass. In this case, make sure that all
atoms constituting the RBG are defined in the input
file since the RBG option does not generate atomic
positions. Such a situation can occur in non-centro-
symmetric space group, as in urea SPG: P -4 21 M ,
since the molecule is located on a C2v site (mm.).
Here, one must enter the entire molecule in the
asymmetric unit.
The elements of the T(6), L(6) and S(9) matrices
are read in "further parameters IFURT " (see
Fullprof guide, line 11.12) following the usual
order ie. 11 22 33 12 13 and 23 for T and L. As
the S matrix is not symmetric, 9 elements can be
required in the general case. The six first elements
are as defined previously, and the three last ones
are respectively S21, S31 and S32.
Similarly to the atomic temperature parameters
betaij, the components of the TLS matrices have
symmetry constraints, which are imposed by the
symmetry of the crystallographic site (not the
molecular symmetry !). These symmetry relations
can be found in the paper by Schomaker and
Trueblood (1968).
The T elements are expressed in angstroms^2, the L
components in radians^2 and the S ones in angstroms*
radians. For convenience, the output to the screen
and to unit 7 (x.out) of the TLS components are
expressed in the following units: angstroms^2 for T,
in degrees^2 for L and degrees*angstroms for S.
Remark : When using this option, one refines the
observed structure factors by assuming that the
atomic temperature factors are constrained ab initio
to satisfy the rigid-body hypothesis. It is well-
known that the RBG/TLS can greatly reduce the
number of atomic and thermal parameters, especially
when the molecule is located at a site of high
symmetry, but the user should be familiar enough
with the TLS hypothesis not to perform inconsistent
refinements.
4- It is advised to use specific rigid body refinement codes as damping
parameters,especially for the rotational parameter which need to be
currently three time higher than the other ones. It is highly
recommended to use the options with screen output (P6 with a negative
value) to control each RBG refinement steps since good constrained
refinements are not so easy to perform.
5- Concerning the refinements: when a main RBG has satellites groups,
the derivatives of the general RBG parameters, i.e. the 3 orientation
angles THETAc, PHIc and CHIc and the coordinates (xo, yo, zo) of the
centre of the group, contain the contributions of the satellites groups.
In contrast, the derivatives of the internal spheric parameters do not
account for these contributions.
6- When this subroutine is used, three additionnal files of fixed names
are created at the end: x#.m, x#.bs and x#.ortep (where # stands for the
number of the phase), containing atomic parameters in a format
suitable to be used with well-known software packages (Molview, Balls
&Sticks and ORTEP). Note that files for Molview are directely
executable. The output for the two other software are incomplete in
the sense that they contain either cartesian coordinates (Balls&
Sticks) or reduced coordinates + atomic temperature parameters
(ORTEP) of atoms located in the asymmetric unit.
MAGNETIC STRUCTURE REFINEMENTS
In the present version of FullProf the default JBT =5 option corresponds
to the calculation of the magnetic structure factor for a conical magnetic
structure. The magnetic intensities are calculated following standard
formula as given, for instance, in the paper by J.M.Hasting & L.M.Corliss
published is PhysRev 126(2),556 (1962). No symmetry operation can be
introduced: all the magnetic atoms within a primitive unit cell must
be given (constraints have to be introduced through the codes of the
parameters). The subroutine MAGMOD, in this case, does not take into
account symmetry for calculations (see the modules FDUM's.FOR for details).
However ISYM must be set to 1, the value of the four parameters
MULT , ICENT , NLAUE , NMAGR should be: 0 1 1 0.
The atom parameters correspond to the following variables:
-> P1,P2,P3,P4 and P5 correspond to x,y,z,B,occ of the atom
-> P6 is the magnetic moment of the atom (in Bohr magnetons)
-> P7 is the half-angle cone of the atom (degrees)
-> P8 is the magnetic phase of the atom (in fractions of 2 pi)
-> P9 of the first atom correspond to Phi (degrees)
-> P10 of the first atom correspond to Theta (degrees)
(Phi,Theta) are the spherical angles(degrees) of the cone axis
The orthonormal system with respect to which are defined the
spherical angles verifies:
X axis coincides with the crystallographic A
Y axis belongs to the plane A,B
Z axis is perpendicular to the plane A,B
The particular implementation of spherical components in magnetic
structure refinements is that Z axis must coincide with C. That
works in all crystallographic systems except for triclinic. The
monoclinic setting must be changed to -> 1 1 2/m
It is recommended to generate the reflections using P-1 as
Space group symbol and use for conical structures the value
IRF =0 (Generates satellites+ fundamentals). For a pure helix
IRF =-1 (only satellites are generated). The number of propagations
vectors must be set to -1 (to generate + and - satellites).
For calculating the magnetic moments in different cells the following
formula should be used:
The magnetic intensity is given by the following formula:
Fm**2 =(p.sinw)**2.Sum(j){m(j) f(H,j) cos(bj) exp(2pii.H rj)}
Fm**2 =p**2.(1+cosw**2)/4.Sum(j){m(j) f(H+-k,j) sin(bj) exp(2pii.Hrj-+fj)}
The correspondence with the parameters P1,..P10 is the following:
rj = ( P1, P2, P3)j
f(H+-k,j) = P5j. FormFactor(H+-k,j) exp (-P4j(sintheta/lamda)**2)
m(j) = P6j
bj = P7j
fj = P8j
The unitary vector defining the axis of the cone is given by:
n = (cos P9 sin P10, sin P9 sin P10, cos P10)
cos w = n . Q/mod(Q) , where Q is the scattering vector
-------------------------------------------------------------------
5.- SINCLE CRYSTAL AND INTEGRATED INTENSITY
REFINEMENTS 5.1: General comments.
The version 3.0.0 (or higher) of FullProf permits the refinement of
integrated intensity data. Single crystal and/or powder integrated intensities
can be included (or used alone) as observations for refining a structural
model. This possibility increases the capabilities of FullProf for handling
other kind of data, but it cannot compete (or substitute) more elaborated
programs specialized in single crystal work.
The structure factor calculation is exactly the same as in powder
diffraction, so all the available features can be directly used with
integrated intensity data.
The R-factors in single crystal work are calculated according to
the following formulae:
Optimized function:
M = Sum{n}[w(n)(F2obs(n)-Sum{k}[F2cal(k)])^2]
The index "n" runs over the observations (1,..Nobs)
The index "k" runs over the reflections contributing to the observation "n"
F2 is the square of the structure factor (intensity corrected for Lp-factor)
RF2 -factor=100*Sum{n}[|F2obs(n)-Sum{k}[F2cal(k)]|]/Sum{n}[F2obs(n)]
RF2w-factor=100*Sqrt(M/Sum{n}[w(n)F2obs(n)^2])
RF -factor=100*Sum{n}[|Fobs(n)-sqrt(Sum{k}[F2cal(k)])|]/Sum{n}[Fobs(n)]
Fobs=Sqrt(F2obs)
Chi2(Intens)=M/(Nobs-Npar)
Notice that RF2w for w(n)=1.0 is not the same value as RF2.
For integrated intensity powder data, F2obs is in fact Sum{k}[jLpF2(k)].
When the option IWGT =2 (unit weights) is used.
The inverse of the normal
matrix is not multiplied by Chi2 as is usual in weighted refinements.
5.2: The extinction correction. 5.3: Mixed refinements.
6.- REFERENCES
7.- DIMENSIONS OF ARRAYS OF THE STANDARD VERSION
LLB, jan. 98