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Variables for use with BGMN

The expression interpreter

Variables in the task description SAV file for BGMN

VAL, VERZERR, STRUC, STRUCOUT, PDBOUT, RESOUT, FCFOUT, OUTPUT, LIST, RU, UNT, DDM, PARAM, LAMBDA, SYNCHROTRON, EPS1, EPS2, EPS3, EPS4, POL, PROTOKOLL, ONLYISO, ITMAX, DIAGRAMM, PLAN, STANDALONEPLAN, GOAL, WMIN, WMAX, CUT, LIMIT2, LIMIT4, LIMIT6, LIMIT8, LIMIT10, ANISOLIMIT, ANISO4LIMIT,

Items in the structure description *.str-file

Definition of the lattice: SpacegroupNo, HermannMauguin, ReflectionCondition, A, B, C, ALPHA, BETA, GAMMA, UNIT
Anisotropic variables: ANISO, ANISOLIN, ANISOSQR, ANISO4
Scaling factor/prefered orientation: GEWICHT, SPHAR0, SPHAR2, SPHAR4, SPHAR6, SPHAR8, SPHAR10
Real structure: B1, B2, k1, k2, k3, sk, H, h, k, l, zweiTheta, RP
Atomic positions: E=, Wyckoff, x, y, z, TDS, B, betaij, U, Uij
GOAL's, quant analysis: GOAL, GEWICHT
BGMN-specific functions: PHASE, sk, B1, k2, ANISO, GEWICHT(h,k,l), GrainSize, TDS,
Advanced feature: subphases: RefMult, iref, GEWICHT[i], B1[i], B2[i], k1[i], k2[i], k3[i], DELTAsk, DELTAzweiTheta,
Advanced feature: Structure factors etc: F, Finv, H
Advanced feature: molecules: set, setgitter, cross, diffvec, normvec, skalpro, distance, angle, T, D, X, Y, Z, WW, WWalt, Straf, Theory, Bondings, BondLevel
Micro absorption correction according to Brindley: my, my[i]
X ray density: density, density[i]

Variables in the task description SAV file for computation of standard profiles

VERZERR, TubeTails, R, FocusH, FocusW, HSlitR, HSlitW, PColl, PCollA, VSlitR, VSlitH, SamplD, SamplW, SamplH, DeltaOmega, SSlitW, SSlitR, SColl, SCollA, DetW, DetH, MonR, EPSG, zweiTheta[i], GSUM, TSlitR, TSlitH, FocusS, FocusA, GEOMETRY, WMIN, WMAX, WSTEP, GEQ, D, T, STANDARDPAR, VAL,

The expression interpreter

BGMN uses a built-in expression interpreter. This interpreter in general uses case-sensitive variable names of unlimited lenght. The number of indices per variable is unlimited. Indexed variables are referred as follows:

name[i,j,k]

Variables may hold numeric values (double format) or strings. In special, a string may hold an expression. Expressions are stored as-is and evaluated every time they are used. Therefore expression evaluation may become recursive: An expression may contain a variable, which refers to a second expression etc. Bracket level is unlimited. A lot of standard functions are predetermined:

abs, sqr, sqrt, sin, cos, tan, asin, acos, atan, log, exp: with one argument. As usual, the argument of the angular functions sin, cos,tan and the result of its inverses (asin, acos, atan) are in radians.
mod, power: with two arguments,
min, max: with variable argument count,
ge, gt, le, lt, eq, ne: This functions accept two or more arguments.
ge, gt, le, lt, eq return 1.0 (TRUE), if the condition holds for each neighboured pair of arguments, starting from the first. If some pair does not hold the condition, 0.0 (FALSE) will be returned immedially, errors in following arguments will not cause this function to cause errors.
ne looks for inequality between any pair (also not neighboured) of arguments. If two arguments are equal, ne returns 0.0 (FALSE). Otherwise, ne returns 1.0 (TRUE).
and, or: with variable argument count. Evaluation of arguments is done until the result is determined (C-like evaluation).
not: with one argument,
ifthenelse: with three arguments. If the first argument is TRUE, then the result of the second expression is returned, otherwise the result of the third. The other argument will cause no error to the result.
ifdef: with variable argument count. Delivers TRUE, if all arguments may be evaluated to a numeric (double) value. In the case one value is undefined (causes an error), ifdef results in an error.
cat: Concatenation of commands, with variable argument count. Arguments may be expressions or assignments. At least one expression must be in the argument list, the rightmost expression determines the return value of the function.
while: looping of commands, with variable argument count. The first argument must be an expression. As long as its value is non-zero and no error occurs, all following arguments are evaluated. Returns the number of loop iterations.
ergibt: with one argument, executes the assignment given as argument. Returns TRUE, if the assignment is succesfull, otherwise FALSE.

Please note the special meaning of multiple equation symbols in value assignments to variables:

a=b+c

assigns the string "b+c" to the variable named "a". Every multiple equation symbol makes one deeper evaluation. e.g.

d==a
e===a

d holds the string "b+c". If the third evaluation is possible at input time, e holds the numeric value of the sum b+c. Otherwise, the multiple evaluation is cancelled (without error) and the string "b+c" is assigned, too.

In the input, the user may define string functions in the manner of:

name(argumentcount):expression

A positive count of argument defines a fixed value, the absolute value of a negative argument count defines a lower limit of argument count. expression may contain the special symbols

#1 #2...

which are replaced by the evaluated numeric value of the first, second... argument. Every argument is evaluated only once. An errorneous argument causes an error only if it will be used. Example:

faculty(1):ifthenelse(eq(#1,0),1,#1*faculty(#1-1))

or using level 3.3.29 or above:

faculty(1):cat(n==#1,ret==1,while(n,ret==ret*n,n==n-1),ret)

BGMN defines a lot of structure-description specific functions with limited validity. Most of them are only valid in the structure description files. Some are only valid in GOAL's, others only in the description of atomic positions (E=...).

Variables in the task description SAV file for BGMN

VAL[1], VAL[2]...

Files with measuring values. BGMN assumes the APX file format of the firm SEIFERT FPM, in general. Files with the extension ".rd" are assumed to be in PHILLIPS format. In this case the variable STEPWIDTH may be uses to assing a non-raster stepwidht (STEPWIDTH != n*0.005)of the measuring file (e.g. PHILLIPS format in conjunction with a scanning PSD from SIEMENS). Files with the extension ".raw" are assumed to be in SIEMENS format. Files with the extension ".gsa" are assumed in GSAS format, restricted to constant angular steps (both the variants STD and ESD of the GSAS data format)

VERZERR

name of the GEQ-file (output of makegeq). This is the recommended case. If only the GER-file (output of geomet) exists, BGMN interpolates it for every measuring point. If no file is available, you can give an expression as value. This expression may depend from the variable zweiTheta (two Θ). It describes the width parameter of a single squared Lorentzian function, which is used instead of the complicated sum of squared lorentzians. The width parameter refers to Θ, unit radian.

STRUC[1], STRUC[2]...

Structure description files for the phases present in the specimen.

STRUCOUT[1], STRUCOUT[2]...

Output of structure descriptions in the same format as the input (*.str).

PDBOUT[1], PDBOUT[2]...

Output of the structures in the *.pdb format (Brookhaven Protein Data Base, e.g. usable for image generation with RasMol)

RESOUT[1], RESOUT[2]...

Output of the structures in ShelX format.

FCFOUT[1], FCFOUT[2]...

Output of observed and calculated F's plus phase angle in ShelX format. I have choosed the No. 5 format from the ShelX 97 manual. Cited from those manual:
Write h, k, l, Fo, Fc, and f (phase angle in degree) ... This is indented for input to somestandard macromolecular FFT programs (such as W. Furey's PHASES program), thereby providing a possible route to a graphical display of the electron density.
New in version 2.5.0!
New in Version 2.5.1: All Fs and the phase angles are corrected for dispersion. This means: They really are fourier coefficents of electron density maps. See (newest) ShelX manual.

OUTPUT

*.par-file (peak parameters of all peaks). Used for diagramm generation with SHOW and for peaklist generation with OUTPUT.

LIST

General result output

RU

Number of background parameters. If omitted, BGMN automatic selects a value depending from the 2Θ range and the data accuracy.

UNT

A single file with pattern data. If this parameter is used, its intensities describes a kind of "amorphous background" and are multiplied with the last background parameter and added to the model during refinement.

DDM

If set to

DDM=Y

the DDM method as described in

L. A. Solovyov
Full-profile refinement by derivative difference minimization
J. Appl. Cryst. 37 (2004), pp. 743-749
http://krsk.info/icct/en/cont/persons/sol/ddm.html

will be used. As inherent to this Method, the number of Background parameters RU is set to zero. The DDM method is indented to cases with complicated background.

PARAM[1], PARAM[2]...

Global parameters for the fit. Needs a starting value in the kind

PARAM[i]=name=startingvalue

Possible extensions are

PARAM[i]=name=startingvalue_lowerlimit
PARAM[i]=name=startingvalue^upperlimit

which may be combined.

LAMBDA

specifies a wavelength file, for example LAMBDA=CU selects the file cu.lam for the wavelength distribution (profile of the K alpha doublet) and cu.ano for the corresponding anomalous dispersion.

SYNCHROTRON

same as LAMBDA, but switches on some specialities for synchrotron radiation. Knows an extended form as

    SYNCHROTRON=0.079776

for specifying an ideal narrow (delta-peak) wavelength distribution at the given wavelength in nanometers. Then, no anomalous dispersion may be specified.

EPS1, EPS2, EPS3, EPS4

describes angular corrections of the measured diagram:

EPS1 describes the shift of X ray tube and/or detector in radian. Positive values of EPS1 correspond to the tube's resp. detector shift towards the Θ=90° position and therefore to shifting the pattern towards lower angle.
EPS2 describes the shift of the specimen out of the goniometer axis. Again, the unit is radian. Positive values of EPS2 correspond to:

GEOMETRY=REFLEXION, GEOMETRY=CAPILLARY:
shift of the specimen out of the zero line and orthogonal to this line opposite of the side of tube/detector, which means shift of the pattern towards lower angle. The shift of the specimen is equal to:
R*EPS2/2
GEOMETRY=TRANSMISSION:
shift of the specimen parallel to the zero line in detector direction. The shift of the specimen is equal to R*EPS2/2
EPS3 corrects for penetration depth. Should only be used with GEOMETRY=REFLEXION, a better way is correction of the profile by penetration depth using the D variable
EPS4 should only be used without modelling the apparatus function (without having runned geomet/makegeq and without using *.ger/*.geq-files)

POL

used in the polarisation factor. Default POL=1 means no monochromator. Cannot be declared as parameter. Should be in the kind

    POL=sqr(cos(2 ThetaMonochromator))

For Cu K_α radiation and graphite monochromator, use

    POL=sqr(cos(26.6*pi/180))
    pi=2*acos(0)

PROTOKOLL

determines, wether a iteration protocol is given or not.
Y/y/J/j: A protocol is printed.
N/n: A protocol is not printed.
Default value is N.

ONLYISO

if this value is set to Y/y/J/j, only a fast isotropic computation is done. All anisotropies and spherical harmonics are ignored. A numeric value controls the exit from iteration. In the case of Y, 1.0E-4 is assumed. Default value is N.

ITMAX

Maximum stepcount while iteration. BGMN uses the 10 fold of the parameter count. In critical cases (e.g. structure solution) this limit should be enlarged.

DIAGRAMM

In every iteration step, a file containing a line per measuring point is written. Each line contains

2Θ I_mess I_calc I_background

, followed by a list of intensities, each for every phase involved in the refinement. This is for graphical observation of the refinement progress (Diagram window in BGMNwin)

PLAN

A simple list, each line contains angle, count and measuring time of a futural measurement. Output of (optional) Optimal Experimental Design.

STANDALONEPLAN

Logical switch. Decides, if the Designed Measurement has to be evaluated together with the unplanned pre-measurement (STANDALONEPLAN=N) or standalone (STANDALONEPLAN=Y). For a single task, I would prefer N, which is the default. However, in the environment of a routine analysis in a factory, which has to been done cyclically every few minutes (specimen does not change very largely), STANDALONEPLAN=Y becomes significant.

GOAL[1], GOAL[2]...

global goal of the experiment. Possible values are:

    GOAL[i]=expression
    GOAL[i]=expression=value
    GOAL[i]=expression=value+-σ

The second line is written in the output SAV file. It contains the result. The third line ist written in the LIST file, supporting a fitted value and an error (1σ) for the expression. If one uses the third line in the SAV-file, Optimal Experimental Design is done and the σ value should be reached after a planned measurement an fit of both measurements at once.

WMIN, WMAX

Angular limits for selection of measuring values, unit degree in 2Θ.

CUT[1], CUT[2]...

Angular limits for deselection of measuring values. Format:

    CUT[i]=wmin:wmax

, units are again degree in 2Θ

LIMIT2, LIMIT4, LIMIT6, LIMIT8, LIMIT10, ANISOLIMIT, ANISO4LIMIT

These variables controls the automatic reduction of degree of spherical harmonics and/or anisotropies. After isotropic calculation, the value of the variable GEWICHT must exceed the LIMITx-fold of its error (1σ). Otherwise, the degree of spherical harmonics is reduced. ANISOLIMIT, ANISO4LIMIT works in the same kind for any variable declared as ANISO or ANISO4. ANISO4 is reduced to ANISOSQR. If not given (which should be mostly the case), BGMN chooses an advanced value depending from the Laue Group of the phase.

Items in the structure description *.str-file

Definition of the lattice

Beside there are other ways for defining a lattice with BGMN, one should use the spacegrp.dat file. Therefore, give at least one of the items

HermannMauguin=...
SpacegroupNo=...

in the structure description file. In addition, one may set

ReflectionCondition=...

as a bool switch for the selection of the reflection (depending on h k l) conditions as given in the International Tables. Zero (false) will omit the reflection, non-zero (true) activates the reflection. And give the non-trivial lattice constants, e.g.

A=... C=...

for tetragonal or hexagonal lattice. The full set of lattice constants (triclinic) must be named

A=... B=... C=... ALPHA=... BETA=... GAMMA=...

In normally, this lattice constants should be parametrized and boundaries should be used, e.g.

PARAM=A=0.314_0.312^0.316

Attention! Units of measure are nanometers, or you must use the key

UNIT=ANGSTROEM

in this structure description file!

Anisotropic variables

Each variable may be parametrized. As an extension, each variable may be parametrized anisotropic by using the key's

name=ANISOLIN
name=ANISOSQR

There are some special keys for backward comptibility:
B1=ANISO stands for B1=ANISOLIN
k2=ANISO stands for k2=ANISOSQR
GEWICHT=ANISO stands for GEWICHT=ANISOSQR
ANISO4 is recommended in the case of complicated micro strain, use k2=ANISO4. This means a fully symmetric product of hkl with a positive definite tensor of forth rank. See:

P. Thompson et al.,J. Less Common Met. 129 (1987) 105
J. Rodriguez-Carvajal et al., J. Phys. Condens. Matter 3 (1991) 3215
Both cited corresponding to an oral presentation of P.W. Stephens on EPDIC 5, Parma, Italy

Each of this key's may be completed by an upper limit, e.g.

B1=ANISO^0.02

This boundary is valid only in the first steps of computation. In this steps isotropic replacements for such variables are used. Therefore, the limit is only a hint for the iteration procedure.

The symmetriy of the anisotropic values is automatically corrected to the lattice symmetry.

Scaling factor/prefered orientation

The commonly used scaling factor is predefined by the variable

GEWICHT

Of course, one may define this variable as anisotropic. For strong and multiple prefered orientation there are possible spherical harmonics. The keywords therefore are:

GEWICHT=SPHAR0/SPHAR2/SPHAR4/SPHAR6/SPHAR8/SPHAR10

Only the even coefficients up to the given order are used. This means 6/15/28/45/66 independent parameters in triclinic lattices. Of course, the symmetry of the spherical harmonics is atomatically corrected to the lattice symmetry. Plus, BGMN guarantees these spherical harmonics to be positive definite. For details see:
J. Bergmann, T. Monecke, R. Kleeberg
Alternative algorithm for the correction of preferred orientation in Rietveld analysis
J. Appl. Cryst. 34 (2001) pp. 16-19

The effective count of parameters is reduced, thereby, for all non-triclinic lattices. SPHAR0 corresponds to an isotropic value.
GEWICHT is corrected with the usual factors for weight content analysis. This includes in special the value as predefined in the variable density, which means that of the first subphase in case of RefMult>1. In General, SPHARx starts with the isotropic value zero. But if no measuring data are given (only theoretic computation), the value 1 is assumed.
If both GEWICHT=SPHARx and GEWICHT=ANSIO are active:

GEWICHT=ANISO dominates over GEWICHT=SPHAR0.
GEWICHT=SPHARx (x>0) dominates over GEWICHT=ANISO.
By defining GEWICHT=ANISO and GEWICHT=SPHARx (x>0) one gets the extended switching SPHAR6->SPHAR4->SPHAR2->ANISO->ISOTROPIC, which makes senso in complicated cases.

Real structure

Having solved the problem of wavelength and apparatus influence into the profil shape, BGMN now must handle the specimens influence to this shape. This is normally done by three variables, two of them may be declared anisotropic:

B1

stands for a lorentzian broadening caused by size effects. It should be parametrized. Units of measure is the inverse of that used for the lattice constants, in common 1/nm. You are encouraged to declare it anisotropic using the key

    B1=ANISO

if the specimens crystals are of anisotropic shape.

B2

Is the square of the broadening of a squared lorentzian, which is more gaussian-like. Using the square of the broadening solves a convergence problem, which will occur for B2=0 by handling the squared lorentzian with itself. In usual, you should not use this variable direct. BGMN predetermines the formula

    B2=k1*sqr(b1)+k2*sqr(1/d)+k3*sqr(cost*max(0.0,cot(twoTheta)))

k1 describes a gaussian-like part of the size effects. It should be parametrized in the way

    PARAM=k1=starting_value_0^1

Values greater 1 leads to negative contents of smallest particles in the particle size distribution. The greater the value of k2, the narrower is the particle size distribution.

k2 may describe the micro strain effect. It is the quare of the usual micro strain. You may describe it anisotropic by using

    k2=ANISO

    k2=ANISO4

But k2=ANISO should be restricted to very special cases, for which you have any hints for the reallity of anisotropic strain.

You should never use k3, except in case you don't use any predetermined specimens function's (which are generated by running geomet/makegeq and sored in *.ger/*.geq files). In such cases, k3 describes a broadening of the line for small angles. Asymmetry is never described, in this way!

You may assign own expressions to B1 and/or B2. There are some predefined variables for doing so:

sk: holds the 1/d-value of the reflection, unit 1/nanometer (or 1/Å in case you use UNIT=ANGSTROEM for this structure file).
h, k, l: hold the Miller indices of the reflection. Attention: In general, reflections are multiple. For each reflection only one triple of Miller indices is used for computation, and intensity is multiplied with the multiplicity!
zweiTheta: holds the 2Θ value of the reflection.
H: holds the multiplicity of the reflection.

The kind of the profile model is controlled by the variable RP, also.

RP=2: means ideal lines, no specimen influence on line shapes.
RP=3: means usage of Lorentzian-broadening B1 only.
RP=4: means usage of both Lorentzian B1 and squared Lorentzian broadening B2. This is the default value.

Atomic positions

In general, the key for starting an atomic position is the position's occupation definition, e.g.

E=C
E=(NA(p),K(1-p))
E=(NA(p),K)

The last two lines are equivalent. All non-weighted elements are used to complete the position's total occupation probability to one.

The next is the Wyckoff symbol in accordance to the spacegrp.dat file, e.g.

Wyckoff=c

The next are the x, y, z values as demanded by the Wyckoff symbol:

x=0.312 z=0.574

For structure refinement, these values may be parametrized:

PARAM=x=0.312_0.31^0.315

The Debye-Waller-Factor is given by the variable TDS. It may be declared as anisotropic:

TDS=ANISO

The isotropic TDS value is equal to the common used B, except for the unit of measure (default nm**2, otherwise use UNIT=ANGSTROEM). The anisotropic TDS values given in the LIST file are dimensionless and are equivalent to the β_ij values. The U_ij values also are given in the LIST file, U_ij values are given in the used unit of measure. If you have given only an isotropic U, please use the equation

TDS=8π²U

If no TDS is defined, a phase-specific of measurement-global expression for TDS is used. Otherwise, TDS is assumed to be zero.

GOAL's, quant analysis

A special feature of BGMN are GOAL's. From above, you know them as global GOAL's. You can, of course, use them in phase-specific or position-specific context. Therefore you must omit the index, e.g.

GOAL=A/C

for determining the lattice constants ratio A/C. A special feature for non-global GOAL's are the so-called auxiliary goals:

goal:name=expression

In opposite to normal assignments, the right side of the auxiliary goal's assignment is evaluated to a numeric (double) value. Furthermore you can use GOAL-time specific functions in auxiliary goals.

Quant analysis is supported by the GOAL's. Therefore, in each phase's structure description file use the auxiliary GOAL

GOAL:phasei=GEWICHT

In the case of three phases, use the three GOAL's

GOAL[1]=phase1/(phase1+phase2+phase3)
GOAL[2]=phase2/(phase1+phase2+phase3)
GOAL[3]=phase3/(phase1+phase2+phase3)

in the SAV file. The values for GEWICHT are corrected for the phase's X ray density (that of the 1st Subphase in case RefMult>1). So they can used for quant analysis, directly.

BGMN-specific functions

PHASE

with one argument serves TRUE, if the string given as argument is identic to the phase identificator given for the phase.

sk

uses three arguments: A set of Miller indices. It serves the 1/d value for the given reflection. Usable only in GOALs

B1

uses the Miller indices as three arguments. Serves the B1 value of this reflection. Usable only in GOALs.

k2

uses the Miller indices as three arguments. Serves the k2 value of this reflection. Usable only in GOALs.

ANISO

First parameter is a variable declared as ANISO, followed by three Miller indices. Serves the value of this variable in the given direction. Usable only in GOALs.

GEWICHT

uses the Miller indices as three arguments. Serves the value of GEWICHT for this direction. Usable only in GOALs. As a special feature, the mean value of GEWICHT is set to the variable GEWICHT at GOAL time. So you can get the value of the prefered orientation's correction for a given direction simply by writing

    GOAL=GEWICHT(h,k,l)/GEWICHT

GrainSize

uses the Miller indices as three arguments. Serves the value of a mean grain diameter in the given direction, which is influenced by B1 and k1. Usable only in GOALs.

TDS

uses the Miller indices as three arguments, Serves the value of the Debye-Waller-factor for the given direction. May be used in a position description and only in GOALs. If you defines a global TDS, you may use this GOAL function outside a position description, too.

Advanced feature: subphases

As an advanced feature, subphase definition may be used for complicated real structures description. Therefore, you must assign a value greater than one to the variable RefMult. Subphases share:

the values of prefered orientation hold in the variable GEWICHT (which is automatic set in dependence from the Miller indices, in the case of GEWICHT=ANISO/GEWICHT=SPHARx)
the lattice constants and therefore the variables sk/zweiTheta, which are automatic set, too.

But you can influence this values subphase-specific as described below. The number of the actual computed suphase is set to the variable iref=1,2,... The scaling factors of the subphases may be set by writing:

GEWICHT[i]=expression

If not defined, BGMN uses the variable GEWICHT. You can use the value of the variable GEWICHT as well as some new parameters in the above expression. So you can define arbitrary subphase's scaling factors. You can define subphase-specific values of the real-structure variables

B1[1], B1[2]...
B2[1], B2[2]...
k1[1], k1[2]...
k2[1], k2[2]...
k3[1], k3[2]...

and/or you can use the variable

iref

in the expressions for non-indexed real structure variables. You can assign arbitrary values to the variable

DELTAsk

and/or

DELTAzweiTheta

and/or these variables indexed with the subphase's number. Their values are used for position correction of the subphase's peaks.

You can use special items for the atomic positions. e.g.

E(1,0,1,0)=...

which means: This atomic position is only used for the first and third subphase, each with weight 1 to the structural amplitude.

As an advanced feature, BGMN serves both the absolute values of the structure amplitudes of the reflection {h,k,l} resp. the inverse reflection {-h,-k,-l} by the variables F resp. Finv. In addition, the multiplicity of the reflection is served by the variable H.

Advanced feature: molecules

As a special feature for structure refinement, you can define a molecule or parts of it in cartesian or atomic (fractional) co-ordinates. In following you can shift and rotate the molecule as a whole or only parts of it (changing bonding lengths, bonding angles or torsion angles in dependence from some refined parameters). As a very advanced feature, you can define some penalty conditions similar to those used in molecular dynamics to avoid molecules from overlapping.

Therefore BGMN uses some special functions:

set

uses 4 parameters. The first is a position descriptor, e.g. C1 for the first carbon atom. The following three are the cartesian co-ordinates of this atom in the molecule. They are assigned to the indexed variables

C1[1] C1[2] C1[3]

according to the example (in further referred as a vector).

setgitter

makes the same task, except that it reads atomic (fractional) co-ordinates. An error occurs, if this function is used before full definition of the lattice constants.

cross

Arguments must be 4 vectors. The first 3 must be defined. Computes the cross product between two connection vectors: The vector between the first and the second position and the vector between the second and the third position. The result equals the vector between the second and the fourth position (the fourth position is set in this kind).

diffvec

Needs three vectors as arguments. Sets the third vector to the difference of the second minus the first.

normvec

Arguments are two vectors. Calculates the second vector as the unit vector in the direction of the first.

skalpro

Needs two vector descriptors. Calculates the scalar product between both and returns it as the function's result.

distance

Needs two vectors as argument. Calculates the distance between both vectors (the atomic distance).

angle

Needs 2, 3 or 4 vectors as arguments.

For 2 arguments it returns the angle between both vectors.
For 3 arguments, it returns the bonding angle between the 3 positions.
For 4 arguments, it returns the torsion angle between the 4 positions.

The result is served in degree!

T

Needs at least 7 parameters. Use it in the kind:

    T(x,y,z,alpha,beta,gamma,E1,...)

Defines an arbitrary unitary transformation of the positions E1,... At first, all positions are rotated for the three euler angles alpha,beta,gamma. At second, all positions are shifted for the values x,y,z. alpha,beta,gamma must be given in degree!

D

Needs at least 4 parameters. Use in in the kind:

    D(A,B,chi,E1,...)

Defines a rotation of the positions E1,... around the axis A-B for the angle chi. chi must be given in degree!

X, Y, Z

Need each one argument: a position descriptor. Returns the (fractional) atomic co-ordinates of this descriptor. Must be used in definition of any atomic position after

    E=...

for defining the values of x,y,z in accordance with the Wyckoff symbol. E.g.

    x=X(C1) y=Y(C1) z=Z(C1)

WW

Needs at least 5 arguments. It defines an interaction energy in accordance to common used values in molecular dynamics. Use it in the way:

    WW(a,m,b,n,(A1,A2,...))
    WW(a,m,b,n,(A1,A2,...),(B1,B2,...))

The interaction energy in common is given as a*r^m+b*rⁿ, where r is the distance between both atoms. The results for all significant atomic pairs (also in neighbour elementary cells etc.) are added and multiplied with the value of the variable Theory (default: zero). This value then is added to the minimized value during Rietveld's fit. The first line means all combinations of one list (e.g. all interactions between carbon atoms of a molecule). The second line means all combinations between two lists of atoms (e.g. all interactions between all carbon and all nitrogen atoms of a molecule).

As a special feature, you can define an occupation probability of the position A (usable for multiple conformations):

    WW(a,m,b,n,(A1,A2(p),...),(B1(q),...))

WWalt

Needs one additional parameter to WW. This last parameter is an interaction probability. You need it for correlated occupation probabilities of two atomic positions. In WW, the interaction probability is computed as the product of the two occupation probabilities.

Straf

Needs one argument: An expression. The square of this expression is used as an energy term. So you can define any arbitrary penalty function.

As an additional feature, you can define assignments

Bondings=E1,E2,...

as many as you want. They are controlled by the variable BondLevel (default value 1). This means: Every atom didn't interact (in WW/WWalt) with itself (BondLevel=0), the next bonded atoms (the atoms must be neighbours in any Bondings list, case BondLevel=1), the next next bonded atoms (BondLevel=2) and so on.

Micro absorption correction according to Brindley

For each phase, there is supported the variable my, which holds the linear absorption coefficient of the phase. For a simple Brindley correction (identic grain size for every phase) please use the auxiliary GOAL

GOAL:phasex=GEWICHT*exp(my*d*3/4)

where d holds the mean grain diameter in microns. This is valid since my is given in the unusual unit µm^-1 In addition the variables

my[i]

hold the linear absorption coefficient of the i^th subphase, which may be of interest in case of RefMult>1. In such case, my holds the linear absorption coefficient of the 1^st subphase.

X ray density of the phase

The variable

density

holds the X ray density of the 1^st subphase (the only, if no RefMult>1 is defined).

density[i]

holds the X ray density of the i^th subphase.

Variables in des task description SAV file for computation of standard profiles

As no other said, all lengths are in millimeters an all angles are in degree.

VERZERR: name of the GER-file (output of geomet) and (if no variable GEQ is defined) the output GEQ-file of makegeq.
TubeTails: File with pattern data for Tube Tails correction. Implementation restriction: This file may contain only one scan. Possible file formats are identic to the VAL[x] entry.
R: Gomiometer radius.
FocusH FocusW: Axial (FocusH) and equatorial (FocusW) dimension of the X-ray tube's focus. FocusW means the optical focus width. Usually, the thermal focus dimensions are printed on the X-ray tube. The optical equatorial focus dimension is reduced by the take-off angle of X-rays from anode surface (usually 6°). Usually, the optical equatorial focus dimension is assumed as the 10th part of the thermal one.
HSlitR, HSlitW: Radius (distance from specimen's center) and width of the equatorial divergence slit. May depend from the variable zweiTheta, which means variable divergence slit. In this case GSUM=Y should be used.
PColl: Divergency angle of the primary soller slit, e.g. 0.5/25 (unit is radian). Default is no collimator.
PCollA: Out-of-plane-angle of primary soller slit.
VSlitR, VSlitH: Radius (distance from specimen's center) and width of the axial divergence slit.
SamplD: Diameter of a round specimen. Default value is infinite (sufficient large). Using a small value, you should give GSUM=Y.
DeltaOmega: Ω twist of the specimen, valid only for GEOMTRY=REFLEXION. Changes profile shapes plus intensities (GEOMET) and changes effective penetration depths depending from zweiTheta (MAKEGEQ). May depend from zweiTheta. Therefore, may be used for simulating grazing incidence, too.
SamplW, SamplH: Length and equatorial dimension of a rectangular, not rotated specimen. Default values are infinite (sufficient large).
SSlitW, SSlitR: Radius (distance from specimen's center) and width of the anti-scatter slit. May depend from the variable zweiTheta, which means variable anti-scatter slit. If used in conjunction with TubeTails, you should use the switch GSUM=Y.
SColl: Divergency angle of the secondary soller slit.
SCollA: Out-of-plane-angle of secondary soller slit.
DetW, DetH: Equatorial (DetW) and axial (DetH) dimension of the receiving slit. DetW may depend on Bragg angle zweiTheta in cases of variable receiving slit, as described for variable divergence slits.
MonR: Radius of a secondary monochromator (distance from specimen's center). It's axial dimension is smaller than those of the detection slit, in most cases. Therefore give MonR and use the monochromator crystal's axial dimension as DetH.
EPSG: Computational accuracy. Default value: 0.7 per cent.
zweiTheta[1] zweiTheta[2]...: 2Θ values, for which geomet computes profile shapes.
GSUM: Logical switch. Values J/j/Y/y means: A variable GSUM is computed and written to each profile in the GER file. GSUM holds the relative intensity of each profile. Use it for small specimens, variable divergence slits etc.
TSlitR, TSlitH: The usage of an additional axial slit near the X-ray tube is supported. These variables describe it's radius and axial dimension. Optional.
FocusS, FocusA: These variables describe a axial shift and an rotation angle (around the line tube-specimen) of the X-ray focus. Optional.
GEOMETRY: Measuring geometry. Default value is REFLEXION. The value TRANSMISSION describes a planar, thin transmission specimen. The value CAPILLARY describes a thin, wire-like specimen in the goniometer axis. In the case CAPILLARY, SamplD or SamplH describes the length (heigth) of the specimen, and T desribes the diameter of the wire (capillary).
WMIN, WMAX: Angular range for the computation done by makegeq. Default range: 20°...140°
WSTEP: Stepwidth of makegeq. Default value is 0.01 degree, higher values are recommended. May depend from zweiTheta.
GEQ: Output file of makegeq. Default value: The value of the variable VERZERR, but with the extension geq.
D: Reciprocal value of the linear absorption's coefficient of the specimen. Default value: zero (no correction of the profile shape for penetration depth)
T: Thickness of specimen (GEOMETRY=REFLEXION/TRANSMISSION) or capillary/wire diameter (GEOMETRY=CAPILLARY). Default value: Infinity (sufficient thick) in the case REFLEXION, zero (thin specimen or capillary) in the cases TRANSMISSION/CAPILLARY.
STANDARDPAR: Name of the *.par file containing only the selected reference lines of the standard specimen. Used for learnt profiles.
VAL[x]: Enumeration of the measured scans, which will be accumulated by the VERZERR program. Used for learnt profiles.