International Union of Crystallography
http://www.iucr.org/iucr-top/comm/cpd/

NEWSLETTER No. 20, Summer 1998
http://www.iucr.org/iucr-top/comm/cpd/Newsletters/

EXTENDED SOFTWARE/METHODS DEVELOPMENT ISSUE

d Benson Kariuki,
achlan Cranswick, "Guest Editor'rn
Arnt-Andreas, "EPDIC6
Fundamental Parameter A
nces in the Rietveld-Analysis

rCell as teaching tool"rogram for laboratory Xuantitative analysis and-as, "AXES a software
Daniel Chateigner, "Practical expe
the Berkeley texture package" p10

ic Algorithms for molecular
optimization problems" p32-33

Synthesizing Line Profiles"& Thierry Roisnel, "FullProf.98
indows 95/NT Applications forDavid Cox and Peter"3rd Canadian Powderin crystallography"
Analysis" p16-17
Syb Gorter & Dean
Diffraction Programs" p18tter p40
S. I? Sen Gmta "ISPD'98 :Powder Diffraction" p18sion on Powder

Diffraction Newsletter p40

1

CPD CHAIRMAN'S MESSAGE
Bob Cernik
Daresbury Laboratory, Warrington, Cheshire, WA4 4AD, UK
E-mail: R.J. Cemik@dl.ac.uk

a great deal of information and I would like to thank him very muchfor his initiative. Our publication of this material does not endorse one
approach over any other, it is intended to keep you informed aboutdevelopments. We are fortunate that an increase in circulation andpromised advertising revenue enables us to send out this extended
issue without spending too much CPD funding. We would welcome
informal submissions at any time from groups developing softwareand methods of potential interest to the powder diffraction community.

This is a busy time for the commission, the CPD is planning toincrease its level of interaction and co-operation with other IUCr
commissions, it will shortly endorse a set of guidelines on Rietveld
refinement and will extend its coverage of powder diffraction into
more applied areas. The field has moved on significantly in terms ofsoftware development. Groups from all over the world have beendeveloping new ways to extract the maximum amount of informationfrom powder profiles for structure solution and refinement. Maximum
entropy, genetic algorithms, optimised direct methods and Monte
Carlo techniques have all made recent advances and the fundamental
parameters approach shows promise for Rietveld analysis. It is very
difficult to know which of these approaches will be more fruitful so I
asked Lachlan Cranswick if he would be prepared to solicit
submissions of current powder structure solution and refinement
developments on behalf of the CPD. I was expecting a small but
significant response, what he obtained, as you can see, was an
overwhelming response. That left a dilemma, publish shortened or thewhole versions or the articles? I decided that in the interests of fairness
we should publish all the information we received. This is not intended
to be a comprehensive catalogue but it does show just how much work
is being put into structure solution at present. We do not have allapproaches represented, genetic algorithms and optimised direct
methods are not discussed in detail. However Lachlan has assembled

The next issue of the newsletter will be edited by professor Siba Sen
Gupta, I would be grateful if you would send any information
regarding events, developments or other activities directly to him. The
next issue will cover powder diffraction in India and Asia and willcontain details of the powder diffraction school in Calcutta thisautumn.

GUEST EDITOR'S COMMENTS
As Hugo Mändar and Toivo Vajakas state most succinctly in their
AXES article, "progress in powder X-ray diffraction has always beenin high correlation with progress in developing of new algorithms,
methods and computer programs for diffraction data processing". It isin this spirit that various biases of this editor have become apparent ininviting contributions to update the community of the status of several
software packages, opinions; and techniques that allow the intelligent
use of software. With an extra eye to the future, two contributions
from non crystallographers were also requested on the subject ofalgorithms. In this case "memetic algorithms", and the possibilities of"evolving new algorithms". I hope these articles are not considered too
off topic; as one obvious future of powder diffraction is the improved
extraction of every drop of information from the diffraction pattern tosolve more complex problems. Mathematical algorithms are afundamental key for putting "nature to the question" by finer degrees
via powder diffraction based methods.

"Wise in our generation, we laugh at the inconsistencies of our forefathers, which,rightly considered as portions of the great cycle of human progress, are rather to berespected as trophies of the silent victory, won by almost imperceptible
gradations...........It is by such indirect means that individuals, each relying on his own
right hand, have been gradually led to endure regular forms of government, and tocherish the abstract idea of justice as indispensable between man and man. Viewed inthis light, the ancient forms of procedure lose their ludicrous aspect, and wecontemplate their whimsical admixture of force, faith, and reason, as we might thefirst rnde engine of Watt, or the "Clermont," which painfully labored in the waters ofthe Hudson - clumsy and rough it is true, yet venerable as the origin and prognosticof future triumphs." (From the introduction to The Wager of Battle; Superstition andForce, Essays on the Wager of Law, The Wager of Battle, The Ordeal, Torture. (1892),
Page 103-104. Henry Charles Lea, University of Pennsylvania)

While past procedures in powder diffraction helped determine ourpresent, it is the prognostic of "future triumphs" based in the here andnow that is worth pondering. On this high note of editorial hyperbole,
now would be a good time to take complete responsibility andapologise for any errors and mistakes that leaked into this issue of thenewsletter. Sincere thanks goes to the contributors who made the time
to contribute their articles and opinions. Appreciation must also go to
SiefertPhilips(http://www.analytical.philips.com/) and(http://www.roentgenseifert.com/) for their support of the CPD
newsletter through their advertisements. It is folly to forget that
"Diffraction does not live by software alone!""Exciting times" and "powder diffraction" are presently equivalentconcepts, especially those who program and develop algorithms; ofwhich the benefits flow to all who use powder diffraction. The aura ofpowder diffraction becoming a mature technique in same vein asroutine single crystal "expert systems" is apparent. This is the time ofcheap desktop computing power; various commercial and freeware
computer programming kits; emerging massively parallel computers;
the Internet for obtaining and distributing code, programs and ideas at
the near speed of light. It is quite popular to discuss and compare how
powder diffraction and crystallography was performed 5, l0,20 and 40
years ago. These often lively and entertaining discussions bring to mymind a favourite portion of Henry Charles Lea's history ofjurisprudence; of which a small extract follows.

Lachlan M. D. Cranswick(Editor, CPD Newsletter No. 20)
Secretary, CCP14(CollaborativeComputational Project for Single Crystal and Powder Diffraction)
Daresbury Laboratory, Warrington, WA4 4AD, UK
E-mail: L.Cranswick@dl.ac.uk
WWW: http://www.ccp14.ac.uWpeopleflachlan/

2Fundamental Parameters Workshop - EPDIC
6, August 1998
Computationally demanding numerical convolutions, indicative of thefundamental parameters approach, have in the past made it an unlikely
approach for routine line profile or Rietveld analysis (e.g. Howard &Snyder, 1989), but this has been overcome with the inclusion of anumber of fast algorithms and by using a direct convolutioninterpolation procedure. Efficiencies in the refinement procedure
together with extremely fast algorithms has resulted in an approachthat is at least three to ten times faster than conventional profile fit
programs - even for non-convolution based fit routines.

The Bruker-AXS GmbH cordially invites you to the following
workshop, which will be held as a satellite meeting accompanying the
6th EPDIC conference in Budapest:"A New Fundamental Parameters Approach in Profile Analysis ofPowder Data"
Line profile shapes are a convolution of (i) the emission profile, (ii) an
instrument component and (iii) specimen aberrations. This approach toline profile analysis is well known latest since the pioneering work of
Klug &Alexander in 1974. Nevertheless, until today current profile fit
routines still apply empirical models to the peaks which do not
distinguish between these contributions and are often inadequate inmodeling observed peak shapes in X-ray data.

The procedures presented at the workshop are expected to overcome
the recent, empirical profile fitting methods.
The topics to he discussed are:
1. Possibilities and limit; of recent profile analysis techniques
2. Fundamental parameter approach vs. conventional fitting techniquesa) Principles & core mathematicsb) Generation of line profilesc) Emission profile, instrument characterisation, sample contributions
3. STANDARDLESS real structure analysis (crystallite size, microstrain,
absorption, ...)
4. Instrument characterisation (axial divergence, horizontal divergence orflat specimen, slit dimensions, ...)
5. Use of any parameter couplings and of any constraints (linear andnon-linear)
6. "How many peaks are there?"
7. Instrument alignment aspects
8. Software

A common problem is the description of peak asymmetry which ismainly a result of axial divergence effects. In addition, the extractionof sample effects, such as crystal size/strain broadening relies on the(time consuming) measurement of a large crystal size, strain free'standard' sample under the same instrumental conditions as the'unknown' sample.
The problem with an empirical/standard approach is that a large
number of refinable parameters are required to accurately describe line
profiles over the whole 2Theta range. This parametrization as well as
the insufficient description of instrumental contributions (such asasymmetry) performed by recent profile fit routines result either ininadequate fits or in erroneous interpretation of the specimen
contributions.

Preliminary date: Monday, 24. August, 16:30 - 18:30.
The final schedule will be provided in the 2nd announcement and at
the EPDIC registration desc.

The new fundamental parameters approach presented in this workshop
uses a convolution based method to synthesize line profiles.
Instrumental and specimen aberrations are convoluted with theemission profile to form the final line profile. Peak position, shape andasymmetry are described by the instrument and sample contributions
resulting in accurate estimates of Bragg angle and profile shape.
Sample related effects, such as specimen absorption, crystallite sizeand strain broadening, are entered as refinable values. The physicalparameters of the diffractometer, such as the receiving slit length,
horizontal divergence, and the primary and secondary Soller slit
angles, are measurable quantities and are not usually refined but can be
if required. This theoretical modeling of line profiles provides
information on diffractometer misalignment and/or geometricirregularities. Significantly the fundamental parameters approach
reduces the number of refined parameters and thus decreases
parameter correlation in general.

Workshop language is ENGLISH. Participation is free.
For further information please contact:
Dr. Arnt Kern
Bruker-AXS GmbH
Oestliche Rheinbrueckenstr. 50
D-76181 Karlsruhe
Fax:++49-721-595-6693
EMail: Amt.Kern@bruker-axs.de

Xnd code: from X-ray laboratory data to incommensurately modulated phases.
Rietveld modelling of complex materials.
J.-F. Berar (*) and G. Baldinozzi (+)

A careful look to the data, often recorded with a simple filter or agraphite monochromator, showed that the radiation impinging on thesample was not perfectly monochromatised: small amounts of parasitic
emission lines (and even W-LM lines related to the filament
evaporation) can pollute the diffraction pattern.

(*) Laboratoire de Cristallographie, CNRS BP 166
F 38042 Grenoble Cedex, France. berar@polycnrs-gre.fr(+) Laboratoire de Chimie Physique du Solide, CNRS ECP
F 92995 Chatenay-Malabry Cedex, France. baldinozzi@cps.ecp.fr

In order to analyse these data, xnd was not limited to the popular two
wavelength choice. Moreover, real materials studied in chemistrylaboratories, often present the coexistence of parasitic phases. Multiple
phase handling was therefore introduced in the refinement code.
These choices have led to a series of consequences for the line shapemodelling. As a matter of fact, each wavelength and each phase have apriori specific profile functions: within the linear systemapproximation, these profiles can be described by the convolution of
the functions related to the experimental geometry and to the intrinsic
profile line shape [2]. Nevertheless, for this rigorous approach, time

Introduction
The Rietveld program xnd [ 1] was first written in the late 80's to takefull profit of data collected with high resolution laboratory
diffractometers. At that time, to reduce significantly the data collection
time, only the significant regions of the pattern were recorded.
Moreover, due to the goniometer encoding, scanning was not
performed with fixed steps and/or fixed counting times. Xnd wastherefore designed according to these requirements.

3

2
08.34245 11
8.34245115.62745
1
0
90.00
90.00
0
90.00
0

consuming calculations have to he performed. The Voigt (or its
approximation by a pseudo-Voigt [3]) function turns out to be an
efficient compromise between accurate line shape modelling andcalculation time for most problems [4, 5, 6]. Within thisapproximation, the line shape parameters can be described in terms of
simple Lorentzian and Gaussian contributions. Moreover, the meaningof these parameters can he straightforwardly related to a proper
physical or instrumental origin [2].

0
1
1

0
0
0.000230.000230.00012
0
0
0

12
12
1
0
0
0

1
1

Following the same leitmotiv, preferred orientation effects were taken
into account using a limited polynomial expansion on the sphericalharmonic basis. These functions were also used to model the sample
anisotropic broadening due to crystallite size or strain effects.

Another example, showing more kinds of dependencies between
variables often occurring in chemistry is related to the site occupancy
in substitutional solid solutions and it requires complex equations to be
set up when more cations share the same site [8].

Some other features were also added to the program: refinablebackground by linear interpolation coefficients or splines, rigid body
constraints and restraints on bond lengths, absorption and anomalous
scattering corrections, x-ray and neutron joint refinements [7]...

Incommensurately modulated phases
Most of the structural studies of incommensurately modulated phases
are developed using single crystal diffraction data. Nevertheless, many
compounds are not easily synthesised as single crystals or theinteresting phases present complex polydomain structures. Therefore,
the study of the structure by single crystal techniques becomes very
complex, or even not possible.

In the following, two peculiar features of xnd are discussed in a moredetailed way.

Simultaneous refinement of multiple data sets
The increasing brightness of radiation sources has allowed the use ofdiffraction experiments to perform real time monitoring of phasetransitions, chemical reactions and in situ studies of reaction kinetics.
These experiments were generally analysed by refining independently
a large number of data sets, the result of the refinement of a given data
set being the ,starting point for the following one. This way ofoperating has two main counterbacks:

The 4D formalism for mono-incommensurately modulated phases(superspace group symmetry, intensity and positioning of satellite
reflections) has been implemented in xnd [9].
Another advantage is represented by the possibility to refine
simultaneously x-ray and neutron diffraction data, taking advantage ofthe different atomic contrast and resolution available from theseprobes. Even in the early stages of the refinement, it is generally easier
to decode the four dimensional Fourier maps obtained from x-ray
diffraction as they are dominated by the heavier scatterers and there areless spurious maxima because of the atomic form factor shape. On theother hand, neutron Fourier maps give more details on the atomic
positions and are very useful in the later stages of the refinements.

it does not take into account that the parameters describing agivendata set are not uncorrelated to the ones of the neighbouring
data sets.
the recording statistic of an individual data set in a real time
monitoring experiment is rather poor.

This complementary use of the different probes is very powerful forthe analysis of the structures of oxide compounds. In particular, therefinement of the incommensurately modulated perovskites-type
structures is a challenging problem as (often) the onset of themodulated phase takes place at a ferroelastic phase transition.
Moreover, light and heavy scatterers are generally present in thesestructures (ferroelectrics, superconductors ...). Therefore, the use ofcomplementary sources of radiation is invaluable to give an accurate
description of the oxygen frameworks. The following example is takenfrom the refinement of a superconducting oxide and shows the blockof an atom presenting both displacive and substitutional modulation
expanded to the second order Fourier term.

Therefore, it is reasonable to try to refine simultaneously all theavailable data defining a limited number of global parameters butallowing them to vary according to a proper external variable (time,
temperature, external electric or magnetic field, ...) The parameter
dependence is expressed within a limited polynomial development
approximating the real behaviour of the parameter. A rather obvious
example of application could he the investigation of the thermal
evolution of the lattice parameters:

Bi(3) BI 8100.7527893 31 1.00 0.25
0.1137175 33 1.00 0.022780 32
1.3653332 52 1.00
# Fourier00.0133801 34 1.00 0000.033348 36
0-0.0095327 35 1.00 000.0032825 39 1.00 00000-0.0026739 37 1.00 0000-0.0019864 33
00.0298094 40
0This approach has some evident benefits as, for most of theparameters, a first order expansion ( N = l ) is often enough to describe
the evolution. In that case the total number of refined parameters isdivided by nearly 2/N_patterns .
Therefore, small continuous variations of a parameter can besignificantly analysed handling all the experiments simultaneously andmore reliable esds for these parameters can be obtained even in thecase of individual data sets having a rather poor statistical quality.
To allow the use of these expansions, the data structure in xnd presents
some peculiar features. All the refinable variables expected to present
similar polynomial dependencies are grouped into blocks. In eachblock, at the beginning of it, a number precises the degree of thedesired polynomial expansion. When no expansion is needed thisnumber is 1, meaning that the parameters therein have the same value
whatever the data set. For a linear expansion this number should be 2,
4 for a cubic expansion and so on. The following example is an excerptof the lattice block for a tetragonal compound presenting a linear
thermal expansion only 4 parameters are needed to fit all the data sets:

-1.00

1.00

1.00
1.00

The refinement of incommensurate phases can be considered a
powerful tool for localising the structural disorder affecting acompound [l0, 11]. Therefore, it is possible to get a better insight ofcomplex and defective phases. This is particularly important since thesmall differences between the ideal and real structure of crystals is
often responsible for the onset of interesting physical properties. Thisis for instance the case of oxygen stoichiometry in superconductors, ofcorrelations between cation displacements in ferroelectrics, etc.

4

on ftp:llftp.polycnrs-gre.frlpub1xnd. A very incomplete
documentation always under heavy development can be found at
http:llRX-Crgl.polycnrs-4gre.frlpubliclxndlxnd.html or on the
CCP14 mirror.
The upcoming versions of xnd should include some new features:
loD0

Finger-Jephcoat asymmetry correction
anharmonic modelling of thermal motion applied to cubic
perovskites
magnetic structures in incommensurate structures
atomic form factor refinements (fo,f,f‘)

n
Y

‘3

24

Y

3

27

3

3

I4

Figure: Example of refinement of the x-ray pattern of a modulated phase

References[l0].

1 B h a r J-F and Gamier P, Accuracy in powder diffraction APD 2nd Conference.
846 212Gaithersburg, USA NIST (1992).
2 Klug H P and Alexander L E, X-ray diffraction procedures, John Wiley and sons(1974) New York.
3 David WIF and Matthewman J C , Profile refinement of powder diffraction patterns using the Voigt function J. Appl. Crystallogr. 18 (1985) 461. David W I F
Powder diffraction peak shapes. Parametrization of the pseudo Voigt as a Voigt jiinction, J. Appl. Crystallogr. 19 (1986) 63
4 Baldinozzi G, Sciau Ph, Pinot M and Grebille D, 1995 Crystal structure of theantiferroelectric perovskite Pb-2 Mg 0-4 , Acta Crystallog,: B 51 668
5 Seshadri R, Martin C , Maignan A, Hervieu M, Raveau B and Rao C N R
Substitution of chromium for univalent copper in superconducting Pb-2 Sr-2 (Ca,Y )Cu-3 0-8+delta, J.Mate,:Chem. 6 (1996) 1585
6 Maignan A, Seshadri R, Martin C, Letouze F and Raveau B Giant negative magnetoresistance in the spin glass insulator Tl-0.94 Sr-2 Cu-0.4 Co-0.6 0-5-delta ,Solid State Commun. 102 (1997) 55 1
7 Baldinozzi G, B h a r J-F and Calvarin G 1997, Segregation and site selectivity in
Zr-doped Y-2 0 - 3 , J. Phys. :Condens. Matter 9 9731-9744
8 Seshadri R, Maignan A, Hervieu M, Raveau B and Rao C N R Structural evolution and electronic properties of La- Sr- Mn 0-, J.Mate,:Chem. 9 (1997) 270
9 Baldinozzi G, Grebille D and Berar J-F, Rietveld refinement ofincommensurate
modulated phases, Proceedings of Aperiodic 97, World Scientific (at press).
10 Baldinozzi G, Goutenoire F, Hervieu M, Suard E and Grebille D, 1996
Incommensurate modulated disorder in Ba-0.85 Ca-2.15 In-6 0-12 , Acta
Crystallog,: B 52 780-789
11 Baldinozzi G, Grebille D, Sciau Ph, Kiat J-M, Moret J and Berar J-F 1998
Rietveld refinement of the incommensurate structure of the elpasolite (orderedperovskite) PB-2 M g Te 0 - 6 , J. Phys. :Condens. Matter 10 (at press)

In incommensurate structure refinements it is necessary to distinguishthe different satellite orders so different R_I (R_F) factors have to be
defined for each set of reflections (Fig. 1). In general, satellite peaks
have low peak to background ratios; therefore, the effect of the
background noise on the estimated integrated intensity of the satellites
is sensible and the R_I factor will be larger for these sets of reflections,even if the structural model is good. A second problem consists in thefrequent overlapping of the satellite peaks with intense average
structure main peaks; in this case, a small error on main peaks and on
the description of their profile will strongly affect the estimation of theexperimental intensities of the satellites. The importance of a very
good equation between experimental and calculated line shapes is to beemphasised and, in this domain, xnd offers a large choice of functions
and combinations of functions, with angle dependent parameters to
optimise the simulation.

Upcoming features
The latest release of xnd is 1.16. The refinement code is written in
ANSI C language and it rans on various platforms (HP9000, SPARC,
SGI, Linux, Power Mac). A compiled version for Microsoft platforms
is also provided. The source code (compressed tar file) can be fetched

BGMN - a New Fundamental Parameters Based Rietveld Program for Laboratory X-ray Sources, it’s Use in
Quantitative Analysis and Structure Investigations
correlation. It is a main source of divergence of the optimization
algorithm, incorrect minima and program crashes.

J. Bergmannl, P. Friede12, R. Kleeberg3
E-mail: bergmann@rcs.urz.tu-dresden,de,friedel@orion.ipfdd.de,kleeberg @mineral.tu-freiberg.de

In addition, the wide-spread Rietveld programs need a lot of intuition
for operation: Having declared an unfavorable set of parameters, theRietveld programs react very sensitively. As a rule, they breakdownwith an error inside the numerical library. In this case, the calculation
which had been terminated compulsorily must be restarted from the
beginning. This termination results from the use of simple optimization
algorithms which cannot consider the physically reasonable ranges ofparameters.

lLudwig-Renn-Allee 14,01217 Dresden, Germany
21nstitute of Polymer Research Dresden e.V., Hohe Str. 6,01069 Dresden, Germany
3University of Mining and Technology, Mineralogical Institute,Brennhausgasse 14,
D-09595 Freiberg, Germany

Common Problems of Rietveld Programs
Rietveld analyses can be executed by a lot of programs. Manyfunctions were added since the first publication.
A special problem for laboratory X-ray sources is the profile model[8]. The foregoing developers paid special attention to extend the
profile model enabling the user to describe the peak shape within awide angular range as exact as possible. In spite of all efforts, it was
not possible to introduce a universal, precise profile model easy to be
used until now. For that reason, the following measuring rule had to be
fulfilled: Use narrow axial divergence collimators (Soller-collimator)
to adapt the peak shape by simple analytical functions over the entire
angular range. Even then difficulties often appeared in the case ofpeaks with 2 0 angles less than 15 degrees. The so-called u-v-w
parameters [7] are widely used for profile shape description. These
three (or more) parameters must be fitted in conjunction with the
crystallographic model parameters. Adaptation results in parameter

BGMN’s Solutions to these Problems
New Profile Model
Splitting up the device function of [15] into an X-ray spectrum part(sum of Lorentzians) and a geometry/divergence part (sum of squared
Lorentzians).
Sample’s function is enriched by a second width parameter of asquared Lorentzian (more Gaussian-like than a pure Lorentzian),
which describes strain/stress in the sample.
Device profile is computed by raytracing method. Input values suchas divergence slit- (also formula for automatic divergence slit), focus-,
detector slit-, sample-dimensions, sample shape, sample thickness,5

estimated linear attenuation coefficient, focus misalignement etc. canbe used to simulate the possible paths of X-rays at given angles.
This “device peaks” are automatic fitted to a predefined residual(e.g. 0.7 %) by a sum of Lorentzians. Their parameters are interpolated
over the whole angular range. These are used in calculation of device
profile part for each experimental peak to describe.
When running the optimization algorithm, all profile parameters
depending on the device are constant. Correlation amongst profile andstructure parameters is eliminated.
See: http://www.mineral.tu-freiberg.de/mineralogie~gmn/index,html

New Refinement Algorithm for Reliable Convergence The
nonlinear least square algorithm is designed basing on a practical bookby [23].Within the central, linear part of the algorithm, a simple
solution of the equation system above the Hesse matrix is replaced by
the RG-CD algorithm (Restricted Gradient-Conjugated Direction)
described in [22]. In its complete version, the algorithm supplies any
in-equation constraints for linear combinations of parameters. Lowerand upper parameter limits can be optionally defined by means of thesimplified version used in BGMN [24].

Error analysis
Beside of the well-known R values, BGMN calculates random error
for all parameters and arbitrary functions of them. Therefore, one candeclare arbitrary functions as so-called GOAL‘S. For every GOAL,
value and ESD are calculated.
Quantitative Phase Analysis
Because of the excellent stability of the algorithm, BGMN enablesroutine quantitative phase analysis without the time-consuming workof programming “refinement strategies” or “analytical tasks” for new
sample groups. Some special methods to use the BGMN features in
QPA are:Use of Parameter Limits
for zero point correction (to avoid correlation with lattice
parameters)
for cell parameters (to avoid meaningless results for minor
phases, to define phases in substitutional series)
for occupation factors (to avoid correlation with PO
correction model)
for peak width (to avoid “background-modeling” by a lotof broad lines of a minor phase)

New Features of BGMN

Use of Anisotropic Parameters
anisotropic line broadening model applicable e.g. forphyllosilicatescomplex models (spherical harmonics of different order)
for preferred orientation correction
BGMN uses statistical tests to reduce the complexity ofmodel in the case of lacking intensity. After running theforegoing refinement of the isotropic parameters. theprogram checks the calculated phase intensity. If it is to low(below a limit to define global in the configuration orindividual in the structure file), BGMN reduces the orderof the spherical harmonics PO model. This may be done
down to isotropy, also for peak broadening. So, BGMN
can start from the same structure model if the phase is amain component or a minor phase.

Description and Correction of Preferred Orientation
To overcome the well-known problems caused by the March function[9], Järvinen has used spherical harmonics firstly [16]. We use amodified version of spherical harmonics until 10th order which canalso be applied for samples of sophisticated orientation distributions.
Parameter correlation and incorrect results can be avoided by defining
the suitable order of the spherical harmonics resp. by the automatic
reducing of the order depending on the measured intensity.
Real Structure Functions
The influence of different real structures on the scattering functions ofpolycrystals has been studied in detail by [18]. In the case of
dislocations, he made the conclusion of gaussian peaks. Its width(squared variance) should be proportional to dislocation density as
well as to length of scattering vector.

Use of Disordering Models
formula interpreter can be used to formulate disorderingmodels into the structure description like individual
broadening and shifting parameters of selected groups of hkl,
e.g. with k# 3n
examples of this approach are published at EPDIC-5 [4].

Basing on [5], [20] has checked BGMN’s model for valid crystallite
size distribution. Equivalent to [5], he found the following formula:withpv= volume percentage of columns having a length D; in parallel= width parameter (half FWHM) of theto scattering vector. bl=
width
simple Lorentzian part of the size broadening. b2(standard deviation (T) of the quadratic Lorentzian part of the size
broadening.
According to this we assume a Lorentz width bl independent from thelength of the scattering vector and a squared Lorentzian width b2 5 bl.
Both influences are greatly discussed in real structure literature, so thedefault formulae for peak widths considers both. Of course, one may
assume other formulae.

Molecular crystals (rigid bodies)
New functions describing that lattice positions are placed by molecules
instead of atoms were introduced. In cases of molecules, rotationalparameters appear in addition to the translational ones. Based on theextended functions for molecules, we can define modifications ofvalence angles, torsion around bondings as well as
stretching/compressing within molecules.
Free programmability
If the functions integrated are not sufficient to solve the special
problem, define new parameters and dependencies by means of theformula interpreter inside the program. This way, it is easy to describe
parameter couplings which are not part of the standard program
capacity (e.g. between different atomic positions).

Use in Serial Analysis
write in the batch file only the command lines
bgmn controlfilel
bgmn controlfile2
and so on, and the refinement will done in fully automaticmanner.
The control file contains only the name of device profile file,measurement file, structure files and output files. Predefining of
background is not necessary. We analyzed series up to 50 samples,
containing up to 12 phases and refining up to 152 parameters without
any problems. Examples of analysis can be visited at
http://www.mineral.tu-freiberg.de/mineralogie~gm~applications.html

Example of Routine Phase Analysis
An example of routine analysis will be presented here. The sample isa commercial slate, used in reconstruction of historical buildings. It
was prepared by stepwise grinding and sieving smaller 20 pn andpacking into standard front-loading sample holder. Special problems
are the strong PO and the Mg-Fe-substitution in chlorite minerals. The
refinement starts without any background separation. The cellparameters of all phases present had to be refined. Substitution of MgFe at 3 positions in chlorite, Ca-Fe and Mg-Fe substitution in ankerite
and the K+ occupation factor in muscovite were also refined.
Anisotropic line broadening models for muscovite and chlorite wereused. Isotropic crystallite size broadening model was introduced for allother phases, for ankerite additional microstrain broadening was

6

assumed. The program had to refine 75 parameters at all. A PentiumII
200MHz processor needed 5 minutes 6 seconds to fit 2467 measuring
values and 915 peaks without any user interaction. The complex PO
starting models of albite, microcline and ankerite have been reduced
automatic to isotropy. The iron substitution in ankerite was calculated
to the predefined limits. The quantitative results are given in table 1.

4 1

G

I

300

c p

52

Figure 2 Asymmetric unit of (IPA-HQ)n(gray = C , light gray = H, dark = 0)
Empirical Force Field Model
The combination of XPD Rietveld refinement with empirical force
field energy minimization can favor a given approximation result [I I],
including nonbonding and penalty functions. Nonbonding terms like
Lennard Jones potential avoid overlapping of atoms. Penalties enablea correct chain continuation [9], [l0] or ring closures [ l l ] ,[12].

1.60
100

0

Atom typeTi (om>

I

r

I

ni w

&j

(kcal*mol-’)
0.12

I
0.165
0.160

Figure 1: Rietveld refinement plot of slate sample. Co-Ka radiation,
Rwp=13.81%, Rexp=9.85%, Durbin-Watson d=l.22

Quartzite IIb

Table 3: Constants of atom types for nonbonding interactions used for (IPA-HQ)nAtomic identifier
052-Clnext
C45-052-CI next

30.11

1

0.15
0.20

15.60

fE rev.&
1.44*106kcai mol-1nm-2
1.44*lo6 kcal mol-’deg-2

ra,cq. resp. S,,,
0.132 nm
115 deg

Table 4 Constants of penalty functions for bonding interactions used for (IPA-HQ)nNote that the ankerite concentration calculated is near the detection
limit but may be significant. The calculated individual PO correction
factors of 001 chlorite and muscovite reflections are about 2.5. This iscommon value for layer silicates in front loading technique.

Other BGMN features used
Major effects for improvement to the reliability factor can be achieved,since sample dependent effects would be respected. These are at first a
preferred orientation of the crystallites, at second respecting possible
micro strains in anisotropic form or at third special Debye-Waller
factors for special atom types, which can be anisotropic also. The
effects are decreasing in the called series.
But’note: Applying of these features should only be done, if one can be
sure having the best result of approximation without.

Structure Refinement of Organic Solids
Using the integrated formula interpreter, solid state structurerefinement of organics is very easy to do by a four step procedure.
Especially for polymers structure proposals are performed withreliability factors below 10% ([9],[10],[11],[12]). Here we present an
overview about (IPA-HQ)n results [9].

The summary of results can be seen in table 5 . We also added theobtained scattering pattern including the approximation in figure 3. All
results (the fractional coordinates and the structure factors F ) are
published in a previous paper [ 17]. An optical expression can be seenat [13]. But note, this can be a structure proposal only because of theavailable experimental information.

Microcline
Ankerite

I

01.58

0.31

00.61

0.11

Table 1: Results of slate quantitative analysis

Monoclinic lattice

Structureless Approximation
The first step, the structureless approximation, results in unit cellparameters and information about symmetry operators.
Symmetryelement
mthoutA-face centering
8-face centenngC-face centering
Body centennga xy,0 glide plane1
1

Q, uniqueaxis b
3 13%

I
I

6.74%

a (4

Space group1.75 (1)5.67 (1)24.1 ( 6 )91.8 (2)1060 (1)2
P 1 n 1 (No. 7)

Denslty(g/cm3)
R, (%)

97

b (4

(4
P (W
c

v (A31

unique axis c
3.44%

7.75%
5.97%

1.50

15.34%

6 08%

7.35%
3 44%

Table 5: Summary of results of structure investigations of (IPA-HQ)nTable 2: Test of symmetry operators for (IPA-HQ)nMolecular Chain Model
A molecule can be described by means of a graph tree model ([6])
using internal coordinates, recalculate the Cartesian ones, shift it to theorigin and orient it to one of the Cartesian planes with one of its mean
axis of inertia. Defining the parameters for global movement (rho x,y,z
and SP vector) and internal conformation (bond length, bond angle andtorsion angle) and the bondings between the atoms, the refinement
procedure can be started.
6

8

10 12 14 16 18 20 22 24
2 8 (dw)

26

28 30 32 34

Figure 3: Approximation of (IPA-HQ)n internal structure parameter7

Summary
BGMN is a newly developed Rietveld program with many
advantageous features likefundamental parameters peak shape model
PO correction uses modified spherical harmonics
possible parametrization of atomic substitution
structure language is interpreted by formula interpreter:- arbitrary variables may be declared as “refineableparameters”- arbitrary refined parameters may be declared anisotropic- crystallographic values like atomic co-ordinates,
substitutions, lattice constants, line broadening etc. may be
defined as arbitrary formulae depending from arbitrary
variables (including parameters)- arbitrary formulae may be declared as result values(GOAL‘S).
structure language is able to handle molecules
structure language is extended for force field description.
This unique feature list enables BGMN to solve different problems.
Until now, BGMN was used successfully in quantitative analysis andstructure investigations of organic solids.

Postscriptum
The authors wish to thank L.M.D. Cranswick for inviting to publish
this paper in CPD Newsletters. They ask to apologize for it’s formality
and length: It has to been written during a single week, only.

References[l] Le Bail, Duroy and Fourquet. Mater: Res. Bull., 23, 1988, 447-452[2] J. Bergmann, http://www.mineral.tufreiberg.de/mineralogie~gm~index,ht~[3] J. Bergmann, R. Kleeberg, T. Taut and A. Haase, Quantitative Phase Analysis
Using a new Rietveld Algorithm -Assisted by Improved Stability and Convergence
Behavior. Advances in Xray Analysis 40(1997) (in press)-[4] J. Bergmann and R. Kleeberg, Rietveld Analysis of disordered layer silicates
MaterSci.Forum (1998) (accepted)[S] E.F. Bertaut, Raies de Debye-Scherrer et Repartition des Dimensions de Bragg
dans les Poudres Polycristallines Acta Cryst. 3 14-18 (1950)[6] G. Biess. Graphentheorie, MIN - 0 L 212, BSB B.G.Teuhner Verlagsgesellschaft
Leipdg, 1988
[7] Cagliotti, Paoletti and Ricci, Nucl. Instrum. V3 223-228 (1958)[S] R.W. Cheary,A. Coelho, J. Appl. Cryst. 25 109-121 (1992)[9] W.A. Dollase, Correction of Intensities for Preferred Orientation in Powder
Diffractometry: Application of the March Model, J. Appl. Cryst. 19 267-272 (1986)[l0] P. Friedel, J. Bergmann, D. Pospiech, D. Jehnichen WAXS and force field constrained RIETVELD modeling of meta-linked fully aromatic copolyesters, 2.
Poly(p-phenylene terephthalate p-phenylene isophthalate) Polymer (subm. 7/98)[ll]P. Friedel, J. Tobisch, D. Jehnichen, T. Taut, M. Rillich, C. Kunert and F.
Bohme. Structure investigations of molecular crystals containing the ring system
cyclo-tris(2,6-pyridyl formamidine) by means of XPD and force field constrained
Rietveld refinement J. Appl. Cryst. (1998) (accepted)[12] P. Friedel, D. Jehnichen, J. Bergmann, T. Taut, and A. Haase, Application of
RIETVELD refinement combined with force field energy minimization to structure
investigation of cyclotris(2,6-pyridyl formamidine) Adv. X-Ray Anal. 41 (1998)(accepted)[13] P. Friedel, http://www.ipfdd.de/people/friedel/homepage.htm[14] W.F. van Gunsteren and H. J. C. Berendsen. Molekudynamik-computersimulationen: Methodik, Anwendungen und Perspektiven in der Chemie Angew. Chem.
102 1020-1055 (1990)[15]T. C. Huang, W. Parrish, Adv. X-Ray Analysis 21 275-288 (1978)[16] M. Javinen, J. Appl. Cryst. 26 525-532 (1993)[17] D. Jehnichen, P. Friedel, J. Bergmann, D. Pospiech and J. Tohisch, Polymer 391095-1102 (1997)[18]M. A. Krivoglaz, X-rays & Neutron Diffraction in Non-Ideal Crystals (1994)[19] A.C. Larson and R.B. von Dreele, General Structure Analysis System Los
Alamos National Laboratory, NM, USA, 1985-96[20] D. Melcher, diploma thesis, TU Dresden 1988
[21] H.M. Rietveld,Acta Cryst. 2 151.152 (1967) and J. Appl. Cryst. 2 65-71 (1969)[22] H. Sadowski, Beiträge zur numerischen Mathematik, 3 131-147 (1975)[23] H. Schwetlick, Numerische Lösung nichtlinearer Gleichungen, Berlin 1979[24] T. Taut and J. Bergmann, Manual “Rietveld Analysis Program B G M N ,Seifert-FPM Freiberg i. Sa, 1998
[25] S.J. Weiner, P.A. Kollman, D.T. Nguyen and D.A. Case, J. Comput. Chem. 7
230-252 (1986)~~~~~~~~The Southampton Combined EXAFS and Powder Diffraction Program
Norman Binsted, Maria Pack, Mark Weller, and John Evans,
Department of Chemistry, University of Southampton, Southampton SO17 lBJ, UK.
E-mail: N,Binsted@dl.ac.uk, mtw@soton.ac.uk, je@soton.ac.uk
WWW: http://www.soton.ac.uM-chemweb/

The complimentary nature of the techniques of EXAFS and X-ray orneutron powder diffraction (PD) often leads to their combined usage inthe study of crystalline materials. For example, X-ray PD is very goodat determining the coordinates of heavy atoms in special positions, butless good at their oxygen neighbours. Metal-edge EXAFS may thenprovide useful constraints on M - 0 distances. There are instances, forexample in mixed-metal periodates such as RbGeIOg [l], where thereflections due to the metal sites exactly overlap (1/3,2/3,1/2 and
2/3,1/3,1/2 sites in P312). The sites differ in their oxygen coordination
distance however, so EXAFS can uniquely resolve them. In otherinstances the short range order seen by EXAFS contrasts with the longrange order seen by PD. Rutile (Ti02) may accommodate highconcentrations of elements such as Ta or Nb, without any change inoverall lattice symmetry but EXAFS would reveal different bonding
distances for Ti, Nb and Ta due to local distortion of the oxygen
framework. In these cases, EXAFS may provide significant additional
information, but is not being used directly to improve the refined
positional coordinates. Moreover, non-nearest neighbour information
is not fully utilised. EXAFS analysis usually involves refinement of aseries of shell distances, perhaps including a few multiple scattering(MS) paths for in-line atoms. In practice, non-nearest neighbour peaks
almost never correspond to simple shells of atoms. Structure to 5 or 6
A may contain dozens of different distances and thousands of MS
paths, which are not well represented by a small set of Gaussian shells.
It is also very unlikely that a refined set of spherical polar coordinates
is compatible with any possible crystal structure.
For these reasons, a program was developed at Southampton [2] whichuses a single model of the crystal structure to fit both PD and EXAFS

spectra (it has been used for np to five different edges from
Gd2Ba2CaCu2Ti3OI4 simultaneously [3]). By modifying thetreatment of disorder used in EXCURV92 (and most other codes)
systematic differences between the techniques have been minimised,
so that in most cases the two methods ‘agree’ on the correct solution.
The PD profile essentially determines the symmetry and cellparameters, but the oxygen positions and distribution of metal atoms
over sites is strongly dependent on the EXAFS. Refinement of thestructure requires only a few more parameters than a Rietveld
refinement - one edge offset per EXAFS spectrum, plus either some
EXAFS Debye-Waller factors or a small set of adjustable parametersfrom which they may be calculated (in [3], two parameters were used
to approximate the DW terms for over three hundred shells and all theMS paths between them). The EXAFS spectra may then be fitted as far
out in R-space as time permits (lo6 path MS calculations are still slow).

Figure 1: The framework structure of GallobicchuliteCag(GU2SiO~)4(0H)8(oxygens excluded).

One of the most interesting applications of the method was to
Gallobicchulite [4], Cag(Ga2SiOg)4(0H)8, a synthetic sodalite. The
structure is that of a P-cage zeolite, with four-membered rings oftetrahedrally coordinated cations (T), linked to form six-memberedrings normal to the (111) directions of the cubic cell, and withintrachannel Ca and OH on cube diagonals (fig.1).
In this material NMR and EXAFS data [5] suggested a high degree ofordering in terms of (Si,Ga) occupancy of sites and Ga-0 bond lengths
consistent with distinct gallium sites. The powder diffraction data,
however, indicated a structure disordered on a large scale, with a single
T-0 distance.

interpret the structure as consisting of domains with one of threepossible orientations within the crystal. The method has thus yielded a
set of positional parameters for a basic cell that is 'invisible' todiffraction methods.
It is hoped to further develop the program in several ways. One is toextend the modelling of local order - for example by using supercellswith lattice distortions for mixed-metal oxide EXAFS while using the
average over constituent cells for PD. Another is to achieve a common
treatment of disorder. The disorder parameters should agree between
EXAFS and PD)as given by:

A is the EXAFS Debye-Waller factor for shell i, and Coi thecorrelation between shell i and the central atom.
A

kid',

Provided the correlations can be obtained and systematic errors in PD
thermal parameters can be eliminated (systematic errors do not seemto be a problem with EXAFS), a common set of refined thermal
parameters can be extracted. This would help reduce correlation
between positions and Debye-Waller factors, so giving more reliable
structures, and also help to distinguish between short range and longrange disorder.

1900-

10

50

SO

130

28.

Figure 2: Fits to Ca~(Ga2Si06)4(0-H)~
using combined rejinement withspace group I4 for EXAFS and 143m f o r neutron data. a). Fit to k3
weighted Ga K-edge EXAFS data (left) and Fourier transform (right),
phase-corrected f o r Ga and 0.b). Fit to powder neutron diffraction profile.

The combined program gave a fit to both neutron PD and EXAFS with
an identical set of refined coordinates however (fig.2), although thiswas only achieved by using two different space groups. With 1-4 thecoordinates produce a pseudo-cubic structure with framework ordering
similar to the sodalite-mineral tugtupite [6]. This fits the EXAFS,
explain? the NMR data, and is consistent with Lowensteins rule [7].
With I43m (and fractional occupancies of some sites) it generates the
PD profile. The relationship between the two cells is exactly equivalent
to averaging over x, y and z orientations of the unique axis in 14. We

Acknowledgements. We are grateful to the EPSRC for funding thiswork, to Daresbury Laboratory for allowing the use of code from
EXCURVE, and to DL theory group for help with computing
equipment. The program uses code from DBW [8],FEFF [9], and the
UKAEA Harwell library [l0].
1. D.B.Currie, W.Levason, R.D.Oldroyd and M.T.Weller, J.Mater.Chem. 1994,4, 1.
2. N.Binsted, M.J.Pack, M.T.Weller and J.Evans, J.Am.Chem.Soc., 1996, 118,10200.
3. M.T.Weller, M.J.Pack and N.Binsted, Angew.Chem.lnt.Ed, 1998, 37, 1094.
4. N.Binsted, S.E.Dann, M.J.Pack and M.T.Weller, Acfa Cryst.B., 1998, in press.
5. M.J.Pack, S.E.Dann and M.T.Weller, Chem.Cummun., 1996, 1341.
6. M.Dano,Acta Cryst.,1966,20, 812.
7. W.Löwenstein, Am.Min., 1954, 39, 92.
8. DBW, program by D.B.Wiles, A.Sakthive1 and R.A.Young, Georgia Institute ofTechnology 1991.
9. J.J.Rehr, J.Mustre de Leon, S.LZabinsky and R.C.Albers, J.Am.Chem.Soc., 1991,
113,5135.
10. AERE Harwell Report R 9185 (HMSO), 1987.

Call for Proposals for Time on the Oak Ridge High Flux Isotope Reactor
Bryan Chakoumakos
Oak Ridge National Laboratory
Oak Ridge, TN 37831-6393, USA
E-mail: kou@ornl.gov WWW. http://neutrons.oml.gov

Interested researchers are invited to apply for time on the neutron beam
instruments at the High Flux Isotope Reactor at the Oak Ridge
National Laboratory (http://www.ornl.gov/). Proposals are accepted at
any time and are reviewed year-round. Approved experiments areusually scheduled within 90 days. Beam time is available at no costfor non-proprietary use.
Application procedures and detailed facility descriptions are found on
our Web site http://neutrons.ornl.gov. If possible, please submit yourproposals by e-mail. Various formats of our proposal form can be
retrieved from our Web site.
Available instruments are triple-axis spectrometers, high-resolution
powder diffractometer, four-circle single-crystal diffractometer,
SANS, reflectometer, double-crystal USANS, a flat-cone geometry
PSD diffractometer ( WAND)*, residual stress diffractometer**.
The 30 m SANS will be "shortened" in the next 1-2 months to makespace for the cold guide hall, but it should be available again in the US
Autumn. We will not have the full 30/35m distance (for highresolution studies) until the cold source installation is completed.
However, we should be able to do "medium resolution" experiments(up to around 100-150 A) in the near future.
Sample environments include: Temperatures = 1.5K to 1900K,
Pressures up to 3 GPa, Magnetic fields up to 7 T, and liquid shear cells.
*The WAND has been recently upgraded with a new, state-of-the-art,
multi-wire, gas-filled, detector.
**Proposals for the residual stress diffractometer are handled by theHigh Temperature Materials Laboratory of the Metals & Ceramics
Division; see http://htm29.ms.ornl.gov/rsuc/index.html.
Neutron Scattering Section
Solid State Division
Oak Ridge National Laboratory
P.O. Box 2008, Bldg 7962
Oak Ridge, TN 37831-6393
423-574-5235 office423-574-6268 FAX
http://neutrons.oml.gov

Practical experience of BEARTEX, the Berkeley texture packagein the plane of octahedra (V05 ,5O0,5), conferring a two-dimensional
behaviour of the conductivity.

Daniel Chateigner
Lab. Physique de l'Etat CondensE,72085 Univ. du Maine - Le Mans, France
E-mail: Daniel.chateigner@univ-lemans.fr
WWW: http://www.univ-lemans.fr/-dchat//danielc/daniel.htm

The aim of this work was to show the relation between the texture andthe conductivity of the Bi4(V0,85Co0,15)2011-6 compound. The
uniaxial pressure-induced and the magnetic field-induced orientations
were studied.

Abstract
The Berkeley Texture Package (Beartex) is demonstrated for its mostusual applications in the field of texture analysis. It is shown how aregular texture analysis can be routinely conducted with this package,in the case of neutron or X-ray data, using several examples
concerning different materials and elaboration processes, on thin films
and bulks. It is demonstrated on several examples how texture cancorrelate physical properties quantitatively, and how it helps
understanding anisotropic measurements.

To create orientations in the polycrystalline samples, two processes
based on the application of a uniaxial pressure (about 2 kbar) and/or amagnetic field (7T) were used on powders. Then we measured the(006) pole figures and normalised them by direct integration in orderto check c axis orientations strengths. The ionic conductivity
measurements were carried out by impedance spectroscopy on single
crystals and on oriented polycrystalline ceramics.

1. Introduction
Quantitative texture analysis (QTA) has now been developed for some
50 years. From the early works thoroughly documented in many books[Bunge, 1982 and 1982a; Wenk, 1985; Matthies et al., 19871,to the up
to date methodologies for the data treatments and using new generation
tools, a tremendous amount of work as been achieved.

The texture of one plate-shaped single crystal was firstly investigated.
In single crystals, the orientation density reaches high values somehow
limited by the experimental resolution. For example, a maximal
density near 4000 m.r.d. was estimated using the (006) pole figure.
The (006) distribution density measured on the 2 kbar uniaxiallypressed sample (P2), has shown a low orientation with a maximal
density equal to 14.8 m.r.d.. Using a pressure of 12.5 kbar, the resulting(006) pole density was slightly larger, with 22 m.r.d.. When amagnetic field of 7 T was combined with the 2 kbar pressure (H7P2),
the maximum (006) pole density reached 33 m.r.d.. Following theseresults, both pressure and magnetic field align the grains with their caxes parallel to the applied force or magnetic field direction, thestrongest orientation being obtained with a combined process.

Used in the former time by geologists, then metallurgists. QTA became
essential in a lot of different fields in science, with the paralleldevelopment of more and more anisotropic materials, due to its
capability to describe the correlation between physical properties andcrystallite orientations. However, as materials are obtained bysophisticated processes (natural or not) giving rise to multiple phasesof different crystalline symmetry with various texture strengths,
crystalline ratios, particle sizes and strain states, QTA is becoming acomplex characterisation procedure.
Among all possibilities to calculate the main texture quantities, wechoose for this paper to illustrate a routine texture analyses using theBerkeley Texture Package (Beartex, Wenk et al., 1998), taking several
examples of materials, and in order to give people a rough approach ofwhat QTA means. People more interested than what is presented here
are invited to consult other formalisms, methodologies and packages.
A general definition of QTA would be out of concerns in this paper andis enough detailed using examples in the paper by Wenk et a1 (1998).
The reader interested in getting familiar with the terms that are used
http://www.univherefindexamplesatlemans.fr/-dchat/beartex/beartex.htm. The study presented on thissite demonstrates the capability of texture analysis to describe heteroepitaxial relationships [Chateigner et Erler, 19971 using classical Xrays. Peoples using neutron diffraction (and position sensitive detector)
and interested in QTA on multiphase samples with low crystal
symmetries may find it in the paper of Chateigner & al., 19971. We
prefer for this example paper to focuss on the correlations between
QTA and anisotropic physical properties. For this we chose three
examples of materials science, anionic conductors (BiCoVOx), highperformance permanent magnets (Sm-Co family) and high temperature
superconductors (YBCO and BSCCO family)."

Table 1 : Summary of the orientation pole densities PO06 and anisotropic
conductivity of single crystal (SC),a 2 kbar uniaxially pressed powder (P2)and a sample oriented by combining axial pressure and a 7T magnetic jield(H7P2).
Taking into account the platelet shape of the single crystals, theconductivity measurements were performed parallel (a//)and
perpendicular (al)to the (a,b) plane. The conductivity a//and al
measured on a single crystal can be considered as the upper and lower
limits which can be attained on a perfect three-dimensionally oriented
material. In contrast, on free powders, the absence of preferredorientation averages out the parallel and perpendicular conduction
effects. Oriented powders have an intermediate conductivity behaviour.
The sample characteristics and the values of the maximum (006)orientation densities are summarised in the table 1. The conductivity
values o// and al are given at 870 K: the values obtained on thesample H7P2 are close to the values measured on the single crystal.
The difference between a//and ol is around 7O.1Oe3 S.cm" for the
single c stal, 50.109 S.cm-' for the sample H7P2, and around 20.10S.cm- for the sample P2. This difference is greater for the sample

2. Anionic conductivity in BiCoVOx ceramics [Muller et al., 19961
Solid electrolytes exhibiting good ionic conductivity by 02-ions areused in oxygen sensors, oxygen pumps, or fuel cells. Their mainfeatures are (i) a high oxide ion conductivity over a wide range oftemperatures and oxygen partial pressures, and (ii) a low fabrication
cost of tubes and membranes with large surface and low thickness.
Therefore, the polycrystalline ceramics represent an importanteconomical and technological challenge.

7

H7P2 than for the sample P2, and shows the effect of the magnetic fieldon the macroscopic conductivity anisotropy, in relation to the degree of
texture.

Among compounds showing such properties, the compound
discovered in 1985 [1,2] and formulated Bi4V2011 is of interest. Its
structure is close to the Aurivillius phase Bi2MoO6. This compound
may be viewed as an intergrowth, along the c axis, of alternating(Bi202)2+ sheets and ( M 0 0 4 ) ~ -perovskite layers. The complete
substitution of Mo6+ ions by V5+ cations induces the creation ofoxygen vacancies to conserve the total electroneutrality. In previous
works [3,4], it has been demonstrated that these vacancies are located

2 2 . Anisotropic magnetic properties in textured SmC0.5 bulks[Legrand et al., 1997/
Solidification in a magnetic field (Bt) of the intermetallic compounds
SmCo5 and Sm2Co17 produces oriented polycrystals. The resulting
high degree of orientation validates a model which explains thephysical orientation mechanism which occurs during the solidification
process.

10

X-ray diffraction pole figure measurements (Figure 3) reveal that caxes deviate by no more than 10" from the B, direction. This figure isin good correlation with the magnetisation curves (Figure 3 - insert).

Due to the association of a rare earth and a transition metal, theferromagnetic phases SmCo5 (1:s)and Sm2Co17 (217) are exhibiting
high saturation magnetisation (Jsl:5 = 0.95 T and J ~ 2 : 1 7= 1.4 T atroom temperature), high Curie temperature (Tc1:5 = 710°C and
Tc2: 17 = 917"C), with a large uniaxial magnetocrystalline anisotropy
along the crystallographic c-axis. The crystal structure of the SmCo5
phase is hexagonal (CaCus-type). The structure of the Sm2Co17 phasecan be generated from that of SmCo5 by an ordered substitution of Co
dumb-bells into some of the Sm sites. Consequently, these two phases
are crystallographically coherent and particularly both have their caxis as the easiest-magnetisation direction [Kumar, 1988]. Sm-Co typepermanent magnets are based on these two ferromagnetic phases.
The produced samples are magnetically characterised
magnetisation measurements carried out in a fluxmeter.

by

Two experiments have been done (Samples 1 and 2). In each case, thematerial was heated up to the fusion by HF induction in an alumina
crucible, then solidified within a few minutes in a vertical thermal
gradient. Sample 1 was solidified without magnetic field, while amagnetic field Bt = 2.5 T was applied for Sample 2. The SEM analyses
show that the samples consist of two phases SmCo5 and Sm2Co17(Figure 1).

4"

00

80

-On

Figure 3: {002/-SmCo5,pole figure of sample 2 measured on a faceperpendicular to Br Maximum density is 70 m.r.d.). Insert: corresponding
magnetisation curves f o r radial and vertical directions.
A direct application of the elaboration process used here is the
production of high energy bulk Sm-Co permanent magnets. To afundamental point of view, the experimental results of orientation incold crucible are consistent with a simple model of anisotropy forcrystallites which orient in the melt during the solidification process.

Texture Influence on critical current density of superconducting
Films, tapes and wires
New high Tc superconductor ceramics crystallise in low symmetry
space groups which give rise to strong anisotropy in their physicalproperties. One of them, the maximum current density (Jc) that thematerial can support is particularly important for potential
applications. The superconductors of concern here are of orthorhombic
symmetry and have Jc's approximately one order of magnitude larger
in the (a,b) plane of the structure than along the perpendicular to it. It
becomes then interesting to texture them in order to get the best current
carrying capability.

Figure 1: SEM micrography of Sample 2: a morphological texture parallelto Bt is formed by the Sm2Co17 phase (dark grey) in the SmCo5 matrix(light grey). The black areas correspond to holes and cracks in thematerials.

The 2:17 phase is aligned parallel to the vertical direction in the 1:5
matrix. This morphological texture has not been observed on Sample 1
and is attributed to the combination of the vertical thermal gradient andthe applied magnetic field. The magnetisation measurements
performed on the whole samples, in two perpendicular directions(vertical and radial) are presented on Figure 1. Sample 2 exhibits easymagnetisation and hard-magnetisation directions parallel andperpendicular to Bt respectively. This is the volumic signature of acrystallographic orientation, the c-axes of the grains lying
preferentially along the vertical direction. On the contrary, Sample 1 israther isotropic and does not reveal the c-axes orientation. It isinteresting to note that Sample 2 is both morphologically andcrystallographically textured

YBCO films on (100)MgO substrates [Pernet et al.. 1994]:
Many texture analyses of thin superconducting films have been
documented in the past. However few quantitative analysis wasoperated up to now. This is mainly due to the strong preferredorientations developed in such films, which make most of themethodologies unusable. The quantitative texture of two series of
YBCO films deposited on (100) MgO substrates by Pulsed Laser
Deposition and Metal Organic Chemical Vapour Deposition was
analysed using X-rays. The film thickness are in the range 150OA2800A.
All the films exhibit c-axis orientation perpendicular to the surface(cl), as revealed by the pole figure analysis. The { 103} pole figures
document a major epitaxial growth orientation with the a and b-crystal
axes of the film aligned with the substrate axes ( l o ) . In addition,some minor in-plane orientations were found with aYBCO rotated by
45" around the normal to film plane from the c l 0 orientation (c145).
The ratio C ~ ~ ~ / orientations
C L O
was measured by integrating the polesin the specific angular ranges. This ratio does not exceed 12% in theworst film. On the other hand, { 102/012} pole figures revealed in somesamples the presence of YBCO crystallites with a or/and b axes
perpendicular to the film surface (al). The ratio al/cl orientations
was calculated. The high intensity level of the poles allow to appreciate
percentages as low as few tenth. The c l 4 5 and al orientations are bothshown to drastically reduce the critical current density Jc (Figure 14),by one order of magnitude for approximately 1% of one or the othertype of misorientation. The Jc variations versus c145 and a 1
misorientations is non linear for both variables.

1.2

-

h

0.8

c I

J

c
v
'3

0

0.5

1

1.5

2

2.5

3

poH (Tesla)

Figure 2: Magnetisation curves of the samples solidified in a verticalmagneticjield Bt = 2.5T (Sample 2, bold lines) or in zero-jield (Sample I ,fine lines). The full and the dotted curve correspond to vertical and radialmeasurements respectively.

11

i

--,

Figure 5: 001 inverse polefigures for the multifilament, tapes and wires samples. The
maximum density is for the multifilament with 46 m.r.d.
Figure 4: Decrease of the critical current density with misorientation defects
observed in YBCO thin films deposited on (100) oriented MgO single crystals.

For comparison we have also measured the texture of P 2223, a sinterforged hot-pressed bar of bulk Bi 2223 powder. The texture which wasmeasured (3.4 m.r.d.) is much weaker in strength than the texture intape T 2223, but similar in pattern with a 001 maximum in thecompression direction. The strength of the texture is comparable to thatof cold-pressed Bi 2223 powders.

Ag-sheathed BSCCO tapes, multifilament and wires [Wenk et al.,1996]:
Bismuth based high temperature superconductors are actually mostamenable to the techniques currently available to manufacture long
lengths of wire or tape with good performance, due particularly to their
low weak link behaviour compared to the yttrium or thallium based
compounds.

Conclusion
We have depicted some regular quantitative texture analysis using theBeartex package. Of course we neither have shown all the possibilities
included in this package, which would concern for example more
specific types of analysis (elastic constants for textured materials,
sound wave velocities, ...), nor we compared it to other existing
program systems. We preferred to focus on general features that one
would have to examine quantitatively the texture of materials. This
allowed us to show how, using routine experiments and calculations,
one can correlate the textural part of the microstructure to physicalproperties achieved in advanced materials.

Superconductor compounds are sheathed in silver, manufactured using
the “oxide powder in tube” method (OPIT). They are shaped as tape orwire, then thermally treated to produce a practical superconductor thatis more adapted for embedding in silver sheaths and consecutive coldor hot deformation and thermal treatment. Multifilamentary
conductors are advantageous since the current is shared by multiple
parallel conducting paths. From the literature, the highest criticalcurrent densities are obtained in general for multifilaments, monocore
tapes, then wires. We used neutron diffraction experiments at ILL toanalyse the texture of these samples. The tapes and wires were cut into
segments ranging from 5mm to 10 mm long, and these segments wereglued together to form a cube, keeping the segments strictly parallel.
Since the elaboration processes are axi-symmetric, all the resulting
textures can be characterised by profiles taken over angular ranges
from normal to parallel to the tape surface, and normal toperpendicular to the wire direction. These profiles are then treatedsimilarly to regular texture analysis, the OD is calculated, then inverse
pole figures (which are a compact representation of axially symmetrictextures) for main sample axes are calculated from it.

References
H.J. Bunge, “Quantitative Texture Analysis”, Ed. H.J. Bunge & C. Esling (1982),
pl-72. Deutsche Gesellschaft fur Metallkunde-Societe Francaise de Metallurgie,
Obernrsel.
H.J. Bunge, “Texture Analysis in Materials Science”, Ed. H.J. Bunge, (1982a), p7576 Bntterworths, London.
D. Chateigner & B. Erler (1997) Material Science & Engineering: B45, 152-161.
D. Chateigner, H.R. Wenk & M. Pernet, J. Appl. Cryst. 30,43-48 (1997).
D. Chateigner, H.R. Wenk & M. Pemet, in press Texture and Microstrncture, 1998.
L. Durand, F. Kircher, P. Regnier, D. Chateigner, N. Pellerin, F, Gotor, P. Simon &P. Odier (1995), Supercond. Sci. & Technol. 8,214-218.
Helming K.(1991), Textures & Microstructures 14-18, 187-192.
K. Kumar (1988), J. Appl. Phys. 6 3 R13.
B.A. Legrand, D. Chateigner, R. Perrier de la Bathie, R. Tournier (1997), J. Magn.
Magn. Mat. 173 20-28
S. Matthies & G. Vinel (1982). Phys. Stat. Sol. B 112, K111.
S.M. Matthies, G.W. Vinel & K.Helming, “Standard Distributions in Texture
Analysis”. Ed. Matthies (1987), p78-87, Akademie Verlag, Berlin.
C. Muller, D. Chateigner, M. Anne, M. Bacmann, J. Fouletier & P. de Rango (1996),
J. ofPhys. D, 29, 3106-3112.
M. Pemet, D. Chateigner, P. Germi, C. Dubourdieu, 0. Thomas, J.P. Senateur, D.
Chambonnet & C. Belouet (1994), Physica C, 2354240,627-628,
de Rango P., Lees M., Lejay P., Sulpice A,, Tournier R., Ingold M., Germi P. &Pernet M. (1991). Nature 349, 770-772.
H.R. Wenk, “Preferred Orientation in Deformed Metals and Rocks. An Introduction
to Modern Texture Analysis”, Ed. H:R. Wenk, (1985), pll-47, Academic Press Inc.,
Orlando FL.
H.R. Wenk, D. Chateigner, M.Pernet, J. Bingert, E.Hellstrom & B. Ouladdiaf(1996), Physica C, 272, 1996, 1-12.
H.R. Wenk, S. Matthies, J. Donovan & D. Chateigner ( 1 9 9 0 J. Appl. Clyst..

All the tape samples showed strong textures with c-axis maxima up to
46 m.r.d. for the multifilament sample (MF 2212). This is visible in the
inverse pole figures (Figure 5). For tapes (T 2212 and T 2223) these
display a maximum at (001) with 37 m.r.d. and 26 m.r.d. respectively.
For the wires (WW 2212 and WLA 2212), the wire direction inverse
pole figures display a maximum region consisting of a girdle at highangles to (001) extending from (100) to (110), and the (001) densities
are much lower than for the tapes because the c-axes form a girdle
distribution, rather than a single maximum.

12

A Fundamental Parameters Convolution Based Approach to Synthesizing Line Profiles
By A.A. Coelho', A.A. Kern2, and R.W. C h e w 3
E-mail: alan.coelho@ibm.net, Arnt-Andreas.Kern@khe.siemens.de,cheary @phys.uts.edu.au
1,2 Bruker Analytical X-Ray Systems GmbH, D-76187 Karlsruhe, Germany
University of Technology, Sydney, Broadway, New South Wales, Australia 2007

A flexible convolution based approach to synthesizing line profiles in
X-ray powder data has been developed. Fundamental to this approach,"the Fundamental Parameters Approach" (FPA), is the fact thatmeasurable geometric parameters are used to generate profile shapes.
With FPA, Bragg angles are intrinsically corrected and profile shapes
accurately described. This description of profile shapes has unmasked[2, 31 small levels of broadening in the Standards Refemce Materialsof L a 6 (SRM 660), Cr203 (SRM 674a) and CeO2 (SRM 674a). Xray lines cannot be fitted with a simple function as their shape changes
significantly over the 28 range. At low angles instrumental effects suchas the finite width and finite length of the receiving slit control thewidth of the line profile and there is appreciable asymmetry. At highangles spectral dispersion takes over and the line shape is controlled by
the emission spectrum of the target. Analyses of X-ray line profiles
from reference materials using the pseudo-Voigt function [8, 7, 4]
found that the shape tends towards Gaussian at low angles andLorentzian at high angles. Pseudo-Voigts fit well at high angles but thefit gets progressively worse at low 28 angles and systematic errors
develop in the integrated intensities when fitting strongly overlappedlines without an asymmetry correction. Of all the single function
profile models currently in use (reviewed in [ 6 ] )none of them gives anaccurate description over the whole 28 range.

Emission Profile and Instrument

Ermrson Profile

Sit

Targetw1mh

Equtonal
Divergmcc

d coy@

Axla1
Divergence
SL'cal(2B)Specimen

Fig. 1: Representation of the most important instrument and sample related
effects contributing to observed line profile shapes.

On the other hand FPA accurately models line profile over the full 28
range for a wide range of instrumental configurations [1]. The line
profiles are synthesized in terms of the emission profile, thedimensions of the diffractometer and the specimen parameters (Fig. 1).
The specimen related effects, such as specimen transparency,
crystallite size and strain broadening, are entered as refinable values.
The physical parameters of the diffractometer, such as the receiving slit
length, horizontal divergence, and the primary and secondary Soller
slit angles, are measurable quantities that can be refined. This isnecessary as in practice one would not expect to obtain refined values
matching the actual diffractometer values exactly; there are too many
second order effects in diffractometer profiles and some instrumental
effects cannot be described accurately enough to make this feasible. It
would not be unrealistic however, to expect refined values within
210% of the instrumental values [3]. Conversely, if physicallyunrealistic values are needed to describe a profile, there is clearly amajor deficiency in the model used to describe the diffractometer.
Specimens of small linear attenuation coefficients produces
appreciable broadening and peak displacement and therefore thisparameter should be refined.

04

Fig. 2: Examples of observed and fitted LaB6 (SRM 660) profiles for an
instrument with no Soller slits. In this case all the profiles are strongly
asymmetric, but are readily accommodated by the applied modelaccounting f o r axial divergence. Note the different 20 axes.

Fig. 3: Examples of observed and fitted profiles f o r the low angle lines of
CeO2 (SRM 674a) and Cr203 (SRM 674a). 5,1" Soller slits in the incident
beam, no Soller slits in the diffracted beam.

The benefits that follow from being able to synthesize and fit X-ray
line profiles accurately in terms of fundamental parameters are
manifold and clearly show up from the excellent description ofobserved line profiles (Figs. 2 and 3). It will be possible to identify
whether or not a diffractometer is operating at its optimum resolution
and determine unequivocally whether or not an observed profile
possesses specimen broadening. Synthesized profiles rather thanprofiles from reference materials can then be used as the basis fordeconvoluting instrumental effects from observed profiles. This should
allow crystallite size analysis and strain analysis to be carried out atmuch lower levels of X-ray line broadening, possibly up to apparent
crystallite sizes = 1 p . We have found that good reference powder
standards for line profile analysis are not readily available. Manymaterials such as powder standards give some degree of specimen
broadening [5].
Computationally demanding numerical convolutions, indicative of thefundamental parameters approach, have in the past made it an unlikely
approach for routine analysis but this has been overcome with theinclusion of a number of fast algorithms and by using a direct
convolution-interpolation procedure. Efficiencies in the refinement
procedure together with extremely fast algorithms has resulted in an
approach that is at least three to ten times faster than conventional
profile fit programs - even for non-convolution based fit routines.

References
1. Cheary, R.W. & Coelho, A.A. (1992), J. Appl. Cryst., 25, 109-121.
2. Cheary, R.W. & Coelho, A.A. (1998), J. Appl. Cryst., Part I, accepted for publication.
3. Cheary, R.W. & Coelho, A.A. (1998), J. Appl. Cryst., Part 11, accepted for publication.
4. Enzo, S., Fagberazzi, G., Benedetti, A. & Polizzi, S. (1988), J. Appl. Cryst, 21 ,536-542.
5. Fawcett, T.G., Crowder, C E., Brownwell, S.J., Zhang, Y., Hubbard, C . ,Schreiner, W., Hamill, G.P., Huang, T.C., Sabino, E., Langford, J.I., Hamilton, R. &Louer, D. (1989), Powder D i f 3,
, 209-218.
6. Howard, S.A. & Preston, K.D. (1989), Reviews in Mineralogy, 20, 217-275.
7. Louer, D. & Langford, J.I. (19881, J. Appl. Cryst., 21, 430-437.
8. Madsen, I.C. & Hill, R.J. (1981, J. Appl. Cryst., 21, 398-405.

Workshop on Using Powder Data to Solve Crystal Structures, May 18th, 1998,
Brookhaven National Laboratory, Upton, USA.
In the opening talk of the afternoon session, Ken Shankland (RutherfordAppleton Laboratory) gave a high-tech presentation of real-spacetechniques that are suitable for organic molecules, in particularpharmaceutical compounds. He emphasized the importance ofappropriate data-collection strategies, such as using longer counting
times at higher angles and the use of differential thermal expansion to
separate overlapping peaks. Questioning claims of progress extrapolated
from "one-off solutions," he showed structures of cimetidine, promazine
HCl, C24HgF10, capsaicin, and ibuprofin, solved by simulated
annealing and genetic algorithms. These techniques are complementary
to direct methods, in that they require detailed knowledge of themolecule's expected bond lengths and angles, so that its internal degrees
of freedom can be described by a collection of several torsion angles (upto ten for the cases shown), the only optimization criterion being theagreement with the experimentally determined structure factors. Jim
Kaduk (Amoco) described the powder structure solutions of several
moderately large molecules (dimethyl 2,6-naphthalenedicarboxylate,dimethyl 2,7-naphthalenedicarboxylate,tremellitic anhydride, anddiammonium terephthalate). He drew attention to the fact that trial
solutions with significant conformational differences can produce nearly
identical fits, and that one must frequently look to subtle features of therefinement to judge the correct structure.

David Cox and Peter Stephens
Brookhaven National Laboratory
E-mail: cox@hnlx7a.nsls.bnl.gov

This workshop was organized as part of the 1998 Annual NSLS Users'
Meeting, and was motivated by the rapid advances in the application of
powder diffraction techniques to the ab-initio solution of unknown
crystal structures during the past few years. In contrast to the wellknown Rietveld profile method for structure refinement, this is arelatively new application which has been driven mainly by thedevelopment of high-resolution synchrotron x-ray techniques, especiallyfor framework structures such as zeolites, fullerene derivatives and othermolecular compounds, and small organic molecules of pharmaceuticalsignificance. A major goal of the workshop was to review advances in
the field since the landmark 1995 Oxford meeting on "Structure
Determination from Powder Data" which followed the EPDIC IV
meeting in Chester and was organized by Bill David and colleagues, theproceeedings of which will appear shortly as a sequel to the popularbook on "The Rietveld Method" edited by Ray Young. Through thegenerosity of a number of sponsors who are acknowledged at the end of
this article, it was possible to invite several speakers from Europe, andthe 80 or so attendees were treated to a state-of-the-art exposition by aninternational cast of speakers from the USA and Europe, where much of
the cutting-edge work in this field is currently taking place. Eight posters
were also submitted for viewing during the lunchtime break.

Robert Dinnebier (U. of Bayreuth) compared standard tools (such as
direct methods) and some unconventional algorithms (extended use ofchemical constraints and rigid bodies, grid searches, the use of pseudoatoms for compact units such as phenyl rings) to a variety of structure
solutions: LiCgHs,. RbC5H5, yellow pigment 14 ( C ~ O H ~ O C ~ ~ O ~ )C(Si(CH3)3)4, Si(Si(CH3)3)4, and CgH50K. He also described the useof maximum entropy to study details of disorder and anharmonic
displacement in L ~ C S ( C H ~ ) ~ .

The proceedings were led off by Henk Schenk (U. of Amsterdam) witha brief and lucid introduction to direct methods (which to date has been
the most important tool for structure solution from powder data),
followed by a description of the POWSIM program, including therequirements for data collection, the decomposition of the powder
pattern into integrated intensities by an iterative procedure which allows
a more reliable estimate of overlapping intensities, and finally structure
solution. Over 20 unknown structures have been solved in this way, thelargest having 28 atoms in the asymmetric unit. Lynne McCusker (ETH,
Zurich) next opened up her structural "toolbox" and pulled out two newtools, texture and structure envelopes, as an aid to solving zeolite
structures. She showed that texture (preferred orientation), normallyabhorred by powder diffractionists, could in fact be put to good use to
extract more reliable intensities from heavily overlapped clusters ofpeaks from pole figure data obtained with a texture gonimeter, resulting
in a dramatic improvement in the number of framework Si and 0 atoms
found directly. She also described how to generate a "structure envelope"(periodic nodal surfaces separating regions of high and low electron
density) which can be used to facilitate computer-assisted modelbuilding of zeolite structures. A third new tool for zeolite structure
determination was discussed by Ralf Grosse-Kunstleve (Yale U,), a
recent graduate of the ETH school of toolmakers. This is the so-called"FOCUS" method, which incorporates crystal chemical information into
the structure determination and combines automatic Fourier recycling
with a topology search specific to zeolites. Zeolites also figured
prominently in the following talk by John Newsam (Molecular
Simulations Corp.), who described approaches to structure
determination based on model construction and simulated annealing
which have had considerable success in predicting and solving new
structures. Recent improvements in the algorithm have overcome someof the previous limitations and improved the performance significantly.
Several examples were given, including recent applications to molecular
structures.

Peter Stephens (SUNY, Stony Brook) presented no new structure
solutions, but instead discussed several aspects of lineshape
management, such as the influence of wavelength on resolution andintensity for analyzer crystal and parallel-blade collimator setups, andthe importance of using the correct geometry (rather than an empiricalapproximation) for the asymmetry of low-angle peaks. The bulk of histalk was devoted to a description of a newly-developed algorithm forhandling anisotropic broadening due to lattice strains in whole-patternfits. This technique, based on a multi-dimensional description of thecorrelations between lattice metric parameters, permits vastly improved
Rietveld fits. One outcome of this work was the ability to locate ahydrogen bond in the structure of sodium-parahydroxy- benzoate, which
was recently solved by ab-initio methods from powder data. In the final
talk, Bob Von Dreele (Los Alamos National Lab.) described some firstattempts at protein crystallography with powder samples, motivated by
the rhetorical question, "how many atoms can be included in a Rietveld
refinement?" In numerical test experiments on a small protein, he foundthat a free refinement was unstable, but by constraining bond lengths, hecould get smooth convergence. With high-resolution data collected at the
NSLS on a powder sample of whale myoglobin, which has 1401 atoms
in a 65,000 A=3 unit cell, it was possible to index the cell, refine lattice
parameters and profile coefficients, and, with appropriate constraints, torefine the atomic structure, in only 30 minutes per cycle on a 133 MHz
pentium laptop!
On this impressive note, Peter Stephens closed the meeting by urging theaudience to make use of the several high-resolution synchrotron
beamlines and laboratory instruments available. A wide variety ofsophisticated tools required for the ab-initio solution of complex
structures have now been demonstrated, and the next phase is to work on
problems where scientifically or commercially important information
results from the application of these new techniques.

However, the growing sense of euphoria over all these achievements was
somewhat dampened in the final talk of the morning session by Dick
Harlow (DuPont Corp.), who reviewed the current status of the $1000
DuPont Challenge, which is to be awarded to the first person to provide
a satisfactory solution of the structure of HAlF4 (an intermediate productin the industrial synthesis of A1F3 catalysts) from powder data collected
at the NSLS. In order to win the prize, the model must also account forneutron data collected from the same material, and the three"reasonable" solutions submitted to date have all failed this test so thechallenge is still open! Prospective contestants should check the Web at
http://www.pitt.edu/-geib/powder.html

The support of the following corporate and institutional sponsors is
gratefully acknowledged: International Centre for Diffraction Data, Air
Products, Amoco, Chevron, Clariant, Mobil, UOP, SUNY X3B1 Powder
Diffraction Facility, X7A PRT.

David Cox and Peter Stephens(Workshop organizers)

15Collaborative Computational Project Number 14 for Single Crystallography
and Powder Diffraction (CCP14)

CCP14, Room C14, Dareshury Laboratory,
Warrington, Cheshire, WA4 4AD, UK.
OldWebsite: http://www.dl.ac.uWCCP/CCP14/
New Website: http://www.ccp 14.ac.uk
E-mail: ccpl4@dl.ac.uk

Secretary: Lachlan M. D. Cranswick (E-mail: L.Cranswick@dl.ac.uk)
WWW http://www.ccp14.ac.uk./people/lachlan/

Examples of freely available software auto-mirrored at the
CCP14 web site include

The CCP14 is continuing in its efforts to provide freely available
crystallographic resources to academics . Recently, significant
numbers of crystallographic software packages have being updated or
created with GUIs (graphical user interfaces), making them highly
suited for teaching and people new to X-ray neutron diffraction.

WinGX Single Crystal Suite/GUI Ortep/GUI Struplo/WinPlaton- by Louis Farrugia of Glasgow University
Powder Cell Powder Diffraction Pattern Calculation andUnit-cell Refinement - by Werner Kraus & Gert Nolze
XFIT for Win95 Peak Profiling - by Alan Coelho and
Bob Cheary
Rietveld Software and Viewers; GSAS. Fullprof, Rietan, XRS-82,
XND, Koalariet, Simref, BGMN, LHPM/Rietica95, etc.

Present CCP14 initiatives include:
Auto-mirroring of Crystallographic Software, Information andResources
Auto-mirroring of Source Code, Algorithms, free C and Fortrancompilers and GUI development kits; wxWindows, Tcl/Tk, etc.
Growing list of tutorials, rnn throughs and help files for people
who make use of single crystal and powder diffraction.

-

CrystallographicNexus CD-ROM Virtual Internet andSoftware Library on CD-ROM for Laboratories Isolated fromthe Internet.
CCP14 is presently producing the Crystallographic Nexus VirtualInternet and Software Library on CD-ROM for laboratories incountries without adequate Internet access. Subject to available
resources, the CCP14 will provide a free crystallographic Nexus CDROM via air-mail on request to laboratories without the ability toaccess the CCP14 site via normal internet connections.

Dealing with Absorption and Microabsorption in Quantitative Phase Analysis

acquisition times of only 5 minutes are sufficient for full-patternquantification purposes. Each sample is prepared as a flat-packed
mount (spinning in its own plane) with the surface at a fixed angle tothe beam and the 120" arc detector is stationary. Near-random intensity
patterns are obtained over a very large angular range using thisgeometry, even for materials prone to preferred orientation in themount. Linear absorption corrections can be applied quickly in astraightforward manner from first. principles [ 12], provided that thephases in the mixture are identified. In order to demonstrate theefficacy of this PSD quantification method, the following two
examples of high- and low-absorber mixtures are shown: (i ) synthetic
hematite-quartz mixture and (ii) natural hematite-bearing clay
(Ruabon Marl). In both of these samples absorption andmicroabsorption effects are extreme when using copper radiation, but
the deliberate use of copper radiation with the PSD is actually very
useful in assessing the magnitude of the microabsorption effect: in
preparing the hematite quantification standard pattern, the sample wassimply ground until the highest background fluorescence was achieved(Figure 1). The mixture sample was similarly ground until thebackground fluorescence stopped rising (Figure 2). These results showthat the microabsorption effect can be minimized with a minimum of
grinding. For quantification purposes, this means that the particle size

Gordon Cressey & Meryl Batchelder
Department of Mineralogy, Natural History Museum, Cromwell Road,
London SW7 5BD, UK.
E-mail: G.Cressey @nhm.ac.uk& merh@nhm.ac.uk

WWW: http://www.nhm.ac.uk/mineralogy/

Powder X-ray diffraction has been applied to quantitative phaseanalysis for over 70 years, and in this time many different methods
have been developed to cope with the difficulties that mixed-phaseanalysis presents [ 1,2]. Traditionally, reference intensity ratio (RIR)
methods [3,4], using either internal or external standards have been themost widely used, and now, with the availability of digital data, fullpattern fitting techniques (including Rietveld methods) are becoming
more popular [5,6,7]. However, all these methods can be timeconsuming, and phenomena such as preferred orientation [8],absorption and microabsorption [9,lO](arising from surface
roughness) still present serious difficulties for quantitative analysis . A
new and rapid phase quantification method [11,12] utilizing a
position-sensitive detector (PSD) overcomes these particular problems
in a unique way. For all quantification tasks the PSD method works
simply by fitting the mixed assemblage pattern with proportionallyreduced 100% phase patterns of components identified in the mixture,and requires no spiking with an internal standard. Furthermore, pattern

16

and surface smoothness of each sample is replicated, and themicroabsorption effect in the mixture is directly proportional to themicroabsorption of the standard phase(s). Therefore, themicroabsorption effect cancels out when proportioning the standard
pattern to fit the mixed assemblage pattern. Results of phase
quantification using this approach [12] are demonstrated for thehematite-quartz mixture (Figure 3) and the natural Ruabon Marl
(Figure 4).

5000

4000

'

RTZ + HEMATITE mutu
01% Qr 10 "01%
Hemat

~

~

c

3000-

2000

~

z (countsx c 43)1000 -

0,

I

I

,

,

,

I

,

,

,

,

10

20

30

40

50

60

70

80

90

100

110

120

W c K J

absorption

Quartz Si02
Hematite Fe,O,

Figure 3. Quantification of a mixture of Quartz + 10% Hematite (by

0

10

20

30

40

50

60

70

80

90

100

110

volume). Microabsorption was first minimized by grinding eachsample to <10 microns. The correction for absorption (from linear
absorption coefficients and densities) is based solely on the fit(apparent volume) measurements and assumes no knowledge of actual
volumes [ 12 ].

120

WC%J
Figure 1. For coarse powder (D), whole pattern intensity is lost becauseof microabsorption: the intensity of both the Bragg peaks andfluorescence background (the undulating signal detected by the PSD)
are lowered. Grinding to a powder of about 10 micron grain size
minimizes the microabsorption effect, but further grinding to 5
microns has little further effect.

?-AsR

I

niFWT TF t / h - . 7 E 1 9 C m 0 6 O z 1 0 . 3 9 . rematte
3' S-SFACE i ? . G n h E S S O h M Cq'3ABSCRCT Oh.S I GCOOPER RAD 41C'.

q t tFFEC-

D 'FRACT O h A k 7 F..3RECLEhCF

40W}

A <37 micron sieve fraction,
ground to 4 0 microns

B c37 micron sieve fraction

C Difference pattern (5 - A)

Figure 4. Phase Quantification of the Ruabon Marl, a natural hematite-

bearing clay. Microabsorption from the hematite standard wasminimized as outlined in Figure 1, and corrections for absorption
applied as in [ 12 ].

Figure 2. If the constituent grains are large, then the Bragg peaks andfluorescence background from the high-absorber phase (hematite
peaks starred) appear too low and will lead to an error inquantification. Grinding to 4 0 microns ensures that microabsorption
is minimized (top pattern).

References[l] Klug HP &Alexander LE. X-ray difraction Procedures (Wiley, New York,)
2nd ed. (1974)[2] Snyder RL & Bish DL. Quantitative Analysis. Reviews in Mineralogy (Min.
Soc. America, Washington, DC), 20 (1989) 101-144.
[3] Chung FH.JAppl Cryst 7 (1974) 519-525.
[41 Chung FH.JAppl Cryst 7 (1974) 526-531.
[51 Smith DK, Johnson GG Jr, Scheible A, Wims AM, Johnson JL, Ullmann G.
Powder Diff 2 (1987) 73-77.
[61 Hill RJ, Howard CJ. JAppl Cryst 20 (1987) 467-474.
[71 Bish DL, Howard SA. JAppl Cryst 21 (1988) 86-91.
[8] Brindley GW. 1980. In: Brindley GW, Brown G, editors. Crystal structures ofclay minerals and their X-ray identification. London: Mineralogical Soc. p 41 1-438(1980).
[9] Wilchinsky ZW. Acta Cryst 4 (1951)l-9.
[l0] Herman H, Ermrich M. Acta Cryst A43 (1987) 401-405.
[ll] Cressey G , Schofield PF. Powder Diff II l (1996) 35-39.
[12] Batchelder M & Cressey G. Clays & Clay Minerals 46 (1998) 183-194.

17

World Directory of Powder Diffraction Programs Release 1998
Syb Gorter and Deane K. Smith

The World Directory of Powder Diffraction Programs is a continuing
project with the goal to identify and catalogue all the programs
available for powder diffraction analysis. It is a joint project of Syb
Gorter of the Program Exchange Bank in the Netherlands and Deane
K. Smith of the USA and is sponsored by the Commission on Powder
Diffraction of the International Union of Crystallography. The maincollection point is Daresbury, Great Britain. This collection point canbe reached at the following address.
ftp://ftv.dl.ac.uk/wdvvl
This site contains programs categorized into 22 areas of activity and 6
subgroups. The directory structure is designed such that one has tochoose first the platform. The next level contains subdirectories named
after the Table numbers in the printed catalogue.

Full pattern profile fitting
Deconvolution
Crystallinity/strain/texture
Rietveld - structure refinement
Quantitative analysis
Structure Determination (powder)
Structure display
Small-angle Scattering
Miscellaneous programs
Epitaxy
Teaching

All programs are available as zip files and can be unzipped on different
platforms using the unzip software available in the first level UNZIP
directory.
Further detailed descriptions on the web for all programs is underconstruction. A printed version published in 1995 by the Program
Exchange Bank is still available (Current price US$ 50, postage andGorterhandling
included).
ContactSyb(sgorter@pobox.LeidenUniv.nl) for a copy.

The table numbers cover the following categories:
Table01.
TableO2.
TableO3a.
Table03b.
Table03c.
TableO3d.
Table04.
TableO5.
Table06.
Table07.
Table08.
Table09.
TablelO.
Tablel 1.
Tablel2a.

Tablel2b.
Tablel 3.
Tablel4.
Table 15.
Tablel 6.
Tablel 7.
Table 18.
Tablel 9.
Table20.
Table21.
Table22.

Crystallographic databases
Analysis packages
Diffractometer Control
File manipulation
Peak Finding
Film reading
d-Generation
Graphical d-1 display
Phase identification
Automatic Indexing
Refinement/indexing
Refinement/error analysis
Metric analysis
Pattern Generation
Small groups profile fitting(no unit cell restraint)

A discount of US$15 is available for payment in cash.
Send orders to:Drs. Ing. S. Gorter
43 van Lennepdreef, NL-2353 NJ Leiderdorp, the Netherlands
E-Mail address: sgorter@poboxLeidenUniv.nl
Fax: (31) 71 582 0827
Phone: (31) 71 527 4415, during business hours or (31) 71 589 1388
Manager of the Program Exchange Bank, the Central Distribution Site
for Powder Diffraction Software
Maintainer of the World Directory of Powder Diffraction Software

ISPD'98 :An International School on Powder Diffraction
Prof. S. P. Sen Gupta
I.A.C.S.,Jadavpur, Calcutta-700 032.

ISPD'98 : An International School on Powder Diffraction (ISPD'98),
sponsored by IUCr and Co-sponsored by ICDD (USA), CSIR, INSA,
DST, DAE (India), will be organized at the prestigious institute ofCalcutta namely, Indian Association for the Cultivation of Science(IACS) for the first-time in this sub-continent. The School, ISPD'98,
will be inaugurated by Prof. Ted Baker, President, IUCr and will beattended by Dr. R. Chidambaram, Vice-president, IUCr, Bob Cernik(Chairman, CPD) Lynne McCusker, Tellgreu, Izumi, John Fabir another eminent speakers. Strong responses have been received and it isexpected that about 200 participants will be attending the School. The
School will have talks and 'hands-on' tutorials on all aspects of Powder
Diffraction including Rietveld method, surface structures etc.
Technical talks will be delivered by representatives from Philips,
Siemens. IUCr funding will be available for young scientists. The
Registration fee (which is a total package) is US $150 (Youngparticipants) and US $ 200 (regular participant). The School will beheld from October 7-10, 1998 during festival time at Calcutta.

These interested may contact
Prof. S. P. Sen Gupta,
Secretary, ISPD'98,
IACS, Calcutta 700 032,
India
Fax : +91-033-4732805
E-mail: ispd98@iacs.ernet.in or msspsg@iacs.ernet.in;
WWW via: http://gandalf.otago.ac.nz:8OO/~eavers/ASC~asca9S.htm

Evolving Techniques in Powder Structure Solution -- an Introduction to the Genetic Algorithm
2 How does a Genetic Algorithm work?

Kenneth D. M. Harris, Roy L. Johnston and Benson M. Kariuki
School of Chemistry, University of Birmingham, Edgbaston,
Birmingham, B 15 2TT, United Kingdom
E-mail: harrikdm@isduxl .bham.ac.uk, roy@tcindy4.bham.ac.uk

Challenges in structure solution from powder diffraction data
Sekd N Pain of Parents and~enera122~
Ofiprtng,,
usbg

The techniques currently available for structure solution from powder
diffraction data can be subdivided broadly into two categories -\\traditional" approaches and "direct-space" approaches.

Mating

The traditional approach [ l , 2, 3] for solving crystal structures directly(ab initio) from powder diffraction data involves extracting theintensities I(hk1) of individual reflections directly from the powder
diffraction pattern, with the structure then solved using the types ofstructure solution calculation used for single crystal diffraction data
(e.g. direct methods or Patterson methods). However, as there isusually extensive overlap of peaks in the powder diffraction pattern, it
is often problematic to extract unambiguous values of the intensities
I(hk1) of the individual diffraction maxima. To overcome this problem
requires either improved techniques for extracting peak intensities(there have been several important recent developments in this area), or
the use of new structure solution strategies (see below) that allow thepowder diffraction profile to be used directly in its "raw" digitized
form.

j,

Intermediate Population of (Np+ 2N,J M a 1 Stmctum(Population PJplus Offspring)
I

I"NaturalMutation

Selection"I

In the direct-space strategy [2, 4, 5], trial crystal structures are
generated in directspace, independently of the experimental powder
diffraction data, with the suitability of each trial structure assessed bydirect comparison between the powder diffraction pattern calculated
for the trial structure and the experimental powder diffraction pattern.
This comparison is quantified using an appropriate R-factor, with the
majority of direct-space methods to date having used the weighted
profile R-factor (Rwp ), as used in Rietveld refinement. We emphasizethat Rwp considers the whole digitized intensity profile rather than the
integrated intensities of individual diffraction maxima; it thus
implicitly takes care of peak overlap and uses the digitized powder
diffraction data "as measured". Alternatively, other definitions of Rfactor based on extracted peak intensities may be used. Clearly, the aimof the direct-space strategy is to find the trial crystal structure
corresponding to the lowest value of the R-factor, and the direct-spacestructure solution techniques are therefore equivalent to exploring a
hypersurface R(X) to find the best structure solution (i.e. the structure
corresponding to the global minimum in R-factor). Here f x g
represents the set (string) of variables (parameters) that define thestructure. In principle, any technique for global minimization may be
used in this context and much success has been achieved in the use ofMonte Car1o [4, 6, 7] and Simulated Annealing [5, 8, 9] searchalgorithms to explore the R(X) hypersurface. Recently, Genetic
Algorithms have also been applied in this field. This paper focuses on
fundamental aspects of applying a Genetic Algorithm to accomplish
global minimization with respect to the R(X) hypersurface.

Figure 1. Flow chart representing the evolution of the population from one
generation (population Pj) to the next generation (population P j+l ) in the
program GAPSS.

Our GA approach for structure solution from powder diffraction data
has been implemented in the program GAPSS [18]. A schematic flow
chart describing the operation of this program is shown in Figure 1.
Our method and program have been discussed in detail elsewhere [ 11,12, 13, 14, 15] (see in particular ref. [13]). In our GA, each memberof the population is a trial crystal structure, defined by the position,orientation and internal geometry of a "structural fragment"(representing an appropriate set of atoms within the asymmetric unit).
The "fitness"of each structure in the population depends on Rwp , andis quantified using the function:

F ( p ) = 1 [ 1 - tanh{27r(2p - 1)}]
2

where

(2)
and Rmin and Rmax are the lowest and highest values of Rwp in thecurrent population. The fitness function defined above has been
designed from our knowledge of the typical nature of Rwp
hypersurfaces.

The Genetic Algorithm (GA) is an optimization technique, based on
the principles of evolution, and involves familiar evolutionary
operations such as mating (crossover), mutation and natural selection[l0]. Through natural selection, the fittest members of a population
survive and procreate, passing their genetic information into
subsequent generations. A crucial feature of the GA approach is that it
operates essentially in a parallel manner, with many different regionsof parameter space investigated simultaneously. Furthermore,
information concerning different regions of parameter space is passed
actively between the individual strings by the mating procedure,
disseminating genetic information throughout the population. The
possibility of using GA techniques in structure solution from powder
diffraction data has been realized independently by two researchgroups. Our approach [ll, 12, 13, 14, 15] described here and theapproach of Shankland et al. [16, 17] differ in the definition andhandling of the fitness function as well as other aspects concerning theway in which the Genetic Algorithm is implemented. Details may befound in the papers cited.

The initial population comprises N P randomly generated structures,and the set X of variables that defines each structure can be regarded
as its "genetic code". Subsequent generations of the population are
produced through well-defined evolutionary procedures (Figure 1).
Mating ("Crossover") involves selecting pairs of structures (withprobability of selection proportional to fitness), and generating
offspring by combining genetic information from the two parents. Any
offspring that are identical to an exisiting structure in the population
are deleted immediately, preventing premature convergence of theentire population towards a single structure. Diversity of the
population is ensured by introducing a few mutant structures withineach generation; these are generated by randomly selecting structuresfrom the population and introducing random changes to parts of their
genetic codes. Natural selection ensures that only the best structures
survive and the overall fitness of the population improves from one
generation to the next.

19

3 Case study: ortho-thymotic acid

C02H
I

Figure 4. Final refined crystal structure of ortho-thymotic acid (hydrogenatoms not shown) viewed along the b axis.

Figure 2. (a) Molecular structure of ortho-thymotic acid. ( b ) Structural
fragment used in the GA structure solution calculation for ortho-thymotic
acid.

The progress of the GA structure solution calculation can be monitoredby constructing an Evolutionary Progress Plot (EPP), which shows thebest (Rmin) and average (Rave) values of Rwp for the population as afunction of the generation number. In the EPP for ortho-thymotic acid
(Figure 3), Rmin and Rave both decrease rapidly in the early
generations. R
flattens out after the 39th generation, with a further
generation. The quality of the structure solution may
drop at the 80tPin

Several structures of varying degrees of complexity have been solved
using our GA method. As an illustrative example, we highlight here thestructure solution of ortho-thymotic acid (Figure 2a), which
represented the first application of our GA method to solve a
previously unknown structure [ l l ] . Measurement of the powder X-ray
diffractogram for ortho-thymotic acid, unit cell determination (a =11.08 A, h = 8.15 A, c = 11.78 A, b = 100.2' ) and space groupassignment (P21/n) have been discussed elsewhere [11]. There is one
molecule in the asymmetric unit.

be judged by comparing the calculated and experimental powder
diffraction profiles following full Rietveld refinement, as well as byassessing the chemical and structural plausibility of the final refinedstructure (Figure 4). Rietveld refinement from the best structure
solution obtained in the GA calculation gave Rwp = 3.2 %.

In our GA structure solution calculation for ortho-thymotic acid, thestructural fragment (Figure 2b) comprised all non-hydrogen atoms inthe molecule. Standard geometries (bond lengths and bond angles)
were used, with the lengths of the two C - 0 bonds in the carboxylic acidgroup taken to be equal. The structural fragment was flexible, with theintramolecular geometry defined by the two torsion angles "1(describing rotation about the C-C bond between the carboxylic acidgroup and the benzene ring) and ~2 (describing rotation about the C-C
bond between the iso-propyl group and the benzene ring), as indicatedin Figure 2b. The position of the structural fragment was defined by the{x, y, z} coordinates of the centre of mass of the molecule and its
orientation by the angles {8; $, cp). Thus, each structure (i) was definedby eight parameters which were divided up into four groups: (xi , yi ,zi I 8i; $i, 'pi I TI^ I ~ 2 i ) .In mating, one offspring was generated by
selecting two groups at random from one parent and combining themwith the two complemantary groups taken from the other parent. The
remaining groups were then combined to generate the second
offspring. Mutations involved making a random change to two of thefour groups. For the groups (xi , yi , zi} and (8i; $, cpi], mutation
involved changing only one of the three parameters.

The final refined crystal structure shown in Figure 4 is completely
reasonable on structural and chemical grounds [ 11] For example, thestructure is found to exhibit the familiar carboxylic acid dimer motif,
without this (or any other type of) intermolecular contact being
imposed during the GA structure solution calculation. The best
structure solution in the plateau region (see Figure 3) extending fromthe 39th to the 79th generation (with Rmin D 19 %) also refines to thesame structure, indicating that the correct structure solution has beenfound relatively early in the GA calculation.

4 Future prospects
The successful application of Genetic Algorithms within theframework of the directspace approach for crystal structure solution
from powder diffraction data has been clearly demonstrated by several
examples, including the example highlighted above. In general, thecorrect structure solution is found after a relatively small number ofgenerations in the GA calculation, suggesting that the GA approach isinherently an efficient means of searching the R(X) hypersurface.
Although there has been a good deal of early success in the applicationof GAS in powder structure solution, there is nevertheless considerable
scope for future development and optimization of the strategies for
implementing GAS in this field. In this regard, we are currently
pursuing the following directions of research [13]: (i) exploring
fundamental aspects of the GA technique, leading towards new andoptimized procedures for searching the R(X) hypersurface; and (ii)developing new ways of defining the hypersurface itself, so that global
optimization may be achieved more efficiently.

25

.
8

= 20

In summary, structure solution approaches employing Genetic
Algorithms represent a valuable addition to the range of techniques(both of the traditional type and the direct-space type) that are currently
available for structure solution from powder diffraction data. The
future application of these techniques promises to reveal new andimportant insights into structural properties of solids across the fullrange of disciplines within solid state and materials sciences.

15

0

20

40

60

80

100

Generation

Figure 3. Evolutionary Progress Plot showing the evolution of Rnzin(darker circles) and R ave (lighter circles), as a function of generation
number; in the GA structure solution calculation for ortho-thymotic acid.

References[I]A. K. Cheetham and A. P. Wilkinson, Angew. Chemie, Int. Ed. Engl. 31, 1557
(1992).
[2] K. D. M. Harris and M. Tremayne, Chem. Mater. 8,2554 (1996).
[3] D. M. Poojary and A. Clearfield, Acc. Chem. Res. 30,414 (1997).
[41 K. D. M. Hanis, M. Tremayne, P. Lightfoot and P. G. Bruce, J. Amer. Chem. Soc.
116, 3543 (1994).
[5] J. M. Newsam, M. W. Deem and C. M. Freeman, Accuracy in Powder
Diffraction 11: NIST Special Publ. No. 846 pp. 80--91 (1992).
[6] D. Ramprasad, G. B. Pea, B. H. Toby, T. J. Markley and R. M. Pearlstein, J.
Amer. Chem. Soc. 117, 10694 (1995).

20

Recent Advances in the Rietveld-Analysis Program Rietan
I

Fujio Izumi,
National Institute for Research in Inorganic Materials,
1-1Namiki, Tsukuba, Ibaraki 305-0044, Japan
E-mail: izumi @nirim.go.jp WWW http://www.nirim.go.jp/-izumi/’-i I

2D(xxI

Five years have passed since RTETANl) was introduced in the wellknown book entitled “The Rietveld Method.” RIETAN has a couple ofversions for angle-dispersive diffraction and time-of-flight (TOF)
neutron diffraction.2) It has been widely utilized particularly in Japanand Asia, contributing to a large number of structural studies. For
example, the structures of the first superconducting copper oxides withfluorite and carbonate blocks were solved with RIETAN.3) This
article reports some recent progress in RIETAN with emphasis on
original technology.

5

1. Principle of partial profile relaxation
The profile function in Rietveld analysis generally contains two typesof profile parameters: primary profile parameter (PPP) and secondary
profile parameter (SPP). The dependence of PPP’s on 0 (angledispersive diffraction) or d (TOF neutron diffraction) is represented
with physical foundations or in empirical ways to afford equations
including SPP’s. For example, in the equation of Caglioti et al.,

t

5

--L-

Iff

I

15

/

20

2.5

26/”

Fig. 1 Observed (plus marks), calculated (solid line), and difference(bottom) patterns of Nu-LTA in a low-28 region. X-Ray diffraction data
were measured with a pair of Soller slits having angular apertures of ( a )58 and (b) 18.

Partial profile relaxation proved to be very effective for analyzing
intensity data including highly asymmetric reflections in low-20
regions. Profile asymmetry, particularly pronounced in the BraggBrentano parafocusing geometry and constant-wavelength neutron
diffraction, may be inadequately approximated with symmetric profile
functions made asymmetric by various procedures. In particular, flatspecimen and specimen-transparency errors in the parafocusing
geometry are difficult to represent analytically. With profile-relaxed
Rietveld refinement, we have been successfully analyzing the crystal
structures of various zeolites which exhibit reflections in 20 regions
lower than 208. Figure 1 exemplifies part of Rietveld-refinement
patterns for a zeolite, hydrated Na-LTA (Linde Type A), whose X-ray
diffraction data were measured with CuKa radiation and two different
goniometers.5)

the full-width-at-half-maximum (FWHM), H b is a PPP specific forreflection k while U, V, and Ware SPP’s common to the whole 0 (d)range. We refine not PPP’s but SPP’s in Rietveld analysis. Suchequations impose a kind of equality constraints on PPP’s, sometimes
failing to express relations between PPP’s and 0 (d) satisfactorily. As
a PPP deviates from an equation relating it to 0 (d),the fit between
observed and calculated profiles gets worse and worse. Such misfit
gives rise to serial correlation committing a prerequisite of Gaussian
distribution of residuals in least-squares methods.
We have devised a new technique called partial profile relaxation:)where the PPP’s of (nearly) isolated reflections specified by the user
are locally refined independently of SPP’s. In Rietveld refinementwith partial profile relaxation, PPP’s of these reflections are all or
partially freed from equations relating PPP’s to 0 (d) and diffraction
indices, hkl. On the other hand, peak positions and integrated
intensities for the relaxed reflections are, respectively, calculated fromlattice and structure parameters in the same fashion as those for theother reflections. Part of PPP’s may be constrained by the equations
applied to reflections not to be relaxed. Though the profiles of only
low-Q reflections can be substantially relaxed except for very simple
structures, better fits in this region lead to improvements in fits in ahigh-Q region.

Other new features implemented in the latest version5) are1) a convenient and user-friendly character-based user interface using
a preprocessor,2) correction of surface roughness on the basis of four models,
3) two peak-shift functions with forms of Legendre polynomials,
4) introduction of the anisotropic profile broadening effect into thesplit-type profile functions,
5) imposing constraints on interatomic distances and bond angles
with outputs from ORFFE,
6) analysis of intensity data measured with variable step widths andcounting times,
7) substantial integration with a MEED program for a maximumentropy method (MEM).7)
The last item will be described separately in the next section.

Partial profile relaxation is especially suitable for samples showing
anisotropic profile broadening. This technique is sound and powerfulin the point that neither assumption nor approximation is required inregard to the dependence of PPP’s on 0 (4. We can even apply more
flexible profile functions to relaxed reflections to improve the fit
between observed and calculated patterns. In principle, profile
relaxation can be introduced not only into Rietveld refinement but into
Pawley refinement.

3. MEM-based visualization and fitting of diffraction patterns
RIETAN has recently been combined with MEED7) to form a joint
software named REMEDY.8) After Rietveld analysis, ’observed’
structure factors, Fa's, are evaluated by partitioning observed
intensities among overlapping reflections in proportion to their profiles
calculated from final parameters in Rietveld analysis. These Fo’s areanalyzed by the MEM to give three-dimensional electron or nuclear
densities, which are more or less biased by a structural model in
Rietveld analysis. We can, however, extract structural details from the
Fo’s by the model-free MEM because the Fo’s contain contributions
that have not been taken into account in the structural model.

2. RIETAN for angle-dispersive diffraction
We have made it possible to analyze angle-dispersive diffraction databy the Rietveld method under partial profile relaxation’) with splittype pseudo-Voigt and Pearson VII profile functions.6) On the use of
the former function, a modified split-type pseudo-Voigt function,
where the FWHM’s of Gaussian and Lorentzian components differ
from each other, can be fit to observed profiles of relaxed reflections.

22Solving Crystal Structures Ab Initio Using Powder Diffraction Data
E, and Z . While a plausible (real space) structure could be obtained for
the E conformation, it did not refine well. Changing to the Z
conformer quickly resulted in identification of a promising low-energy
structure, one which refined well.
The ester groups are rotated 20” out of the plane of the naphthalene
ring. This rotation “costs” about 1 Kcal/mole/ester group. The crystal
structure consists of layers perpendicular to the a-axis (Figure 1). The
aromatic rings are inclined, and stack parallel to c, with “side-to-side”
interactions along b. These layers interact only loosely with theirneighbors along a, with only end-to-end contacts between the layers.
The twist of the ester groups helps the molecules interlock within thelayers. The small energy penalty of the rotation results in a very
efficient and beautiful packing.

James A. Kaduk,
Amoco Corporation, P.O. Box 301 1 MC F-9, Naperville IL 60566 USA
E-mail: kaduk@amoco.com

Many technologically-important materials do not form the single
crystals “necessary’ for determining their solid state structures using
conventional crystallographic techniques. Knowledge of the crystal
structure of a material makes it possible to rationalize/explain/predict
many other properties, and facilitates the use of diffraction techniques
to obtain morphological and mesostructural information from thepowder data. Having the structure “in hand” when it is needed saves
time and money; the effort of determining crystal structures thus is asort of “intellectual capital investment”, and can be justified as such.
Solution of a crystal structure “asks a lot” from the powder data. The
powder crystallographer is wise to use all information available about
the compound. Such information includes chemical connectivity, local
coordination, and stoichiometry. For small organic molecules wegenerally have the advantage that the molekular structure is known
from spectroscopic techniques; it is “only” the crystal structure whichmust be determined. Several different techniques for solving
structures using powder data are described here.

Dimethyl 2,7-naphthalenedicarboxylatePaDimethyl 2,6-naphthalenedicarboxylate

Figure 2. The crystal structure of dimethyl 2,7nuphthalenedicarboxylate,viewed down the monoclinic b-axis.

A common engineering practice is to modify polymer properties by
incorporating a co-monomer to alter the packing of the polymer
chains, and thus the physical properties of the polymer. Dimethyl 2,7naphthalenedicarboxylate (27NDC) is of interest as a potential comonomer in PEN applications. The crystal structure of 27NDC
provides the framework for understanding the physical properties, andsheds light on how it may affect polymer chain conformations.
The powder pattern could be indexed on a primitive monoclinic cell,and the space group was ambiguous. The density is such that Z = 2.
Space group P21 was assumed, and verified by successful solution andrefinement; no additional symmetry was detected in the refinedstructure.

Figure 1. The crystal structure of dimethyl 2,6-naphthalenedicarboxylate,viewed down the monoclinic b-axis.

Poly(ethy1ene 2,6-naphthalenedicarboxylate), PEN, is a promising
polymer for use in applications requiring superior physical properties
to those of poly(ethy1ene terephthalate), PET. The commercial
monomer, dimethyl 2,6-naphthalenedicarboxylate(NDC) is preparedby esterification of 2,6-naphthalenedicarboxylic acid, which isprepared by homogeneous oxidation of 2,6-dimethylnaphthalene(DMN). Determining the crystal structure of our commercial material
seemed like a good idea.

A 27NDC molecule was built in Cerius2. The ester groups wereoriented in the Z conformation observed in NDC. The molecule waspositioned roughly in the cell; the long a and short c cell dimensions
put severe constraints on the orientation of the molecule. This
structure was used as input to the STRUCTURE-SOLVE module of
Insight11 [5]. This module implements a Monte Car1o simulated
annealing procedure, in which the metric is not energy, but theagreement of the observed and calculated power patterns. Initial runs
used a rigid planar molecule; in later runs the ester torsion angles werealso allowed to vary. The best solution was used as input to a Rietveld
refinement. In the initial refinements, the methyl carbons wereomitted; large peaks occurred in a difference Fourier map at thepositions predicted by STRUCTURE-SOLVE.

This structure solution is an example of “trial and error”. The powder
pattern of NDC can be indexed on a primitive monoclinic cell, with Z= 2. The space group was unambiguously determined as P21/c. It
therefore seemed likely that the molecules resided on centers of
symmetry. The two shorter cell dimensions are similar to those of 2,6dimethylnaphthalene, providing some indication of the orientation of
the molecule. The NDC molecule was placed at a center, andmanipulated using Cerius2 [4], simultaneously monitoring both thereasonableness of the structure (intermolecular contacts) and theagreement of the observed and calculated powder patterns. This was ahumbling exercise, since it demonstrated just how sensitive thediffraction pattern is to molecular orientation!

Both ester groups are in the Z conformation, but they are rotated only
6 and 11” out of the ring plane. The crystal structure (Figure 2)
consists of layers of molecules perpendicular to a. In an individual
layer, all of the 27NDC molecules are parallel, but the tilt differs inadjacent layers.

Solving the structure was complicated by the fact that there are twopotential low-energy centrosymmetric conformations of the molecule,

24

. .,

:I..

".*'..

-..,.
--.,

. .

-.-. .

. ..

.

.. .

.. .

... .

A
for automaticquantitative phase analysis

+
+
+

+

+
+

+
+

Windows graphical user interface
Full power of BGMN@algorithm
Calculation and separation of instrumental function
Constraints for all parameters definable
Automatic background determination during refineme
Spherical harmonics model for correction of preferred orientation
Calculation of amorphous content with internal standard
Extendible phase database with structure information

Bogen st rasse 4 1 D-22926 Ah rensburg

26

http:// www.roentgenseifert.com
eMail: ROENTGEN.SEIFERT@t-online.deTel.: +49(0)4102 8074, Far: +49(0)4102 807-189

However, especially for low-symmetry crystal structures the given
manipulation tools enables a successful variation of structure models
what has been proved e.g. by RECK (1994). For education it is useful
to demonstrate the influence of local symmetry on the crystal structure
but also on the resulting powder pattern. So one can study the influenceof the the position of heavy atoms within the unit cell or the
dependence of the orientation of molecule fragments etc.
(see http://www.bam.de/a-v/v-l/powder/e-cell.htm1).
Fig.3 The subgroups have been subdivided in 4 classifications. In analogy
to the transformation the existing subgroups can be chosen by selection.

Powder diffraction simulation
The different examples given below show clearly that the advantage of
PowderCell is based on the combination of structure visualizer andpowder pattern generation. Even of the last one we maked a point
because from the comparison of experimental and theoretical curve
results the quality criterion for the used or created structure model. In
contrast to that the structure viewer really represents only the means toan end.

PowderCell represents one of the first programs which is able to derive
the subgroups of a crystallographic space-group type. The used data
are based on extensive derivations of MULLER (1994), who puts theseat our disposal. The subgroup procedure allows to reduce thesymmetry density of a given crystal structure. To this end all possible
maximal subgroups classified in translutionengleiche andklassengleiche will be displayed and the user must only select the rightone (Fig.3). Also here the user of the program gets the complete
transformation of the crystal structure containing the adapted lattice
parameters as well as the complete number of atoms of the asymmetricunit corresponding to the new symmetry. Especially the last one is thehighlight of this procedure because it simplifies the work with suchproblems, e.g. the investigation of phase transitions or theinterpretation of the influence of lower symmetric external effects on
the atomic arrangement within the crystal. Thus it should be possible
to demonstrate structure similarities or to transfere one structure intoanother. Furthermore the Wyckoff splitting can be investigated bydecreasing of symmetry density step by step. Please notice that the
subgroup relations are defined for the first setting only, i.e. sometimes
it is necessary to transform the derived subgroup into a conventionalsetting before the next decrease of symmetry can be carried out. The
invariance of the resulting powder pattern is a good criterion for thecorrectness of the used procedure and can be observed quasisimultaneously. The apparent change of the extinction laws, of thereflection indexing, of the multiplicities is suitable to show that a lot of
crystallographic conventionts are based on the mathematicaldescription used. The derivation of subgroups enables also thedemonstration of the difference between systematic and accidental
extinctions.

The generation of the powder pattern considers several parameterswhich influence the resulting diffractogram - Fig.4. The mostimportant fact is that these parameters can be changed very user
friendly. On the work sheet experiment the X-radiation can beselected from a set of 11 different anode materials, the anomaleous
dispersion or the al/a2 doublet can be switched on/off, the angle range
can be set as wished. Thus the influenceof the different parameter can
be studied intensively, especially if one considers additionally thatthese are dependent on the used crystal symmetry, lattice parametersand element distribution. However, the resulting reflection intensities
must be convoluted using suitable profile functions. Furthermore thechange of the peak width in dependence on the diffraction angle must
be considered by the use of a 3 parametric model function (Caglioti(1958)). On the other hand preferred orientations influence the integral
intensity thereby that the effective multiplicity varies.

Using the subgroup relations it is very easy to show e.g. the corellation
between the different modifications of BaTiOg observed in formerdays and described by the space groups P m3m, P 4mm, R 3m and A
mm2. Thus it is really possible to derive the different modifications
from the Perowskite structure (P- m3m). However, also ordered
strcutures like Ni3AI (g' precipitates in nickel-base superalloys structure type: L12) can be extracted from the disordered structure of
the g phase: Ni0.75A10.25 (structure type: Al).

Fig. 4 Free dejinable parameters for the powder dijfraction simulation in
dependence on each phase. The phase-independent, general parameters
can be set in experiment.

From these a lot of demonstrations are imaginable e.g. how does theuse of variable slit system or primary monochromator influences thepowder pattern; when the anomaleous dispersion must be considered;
how one may detect the character of preferred orientation, how differs
X-ray and neutron diffraction patterns etc. Very often these are verypractice-oriented questions, so that the simulations of such problems
may support the teaching very effectively.

Structure manipulation
The lost of symmetry caused by derivation of subgroups is equivalent
to a decrease of local symmetry, i.e. an atom located on a special
position will be transfered to a location described by a more generally
position. The result is that often the atom is not more fixed on thisposition but gets the ability to move within the unit cell. This has been
carried out in PowderCell.

Data and graphical output
PowderCell enables the user to print directly all data displayed or listed
in the program in any form, e.g. the structure data, the comment, thereflection table and the used experimental conditions. Furthermore it ispossible to print the crystal structure as well as the powder pattern
directly. However, it is more important to export the graphs because in
PowderCell one cannot edit the pictures (Fig. 5). For the crystal
structure representation the use of POVRay, a freeware raytracing
program, has been supported (www.povray.org). POVRay generates
photorealistic pictures using the exported scripts (Fig. 5).

To this end parts of the crystal structure must be selected. These will
be visualized as hatched atoms. The tools for moving allow to rotate ortranslate the selected parts. Thus it is possible to shift along the basis
vectors or along a direction defined by two atoms. Rotations areallowed around a given atom, the center of gravity of selected atoms or
arround a direction defined by two atoms again.
Until now the manipulation is not Wyckoff position sensitive i.e. it is
impossible to translate or rotate under condition of preservation of thelocal symmetry. Quite the reserve, the symmetry of the new position
will be analysed again and all symmetry-equivalent positions will be
generated.

28

CSD/ICSD databanks. Arguments in this sense are found in themultiplication of methods allowing to locate molecules or known
fragments. All crystal systems were the subject of SDPD, themonoclinic and orthorhombic systems being the more generally
studied with respectively 42.4 and 30.1%. Instruments selected weretraditionally either neutron reactors (65), synchrotron radiation sources(64) or in-laboratory conventional X-ray diffractometers with (94) orwithout (143) incident beam monochromator. In fact these numbers do
no reflect the possible joint use of 2 or 3 of these instruments. Neutrons
were used scarcely alone (22), many neutron cases correspond tostudies of liquid-solid state phase transitions at low temperature (Fitch
and Cockcroft). That the most complex structures will soon be solved
from synchrotron data is evidence. We should first agree on what is acomplex structure and define complexity criteria.
Anyway,conventional X-rays have not really been outperformed yet bysynchrotron radiation in quantity (237 and 64 applications,
respectively) nor in quality (no real gap in complexity is observed,
although it should be).

Some times ago, it was stated that we were unable to determine
structures as large as those we could refine by the Rietveld method.
The new paradox is that we can locate now molecules in much bigger
cells than we could refine without constraints. Due to resistance tochange, habits listed in the SDPD-Database have chances to give us thetendencies for the years to come. Few softwares dominate each step of
the SDPD whole process, they will probably extend their domination
unless more efficient ones appear. Not all softwares are in the publicdomain so that some methods are the exclusivity of developers or
teams repeating structure determinations by their own way. SDPD will
not expand faster before a larger distribution of these new softwares.
If your works is lacking in the database, please send the references(annel@fluo.univ-lemansfr).
1. W.H. Zachariasen, Actu Ctystallogr: 1 (1948) 265-268
2. http://fluo.univ-lernans.fr:8001/iniref.html

Line Profile Analysis and the Rietveld Method: crossing paths?
Matteo Leoni* and J. Ian Langford'*Dipartimento di Ingegneria dei Materiali, Universita di Trento,
38050 Mesiano (TN), Italy&School of Physics & Astronomy, University of Birmingham,
Birmingham B1S 2TT, UK
E-mail: Matteo.Leoni@ing.unitn.it & j.i.langford@bham.ac.uk

Is a combination of the Rietveld Method (RM) and Line Profile
Analysis (LPA) possible? Or, in other words, is it possible to obtainmeaningful microstructural information from pattern refinement?
Opinions in the scientific community are divided, but the answer isprobably "Yes, provided we are aware of what we are doing", with theadditional proviso that, at least for the time being, sample
imperfections are not too complicated. However, in all cases thephysical meaning and validity of a solution have to be carefully
checked against one's experience and intuition and, if practicable,
information from other techniques. While the traditional Rietveld
recipe for pattern generation and refinement is mostly unequivocal, thecorrespondence between an observed broadened peak and a set ofphysically sound microstructural parameters is not: a given line-profile
shape can be compatible with different broadening models.
The question of profile shape is of course central to obtaining precise
and meaningful results from the structure refinement, but empiricalshape and shape-trend functions have mostly been used since theoriginal work of Rietveld. From the technical point of view it is quite
easy to embed in the refinement procedure a routine for the generationof profile shapes based on microstructural parameters. More-or-lessindependently, some authors (Scardi and Lutterotti, Delhez andMittemeijer, Cheary and Coelho, von Dreele, Bergmann, for example)
have gone some way towards accomplishing this in recent years byusing different approaches and models, but rarely has a convincing
analysis of the validity of the results been carried out. Clearly both the
RM and LPA are defined mathematically over a wide range ofparameters, but, owing to the phenomenological nature of the models
which often underlie the mathematical analysis, and also to various
approximations, the results can be of limited physical significance.
This in turn means they must be taken cum grano salis, unless avalidation a priori carried out with traditional methods is undertaken.
For example, extremely high values for crystallite size or microstrain
derived from Rietveld refinement have been reported in the literature.
These cannot be justified by any model since the criteria on which themodels are based have not been met.
It must be stressed that LPA is limited in its application and has not yet
been developed as a global tool. It merely gives an explanation for lineprofile shapes in somewhat restricted cases. There are various models,applied singly or simultaneously, which are only valid when certain
sources of broadening are present, such as crystallite size, stacking

faults, dislocations, microstrain or composition gradients, etc.. A
definitive microstructural refinement tool, able to handle all of thesehas not yet been established, though some proposed procedures
perhaps represent a move in the right direction; those derived from
integral breadth methods (English and Dutch schools) and single-peakFourier approaches (Italian school) seem the most reasonable to be
included in Rietveld codes. Due to their nature, and since they canaccount for anisotropic broadening, they can permit a directcomparison to be made with traditional profile analysis techniques,
such the Warren-Averbach method. However, even in this case, validity
is restricted by the limitations of the underlying theories, i.e. limited
crystallite size and non-specific microstrain, both presenting simple
distributions. Improvements in the field may well be reported in the
future, but the best solution is likely to be a comparative one.
A few words should be added on purely quantitative aspects, related tothe instrumental contribution to the profile shape. Recent additions to
the literature show the possibility, in limited cases, of calculating the
instrumental profile shape for a given geometry; actual measurements
are, in fact, conducted on suitable standard materials that are notguaranteed to be defect-free (even the NBS line-profile standard has
been proven to be slightly defective). On the other hand, since it is
impossible to be certain that calculations take into account all
instrumental effects, quantitative values have to be considered good
estimates within the reliability of the instrumental profile. (This isvalid also for traditional LPA.) Even this field is still open and adefinitive solution is still awaited.
In conclusion, the state-of-the-art allows for a microstructuralrefinement in the Rietveld method, but clearly the nature of any
structural imperfections present in the sample must be ascertained by'traditional' methods beforehand; characterization of microstructure ismore than simply reporting values of 'size' and 'strain'. Also, prior to
attaching any physical significance to the results, a check on the rangeof validity of the model employed and, whenever possible, a crosscheck of the results, should be carried out. However, even when the
results are not physically meaningful, a profile shape model whichadequately accounts for anisotropic sample broadening can enhance
the quality of pattern fitting and hence the quality of the refinedstructural data.
Since the literature on the subject is vast and growing continuously, a
dedicated Website, intended to expand with further contributions fromthe scientific community, is being set-up by the authors under the URL
http://bragg .ing.unitn.it/sizestrain/
Mirroring and further notes will be available on the CCP14 Website
http://www.ccpl4.ac.uk

AXES - a software toolbox in powder diffraction
crystalline structure analysis using Williamson-Hall Plot
(Mändar, et al. 1998; see Figure 3.) and Fourier analysis of peak
shapes;diffraction peak shape simulation using interference functions
and column length distribution functions.

By Hugo Mandar and Toivo Vajakas
Department of Physics, University of Tartu, 4 Tahe Str., EE2400 Tartu, Estonia.
E-mail: hugo@physic.ut.ee

Introduction. Progress in powder X-ray diffraction has always been inhigh correlation with progress in developing of new algorithms,
methods and computer programs for diffraction data processing. This
paper gives an overview about the history and basic features of aprogram system AXES.

I
Figure 3.

Dialogue for ev\aluation of cry stallite size arid
lattice deformation on the bases of Voigt
analysis and Williamson-Hall Plot

The source size of the program has grown more than three times
containing now about 8200 lines Full set of AXES tools is in form ofcompiled program available in a version A, which is distributed asshareware and requires a licence A selected set of tools sufficient for
diffraction data preprocessing, peak detection, fitting, indexing, cellrefinement, crystallite size estimation and preparation of input files for
Rietveld analysis is available free of charge in version B for educationfrom ftp://ftp.physic.ut.ee/pub/pc/axes and the program suite
CCP14 The current version of AXES 1 9 (including also the external
programs and databases) should meet the needs both a professional
crystallographer and a beginner in the field of powder diffraction

searchimatch
Historical background. Developing of AXES started in1992 in theframework of a cooperation between Universities of Konstanz(Germany) and Tartu (Estonia). The basic idea of the elaboration of ourprogram was to get a user-friendly X-ray powder diffraction structure
analysis package which includes available programs oriented for asingle task and which can be used to perform a full route of analysis
starting from data collection and finishing with structure visualization.
This kind of program, called GUFI, was under development since 1987
in University of Heidelberg by Robert E. Dinnebier (Dinnebier, 1993).
We selected GUFI (and its source language - Borland Pascal 6.0) as an
initial platform and started to contribute to this project. Until 1994 thefollowing programs and features were included or advanced:
call of structure visualization programs (SCHAKAL, ORTEP,
ORTEX, MOLDRAW);
individual and whole pattern fitting (Mandar, et al. 1994);
compare multiple diffraction patterns and peaks in graphics;
search/match on the bases of ICDD/PDF-2 database (Vajakas& Mändar, 1994, see Figure 1. and Figure 2 );manual background detection;a version of long patterns (190000 points);
online help,
improvement of 28 & I calibration algorithms and graphicaluser interface (GUI).

Figure 4. Layout of' Fitting Manger dialogue

Example. The following example on the bases of the IUCr CPD
Round Robin on Quantitative Phase Analysis sample No. 1G shows
how AXES helps preparation of initial data for Rietveld analysis.
From 27 different import/export formats of diffraction data available in
AXES we use the Diffrac 3.x format to read in the pattern. For Rietveld
program the pattern is saved in FULLPROF *.DAT format.
Visual evaluation of background line gives often better estimatescompared with analytical functions or Fourier filtering methods.
Commands in dialogue Background Manual facilitate graphicaldetection of background curve which thereafter is saved in
FULLPROF *.BAC format.
Set of dialogues Pattern Fitting: Peak Parameters, WPPF

Figure 2. Pattern search results of CPD-RR sample 1
The phases which are present in the sample are detected b!
their higher values of Figure-Of-Merit (FOM) comparedwith others proposed by search algorithm
Commercialisation of GUFI in 1994 urged us to continue the project ina separate direction. The new program, after extracting the GUFI
specific pattern processing dialogues and algorithms, and porting it to
Pascal 7.0 with DPMI support, was called AXES. Since this time thefollowing main tools have been included:
structure data import/export for POWDERCELL, ICSD,LAZY-PULVERIX, GSAS, MOLDRAW, SCHAKAL;
set of dialogues for preparation of input data for FULLPROF(Mandar, et al. 1996);

31

Parameters and Fit Manager (see Figure 4.) are used for calculation of
initial values for peak shape parameters (u, v, W, mo). For a large
number of peaks it is sufficient to fit peaks in three ranges - in the
beginning, middle and end of the pattern, including 4-6 peaks in eachrange. A default fitting first with Gaussian and next with Pearson VII
type function gives u=0.015, v=-0.004, w=0.020, m0=9.

parameters (except the maximum number of refinable parameterswhich has to be given in Refin. Models dialogue), this is done by
AXES. In case of complicated models, where the codewords are
fractional, the user has to edit a *.PCR file directly. This can be done
by a text editor accessible from inside the main dialogue of the *.PCR
editor.

Now follows preparation of parameter files for Rietveld analysis. The
shape parameters are entered in dialogue Phase Refinable General
Parameters (see Figure 5) of the FULLPROF *.PCR Editor. The other19 dialogues of this set are used for preparation, inspecting and editing
the refinement model of the sample. In case of structures containing
many atoms in the unit cell, the user has a facility to import structure
data from different sources: ICSD database, GSAS *.EXP file, input
files of structure visualization programs (e.g. MolDraw, PowderCell).

Export and import of current set of parameters is done automaticallyby starting and finishing of FullProf. Fitting quality can now beassessed in graphics (see Figure 6.) using commands in dialogue
Compare. The curves and marked points in the current graphics
window can be saved into an ASCII file in x-y (an n column) format
which is easily retrieved by any graphics drawing programs.

Perspectives.
AXES is a MS DOS program but runs
successfully in MS Windows. Perspectives of advancement areconnected with porting it from DOS to Windows. Delphi had been
selected as a new software platform and preliminary work was started
in 1997.
References
Dinnebier, R.E. Entwicklung eines Programmsystems zur Messung und Auswertungvon Rontgen-Pulverdaten. Ph.D. Thesis, Mineralogisch-Petrografisches Institut,
Universitat Heidelberg, 1993.
Mändar,H., Felsche,J., Mikli,V., Vajakas,T. AXES 1.9: new tools for estimation of
crystallite size and shape by Williamson-Hall analysis. J.Appl.Cryst., 1998, May, 24
pp. (submitted).
Mändar,H., Vajakas,T., FelscheJ., Dinnebier,R.E. AXES 1.4 - a program the forpreparation of parameter input files for FULLPROF, J. Appl. Cryst., 1996,29,304.
Mändar, H., Vajakas, T., Haav, A., Felsche, J. A new single-profile and whole-powder-pattern fitting method in a XRPD program GUFI. Zeitschrift fürKristallographie. Supplement Vol. 8 (15th ECM. Book of Abstracts), Dresden,
28.Aug.-2.Sept., 1994, 135.
Vajakas, T., Mändar, H. Phase identification with X-ray powder diffraction data
evaluation program GUFI. Abstracts to "International Conference Powder
Diffraction and Crystal Chemistry PD-94': Saint Petersburg, Russia, June 20-23,
1994, p.29-30.

F i ~ i i5.
l~!Nxei-~ed. d c u l n t e d a d iirilcrcncc c i m e5
shoun in gfiiphical use11interface of XLTS. Sixteen
patterns and a din'erence curve can be visualized andanelysedusing seven functions of GUI.

The most important facility of these dialogues is that in general, theuser does not need to take care of counting, ordering and format of

Memetic Algorithms for molecular conformation and other optimization problems
A main difference between GAS and MAS is that the latter approachtries to use all possible knowledge available to solve the problem.
Some SS procedures can be be classified as MAS too, though none of
the approaches properly includes the other. In essence, MAS constitutean exercise of humbleness and common sense; if several alternativealgorithms for the problem already exist, it should be a wise idea to usethem together. This is of particular interest for the practitioner, who has
been relying on a well-known code which enables to give locally
optimal solutions but requires some extra global optimization (adding
stochasticity to the search). Thus MAS are sometimes called "Hybrid
Genetic Algorithms", or "Lamarkian Evolutionary Algorithms" oreven "knowledge-augmented GAS". Other denominations include"Genetic Local Search" or "Parallel Genetic Algorithms". They areeasy to be recognized from the so-called "standard GAS" since in MAS
the new configurations (children) are created from highly evolved"parents" from previous generations. The independent evolution ofparents is done using knowledge about the problem. In non-linear
settings this generally achieved using gradient information. In
combinatorial optimization problems they generally use some local
search or constructive algorithm but truncated exact procedures (liketruncated branch-and-bound or branch-and-cut techniques) can also be
used. In all cases the existence of theorems and properties related tothe structure of the optimum configuration greatly help to reduce thewhole search process.

Pablo Moscato
Departamento de Engenharia de Sistemas,
Faculdade de Engenharia El'etrica, Universidade Estadual de Campinas,
C.P. 6101, Campinas, SP, CEP 13081-970, BRAZIL
E-mail: moscato@densis.fee.unicamp.br
WWW: http://www.densis.fee.unicamp.br/-moscato/(mirrored at CCP14)

With the name of 'Memetic Algorithms' we recognize a class ofmetaheuristics which constitutes an emerging paradigm for
optimization. For more than a decade now it has been applied withsuccess to a large variety of combinatorial and nonlinear problems. In
the last four years, and mostly in the last two, several techniques
introduced in molecular optimization problems can be characterized inthis way. We try to just introduce here the new techniques while weseek to emphasize the relation with previous and current work in
Memetic Algorithms and Scatter Search. Memetic Algorithms (MAS)is a population-based approach to optimization [28]. It can be appliedboth to nonlinear and discrete (combinatorial) optimization problems.
They are orders of magnitude faster than Genetic Algorithms in someproblem domains. We call it a 'metaheuristic' since it is a general
purpose strategy that guides other basic heuristics or truncated exact
methods. Other metaheuristics, like Simulated Annealing (SA) or
Guided Local Search (GLS) (which guide some underlying "Hillclimbing" procedure), are applied to a single "optimizer" and thus they
can not be categorized as 'population-based. Basic Tabu Search (TS)techniques also use a single optimizer, but more evolved
metaheuristics like Scatter Search (SS), also use procedures based in"multiple-point" optimization. Genetic Algorithms (GAS), also try to
evolve solutions in configuration space by using a "population" of
individuals which represent alternative solutions of the problems.
Good reviews stressing the similarities and differences of theseapproaches can be found in [l0] [ I l l and [28] (the latter, written in
1990-92, anticipates the relevance of MAS in protein landscapes).

The term "memetic" comes from R. Dawkins introduction of the term"meme" to denote an analogous to the gene but in the field of cultural
evolution. In a Caltech report written in 1989 we discussed several
MAS for combinatorial optimization and we conjectured the reasonsfor its success over the standard GAS approaches. Currently, a home
page we maintain contains links to all available papers and relevantbibliography for MAS. In this note, due to length constraints, we will
omit most of the references available from the web page. The Caltech

32report that gave its name to the, at that time incipient, field discussed a
hybrid of GAS and SA developed with M.G. Norman in 1988.
Currently, several papers are applying hybrids of GAS with SA or othermethods to a variety of molecular optimization problems [39] [34] [33][22] [1] [49][37] [I8] [21] [12] [I9][do] [3] [27] [8] [23] P51. In
all of them, the authors of these papers refer to their metaheuristic as"genetic", probably being unaware about the existence of other MAS.
For instance, Fu et al. in [9] say that GAS "combined with conjugatedgradient or molecular dynamics has been demonstrated to be efficientfor the ground-state configuration search in materials research, e.g.
fullerene formation, in this paper, based on the generalized tightbinding molecular dynamics, we apply the GA to study the surface
reconstruction of Silicon (001) for the first time". Hybrid population
approaches like this can hardly be catalogues as being 'genetic', but
this denomination has appeared in previous work by Deaven and Ho[5] which got extra recognition due to an article by J. Maddox in
Nature [24]. Other applications include cluster physics. Niesse andMayne in [29] said: "In a recent paper, Gregurick, Alexander, andHartke [S. K. Gregurick, M. H. Alexander, and B. Hartke, J. Chem.
Phys. 104, 2684 (1996)] proposed a global geometry optimization
technique using a modified Genetic Algorithm approach for clusters.
They refer to their technique as a deterministic/stochastic genetic
algorithm (DS-GA). In this technique, the stochastic part is a
traditional GA, with the manipulations being carried out on binarycoded internal coordinates (atom-atom distances). The deterministic
aspect of their method is the inclusion of a coarse gradient descentcalculation on each geometry. This step avoids spending a large
amount of computer time searching parts of the configuration space
which correspond to high-energy geometries. Their tests of thetechnique show it is vastly more efficient than searches without thislocal minimization". Other papers in the area of cluster physics include[30] [16] [31] [37] [I5] [6]. Other evolutionary approaches to avariety
of molecular problems can be found in: [36] [32] [8] [26] [25] [14][13]. Their use for design problems is particularly appealing, see: [18][38] [2]. They have also found a way into protein design [7] [20],probably due to their landscape structure [28].

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algorithm for folding protein structures using NMR restraints. Protein Science,7(2):491--499, Feb. 1998.
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molecular design. Journal of Computer-aided Molecular Design, 10(4):337--358,
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[3] T. Dandekar and P. Argos. Identifying the tertiary fold of small proteins withdifferent topologies from sequence and secondary structure using the genetic
algorithm and extended
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[6] D.M. Deaven, N. Tit, J.R. Morris, and K.M. Ho. Structural optimization of
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[8] R. Doll and M.A. VanHove. Global optimization in LEED structure
determination using genetic algorithms. Surface Science, 355( 1-3):L393--L398, Jun.
1, 1996.
[9] R.T. Fu, K. Esfarjani, Y. Hashi, J. Wu, X. Sun, andY. Kawazoe. Surface
reconstruction of Si (001) by genetic algorithm and simulated annealing method.
Science Reports of The Research Institutes Tohoku University Series A-Physics
Chemistry And Metallurgy, 44(1):77--81, Mar. 1997.
[l0] F. Glover. Genetic algorithms and scatter search - unsuspected potentials.
Statistics And Computing, 4((2)):131--140, Jun. 1994.
[1 1] F. Glover. Scatter search and star-paths - beyond the genetic metaphor. OR
Spektrum, 17((2-3)):125--137, Sep. 1995.
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SIMD-MIMD platform. International Journal of Modem Physics C, 8(2):239--252,
Apr. 1997.
[31] W.J. Pullan. Structure prediction of benzene clusters using a genetic algorithm.
Journal of Chemical Information and Computer Sciences, 37(6):1189--1193, Nov.Dec. 1997.
[32] M.L. Raymer, P.C. Sanschagrin, W.F. Punch, S. Venkataraman, E.D. Goodman,
and L.A. Kuhn. Predicting conserved water-mediated and polar ligand interactionsin proteins using a k-nearest-neighbors genetic algorithm. Journal of Molecular
Biology, 265(4):445--464, Jan. 31, 1997.
[33] K. Shankland, W.I.F. David, and T. Csoka. Crystal structure determination frompowder diffraction data by the application of a genetic algorithm. Zeitschrift Fur
Kristallographie, 212(8):550--552, 1997.
[34] K. Shankland, W.I.F. David, T. Csoka, and L. McBride. Structure solution of
ibuprofen from powder diffraction data by the application of a genetic algorithm
combined with prior conformational analysis. International Journal of
Pharmaceutics, 165(1):117--126, Apr. 20, 1998.
[35] K.Y. Tarn and R.G. Compton. GAMATCH - a genetic algorithm-based programfor indexing crystal faces. Journal of Applied Crystallography, 28:640--645, Oct. 1,
1995.
[36] A.H.C. vanKampen, C.S. Strom, and L.M.C Buydens. Lethalization, penalty
and repair functions for constraint handling in the genetic algorithm methodology.
Chemomehics And Intelligent Laboratory Systems, 34( 1):55--68, Aug. 1996.
[37] R.P. White, J.A. Niesse, and H.R. Mayne. A study of genetic algorithm
approaches to global geometry optimization of aromatic hydrocarbon rnicroclusters.
Journal of Chemical Physics, 108(5):2208--2218, Feb. 1, 1998.
[38] P. Willett. Genetic algorithms in molecular recognition and design. Trends in
Biotechnology, 13(12):516--521, Dec. 1995.
[39] C.R. Zacharias, M.R. Lemes, and A.D. Pino. Combining genetic algorithm andsimulated annealing: a molecular geometry optimization study. THEOCHEMJournal of Molecular Structure, 430(29--39), Apr. 14, 1998.
[40] M. Zwick, B. Lovell, and J. Marsh. Global optimization studies on the 1-dphase problem. International Journal of General Systems, 25(1):47--59, 1996.

33

Computer programming and mathematical modeling using evolutionary computation
Roland Olson,
Qstfold College, 0 s Alle 11,N-1757 Halden, Norway
E-mail: Roland.Olsson@hiof.no, WWW: http://www-ia.hiof.no/-rolandol

The editor of this newsletter asked me to speculate a little about the
future of the ADATE system and other similar techniques that are yet
to be invented and so I certainly will. However, please keep in mind
that my crystal ball may not be particularly reliable even though it isbetter polished and maintained than any other I have seen so far.. .

The production of computer software and mathematical models is oneof the cornerstones of modem society, both as an independent industry
and as an integrated part of general industrial and research activity.
Products as diverse as washing machines, mobile phones,
spectrographs, combustion engines and web-browsers are controlled
by software with rapidly increasing complexity, correctness problems
and cost of development. The reason for this trend, which sometimes
is referred to as the software crisis, is that programming is a highly
creative activity that often is a form of art rather than science or wellplanned engineering.

The key issue in the success of the ADATE system is scalability whichmeans that neither specification difficulty nor simulation time increase
unreasonably much as the synthesized programs become more andmore complex.
The problem of writing specifications is similar to the problem
of writing pedagogical textbooks for schools, be it a university or anelementary school, but a “textbook” for “individuals” produced by the
ADATE system must start at a lower level than even textbooks forelementary school. It is relatively easy to write such ADATE“textbooks” for mathematical and logical problems, but more difficult
when considering human skills that are more or less directly
programmed in our genes, for example pattern recognition, motor
control and language. Note that the problems of writing effective
algorithms for the latter problems are largely unsolved using
traditional methods and that EC may be the best way of creating suchalgorithms.

The development of accurate mathematical models in the naturalsciences usually builds on a larger scientific foundation thanprogramming, but is still often an empirical science where intuition ismore important than pure deduction. There are very many applications
where adequate mathematical models are lacking even thoughsubstantial measurement data are available. Some of theseapplications, for example determining the three-dimensional structureof a protein from data obtained using X-ray diffraction, are both
important and still not well developed. For instance, the threedimensional structures of the estrogen receptors alpha and betaremained undetermined until last year even though these structures are
essential for the effective design of drugs against common diseases
such as osteoporosis and breast cancer.

There is often a fundamental difference between directly writing a
program for a given class of problems and writing a textbook teaching
how the problems may be solved. For example, we cannot write
programs that effectively deal with the complexities and intricacies ofhuman language but we can indeed develop ADATE textbooks for all
the important facets of human language. Note that full mastery of suchtextbooks requires generalizing ability and levels of cognition that areso far unseen in any existing algorithms.

The field of evolutionary computation (EC) contains techniques bothfor automatic programming and automatic modeling where a computer
independently produces programs or models using some form ofsimulated evolution.

Actually, there is no clear theoretical obstacle that would prevent the
ADATE system from producing programs with such cognitive
capabilities. The main obstacles are practical, in particular the timerequired to simulate the evolution of complex programs.

The most well known techniques in evolutionary computation are
evolutionsstrategie (ES), evolutionary programming (EP), genetic
algorithms (GA) and genetic programming (GP). The first three dealalmost exclusively with mathematical modeling but the fourth has to asmall extent also been applied to automatic programming even though
the focus is on modeling also for GP. There are numerous other EC
techniques, many of which should not be viewed as an offspring fromone of the four above and also many hybrids between EC techniquesand standard combinatorial optimization methods such as the simplex
method, simulated annealing and tabu search .

In natural evolution, nature has employed extremely massive
parallelism and a computational effort that we have just begun tocomprehend. ADATE is governed by laws of evolution that are likely
to be more optimized and well-designed than the seemingly primitive
laws of Darwinian evolution. Therefore, an evolution simulation
leading to human levels of cognition can conceivably be carried out
using ADATE with a computational effort many orders of magnitude
smaller than that of natural evolution.

I have just returned from a stimulating week at the 1998 IEEE World
Congress on Computational Intelligence, which included theInternational Conference on Evolutionary Computation, and foundthat the field is more diverse than ever and that navigation in this jungleof alternative methods is difficult even for someone who has been
active in EC for more than a decade. It is important to have in mind thatno matter what inductive mathematical modeling problem you areinterested in , there are at least a half dozen rather different methods tochoose from and that not one of them is likely to be the “best” method
for your problem but only provide you with a starting point for yourown method development.

My research priority over the next years is to determine and enhance
the scalability of the ADATE system, for example obtaining
relationships between the complexity of synthesized programs and thecorresponding simulation time. Hopefully, these relationships will beclear enough to allow extrapolation to orders of magnitude higher
complexities, which may tell us how powerful computers we need to
produce algorithms highly skilled in human language, logic,
mathematics and general science. Maybe the world’s leading powder
crystallographer in 30 years is an algorithm generated throughsimulated evolution on a parallel computer with ten million Merced-9
CPUS?

Let me now turn to automatic programming using simulated evolution
which is more difficult than automatic modeling but also more generaland potentially more rewarding. During the last 6 years, my main
professional occupation has been to develop ADATE (Automatic
Design of Algorithms through Evolution), that currently can produce
general programs of moderate complexity from first principles whichmeans that as much code as possible is produced through artificial
evolution and that the system is fed a minimum of knowledge before
the evolution begins. One can say that the system starts out as a “babymachine” or a “blank sheet” and typically does not even knowelementary algorithms such as how to add natural numbers. However,it can learn for example addition, multiplication, sorting, string
processing and other moderately complex algorithms in a few days ofevolution simulation.

The 1997 prototype for the ADATE system is available at

http://www-ia.hiof.no/-rolandoladate-intro.htm1
It is certainly not yet ready for powder crystallography or anything likeit.

34

FullProf.98 and WinPLOTR New Windows 99/NT Applications for Diffraction.
Interactive calculations (sum, difference, multiplication, centroid,
integration) with the diffraction patterns in the current plot.
Interactive profile fitting to independent pseudo-Voigt functions
using the non-linear least-squares Marquard algorithm (see Fig. 2).
All starting parameters and refinement flags can be selected byclicking with the mouse.

Juan Rodriguez-Carvajal and Thierry Roisnel
Laboratoire Leon Brillouin (CEA-CNRS), Centre d'Etudes de Saclay
91 191 Gif sur Yvette Cedex, FRANCE
E-mail juan@hali saclay cea fr & roisnel@llb saclay cea fr
WWW http //www-llb cea fr/winplotr/winplotr htm

The program FullProf is widely used in powder diffraction data
analysis on different computer environments. During the first half of1998 profound changes have been introduced in its source code. The
most important is the complete transformation of the source code to
the new standard Fortran 90, using the new syntax and features(suppression of COMMON statements, introduction of modules,
interfaces, types, etc). This is now distributed as the beta-version of
FullProf.98 (only for DOS/Windows 95/NT at present).
Simultaneously, the program WinPLOTR has been developed in
Fortran 90 for the Windows 9 5 / N T platform (Lahey Fortran 90
compiler and RealWin to access the Windows API from Fortran 90).
This program can be used for various purposes: visualisation of
powder diffraction patterns, interactive profile fitting and as a GUI for
FullProf.98 and other programs. The program WinPLOTR has all thefeatures of a conventional Windows application using the mouse to
select menus, tools in the toolbar, to answer to dialog boxes, to resize
and to move windows, to scroll, etc. When a diffraction pattern isdisplayed in the graphic window the drag operation (pressing, moveand release) is available with the left mouse button to zoom the patternplot. Click with the right mouse button redisplays all the data points ofthe pattern. In any case the move of the mouse inside the graphic
window gives information (in the status bar) about the X and Y
positions, in physical units. Among the features of WinPLOTR wecan point out the following:

Figure 2: Aspect of the screen after an interactive profile refinement
session.

Direct launch of FullProf from the pop-up menu or by clicking abutton. Automatic plot of the CODFIL.prf file. The file
CODFIL.pcr can be directly accessed by an editor selected by theuser and stored in the winplotr.s e t file. By default Notepad
is used.
Visualisation of the hkl indices of reflections selected with themouse when an observed-calculated pattern coming from
FullProf is in the current window.

All the main arrays have the ALLOCATABLE attribute. The actual
dimensions can be controlled by the user, at run-time, through thetext file winplotr.set. This file serves to store the settings ofthe program. The current settings can be saved from the program
itself.

The Windows beta-version of FullProf.98 has the same features as theversion 3.5 of FullProf but a step-wise refinement option is available
in which the observed versus calculated profile is displayed at eachcycle and the user is asked to accept or not the continuation of therefinement (see Fig.3).
A summary of the most important features of FullProf.98 is given
below:The program can treat multi-phase diffraction patterns (up to 8
phases of X-rays, laboratory and synchrotron sources, or neutrons,
constant wavelength and time of flight (TOF).
One or two wavelengths can he used (eventually with different
profile parameters).
The background can he fixed, refinable, adaptable, or adjusted by
Fourier filtering.
There are different choices of peak shape for each phase:
Gaussian, Lorentzian, modified Lorentzians, pseudo-Voigt,
Pearson-VII, Thompson-Cox-Hastings (TCH) pseudo-Voigt,
numerical, split pseudo-Voigt, convolution of a double exponential
with a TCH pseudo-Voigt for TOF
The absorption correction is available for different geometries.
The micro-absorption correction is implemented for the BraggBrentano set-up.
There are two methods for magnetic structure refinement(crystallographic and spherical representation of the magnetic
moments). The first describes the magnetic structure in themagnetic unit cell. The second makes use of the propagation
vector formalism using the crystallographic unit cell. This second
method is necessary for incommensurate magnetic structures.

Figure 1: Screen copy of the main window of WinPLOTR, showing azoomed region of several difjraction patterns of ErFe4Ge2 at different
temperatures. The small window shows the positions and intensities ofseveral peaks selected by the user:

Total control of the style, colours, size of symbols, fonts, line
width of graphics.
Selection of points for background and peaks that can be stored ina file (see Fig. 1).
Many formats for the diffraction data files can he read: those of
FullProf, GSAS and some others. Multiple patterns can be plot byaccessing to a buffer file.
The graphics can be saved as Postscript and HPGL files or printed
directly.
Selection of the units of the X-axis: 28(deg.)/TOF(~sec.),sine/h(A'), Q(A-'), d@).

35

The structural or magnetic model may be supplied by an external
subroutine for special purposes (polymers, small angle scatteringof amphifilic crystals, description of incommensurate structures inreal direct space, etc).
Single crystal data or integrated intensities can be used as
observations (alone or in combination with a powder profile).
Neutron (or X-ray) powder patterns can be mixed with integrated
intensities of X-ray (or neutron) from single crystal or powder
data.
A Montecarlo search for starting configurations, in a user-definedparameter box, is available for use with integrated intensity data.
The multi-pattern capabilities are not currently available in the betaversion but they will be introduced in future versions. The version withallocatable arrays (all dimensions controlled by the user at run time) is
not presently distributed because there is a loss of the performance bya factor of 3 with the Lahey compiler.
There is a project for a general GUI for FullProf.98 that is beendeveloped by Alain Bouvet (ILL, Grenoble). This GUI will be directly
multi-platform because is written in Java ; it will allow the creation,from the scratch, of the main input file using pop-up menus andbuttons. The graphic capabilities of the first version will probably not
be as powerful as those provided by WinPLOTR but it should beenough for many purposes.
Beta versions of FullProf.98 and WinPLOTR are freely available
from:

Figure 3: Layout of the screen during the execution of FullProf.98 in stepwise mode when launched from WinPLOTR.

Automatic generation of reflections for an incommensurate
structure with up to 24 propagation vectors. Refinement ofpropagation vectors in reciprocal lattice units.
hkl-dependence of FWHM for strain and size effects.
Profile Matching. The full profile can be adjusted without priorknowledge of the structure: it needs only good starting cell andprofile parameters.
Quantitative analysis without need of structure factor calculations.
Chemical (distances) and magnetic (magnetic moments) slack
constraints.
Form factor refinement of complex objects (plastic crystals). Rigid
body-TLS model.

ftp://charybde.saclay.cea.fr/pub/divers/ful~prof.98/windows/winfp98.zip(both programs)

ftp://charybde.saclay.cea.fr/pub/divers/WinPLOTR/winplotr.zip(WinPLOTR alone)

3rd Canadian Powder Diffraction Workshop

Queen’s University), magnetic Bragg diffraction with neutrons (JohnGreedan, McMaster University), and the implementation of rigid bodyrefinements in GSAS (Ian Swainson, National Research Council).

University of Waterloo, Waterloo, Ontario, Canada. June 12-13, 1998.
Ian Swainson (NRC, Canada) and Bruce Torrie (University of Waterloo, Canada)
E-mail: Ian.Swainson@nrc.ca

The workshop was aimed at demonstrating the uses and methods ofrefining powder diffraction data collected from both X-ray and neutron
sources. There were 24 participants in the workshop from across North
America. The speakers came from chemistry, physics and mineralogy
backgrounds and had familiarity with both sources of radiation. This
broad experience helped in dealing with the questions from theparticipants who came from a wide variety of backgrounds.

Both afternoons were taken up with practical sessions using thecomputer facilities of the physics department of the University ofWaterloo.
The workshop registration fee was kept low so that as many people aspossible could attend: $100 for students and $125 for others. This wasmade possible by the support of the University of Waterloo and theCanadian Institute of Neutron Scattering. A big thank you goes out tothe speakers as well for their contributions. It was good to see thesession so full and we hope to repeat the event in the future.

The workshop began with introductory talks by Angus Wilkinson(Georgia Tech) who gave an introduction to powder profile refinement
and Bob Von Dreele (LANSCE) described profile refinement with
GSAS. Later in the session more specific talks were given including an
overview of “ab initio” methods for use with powder data (Angus
Wilkinson), methods of quantitative phase analysis (Ron Peterson,

Ian Swainson (NRC) and Bruce Tome (University of Waterloo)

36

GUI-based tools for Powder Diffraction Analysis Using Tcl/Tk

Brian Toby
NIST Center for Neutron Research
National Institute of Standards & Technology
Gaithersburg, MD 20899, USA
E-mail: Brian.Toby @NIST.gov W W W http://rrdjazz.nist.gov/-tobyl

The most recent version of the program accepts reciprocal unit cells.
Dick Harlow has had considerable success indexing diffractogramsfrom materials with low symmetry unit cells by determining two
reciprocal cell parameters and the angle between them from electron
diffraction data. The remaining unknown parameters can then be foundusing this program. Peak fitting is done with the GPLSFT programfrom Dave Cox et al, which incorporates the Finger-Cox-Jephcoat
assymetry correction.

Over the last few years we have been using a script language, Tcl/Tk
to create graphical user interface (GUI) based programs for use inpowder diffraction applications. Tcl/Tk is available for free (seehttp://www.tcltk.com for more information) and runs on virtually allcomputer platforms. At the NIST Center for Neutron Research, we dovirtually all our code development for Silicon Graphics and PCs
running Linux, but much of the code runs with no modification onother UNIX platforms and often with only minor debugging in
Windows.

One of the nicest features of the code is built into the BLT graphics
package that we use. Any part of the graphical display can be "zoomedin" by using a mouse to draw a box around the feature.
(http://rrdjazz.nist.gov/-tobykmpr. html)

LOGIC

Tcl/Tk is easy to learn, even for fossils such as the author (who learned
to program on computer cards). Below I describe a few programs thatare in use at the NCNR and are freely available over the web. Whilethese programs are quite useful in their current form, I would like toencourage others to add more functionality and I would particularly
like to get some help with Windows debugging.

This program is used to locate entries in the ICDD-JCPDS databasethat match a set of constraints, such as chemical composition, peak
positions, etc. It can be used either with a GUI or a Web interface. It
provides a nice example of how FORTRAN subroutines can be
integrated into Tcl/Tk code and has been debugged both with Unix andWindows-95. It is in use in a number of labs around the world, but I do
not have much use for the database and currently do have a copy of thedatabase so I am not planning any additional development for thisprogram. (http://rrdjazz.nist.gov/-toby/logic.html)

CMPR

*

.

The goal of this program is to be a "Swiss army knife" for powder
diffraction. At present, its current functions are the display ofdiffraction data, peak fitting and manual indexing. Manual indexing isdone by generating allowed reflection positions for an arbitrary unit
cell and then watching these positions move as the lattice constants arechanged via sliders. Reflections extinctions can be tested by entering
a symmetry operation or space group. Extinct reflections are thenhighlighted.

GSAS GUIThis is not a full GUI implementation of GSAS, but it does provide a
GUI shell that allows the various GSAS programs to be started from amenu and toolbar interface. The menus and toolbars are userconfigurable. It provides a few unique tools. For example, it has aplotting program, liveplot, that shows the observed and computed
diffraction patterns; the display is updated automatically as therefinement progesses. A second tool, textview (viewlst) eases the taskof examining the .LST file that contains the GSAS output. A recent
improvement to liveplot allows CMPR to be used to generate peak
positions from an arbitrary unit cell which are then superimposed on
the Rietveld output. This aids in identification of supercells andimpurity phases. (http://rrdjazz.nist.gov/-tohy/gsastcl.html andhttp://rrdjazz.nist.gov/-toby/gsastcl-cfg.htm1)

37

Aspects on using Java in crystallography
Steffen Weber
NIRIM, Namiki 1-1, Tsukuba, Ibaraki 305, Japan
E-mail: weber@nirim.go.jp W W W http://www.nirim.go.jp/-weberl

the applet's output cannot be easily obtained (apart from using screen
capture utilities). Applets are useful for educational and demonstration
purposes and make good programming exercises while learning Java.
Several examples of crystallographic applets can be found on theauthors homepage [4]. Apart from applets, which are embedded in a
webpage and require a webbrowser or the JDK'sappletviewer there are
the stand-alone Java applications which can be run like any othersoftware. Applications are what crystallographers are really interested
in. Note that depending on its purpose and extent a Java program canbe written in such a way that it can run both as an application or anapplet. Java applications can use the full palette of the available APIs.
Until the present version of the JDK (JDK1.1.6) the GUI of a Java
program may have a slightly different look on different operating
systems, because the corresponding os dependent window managers
are being accessed. With the next JDK1.2 the developer may choose to
use Java's new Abstract Windowing Toolkit (AWT) extension named
Swing. A GUI created using Swing would look the same independent
from the underlying os.

Introduction
Java is a relatively new programming language and it is still underdevelopment. Since the number of people working in the field of
crystallography, who are interested to learn more about Java is growing
I would like to point out some of Java's features that are of interest to
crystallographers and leave it to the reader to access other sources onmatters of Java language specifications etc. As a continuously growing
language Java offers almost anything you might need to develop highperformance applications. The parts of Java that serve as standard
libraries of ready-to-use methods are called Application Programming
Interfaces (API). Among the newer developments are APIs forserial/parallel port communication, 2D/3D graphics, advanced image
processing, speech recognition etc. Java's perhaps biggest advantages
are its cross-platform portability, the easiness by which Graphical User
Interfaces (GUI) can be created and multi-threading, which allows a
program to perform multiple tasks independent from each other. Javais an interpreted language. The Java compiler generates so-called
bytecode which is recognized by the file extension *.class. A Java
interpreter will then convert this bytecode into machine dependent
binary executable code. This interpreter, also referred to as Java Virtual
machine (JVM), is available for many operating systems (OS), such as
MS-Windows95/NT, Unix, Linux and the Mac os. Everything neededfor developing and running Java programs can be downloaded for freefrom the Internet in form of the Java Development Kit (JDKTM) [I].
The JDK, however, does not include an Integrated Development
Environment (IDE), which is usually available for other programming
languages. However, such IDEs for Java can be obtained ascommercial third-party products especially for MS-Windows9YNT.
One of the first Visual IDEs, which is actually written in Java andtherefore runs on any os with a JVM is Xelfi from Xelfi Technologies[2]. It has the look and feel known from Delphi's IDE. Among the nonvisual development tools for MS-Windows95/NT ED4W from
SoftAsItGets [3] is perhaps the best. Visual IDEs allow you to build
your GUI by dragging components from a palette and dropping themin the design area. The frame work code is generated automatically andone only has to fill in the actual code. Note that some of the Javadevelopment tools available allow only the creation of applets,
sometimes even without the possibility to actually write a single line ofcode. If you are interested in developing applets and applications you
should choose an IDE, which offers both or just stick to the JDK and
use your preferred text editor for coding. When writing Java programs
it is a good practice to first create the whole GUI with menus, buttons
etc. and write the actual code after that. The Java beginner should try
to translate a functional program written in another language into Java.
This can be done quite easily due to language similarities as in the caseof C/C++. In such a translation note that arrays in Java start with index
zero, unlike one as in Turbo Pascal for example. The absence ofpointers in Java is another bonus, since one does not have to worry
about memory allocations. It just be mentioned here that one of thenewer concepts in Java's component architecture are JavaBeans, which
are reusable components that are required by Visual IDEs. By writing
your code as beans you may extend the palettes of components
available for the creation of other programs. An example for a
JavaBean is the Molecule Viewer bean from JavaSoft, which can also beseen in applet form on many websites.

2. Calculation intensive programs
In case of computationally based programs, such as least squares
refinement programs, Java may turn out to be too slow. One also mightneed to interface with some specialized hardware or drivers or one
simply might want to reuse already available codes and libraries. In
such cases one may use a combination of Java code and C code. C codeis faster, and one does not have to recode already available code, apartfrom some modification for exchanging data types. FORTRAN
programs can be converted to C code using some FORTRAN-to-Ctranslator utility.

2.1 Linking native code
When linking C code to your Java program using the Java Native
Interface (JNI) cross- platform portability is decreased, since aplatform dependent C-compiler has to be used if one wants to transfer
the program to another os. This will create some dynamic loadable
library (DLL). On the Windows platform this is a *.dll file and under
Unix a *.so file. This library file is loaded when a Java program
containing native methods is started. One then has the possibility to
exchange data between the Java side and the native side. From within
the C code also system calls to other external programs can be done
easily. One therefore can write a Java program where the only functionof the Java side is to serve as a GUI while all computations are actually
done using native code.

3. Graphics intensive programs
One of the strongest sides of Java is its graphics handling capabilities.
Even with the standard APIs extensive graphics and image processing
can be achieved (without specific 2D/3D APIs). With the new APIs in
the forthcoming JDK1.2 those features will even leap to a much higher
level.

3.1 Creating and saving images, image processing
Graphics are displayed in Java's canvas component, which also
includes mouse tracking possibilities. Thus the mouse can be used forexample to shift, rotate and zoom images or to index Bragg reflexions
in a diffraction pattern simulation. One can either just draw onto the thecanvas and/or display images that are either loaded as GIF or JPEG
files or calculated pixel by pixel. The latter is of particular importance,since no input graphics is needed. One may just declare a onedimensional array of size [image-width*image-height], each arraycomponent standing for an integer value that contains the alpha and
RGB information (alpha=transparency, red, green, blue). One maythen calculate/manipulate each pixel at will and then use theMemoryImageSource() class to actually create the image to be
displayed. One may also make copies of an image to apply special
filters (brightness, contrast etc.), the source code of which can be foundin many books or on the Internet. The author used this method among
others to read 10 Mbyte large binary files representing Imaging Plate

1. Java applications versus applets
It would be wrong to think that Java is just a language for writing niceapplets to enhance the attractiveness of web pages. Applets have severe
limitations that a developer has to be aware of, since it might influence
one's programming style. For example applets can neither read fromnor write to the local hard disk. Therefore an applet cannot read input
files in the usual sense or create temporary files for later use in the
programs execution. Data files can be accessed as URL documents,
which is quite another thing. Furthermore one cannot print directlyfrom within an applet or save output graphics. Therefore hardcopies of38

data, in order to display them on-screen. Since one has access to eachpixel value one can easily write a peak search routine for example. If
you were to compare two diffraction pattern images you could lay thesecond one over the first one with the background color of the second
image switched to transparent. If you want to manipulate a GIF/JPEG
image you may load it and obtain its pixel values using the
PixelGrabber() class. Until now one has to use third-party Javapackages if one wanted to save the contents of a canvas in form of a
GIF file for example. The 2D API of the JDK1.2, however, will include
the possibility to save the images as JPEG files, which may then be
viewed or imported by other software.

This is now possible with the early release of the new serial/parallel
port communication API (javax.comm). With this API one may specify
port settings and open connection to an external device. If one wishes
to execute the software on Windows and Unix platforms one only
needs to specify the correct port identifier name which may be of theform "COM1" or "/dev/term/a". A software example for controlling a
Mac-Science goniometer can be seen at [7]. That program uses a
separate thread for the measurement. Thus access to the GUI is
maintained and the execution may be stopped, paused, continued at
any time. Java furthermore offers an internal counter in units ofmilliseconds, which gives the developer more control over the speed ofstepping motors.

3.2 Molecular graphics, 3D visualization

5. Realizing Software Documentations
Maybe the first applications that interested crystallographers wereapplets that were able to display molecules in 3D such as the above
mentioned Molecule Viewer or the JaMM applet by J.N.Huffman [5].
The author is currently working on an application [6] with the intention
to include more features then applets can offer. Such programs can berealized quite easily with Java. Since mostly non-penetrating balls andsticks are used no real 3D engine is needed for such a program. This
only becomes necessary for displaying coordination polyhedra orinterpenetrating atoms. The above mentioned programs use either
shaded atoms that are calculated and created with theMemoryImageSource() class or loaded as small GIF files. In contrast
when a molecule is displayed using VRML (Virtual Reality Modelling
Language) atoms are rendered as polygonized spheres, which allows
for simpler interpenetration algorithms. The key features needed toprogram graphics animation is fast repainting and the possibility to
avoid flickering. Both can be achieved easily with Java. When
dragging the mouse for rotating a molecule the canvas' repainting
routine is called automatically. To achieve flicker-free animation one
uses double buffering, whereby the next image (frame) is first drawn
onto some image buffer and only displayed-when it is finished. The
same technique could be used to display some graph representing
dynamically changing data. To make sure that atoms are correctly
drawn from the back to the front one uses the z-buffering technique(useful only for raster graphics; z-value of each pixel is saved in a
special buffer) or one can order the z-coordinates of the atoms with aquicksort algorithm (this is better for vector graphics; eg.: if you also
want to produce PostScript output). The same simple 3D routines,
which are basically the rotations around the three principal axes andthe quicksort routine may be used for other visualization tasks incystallography such as the display of reciprocal lattice points forindexing diffractometer data. Using mult-threading one may also
create a separate thread that keeps the animation going while the GUI
can be accessed to perform other tasks.

One possibility to realize documentations, tutorials, online help andsupport information is to do it all in HTML format and integrate aHTML browser component into your software. Since Java programs
are network-aware you may put all files on your webserver and usersof your software will access those files, which gives you the possibility
to provide the users always with the latest updated documentations. At
present there is good HTML browser component available from
ICEsoft A / S [8]. If you want to see it in action you may look at thesoftware JSV [6] where it is implemented.

6. Some of Java's downsides
The two major shortcomings concern speed and printing. Java beeing
an interpreted language is bound to run slower than when executing
compiled native code. A solution to this is the use of Just-In-Time (JIT)
compilers, which convert Java's bytecodes into native processor
instructions before execution. This may increase the performance by
up to 10 times. JIT compilers are already implemented in current
webbrowsers and will be part of JDK1.2. The Java microprocessor
chip, which will run Java programs as fast as native code is anotherdevelopment to solve this problem. The other problem is printing. Till
JDK 1.1.6 there is no easy way to print out your graphics, however, the
new 2D API in JDK1.2 will provide solutions at least for the Windows
and Solaris platforms. If you do not want to depend on developmentsin this area, you may code PostScript output capabilities into yoursoftware [9] (contact author for tips on PostScript). Furthermore notethat your Java code can be retrieved from the bytecode (*.class files)
by using some Java decoder. If you want your code to be unreadable
you may use for example MochaSoft's Source Obfuscator [l0] before
compilation.

7. Conclusion
Java is very suitable for such crystallographic applications that require
either a GUI, extensive graphics features or both. Its cross-platform
portability may save coding time and allow a wide distribution of one's
software. Both very welcome to the developer. For computationallybased programs (eg. refinement software) native C code should belinked to the Java program, which, however, decreases its crossplatform portability.

4. Serial port communication

\ 1ci

JiTC

,j

I loo

P

I terta--References
1. Javasoft home at http://www.javasoft.com
2.Xelfi Technologies at http://www.xelfi.com
3.SoftAsItGets at http://www.getsoft.com
4. S.Weber's homepage at http://www.nirim.go.jp/-weher
5. JaMM at http://www.cica.indiana.edu/-jnhuffmaLJaMM/java.htnd
6. http://www.nirim.go.jp/-weher/jsv.html
7.http://www.nirim.go.jp/-weher/ipc.html
8. ICEsoft A / S at http://www.icesoft.no
9. PostScript Language Tutorial and Cookbook, Adobe Systems Incorporated,
Addison-Wesley Publishing Company, 1986
10. MochaSoft at http://www.mochasoft.dk
11. Tonny Espeset: Kick Ass Java Programming, 1996, Coriolis Group Books
12. Mastering Java, 1996, SYBEX, San Francisco
13. Glenn Vanderburg, et al.: Maximum Java 1.1, 1997, Sams.net Publishing

A very interesting field for the application of Java programs might be
the creation of control software for goniometers, diffractometers etc.

39What's On
8-12 Feburary 1999
Australian X-ray Analytical Association (AXAA99)
Analytical X-rays for Industry and Science
Melbourne, Victoria, Australia
Contact: Dr Mick Gould
13 Jeffrey St, Mt Waverley, 3149, Victoria, Australia
Fax: +(613) 9887-8773;
Tel: +(613) 9887-8003;
E-mail: ca@netwide.com.au
WWW: http://www.latrobe.edu.au/wwwlaxad

7-10 Octobel; 1998
ISPD'98: An International School on Powder Diffraction,
Indian Association for the Cultivation of Science
Contact: Prof. S. P. Sen Gupta
I.A.C.S., Jadavpur, Calcutta-700 032, India
Fax : +91-033-4732805
E-mail: ispd98@iacs.ernet.in or msspsg@iacs.ernet.in;
WWW via:
http://gandalf.otago.ac.nz:800/rwea~ers/ASCA/asca98.htm
13-15 Octobel; 1998
3rd Conference of the Asian CrystallographicAssociation(AsCA'98)
Hotel Equatorial Bangi, Selangor, Malaysia.
Contact: Prof. A. Hamid Othman
Jabatan Kimia, University Kebangsaan, Malaysia
43600 Bangi Malaysia
Fax: +6-03-8258828
E-mail: hamie@pkrisc.cc.ukm.my
Int. Org. Com. Chairman: Prof. Shin-Lin Chang(slchang@phys.nthu.edu.tw)
Int. Prog. Corn. Chairman: Prof. T. Yamanaka(b61400a@center.osaka-u.ac.jp)
WWW: http:/lgandalf.otago.ac.nz:8OO/rweavers/ASC~asca98.htm-

4-13 August 1999
18th Congress and General Assembly of the International Unionof Crystallography,
Glasgow, Scotland, UK
Contact: Dr. C. Gilmore, Department of Chemistry, University ofGlasgow,
Glasgow G12 8QQ, UK
Fax: +44 (41) 330 4888;
E-mail: iucr99@chem.gla.ac.uk
WWW: http://www.chem.gla.ac.uMiucr99/

CALL FOR CONTRIBUTIONS TO THE NEXT CPD
NEWSLETTER
The next issue of the CPD Newsletter will be edited by S. P. Sen Gupta to appear in late
1998. He would greatly appreciate contributions from readers on matters of interest to thepowder diffraction community, e.g. meeting reports, future meetings, developments in
instruments, techniques and computer programs and news of general interest. Please send
articles and suggestions directly to him (address is Prof. S. P. Sen Gupta, I.A.C.S.,
Jadavpur, Calcutta, 700 032, India; Fax : +91-033-4732805; E-mail: msspsg@iacs.ernet.in)

HOW TO RECEIVE THE IUCR CPD
NEWSLETTER
If you would like to be added to the mailing list for Newsletters of the IUCr Commission
on Powder Diffraction or you have changed your address, please contact

Prof. R.J. Cernik,
Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, UK;

Fax: +44 (1925) 603 124
E-mail: R. J.Cernik @ dl.ac.uk

40