Fullprof Intro

8/11/2019 Fullprof Intro

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Introduction to the Program F ULL P ROF : Refinement of Crystal andMagnetic Structures from Powder and Single Crystal Data

Juan Rodrguez-Carvajal

Laboratoire Lon Brillouin (CEA-CNRS), CEA/Saclay, 91191 Gif sur Yvette Cedex,FRANCE.

In these notes an introduction to the program FullProf is presented. After a brief introductionsummarizing the history of the program we present the main elements of the Rietveld methodand how to use the program in routine work for refining crystal and magnetic structures. Themost specialized topics (microstructure effects, flipping ratio refinements, the use of specialform-factors, time of flight neutron powder diffraction) will not be treated here. A fullexample of Simulated Annealing run, for localizing hydrogen atoms using neutron powder

diffraction, is discussed in more detail. These notes have been written taking parts of themanual and other tutorial documents that are available in the FullProf Web site.

Introduction

The program FullProf has been mainly developed to perform Rietveld analysis [1] of neutronor X-ray powder diffraction data collected at constant, or variable, step in scattering angle 2 or using the technique of neutron time-of-flight (TOF). Single Crystal refinements can also be

performed alone or in combination with powder data. However, the program has somestructure determination capabilities by using the Simulated Annealing method for globaloptimization.The first versions of the program FullProf were based on the code of the DBWS program [2],which was also a major modification of the original Rietveld-Hewat program. The program

FullProf has been re-written using the full capabilities of the new Fortran 95 standard during1997-1998. It is progressively being transformed in a program based in the CrystallographicFortran 95 Modules Library [3]. The program works with some allocatable arrays so the usercan directly control the dimensions of important arrays at run time. In this paper we shalldescribe some elementary points concerning the methods implemented in the program andhow to use it. For further details the user should consult the manual and tutorials. TheWindows version of the program and all the suite of programs related to FullProf are nowdistributed within the FullProf Suite installer ( setup_FullProf_Suite.exe ). This installer,additional documents and tutorials, can be found in the FullProf Web site [4].

The Rietveld Method

A powder diffraction pattern can be recorded in numerical form for a discrete set of scatteringangles, times of flight or energies. We will refer to this scattering variable as T . Then, theexperimental powder diffraction pattern is usually given as two arrays { } 1,...,,i i i nT y = . In thecase of data that have been manipulated or normalized in some way the three arrays{ } 1,...,, ,i i i i nT y = , where i is the standard deviation of the profile intensity i y , are needed inorder to properly weight the residuals in the least squares procedure. The profile can be

modeled using the calculated counts ci y at the ith step by summing the contribution fromneighboring Bragg reflections plus the background:


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, , ,h

( )h hc i i i y S I T T b

= + (1)

The vector h (=H , reciprocal lattice vector, or H +k for magnetic structures of propagation

vector k ) labels the Bragg reflections, the subscript labels the phase and vary from 1 up tothe number of phases existing in the model. In FullProf the term phase is synonymous of a

same procedure for calculating the integrated intensities , I h . This includes the usual

meaning of a phase and also the case of the magnetic contribution to scattering (treatedusually as a different phase ) coming from a single crystallographic phase in the sample. Thegeneral expression of the integrated intensity is:

{ }2, ,h h I L AP C F = (2)

For simplicity we will drop the -index. Sometimes we will refer to the whole arrays{ }i y and { }ci y as obs y and calc y respectively. The meaning of the different terms appearing in(1) and (2) is the following:

S is the scale factor of the phase Lh contains the Lorentz, polarization and multiplicity factors F h is the structure factor (crystal structures) or the modulus of the magnetic

interaction vector (magnetic structures). Ah is the absorption correction P h is the preferred orientation function

is the reflection profile function that models both instrumental and sampleeffects

hC includes special corrections (non linearity, efficiencies, special absorptioncorrections, extinction, etc)

ib is the background intensity

In the following sections we discussed the different terms in more detail. The RietveldMethod consist of refining a crystal (and/or magnetic) structure by minimizing the weightedsquared difference between the observed { } 1,...,i i n y = and the calculated (1) pattern

{ }, 1,...,( )

c i i n y

= against the parameter vector

1 2 3( , , ,... )

p = . The function minimized in

the Rietveld Method is:

{ }22 ,1

( )n

i i c ii

w y y =

= (3)

with 21i

iw = , being2i the variance of the "observation" i y . In more complex cases the user

may consider several diffraction patterns, or some chemical constraints. For those cases thegeneral expression of the function to be minimized is:


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{ } { }222 2 2 2

1 1 1 1

1( ) ( )

N N n m

T P P G P i i ci j cj P p i j gj P

w y y c g g = = = =

= + = + (4)

Where 2 P and2G are the chi-square of the pattern P and the chi-square of soft constraints.

The weight factors p are provided by the user and are internally normalized in order to get

1

1 N

P P

=

= , for the N patterns. The quantity j g is the prescribed value of a constraint (distance,angle, valence, magnetic moment, etc) with standard deviation gj .The smaller the value of

gj the higher is the strength of the constraint. The calculated value of the constraint ( )cj g

is performed as a function of a subset of components of the vector parameter .Thenormalization constant c is taken as the current value of the global reduced chi-square for allthe diffraction patterns. For simplicity we shall consider the expression (3) to explain somestandard points concerning the least squares optimization. If the optimum set of free

parameters is opt , the necessary condition for a minimum of (3) is that the gradient of

2 should be zero:2

0opt

= A Taylor expansion of ( )ic y around an initial guess 0 allows the application of an iterative

process. The shifts to be applied to the parameters at each cycle for improving 2 areobtained by solving a linear system of equations (normal equations)

0A b= (5)

where the components of the p p matrix A and vector b in the Gauss-Newton algorithm,used within FullProf , are given by the expressions:

, 0 , 0

, 0,

( ) ( )

( )( )

c i c ikl i

i k l

c ik i i c i

i k

y y A w

yb w y y

=

=

(6)

The shifts of the parameters0

obtained by solving the normal equations are added to the

starting parameters giving rise to a new set01 0

= + . The new parameters are consideredas the starting ones in the next cycle and the process is repeated until a convergence criterion

is satisfied. The shifts applied to the current parameters may be pre-multiplied by a userdefined factor that depend on each individual parameter (through the codeword) and arelaxation factor. The standard deviations of the adjusted parameters are calculated by theexpression:

1 2( ) ( )Ak k kk a = (7)

Where the reduced chi-square is defined as:2

2

n - p

= (8)

The quantity a k is the coefficient of the codeword for the parameter k . The2

quantity used

in the above formula is always calculated for the points in the pattern having Braggcontributions, thus i could be greater than the corresponding value calculated with other


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programs. In FullProf the quantity 2 is also calculated for all points considered in therefinement, so the user can easily re-calculate the alternative value of the standard deviation.In normal least square refinements the weighting scheme is based in fixed variances of the

profile intensities. This is appropriate when the statistics is good enough to be considered asGaussian. For low counting statistics a maximum likelihood refinement is more appropriate.This is equivalent to calculate the variance according to the model instead of usingexperimental fixed variances that are very bad estimated when low counting rate is dominant.In such a case the weights of the observations are calculated at each cycle as:

2,1i calc iw = supposing a Poissonian distribution and correcting for eventual normalization

factors used in the input data file to estimate the experimental variances.

Single Crystal, or Integrated Intensity, data

The program FullProf is also able to refine the crystal and magnetic structure using singlecrystal data, even if they correspond to a twinned crystal. The method is completely analogueto the Rietveld method, except that is more simple because all the complexities related with

background and peak shapes are absent. The function optimized when using integratedintensities is:

2 2 2, ,( )n obs n calc k

n k

M w G G= (9)The index n runs over the observations (1,.. N obs). The index k runs over the reflectionscontributing to the observation n (in case of twinned crystals or overlapped integratedintensities coming from powder data). 2G is the square of the structure factor (intensitycorrected for Lp-factor). In case of powder diffraction 2 2( )k k k G I jLpF = = , so clusters ofintegrated intensities are used.

Getting started with the Rietveld method using FullProf

The minimal input for the program FullProf is a file of extension . pcr , which calledhereafter a PCR file, containing the structural and peak shape information. The code of thefile (let us call it CODFIL for CODFIL.pcr) serves for naming different output filesdistinguished by their extension. The PCR file may just be the unique input when a simulationis performed. For treating experimental data, at least a file containing the profile intensities,or the reflection indices and structure factors for single crystals, is needed. The extension ofthis file is usually . dat but any other extension is admissible. Below we give a descriptionof the examples contained in the file pcr_dat.zip (this file is accessible in the site given in[4]). We shall discuss some elementary rules and comments about the problems the user canexperience in running the program. The Commission on Powder Diffraction of theInternational Union of Crystallography has published some guidelines for Rietveld refinement[5] that can be used to complete the rules provided in this paragraph.Rietveld refinement has nothing to do with structure determination . To start refining astructure an initial model (even if incomplete) is necessary. This model is supposed to beobtained from a crystal structure solver program or by any other mean.For starting a profile refinement from the scratch, the best is to copy one of the PCR filesaccompanying the distribution of FullProf , and modify it according to the users case: x-ray

or neutron diffraction, crystal or magnetic structure refinement, synchrotron, TOF neutrons,etc. The provided PCR files in the archive pcr_dat.zip can be used as templates. Of course the


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closer to the users case is the initial PCR file the easier is to modify it. An important aspect isthe format of the profile intensities data file that must be correctly given before attemptingany kind of refinement.The user must be aware of the way he(she) can control the refinement procedure: the numberof parameters to be refined, fixing parameters, making constraints, etc. The control of the

refined parameters is achieved by using codewords . These are the numbers xC that are enteredfor each refined parameter. A zero codeword means that the parameter is not being refined.For each refined parameter, the codeword is formed as:

( ) (10 ) xC sign a p a= + where p specifies the ordinal number of the parameter x and a (multiplier) is the factor bywhich the computed shift (see equation 5) will be multiplied before use. The calculated shiftsare also multiplied by a relaxation factor before being applied to the parameters.Recently, we have developed a Windows GUI, called EdPCR , to control the PCR file, so thatthe user can control everything without been concerned with numbering the different

parameters. All this part is automatically performed by EdPCR , by using the mouse and

clicking on the appropriate boxes. To access EdPCR one can use a button existing in thetoolbar of the visualizing program WinPLOTR [6]. The menu item Templates in EdPCR allows to import CIF or SHELX files to create, from the scratch, a PCR file that can bemodified afterward.

A stepwise method for Rietveld refinement

Although the principles behind the Rietveld profile refinement method are rather simple, theuse of the technique requires some expertise. This results merely from the fact that Rietveldrefinement uses a least-squares minimisation technique which, as any local search technique,gets easily stuck in false minima. Besides, correlation between model parameters, or a badstarting point, may easily cause divergence in early stages of the refinement. All thesedifficulties can actually be readily overcome by following a few simple prescriptions:

Use the best possible starting model: this can be easily done for background parameters and lattice constants. In some cases, in particular when the structuralmodel is very crude, it is advisable to analyze first the pattern with the profilematching (Le Bail) method in order to determine accurately the profile shape function,

background and cell parameters before running the Rietveld method. Do not start by refining all structural parameters at the same time. Some of them affect

strongly the residuals (they must be refined first) while others produce only littleimprovement and should be held fixed till the latest stages of the analysis.

Before you start, collect all the information available both on your sample(approximate cell parameters and atomic positions) and on the diffractometer andexperimental conditions of the data measurement: zero-shift and resolution function ofthe instrument, for instance. Then a sensible sequence of refinement of a crystalstructure is the following:

1. Scale factor.2. Scale factor, zero point of detector , 1rst background parameter and lattice

constants. In case of very sloppy background, it may be wise to actually refineat least two background parameters, or better fix the background using linearinterpolation between a set of fixed points provided by user.

3. Add the refinement of atomic positions and (eventually) an overall Debye-Waller factor, especially for high temperature data.


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4. Add the peak shape and asymmetry parameters (or better: use an externalinstrumental resolution file adapted to the diffractometer providing the data).

5. Add atom occupancies (if required).6. Turn the overall temperature factor into individual isotropic thermal

parameters.

7. Include additional background parameters (if background is refined).8. Refine the individual anisotropic thermal parameters if the quality of the data is

good enough.9. In case of constant wavelength data, the parameters to correct for instrumental

or physical 2 aberrations with a COS or SIN angular dependence.10. Microstructural parameters: size and strain effects.

In all cases, it is essential to plot frequently the observed and experimental patterns. Theexamination of the difference pattern is a quick and efficient method to detect blunders in themodel or in the input file controlling the refinement process. I may also provide useful hintson the best sequence to refine the whole set of model parameters for each particular case.When large and unrealistic fluctuations of certain parameters occur from one cycle to thenext, examine the correlation matrix: if large values (say larger than 50%) are observed,refine separately the corresponding parameters, at least in the early stages of the refinement.Finally it must be remembered that there is a limit to the amount of information that can beretrieved from a powder diffraction pattern. Indeed structures with up to a hundred or morestructural parameters can be refined from neutron powder data but such refinements must be

performed with great care; for refinements involving a large number of variables the physicalsignificance of certain parameters must be carefully examined. For instance thermal and

profile parameters can become poorly defined and act as a dumping ground for systematicerrors; then it is preferable to fix their values to a physically reasonable number and exclude

them from the refinement.When the uncertainty concerns the atomic parameters, it may help to provide some externalinformation to the program. This can be achieved for instance by using strict constraints. Forinstance the displacement (thermal) parameters of chemically similar but crystallographicallydistinct atoms may be constrained to be identical, or the occupancy of two distinct and partlyoccupied sites of a structure may be compelled by the chemical analysis of the material. Forcomplex structures it may be necessary to use soft constraints on distances and angles, oreven rigid body constrains.If there are difficulties from the very beginning (for instance a singular matrix at the firstrefinement), start refining the scale factors only and examine the observed versus calculated

pattern using WinPLOTR . These will most of the time reveal a glaring blunder in the inputdata (zero-shift, step size, angular limits etc).

Examples. Content of pcr_dat.zip

To test the installation of the program, or for training purposes, a list of complete examplesare provided together with FullProf . The content of the file pcr_dat.zip is now distributedwithin the FullProf Suite installer. Anyway it can be obtained as a separate file in the samearea as the program.The files contained in pcr_dat.zip have been selected in order to illustrate the use of FullProf in a variety of situations. In no way the proposed models pretend to be the most adequate tothe data. In some cases there is a clear disagreement between the data and the model. The usermay try to improve the models including new parameters that have a clear physical relevance.Increasing the number of parameters just for getting more nice fits may result in non sense


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values. At present the files contained in the archive pcr_dat.zip are given in the followingtable:

PCR Code Purpose Data FileCe1 refinement of a CeO 2 standard ceo2.datCe2 " "Rutana Conventional X-ray diffraction pattern: Rutile+Anatase Rutana.datTbbaco Conventional X-ray diffraction pattern: Tb 2BaCoO 5 Tbbaco.datTbba Conventional X-ray diffraction pattern: Profile Matching "Tb Search for Tb,Ba and Co by Montecarlo with prev. output Tb.intPbSOx Crystal structure refinement of PbSO 4 with X-rays Pbsox.datPbSO Profile matching to obtain an overlapped intensity file "PbSOm Search for Pb by Montecarlo using previous output pbsom.intPb Profile matching test of PbSO4 neutron data Pbso4.datPbSO4 Crystal structure refinement of PbSO 4 "PbSO4a Crystal structure refinement of PbSO 4 (anisotropic b's) "Pb_ho Artificial multipattern refinement Pbso4.dat,Pbsox.dat,

Hobk.datPb_sing Example of new format of PCR file adapted for multipattern

refinementsPbso4.dat

Pb_san Example of Simulated Annealing: solves the structure of PbSO 4 Pb_san.intC60s Compares C 60 x-tal data to form-factor SPHS sin(Qr)/Qr C60.intC60 Refinement of C 60 x-tal data using symmetry adapted cubic

harmonics. Form-factor type SASH.C60.int

Dy Four different ways of refining the crystal Dy.datDya and magnetic structure of DyMn 6Ge6 "Dyb "Dyc "Hocu Refinement of the magnetic structure of Ho 2Cu2O5 (D1B data) Hocu.datHobb Refinement with integrated intensities (Nuc+mag) Hobb.int

Hob Montecarlo search for mag. moments in Ho2BaNiO5 "Hobk1 Three different ways of refining the crystal Hobk.datHobk2 and magnetic structure of Ho2BaNiO5 "Hobk3 "Cuf1k Refinement of crystal & magnetic structrure of CuF 2.

Microstructural effects (D1A data)Cuf1k.dat

Pb_san Example of Simulated Annealing: solves the structure of PbSO 4 Pb_san.intLa Two ways for strain refinement in La 2 NiO 4 (D1B) La.datLab with low resolution neutron powder data "Monte Montecarlo test with single crystal data Monte.intHmt Rigid body-TLS refinement of published single X-tal data Hmt.intUrea Test Rigid body with satellites (simulated data) Urea.dat

Pyr Test Rigid body with general TLS refinement (sim. data) Pyr.datYcbacu YBaCuO with Ca. Data from D1A Ycbacu.datArg_si Corrected TOF data of Si from SEPD at Argonne Arg_si.datCecoal TOF data from POLARIS at ISIS CecoalCecua1 TOF data from POLARIS at ISIS Cecua1.datLamn_3t2 Constant wavelenght neutron data from 3T2 (LLB) of LaMnO 3 Lamn_3t2.datLamn_pol TOF data from POLARIS at ISIS on the RT phase of LaMnO 3 Lamn_pol.datSi3n4r Quantitative phase analysis. Two polymorphs of Si 3 N4. (Studvik) Si3n4r.datSin_3t2 As above but data taken at 3T2 (LLB) Sin_3t2Pb_san Example of Simulated Annealing: solves the structure of PbSO 4 Pb_san.intMaghem Refinement of Fe 2O3-Fe 3O4 at RT (D1A data) Maghem


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In general, the user must first run the program to verify that the provided PCR files behavecorrectly. After that, the user should make a copy of the control files for saving them beforerunning his(her) own options. The best way is to modify the given values for different sets of

parameters and run the program. The beginner must make extensive use of editor-plot cycles.The plot of the file CODFIL.prf is of absolutely necessity for knowing the behavior of the

program under bad (or inaccurate) input parameters.

To use the above files for training, the inexperienced user must start with the simplest cases,that is ce1.pcr and ce2.pcr used to process the file ceo2.dat . This file corresponds to a datacollection on cerium oxide with a laboratory X-ray powder diffractometer, using CuK doublets. Other simple examples with conventional X-rays are: the rutile-anatase mixture, thatallow a quantitative analysis of the relative fraction of each component, and the diffraction

pattern of Tb 2BaCoO 5 presenting micro-absorption effects that produce some negativetemperature factors. The user can modify the input file in order to input the micro-absorptioncorrection and look for the changes in the results. The next files to be processed are those ofPbSO 4. The data file correspond to a laboratory X-ray diffraction pattern ( pbsox.dat ) and to aneutron powder diffraction pattern ( pbso4.dat ) obtained on D1A (ILL) that was used in aRound Robin on Rietveld refinement [7]. For a person working mainly with crystal structuresthe next files to be studied are: ycbacu , hmt and urea for powder diffraction.

Some files to be used with single crystal data are also given: c60 . The first one uses asimplistic model (just a spherical shell) for describing the C 60 molecule that gives relativelygood results. The user can try this file as an example of special form factor refinement. Thefree parameter is the radius of the C 60 molecule.

If the user is interested in magnetic structures it is worth to read the article [8], and references

therein, for an introduction to the way the formalism of propagation vectors is implemented in FullProf , taking into account that slightly different conventions (see the mathematical sectionof the manual) have finally been adopted concerning the sign of phases. The user can start

practicing with the rest of the files in the following order.

la, lab : refinement of the low temperature phase crystal and magnetic structure ofLa 2 NiO 4. The data are from a medium-low resolution neutron powder diffractometer(D1B at ILL). This phase present a microstrain that is refined using two equivalentmethods in the two files. The magnetic structure is very simple. A peak from animpurity phase is near the first magnetic peak.

The files hobb , hob , hobk1 , hobk2 , hobk3 concern the refinement of the crystal andmagnetic structures of Ho 2BaNiO 5 at 1.5K, using different methods and conditions.The user can verify that hob.pcr can solve the magnetic structure of Ho 2BaNiO 5 justtesting random configurations. This is a very favorable case and this method cannot beapplied for general magnetic structure determination. The data are from D1B at ILL.

Hocu : refinement of the magnetic structure of Ho 2Cu 2O5. The data have been taken onD1B diffractometer at the ILL. Magnetic scattering dominates nuclear scattering. Thecrystal structure cannot be refined with these data.

Cuf1k : refinement of the magnetic structure of CuF 2. The data have been taken onD1A diffractometer when it was installed provisionally at the LLB. Nuclear scatteringdominates magnetic scattering. The diffraction pattern cannot be refined properly

without taking into account microstructural effects.


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The program recognizes the use of simulated annealing by putting the variable Nre equal tothe number of parameters to be eventually varied, and Cry =3 at the beginning of the PCRfile (see appendix of the manual for details).In the example above the three angles (in radians) defining the orientation of the molecule areselected as parameters 1, 2 and 3. The admissible range of values are given in a list followed

by an indicator telling to the program how to treat the boundaries. The number 1 followingthe value of the initial step (0.5 radians) indicates that periodic boundary conditions areapplied.

The flag InitConf is important for selecting the treatment of the initial configuration. IfInitConf = 0 the initial configuration is totally random. If InitConf =1, the initialconfiguration is the one given by the values of the parameters in the PCR-file. This last optionis useful when one tries to optimize an already good starting configuration, by controlling the

box limits and the steps.

The other critical point is to select between the two algorithms. This is controlled by the valueof the variable Nalgor . If its value is zero, the Corana [11] algorithm is selected. This

=> **** SIMULATED ANNEALING SEARCH FOR STARTING CONFIGURATION ****=> Initial configuration cost: 77.53=> Initial configuration state vector:=> Theta Phi Chi=> 1 2 3=> 1.3807 2.4672 -3.0110=> NT: 1 Temp: 8.00 (%Acc): 23.50 : 5.2360 : 44.4302. . . . . . .

=> NT: 6 Temp: 4.72 (%Acc): 30.50 : 0.3496 : 23.8774. . . . . . . .=> NT: 11 Temp: 2.79 (%Acc): 39.33 : 0.1440 : 13.4990. . . . . . . .=> NT: 21 Temp: 0.97 (%Acc): 38.50 : 0.0530 : 6.3417. . . . . . . .=> NT: 33 Temp: 0.27 (%Acc): 36.17 : 0.0179 : 4.3854

=>BEST CONFIGURATIONS FOUND BY Simulated Annealing FOR PHASE: 1=> -> Configuration parameters ( 71 reflections):=> Sol#: 1 RF2= 3.928 ::=> Theta Phi Chi=> 1 2 3=> 0.9401 0.1464 2.7477

=> CPU Time: 25.177 seconds

=> 0.420 minutes

Figure 2 : Simplified screen capture of the FullProf output when running in thesimulating annealing mode for the example of Figure 1. The first picture of the structurecorresponds to the starting configuration. The final result is also displayed.


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algorithm does not use fixed steps for moving the parameters defining the configuration,instead the program starts by using then whole admissible interval as initial step for all

parameters and then adapt progressively their values in order to maintain an approximate rateof accepted configurations between 40% and 60%. If Nalgor =1 the same algorithm is used

but the starting steps are those given in the file. For Nalgor =2, the normal SA algorithm(fixed steps) is used. The last method, used with appropriate boundary box for parametersand InitConf =1, is better when one tries to refine a configuration without destroying the

starting configuration.Within the distribution of FullProf there is a simple example of simulating annealing work

using neutron diffraction data from D1A on lead sulfate PbSO 4. The file is Pb_san.pcr , wherethe user finds a particular case of how to prepare a PCR file adapted for simulated annealing.In this example the atoms are treated independently using the correct space group and anartificial constraint is used: several atoms are constrained to have the same y fractionalcoordinate. We know that all these atoms are in a special position of the Pnma space group ( y should be or ), but the file is prepared in such a way as to illustrate the use of constraints.Starting from a random configuration for all the free parameters (including the special ys) the

program finds progressively the good atom positions when the appropriate values of thecontrol parameters are used. The user may play with the different parameters (startingtemperature, number of Monte Carlo cycles per temperature, type of algorithm, number ofreflections to be used, etc) to experience when the method is able to solve the PbSO 4

structure.

Calculated Neutron powder diffractionpattern without Hydrogen atoms

Where are the hydrogen atoms?

Calculated Neutron powder diffractionpattern without Hydrogen atoms

Where are the hydrogen atoms?

Figure 3 : Comparison of the calculated versus observed neutron powderdiffraction pattern of Sr acid oxalate hydrate, using the represented crystalstructure solved by X-ray powder diffraction [13].


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Another interesting case is that of searching hydrogen (deuterium) atoms when the rest ofatoms are already known. We shall take as an example the case of Sr acid oxalate hydrate thatwas solved by conventional Fourier synthesis [12, 13].

The non hydrogen atoms structure was solved ab initio from X-ray powder diffraction usingdirect methods [13], but the calculated neutron powder diffraction pattern without hydrogenatoms was very poor (see Fig. 3). A profile matching refinement of the neutron diffraction

!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More14 0 0 0.0 0.0 1.0 0 4 0 0 0 966.691 0 5 0

!P 21/n


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pattern, putting the option to generate a file containing cluster of integrated intensities, provided the input file (extension . int ) necessary to run a simulated annealing work. Forsearching the hydrogen atoms, it is not necessary to use a large number of reflections. Onlythe reflections up to 47( ) in 2 are sufficient to find the hydrogen positions. The PCR file are

prepared by putting all known atoms in their fixed positions (according to the results obtained

by X-ray diffraction) and three additional hydrogen atoms (according to chemical analysis) inarbitrary positions. The limits for the free parameters (positions of hydrogen atoms) are put inthe appropriate place (see Figure 4), and the file is ready for run. The final result after runningthe simulated annealing job followed by Rietveld refinement of the proposed solution isdisplayed in Figure 5. The files corresponding to this case, and a PDF file with more detailsabout the problem, can be obtained from the Internet [14]

The user should experiment for their own cases in order to select good control parameters.For instance the appropriate starting temperature depends strongly on the number of free

parameters, the step sizes and the constraints. For solving a structure (crystallographic ormagnetic) from the scratch it is important to select a temperature for which the percentage ofaccepted configurations is high (or the order of 80%) in order to let the procedure explore a

large set of configurations. The number of Monte Carlo cycles per temperature should be afactor (from about 15 to 50) the number of free parameters.

Two types of oxalate groups

The chemical formula is Sr(HC 2O4). (C 2O4) . H 2O

Where are the hydrogen

atoms?

Chains along cC2O4 HC2O4 H

Isolated C 2O4

And water molecules




atoms?


Isolated C 2O4

And water molecules




atoms?


Isolated C 2O4

And water molecules



atoms?

Chains along cC2O4 HC2O4 HChains along cC2O4 HC2O4 H

Isolated C 2O4Isolated C 2O4

And water moleculesAnd water molecules

Figure 6 : Results obtained from simulated annealing and further Rietveld refinement of thecrystal structure of Sr acid oxalate hydrate.


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There is no guarantee that the optimum solution will be found, however if the final R-factorsare lower than say 25% the structure provided by the program may contain some recognizablefragment that serves to start normal Rietveld refinement cycles together with Fouriersynthesis. For using the GFourier program [12], distributed in the same site as FullProf , it isimportant to use the value Jfou =4 in the PCR-file, to output an appropriate set of structurefactors and an input file (extension inp) for GFourier .

AcknowledgementsIt is a pleasure to thank here all my colleagues that have contributed with discussions, writing

pieces of code, or are presently contributing with companion programs to FullProf : ThierryRoisnel, Javier Gonzlez-Platas, Aziz Daoud-Aladine, Carlos Frontera, Laurent Chapon andVincent Rodriguez. I would like to thank many users for giving me a feedback without whichthe program could not be improved.

References:

[1] H.M. Rietveld, Acta Cryst . 22 , 151 (1967); H.M. Rietveld, J. Applied Cryst . 2, 65 (1969).[2] D.B. Wiles & R.A. Young, J. Applied Cryst . 14 , 149 (1981); D.B. Wiles & R.A. Young, J.

Applied Cryst . 15 , 430 (1982)[3] J. Rodrguez-Carvajal and J. Gonzlez-Platas: Crystallographic Fortran 90 ModulesLibrary (CrysFML): a simple toolbox for crystallographic computing programsCommission on Crystallographic Computing of IUCr, Newsletter 1, January 2003. Availableat http://www.iucr.org/iucr-top/comm/ccom/newsletters/ .[4] The most recent versions, for different platforms, of the program FullProf can be found at

the ftp-area: ftp://ftp.cea.fr/pub/llb/divers/fullprof.2k . Different mirrors of this site can befound at http://www.ccp14.ac.uk .

[5] L.B. McCusker et al ., J. Appl. Cryst . 32 , 36 (1999).[6] J. Rodrguez-Carvajal and T. Roisnel, FullProf.98 and WinPLOTR New WindowsApplications for Diffraction. Commission on Powder Diffraction, IUCr, Newsletter 20 , May-August (1998). J. Rodrguez-Carvajal, Recent developments of the program FullProf .Commission on Powder Diffraction, IUCr, Newsletter 26 , December (2001).J. Gonzlez-Platas and J. Rodrguez-Carvajal, EdPCR a GUI for FullProf (unpublished)[7] R.J. Hill, J.Appl.Cryst 25 , 589 (1992).[8] J. Rodrguez-Carvajal, Physica B 192 , 55 (1993).[9] S. Kirkpatrick, C.D. Gellat, Jr., M.P. Vecchi. Science 220, Nr. 4598, 671 (1983)[10] J. Rodrguez-Carvajal, Materials Science Forum 378-381 , 268 (2001); see alsoProceedings of the XVIII Conference on Applied Crystallography, Ed. Henryk Morawiec andDanuta Strz, World Scientific, London 2001, pp 30-36.[11] A. Corana, M. Marchesi, C. Martini, S. Ridella, ACM Trans. Math. Softw. 13 , 262 (1987) [12] J. Gonzlez-Platas and J. Rodrguez-Carvajal, GFourier : a Windows/Linux program tocalculate and display Fourier maps . Program available within the FullProf Suite .[13] G. Vanhoyland et al . J. Solid State Chem . 157 , 283 (2001).[14] The file sr_oxalate.zip contains the data and PCR files to practice with simulatedanneling. The file ECM-21-Workshop.zip contains a PDF file corresponding to a presentationon several aspects of FullProf includint a tutorial for the oxalate case. Both files can be foundat ftp://ftp.cea.fr/pub/llb/divers/Rietveld-exercises .

Fullprof Intro

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