introduction to the program fullprof refinement of

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Introduction to the Program FULLPROF:Refinement of Crystal and Magnetic Structures

from Powder and Single Crystal Data

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Juan Rodriguez-Carvajal

Institut Laue-Langevin

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Introduction to the Program FULLPROF: Refinement of Crystal and

Magnetic 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 programFullProfis presented. After a brief introduction

summarizing the history of the program we present the main elements of the Rietveld method

and how to use the program in routine work for refining crystal and magnetic structures. The

most specialized topics (microstructure effects, flipping ratio refinements, the use of special

form-factors, time of flight neutron powder diffraction) will not be treated here. A full

example 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 theFullProfWeb site.

Introduction

The programFullProfhas been mainly developed to perform Rietveld analysis [1] of neutron

or 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 some

structure determination capabilities by using the Simulated Annealing method for global

optimization.

The first versions of the programFullProfwere based on the code of the DBWS program [2],which was also a major modification of the original Rietveld-Hewat program. The program

FullProfhas been re-written using the full capabilities of the new Fortran 95 standard during

1997-1998. It is progressively being transformed in a program based in the Crystallographic

Fortran 95 Modules Library [3]. The program works with some allocatablearrays so the user

can directly control the dimensions of important arrays at run time. In this paper we shall

describe some elementary points concerning the methods implemented in the program and

how to use it. For further details the user should consult the manual and tutorials. The

Windows version of the program and all the suite of programs related to FullProf are now

distributed within the FullProf Suite installer (setup_FullProf_Suite.exe). This installer,

additional documents and tutorials, can be found in theFullProfWeb site [4].

The Rietveld Method

A powder diffraction pattern can be recorded in numerical form for a discrete set of scattering

angles, times of flight or energies. We will refer to this scattering variable as T. Then, the

experimental powder diffraction pattern is usually given as two arrays { }1,...,

,i i i n

T y=

. In the

case of data that have been manipulated or normalized in some way the three arrays

{ }1,...,

, ,i i i i n

T y =

, wherei is the standard deviation of the profile intensity iy , are needed in

order to properly weight the residuals in the least squares procedure. The profile can be

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

h

( )h hc i i iy 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 thephaseand vary from 1 up tothe number of phasesexisting in the model. In FullProf the term phaseis synonymous of a

sameprocedure 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 (treated

usually as a differentphase) coming from a single crystallographic phase in the sample. The

general expression of the integrated intensity is:

{ }2,,

hh

I L APC F

= (2)

For simplicity we will drop the -index. Sometimes we will refer to the whole arrays{ }iy and { }ciy as obsy and calcy 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

Fh is the structure factor (crystal structures) or the modulus of the magnetic

interaction vector (magnetic structures).

Ah is the absorption correction

Ph is the preferred orientation function

is the reflection profile function that models both instrumental and sampleeffects hC includes special corrections (non linearity, efficiencies, special absorption

corrections, extinction, etc)

ib is the background intensity

In the following sections we discussed the different terms in more detail. The Rietveld

Method consist of refining a crystal (and/or magnetic) structure by minimizing the weighted

squared difference between the observed { }1,...,i i n

y=

and the calculated (1) pattern

{ }, 1,...,( )

c i i n

y=

against the parameter vector1 2 3

( , , ,... )p

= . The function minimized in

the Rietveld Method is:

{ }22

,

1

( )n

i i c i

i

w y y=

= (3)

with 21

iiw = , being

2

i the variance of the "observation" iy . In more complex cases the user

may consider several diffraction patterns, or some chemical constraints. For those cases the

general expression of the function to be minimized is:


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{ } { }

222 2 2

21 1 1 1

1( ) ( )

N N n m

T P P G P i i ci j cj

P p i j gjP

w y y c g g = = = =

= + = +

(4)

Where2

P and2

G 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

1N

P

P

=

= , for theNpatterns. The quantity jg 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 ( )cjg

is performed as a function of a subset of components of the vector parameter .The

normalization constant cis taken as the current value of the global reduced chi-square for all

the diffraction patterns. For simplicity we shall consider the expression (3) to explain some

standard 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

0

opt

=

A Taylor expansion of ( )ic

y

around an initial guess0allows the application of an iterative

process. The shifts to be applied to the parameters at each cycle for improving 2 are

obtained 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 withinFullProf, are given by the expressions:

, 0 , 0

, 0

,

( ) ( )

( )( )

c i c i

kl i

i k l

c i

k i i c i

i k

y yA w

yb w y y

=

=

(6)

The shifts of the parameters0obtained by solving the normal equations are added to the

starting parameters giving rise to a new set01 0

= +

. The new parameters are considered

as 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 a

relaxation factor. The standard deviations of the adjusted parameters are calculated by the

expression:1 2( ) ( )Ak k kk a

= (7)

Where the reduced chi-square is defined as:2

2

n - p

= (8)

The quantity akis 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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closer to the users case is the initial PCR file the easier is to modify it. An important aspect is

the format of the profile intensities data file that must be correctly given before attempting

any kind of refinement.

The user must be aware of the way he(she) can control the refinement procedure: the number

of 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 by

which the computed shift (see equation 5) will be multiplied before use. The calculated shifts

are also multiplied by a relaxation factor before being applied to the parameters.

Recently, we have developed a Windows GUI, calledEdPCR, to control the PCR file, so that

the 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 be

modified afterward.

A stepwise method for Rietveld refinement

Although the principles behind the Rietveld profile refinement method are rather simple, the

use of the technique requires some expertise. This results merely from the fact that Rietveld

refinement 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 bad

starting point, may easily cause divergence in early stages of the refinement. All these

difficulties can actually be readily overcome by following a few simple prescriptions:

Use the best possible starting model: this can be easily done for backgroundparameters and lattice constants. In some cases, in particular when the structural

model is very crude, it is advisable to analyze first the pattern with the profile

matching(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 affectstrongly the residuals (they must be refined first) while others produce only little

improvement 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 and

experimental conditions of the data measurement: zero-shift and resolution function of

the instrument, for instance. Then a sensible sequence of refinement of a crystal

structure 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 refine

at least two background parameters, or better fix the background using linear

interpolation 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 external

instrumental 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. The

examination of the difference pattern is a quick and efficient method to detect blunders in the

model or in the input file controlling the refinement process. I may also provide useful hints

on 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 the

next, 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 be

retrieved from a powder diffraction pattern. Indeed structures with up to a hundred or more

structural 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 physical

significance of certain parameters must be carefully examined. For instance thermal and

profile parameters can become poorly defined and act as a dumping ground for systematic

errors; 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 external

information to the program. This can be achieved for instance by using strict constraints. For

instance the displacement (thermal) parameters of chemically similar but crystallographically

distinct atoms may be constrained to be identical, or the occupancy of two distinct and partly

occupied sites of a structure may be compelled by the chemical analysis of the material. For

complex structures it may be necessary to use soft constraints on distances and angles, or

even rigid body constrains.

If there are difficulties from the very beginning (for instance a singular matrix at the first

refinement), 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 input

data (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 examples

are provided together with FullProf. The content of the file pcr_dat.zip is now distributed

within the FullProf Suite installer. Anyway it can be obtained as a separate file in the same

area as the program.

The files contained inpcr_dat.ziphave 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 to

the data. In some cases there is a clear disagreement between the data and the model. The user

may 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 archivepcr_dat.zipare given in the following

table:

PCR Code Purpose Data File

Ce1 refinement of a CeO2standard ceo2.dat

Ce2 " "

Rutana Conventional X-ray diffraction pattern: Rutile+Anatase Rutana.dat

Tbbaco Conventional X-ray diffraction pattern: Tb2BaCoO5 Tbbaco.dat

Tbba Conventional X-ray diffraction pattern: Profile Matching "

Tb Search for Tb,Ba and Co by Montecarlo with prev. output Tb.int

PbSOx Crystal structure refinement of PbSO4with X-rays Pbsox.dat

PbSO Profile matching to obtain an overlapped intensity file "

PbSOm Search for Pb by Montecarlo using previous output pbsom.int

Pb Profile matching test of PbSO4 neutron data Pbso4.dat

PbSO4 Crystal structure refinement of PbSO4 "

PbSO4a Crystal structure refinement of PbSO4(anisotropic b's) "

Pb_ho Artificial multipattern refinement Pbso4.dat,Pbsox.dat,

Hobk.dat

Pb_sing Example of new format of PCR file adapted for multipatternrefinements

Pbso4.dat

Pb_san Example of Simulated Annealing: solves the structure of PbSO4 Pb_san.int

C60s Compares C60x-tal data to form-factor SPHS sin(Qr)/Qr C60.int

C60 Refinement of C60 x-tal data using symmetry adapted cubic

harmonics. Form-factor type SASH.

C60.int

Dy Four different ways of refining the crystal Dy.dat

Dya and magnetic structure of DyMn6Ge6 "

Dyb "

Dyc "

Hocu Refinement of the magnetic structure of Ho2Cu2O5(D1B data) Hocu.dat

Hobb 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.dat

Hobk2 and magnetic structure of Ho2BaNiO5 "

Hobk3 "

Cuf1k Refinement of crystal & magnetic structrure of CuF2.

Microstructural effects (D1A data)

Cuf1k.dat


La Two ways for strain refinement in La2NiO4 (D1B) La.dat

Lab with low resolution neutron powder data "

Monte Montecarlo test with single crystal data Monte.int

Hmt Rigid body-TLS refinement of published single X-tal data Hmt.int

Urea 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.dat

Arg_si Corrected TOF data of Si from SEPD at Argonne Arg_si.dat

Cecoal TOF data from POLARIS at ISIS Cecoal

Cecua1 TOF data from POLARIS at ISIS Cecua1.dat

Lamn_3t2 Constant wavelenght neutron data from 3T2 (LLB) of LaMnO3 Lamn_3t2.dat

Lamn_pol TOF data from POLARIS at ISIS on the RT phase of LaMnO3 Lamn_pol.dat

Si3n4r Quantitative phase analysis. Two polymorphs of Si3N4. (Studvik) Si3n4r.dat

Sin_3t2 As above but data taken at 3T2 (LLB) Sin_3t2


Maghem Refinement of Fe2O3-Fe3O4at RT (D1A data) Maghem


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In general, the user must first run the program to verify that the provided PCR files behave

correctly. After that, the user should make a copy of the control files for saving them before

running 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.pcrand ce2.pcrused to process the file ceo2.dat. This file corresponds to a data

collection 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, that

allow a quantitative analysis of the relative fraction of each component, and the diffraction

pattern of Tb2BaCoO5 presenting micro-absorption effects that produce some negative

temperature factors. The user can modify the input file in order to input the micro-absorption

correction and look for the changes in the results. The next files to be processed are those of

PbSO4. The data file correspond to a laboratory X-ray diffraction pattern (pbsox.dat) and to a

neutron powder diffraction pattern (pbso4.dat) obtained on D1A (ILL) that was used in a

Round Robin on Rietveld refinement [7]. For a person working mainly with crystal structures

the next files to be studied are:ycbacu, hmtand ureafor powder diffraction.

Some files to be used with single crystal data are also given: c60. The first one uses a

simplistic model (just a spherical shell) for describing the C60molecule that gives relatively

good results. The user can try this file as an example of special form factor refinement. The

free parameter is the radius of the C60molecule.

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 inFullProf, taking into account that slightly different conventions (see the mathematical section

of 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 ofLa2NiO4. The data are from a medium-low resolution neutron powder diffractometer

(D1B at ILL). This phase present a microstrain that is refined using two equivalent

methods in the two files. The magnetic structure is very simple. A peak from an

impurity phase is near the first magnetic peak.

The files hobb, hob, hobk1, hobk2, hobk3 concern the refinement of the crystal andmagnetic structures of Ho2BaNiO5 at 1.5K, using different methods and conditions.The user can verify that hob.pcrcan solve the magnetic structure of Ho2BaNiO5 just

testing random configurations. This is a very favorable case and this method cannot be

applied for general magnetic structure determination. The data are from D1B at ILL.

Hocu: refinement of the magnetic structure of Ho2Cu2O5. The data have been taken onD1B diffractometer at the ILL. Magnetic scattering dominates nuclear scattering. The

crystal structure cannot be refined with these data.

Cuf1k: refinement of the magnetic structure of CuF2. The data have been taken onD1A diffractometer when it was installed provisionally at the LLB. Nuclear scattering

dominates magnetic scattering. The diffraction pattern cannot be refined properly

without taking into account microstructural effects.


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The files dy, dya, dyb, dyc use different methods to refine the incommensuratemagnetic structure of DyMn6Ge6. This is a conical structure that can be refined using a

real space approachas in dyand dyaor using Fourier components of the magnetic

moments, which is the general formalism of FullProf for handling magnetic

structures. This is the case of files dyband dyc.

The only right way to learn about crystal and magnetic structure refinements is practicing

with real data as those given in the pcr_dat.ziparchive, or better, with the data collected by

and of interest to the user.

Solving or completing structures by Simulated Annealing

An option for helping to solve crystal and/or magnetic structures has been implemented in

FullProf. This is a simulated annealing module able to handle two types of algorithms: fixed

and variable steps for generating new configurations. The simulated annealing technique [9]

works, at present, only with integrated intensities. A short report about the technique and the

implementation inFullProfmay be found in reference [10], here we show just some examplesof using the method .

To solve a crystal or a magnetic structure a complete list of atoms with all their attributes

(thermal parameters, magnetic moments, etc) should be given as if everything were known.

An example of simulating annealing PCR file is given in Figure 1.

The use of codewords is totally supported so that any usual constraint may be used in the

search. Of course the initial values of the parameters are arbitrary provided the hard

constraints through the codewords are respected. In fact the meaning of the codewords is the

same as in least square refinements, the multipliers and signs are applied to the shiftswith

respect to the previous values of the parameters. The scale factor may be treated automatically

so that no codeword should be given to this parameter.

Para-di-Iodo-Benzene (Sim.Annealing)!!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More

6 0 0 1.0 0.0 0.0 4 4 0 0 0 0.00 0 0 0!P b c a


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The program recognizes the use of simulated annealing by putting the variableNreequal 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 are

selected as parameters 1, 2 and 3. The admissible range of values are given in a list followedby an indicator telling to the program how to treat the boundaries. The number 1 following

the value of the initial step (0.5 radians) indicates that periodic boundary conditions are

applied.

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 option

is 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 variableNalgor. 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 theFullProfoutput when running in the

simulating annealing mode for the example of Figure 1. The first picture of the structure

corresponds to the starting configuration. The final result is also displayed.


12/15

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 rate

of accepted configurations between 40% and 60%. IfNalgor=1 the same algorithm is usedbut the starting steps are those given in the file. ForNalgor=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 refinea 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 PbSO4. The file isPb_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 an

artificial constraint is used: several atoms are constrained to have the same y fractional

coordinate. We know that all these atoms are in a special position of thePnmaspace 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 specialys) the

program finds progressively the good atom positions when the appropriate values of the

control parameters are used. The user may play with the different parameters (starting

temperature, number of Monte Carlo cycles per temperature, type of algorithm, number of

reflections to be used, etc) to experience when the method is able to solve the PbSO4

structure.

Calculated Neutron powder diffraction

pattern without Hydrogen atoms

Where are the hydrogen atoms?

Calculated Neutron powder diffraction

pattern without Hydrogen atoms

Where are the hydrogen atoms?

Figure 3: Comparison of the calculated versus observed neutron powder

diffraction pattern of Sr acid oxalate hydrate, using the represented crystal

structure solved by X-ray powder diffraction [13].


13/15

Another interesting case is that of searching hydrogen (deuterium) atoms when the rest of

atoms are already known. We shall take as an example the case of Sr acid oxalate hydrate that

was solved by conventional Fourier synthesis [12, 13].

The non hydrogen atoms structure was solved ab initiofrom X-ray powder diffraction using

direct 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


14/15

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. For

searching the hydrogen atoms, it is not necessary to use a large number of reflections. Only

the reflections up to 47() in 2are sufficient to find the hydrogen positions. The PCR file areprepared 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 in

the appropriate place (see Figure 4), and the file is ready for run. The final result after running

the simulated annealing job followed by Rietveld refinement of the proposed solution is

displayed in Figure 5. The files corresponding to this case, and a PDF file with more details

about 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 or

magnetic) from the scratch it is important to select a temperature for which the percentage of

accepted 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(HC2O4). (C2O4) . H2O

Where are the hydrogen

atoms?

Chains along c

C2O4 HC2O4 H

Isolated C2O4

And water molecules




atoms?

Chains along c

C2O4 HC2O4 H

Isolated C2O4

And water molecules




atoms?

Chains along c

C2O4 HC2O4 H

Isolated C2O4

And water molecules



atoms?

Chains along c

C2O4 HC2O4 HChains along c

C2O4 HC2O4 H

Isolated C2O4Isolated C2O4

And water moleculesAnd water molecules

Figure 6: Results obtained from simulated annealing and further Rietveld refinement of the

crystal structure of Sr acid oxalate hydrate.


15/15

There is no guarantee that the optimum solution will be found, however if the final R-factors

are lower than say 25% the structure provided by the program may contain some recognizable

fragment that serves to start normal Rietveld refinement cycles together with Fourier

synthesis. For using the GFourierprogram [12], distributed in the same site asFullProf, it is

important to use the value Jfou=4 in the PCR-file, to output an appropriate set of structure

factors and an input file (extension inp) for GFourier.

Acknowledgements

It 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: Thierry

Roisnel, Javier Gonzlez-Platas, Aziz Daoud-Aladine, Carlos Frontera, Laurent Chapon and

Vincent Rodriguez. I would like to thank many users for giving me a feedback without which

the 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 Modules

Library (CrysFML): a simple toolbox for crystallographic computing programs

Commission on Crystallographic Computing of IUCr,Newsletter 1, January 2003. Available

athttp://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 be

found 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 Windows

Applications 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, EdPCRa GUI forFullProf (unpublished)

[7]R.J. Hill, J.Appl.Cryst 25, 589 (1992).

[8] J. Rodrguez-Carvajal,Physica B192, 55 (1993).

[9] S. Kirkpatrick, C.D. Gellat, Jr., M.P. Vecchi. Science220,Nr. 4598, 671 (1983)

[10] J. Rodrguez-Carvajal, Materials Science Forum 378-381, 268 (2001); see also

Proceedings of the XVIII Conference on Applied Crystallography, Ed. Henryk Morawiec and

Danuta 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 to

calculate and display Fourier maps . Program available within theFullProf 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 simulated

anneling. The fileECM-21-Workshop.zipcontains a PDF file corresponding to a presentation

on several aspects ofFullProfincludint a tutorial for the oxalate case. Both files can be found

at ftp://ftp.cea.fr/pub/llb/divers/Rietveld-exercises.
https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==https://www.researchgate.net/publication/238135204_Crystallographic_fortran_modules_library_CFML_a_simple_toolbox_for_computing_programs?el=1_x_8&enrichId=rgreq-53de0cc2bac6fc4694a28e336e88790b&enrichSource=Y292ZXJQYWdlOzI2NzM3NTYxMDtBUzoxNjIwNjQzODc1NTEyMzJAMTQxNTY1MDU2OTUzOA==

introduction to the program fullprof refinement of

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