A user's guide to – Rfit2000 Contents 1. Introduction 2. How
Contents
1. Feigin L A Kristallografiya 1995 v 40 n 5 p 801 808 russian and english 6 Konovalov O V Feigin L A Shchedrin B M Statistical evaluation of the accuracy of structure parameters determination from X ray and neutron reflectivity data Kristallografiya 1996 v 41 n 4 p 640 643 7 Konovalov O V Samoilenko I I Feigin L A Shchedrin B M Application of normalizing function in the simulation of X ray and neutron reflectivity data Kristallografiya 1996 v 41 n 4 p 635 639 8 Konovalov O V Feigin L A Shchedrin B M Allowance for apparatus distortion in modeling the srtucture of Langmuir Blodgett films from reflectivity data Kristallografiya 1996 v 41 n 4 p 629 634 9 LI Samoilenko O V Konovalov L A Feigin B M Shchedrin L G Yanusova Processing of experimental reflectivity data within the REFLAN software package Kristallografiya 1999 v 44 n 2 p 310 318 10 O V Konovalov I I Samoilenko L A Feigin B M Shchedrin L G Yanusova Statistical substantiation of parametrization of a film model in reflectometry Kristallografiya 1999 v 44 n 2 p 319 323 P2. allow to describe periodic structures with different structures at interfaces The general format of file with model description is WL dWL dtTheta dDet VdTheta VdDet BU RU AU NRU d BU 1 5 BU 1 B BU 1 o BU 1 d BU 2 5 BU 2 B BU 2 o BU 2 d AU AU 8 AU AU d_ Sub 0 Here B AU AU o AU AU B Sub WL is wave length of irradiation in Angstrom dWL is FWHM of wave length dispersion in Angstrom dTheta VdTheta define FWHM of incident beam divergence so that FWHM dTheta VdTheta Theta VdTheta takes in account variation of beam divergence with Theta Units of FWHM dTheta Theta are degree dDet VdDetect define angular aperture of slit before detector DFW so that DFW dDet VdDet Theta VdDeta takes in account variation of slit width with Theta Units of DFW dDet are degree BU RU AU number of slubs in the model of the film for each group Any number may take zero To have unique format of data reading the thickness of the Substrate must to have any value for example 0 3 4 File of constrains on parameters of model This file Imt defines a domain of interest a domain where we search the solution The limits file contains minimal and maximal values allowed for each parameter Format of LMT file is similar to MDL file The LMT files do not have first two lines of MDL file On the place of one value in the MDL file LMT file has 3 values that are minimal and maximal values of interval
3. files First column is incident angle in degree or 1 A Second column is measured intensity Third column is the intensity calculated for the best model with taking in to account of instrumental resolution The bst file contains parameters of the best model and if it was requested an estimation of uncertainties of the variable parameters This file may contain three models One model that was found during fitting session Second model that was found after Newton step Third model that was found after optimization of Newton step The final curve that is in the pet file is calculated for the model with that have the smallest y value of these 3 models 6 Questions and bugs Please do not hesitate address to Oleg KONOVALOV E mail konovalo esrf fr 7 References 1 NUMERICAL RECIPES The art of scientific computing William H Press Brian P Flannery Saul A Teukolsky William T Vetterling Cambridge University Press 1986 Chapter 10 4 Downhill Simplex Method in Multidimensions 2 Lekner J 1987 Theory of reflection Dordrecht Martinus Nijhoff Lekner J 1991 Physica B Utrecht v 173 p 99 111 Parratt L G Phys Rev v 95 1954 p 359 Born M Wolf E 1980 Principles of optics 6th ed New York Pergamon Pres 5 Samoilenko I I Shchedrin B M Feigin L A Global minimization in reconstraction of the scattering length density profile by X ray reflectivity data Phys B v 221 1996 p 542 546 Samoilenko I I Shchedrin B M
4. of the parameter variation and integer number that defines the status of the parameter The status is one of following e 0 means parameter fixed and does not change in the session e 1 parameter should be fit e n negative integer value means that corresponding parameter takes the same value as the parameter in the line n Lines are counted from the top to down 4 Run Click on file RFIT2000 EXE To be able to fit or simulate data you should fist define a name of command file To do this click option lt File gt and then lt Set Command File gt As far as the name of command file is defined the option lt Run gt becomes enable Click on lt Run gt and redefine setting if there is a reason When settings is defined click lt OK gt The fit or simulate session will start To interrupt fitting you should fist click on main window and then CtrI Q During the fit information about number of done iterations the best y and the worst x of the simplex tolerance and stage local or global is updated in appropriate window Each time when program finds a model with the x better than the last one a plot window will be updated 5 Out put files Three new file with extensions bst pcet loc appear on the disk after fitting session All of them have the same name as the name of the model file The loc file contains values of variable parameters of the model at found local minima during the session The pet file is the 3 column
5. A user s guide to Rfit2000 Contents 1 Introduction 2 How to run program 3 Input files and its format 3 1 Command file 3 2 File of experimental data 3 3 File with model description and initial parameters 3 4 File of constrains on parameters of model 4 Run 5 Out put files 6 Questions and bugs 7 References 1 Introduction The RFIT2000 program is created to fit X ray and neutron reflectivity data The search of global minima is done via successive descent from local minima 5 This method can be treated as a loop of two stages repeated consequently The first stage is the local minimization of the 7 like criterion and the second one is the descent from the most recent local minimum This is a way how program search the global minimum Minimal requirement for a computer any PC with any Windows operation system The program fits the model parameters to experimental data Local minimization procedure is based on the algorithm called Downhill Simplex Method 1 One of the three methods to calculate reflectivity may be chosen optionally e Fourier transformation of electron density 2 e Parratt algorithm 3 e Matrix method 4 The reflectivity is calculated with taking into account an instrumental resolution function That usually is not delta function due to wave length dispersion divergence of the incident beam and finite aperture of a detector Moreover the resolution function is function of scattering v
6. ector Q 4 1 sin 0 A Where x is pi number 0 is grazing angle and is wave length Optionally the program makes statistical analysis of found solution 6 that gives estimation of parameters uncertainties The merit function has the next form 2 eee oe yee fen dI exp Where j 1 N and N is total number of experimental point M is number of variable parameters and K scaling factor To learn more details about merit function and application of instrumental resolution in the program see ref 6 7 8 2 How to run program Just click on file RFIT2000 EXE There are four supplementary input files needed for the program operation 1 Command file 2 File with experimental data 3 File with model description and 4 File with constrains on model parameters There are examples of input and output files input glob inp glob dat glob mdl glob Imt output glob loc glob pct glob bst These file will help to understand instructions given below and serve as a test 3 Input files format 3 1 Command file The definition of input files names and some miscellaneous information contains in command file This file contains following information Names of experimental data file dat Operation mode Fit or Simulation Apply or not the scaling of the data Presence or absence of uncertainty column error bar in the experimental data Name of model file with parameters of initial guess mdl Name of file with the constrain
7. iption and initial parameters This file contains parameters that characterize instrumental resolution model description and parameters of the model An example file has name glob mdl All extensions are allowed except of BST PCT and LOC that reserved for extension of output files In RFIT2000 a model of scattering density profile of the film is represented as a pile of homogeneous slabs A slab is a fundamental building block defined by 4 parameters thickness d in Angstrom real 5 and imaginary B part of complex refractive index N i f and a value of roughness of the toppest interface o Instead of 6 and B the scattering power density profile could be determined with real and imaginary pert of the SLD scattering length density or electron density el A Top is towards the media from which irradiation comes and bottom is towards the substrate All slabs are associated with three group The group in the middle of film has special property This group describes the set of slabs that are periodically repeated NRU times This is made to be able to model periodical structures So to describe the whole group a description of one Repeat Unit is enough This unit consists of RU slabs The others groups relatively to theirs location to central group have names Before repeat Units BU slabs and After repeat Units AU slabs BU part is at the interface Ambient Film AU part is at the interface Film Substrate Sub This 3 groups
8. s on parameters min max mt Tolerance limit to stop fitting 2 x max X min X max Xmin Default is 10 Number of maximum iteration in the fit session Default is 60000 Cutoff Level Default is 0 If the calculated intensity below the cutoff level then intensity takes the value of this level e Calculation Method One of three Matrix Parratt Fourier An example of command file has name glob inp If the experimental data is not normalized on intensity of incident beam the option APPLY SCALING have to be selected There is no difference between Matrix and Parratt method of calculation in terms of result However Matrix method takes less time in case of structure with a multiple repetition of a unit 3 2 File of experimental data An example of such a kind of file has name glob dat The extension DAT for experimental data is not obligatory The data are expected to be in a 2 or 3 column format The first column is the grazing angle in degree or reciprocal Angstrom The second column is the specular intensity or reflectivity Iexp Third column optional is the error bar for experimental data at given point dlexp Usually it is statistical errors of determination of Iexp Error bar is used to weight the difference between experimental and calculated values If the third column is missing then question will appear in dialog to choose as weighting method fraction of the intensity or Fresnel curve 3 3 File with model descr
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