A Combined Fit of X-ray/Neutron Total Scattering
Contents
1. The RMCProfile code fits only the diffuse component of electron scattering and therefore Bragg peaks must be excluded from the fitted pattern This is accomplished by using masks which are placed on top of all the Bragg spots in the pattern The mask has an ellipsoidal shape inscribed into a rectangular The user selects the size of the mask by defining the upper left and lower right corners of this rectangular using mouse clicks as prompted by the program Once the user selects one Bragg peak the program automatically locates and masks its pair related by the 180 rotation around the centre Finally the user selects the quarter of the diffraction pattern to be included in the fit only one quarter is fitted to reduce the computation time using a mouse click in the corresponding corner of the diffraction pattern Once this action is completed the program ED exe creates an input file for use by RMCProfile The name of this file must be specified in the DIFFUSE SCATTERING card of the dat file 4 Restraints on peak tails in partial PDFs DISTANCE WINDOW and MINIMUM DISTANCES constraints frequently cause unphysical spikes discontinuities in partial PDFs at the distance limits set by these constraints usually these limits and the spikes occurs in the tail portions of the PDF peaks This effect is most pronounced in the case of two closely overlapped partial PDFs that exhibit opposite signs of the Faber Ziman coefficients In2. c Perform self consistent FEFF calculations of the scattering paths in a separate folder for each cluster In the FEFF input file set the amplitude reduction parameter S to a value less than 0 1 to let FEFF estimate this parameter from the atomic overlap integrals Identify scattering paths to be used in the fit d Use Artemis or similar to fit the experimental EXAFS using selected scattering paths For all paths set S amp parameter in the GDS section to a value calculated by FEFF FEFF8 20 provides satisfactorily estimates for So which are specified in the header of the chi dat output file The fitted value of S may deviate from the theoretical due for example to inhomogeneous sample significant deviations likely indicate a problem and should be considered seriously If multiple experimental EXAFS datasets are available a simultaneous fit is recommended Each dataset should be assigned a single value of Eo e Return to the EXAFS data reduction software e g Athena and adjust Eo to the fitted value to convert EXAFS oscillations from the energy to k space Repeat the fit in Artemis using these modified data and obtain a new value of Eo Repeat this procedure iteratively until Eo lt 0 5 eV This process minimizes systematic errors caused by the incorrect choice of Eo f In Artemis fit the background if possible and save the experimental data and the background as chi k g Use any spreadsheet software
3. 2 1 3 Double and Triple Scattering In the Nearly Collinear Chains Double and triple scattering paths that yield significant contributions to EXAFS involve nearly 30 collinear chains Figs 1 2 containing the intervening atom i e atom j in Figs 1 2 in the first coordination shell of the absorber In principle scattering amplitudes and phase shifts depend on all three angles within the atomic triangle formed by the absorber and the scatterers However the present code assumes that for the nearly collinear chains these parameters are determined entirely by the angle this simplifying yet sufficiently accurate assumption was introduced to speed up the calculations A utility program EXAFS_INTER exe is used to calculate the amplitudes and phase shifts as a function of on a mesh selected by the user and write the resulting data for all double and triple scattering paths into myn2n3 e2 and n m n3c3 files respectively as detailed in Section 5 2 2 1 4 Double and Triple Scattering In the Nearest Coordination Spheres Another important geometry for double scattering involves triangular paths with the scatterers located in the 1 and 2 coordinations shells around the absorber Figs 1b In this case the effective amplitude factors and phase corrections are determined primarily by the 9 angles Again a utility program EXAFS_INTER exe is used to calculate the nij amplitudes and phase shifts as a function of on t
4. F 2 k F k oo k 1 1 r yo jno ni 2 0 eff and the effective phase correction is Qin Ok arg Ch hp E D gt k F Oi 2 k Here 79 is the distance between the atoms i and j in the cluster used in FEFF calculations Similarly the contributions of the triple scattering paths Fig 2 that involve either one or two scatterers are calculated according to the approximate formulae Ae O k eff Pe ra sinky 28 k la gt kK exp 27 A k 4a yY Jn reg Vijttin Fig 2a o _ SRE A ij 4 l hi Teff 2rij Fig 2b sin 2kry 26 k la p a k exp 2ry A k 4b 2 eff 3 o _ SSF ijn kr r ij in k sin 2kr y 28 k lr pf k exp 2r g A k 40 y Veg Tij in Fig 2c a gE l n b ge 7 Se n Fig 2 Schematic representations of triple scattering paths that involve two scatterers a c and a single scatterer b Triple scattering paths that involve three different scatterers are neglected in the present RMC refinements because of their small effect on the EXAFS signal Calculations of the effective amplitude factors and phase corrections are time consuming Therefore these characteristics are calculated prior to RMC refinements on the appropriate k and meshes as described below in Sections 2 2 2 3 During the refinements the scattering amplitudes for the intermediate values of are calculated using linear interpolation
5. e g Excel to subtract the background from the experimental data The background subtraction option in the current version of Artemis appears to work incorrectly h Save the background subtracted experimental data in the following format 1 line number of experimental points 2 line title Subsequent lines k A and chi k values in xy format 2 4 Creating EXAFS files In the following the file structures are illustrated using perovskite like SrAl Nby O3 as an example EXAFS data for Sr and Nb are stored in the files I Sr back dat and I Nb back dat respectively In the cfg file the atom types are specified as 1 Sr 2 Nb 3 Al 4 0 Create a separate folder for each absorber type and perform FEFF calculations for all the absorbers a Each of these folders should contain the following files subfolders 1 EXAFS INTER exe file 2 FEFFxxx exe file 3 experimental EXAFS datafile 4 feff inp file generated by Artemis 5 path dat file generated by FEFF and 6 a subfolder called store where the output files will be stored b Rename the path dat file created by FEFF to pathbackup dat An example of the path dat file and the description of its structure are presented in Appendix A1 c Open feff inp file and change the CONTROL card parameters to CONTROL 0 0 0 0 1 1 for FEFF820 exe or to CONTROL 0 0 1 1 for FEFF6l exe d Identify the paths to be included in the fit e Run EXAFS INTER exe Respond to the pr
6. experimental data sets and store the parameters in the nsel file see Section 5 1 2 1 2 Double and Triple Scattering The exact equation for a double scattering i e a three leg path Fig 1 contribution that involves an absorber i and scatterers j and n is expressed as S RF O ed k F Oi gt k krr r ij jn ni a ImC exp i 2kr y 26 k 1 2ry A kK 2 Here re Tirinti ni is the effective scattering path length F k F KOA k expli p is the complex scattering amplitude for an atom j and C cos and the scattering angle 7 ijn is the angle dependent parameter in the plane wave approximation C 0 J ort Ner On l Fig 1 A schematic representation of double scattering in a three leg path The scattering process involves an absorber i and scatterers j and n The FEFF code provides two real functions as an output C JE CA k F Opi k r2 effective pa k eff r r r ij jn ni gee k arg Cp F Opn OF Oni K nij These functions can be substituted into Eq 1 to calculate an EXAFS signal as implemented for example in the IFEFFIT Artemis software Similarly in the present RMC calculations the contribution of double scattering to EXAFS is calculated using the approximate formula S RFI 9 k ea 4 mO 26 k l 97 9k exp 2r A K 3 i jn ni where the effective amplitude factor is 4 CW
7. scattering path A value of the scattering angle for the selected path will be displayed Enter the minimum and maximum values in degrees for the angular range to be sampled An output file 212n3c2 will be generated Enter the number xxxx of the feffxxxx dat file corresponding to the triple scattering path An output file n n n3c3 will be generated In order to include similar scattering processes for another set of the distant and intervening scatterers select option 3 again and follow the same procedure Option 4 Enter the types of scatterers for a double scattering not chain like process Several nonequivalent paths may exist that include the same types of scatterers Enter the total number of these paths and then the numbers xxxx of the corresponding feffxxxx dat files in the ascending order for the internal angle angle Onij for a triangular path is defined in Fig 1 As the number of the feffxxxx dat file corresponding to the the smallest angle is entered a value of this angle will be displayed Enter the minimum and the maximum values in degrees for the angular range to be sampled The procedure will be repeated for every double scattering path with the specified scatterers The angle intervals selected for different non equivalent paths involving the same scatterers should not overlap In order to specify the double scattering processes for other types of scatterers select option 4 again Option 5 Enter the types of scatterers
8. than the target values In particular positive Nb Nb and O O displacement correlations were recovered and the incorrect K K correlations while still present decreased considerably Clearly including the information encoded in electron diffraction improved considerably a correctness of the recovered displacement correlations A5 Algorithm for removal of incoherent scattering from neutron S Q Strong incoherent neutron scattering that arises for example in samples containing hydrogen H has to be subtracted from the data to obtain a properly normalized S Q Here we implemented a robust procedure for subtracting this incoherent background from the experimental data using RMCProfile and utility Incoh_subtr exe This utility program first calculates the difference between the experimental S x Q and the Scaic Q calculated using RMCProfile for an atomic configuration representing the average structure with random atomic displacements and then fits this difference using an empirical 5 parameter analytical function Q Ae O F O D E where A B C D and E are adjustable parameters The analytical expression was selected over a polynomial or a B spline also tried because it does not introduce any oscillations of the kind that may arise due to real structural correlations This fitted baseline function represents a contribution of incoherent scattering as well as all other additive corrections that need to be subtracted form the data
9. this case the artificial spikes in the two PDFs cancel each other so that the total PDF exhibits no discontinuities therefore no driving force for healing these spikes exist during fitting of the total PDF The problem can be alleviated by imposing restraints on the peak tails in partial PDFs as implemented in the current version of RMCProfile These restraints can be applied to the low r and or high r tails of any peak in any partial PDF For each restraint a user has to specify the 7min left and Fmax right limits of the interval over which the constraint is applied along with the tail function Z r This function is defined as a fourth order polynomial with a zero constant term 4 L r gt a r n 5 n l 12 where r is set tO 7min and Fmax for for the low r tail and high r tails respectively The coefficients a must be obtained by fitting L r to the tail of interest using any suitable computer software For a given partial PDF g r the program checks the inequality g r gt L r for all heigl after each RMC move If the condition is satisfied the penalty function having a user specified weight is added to the residual The restraint for each low r tail to be constrained is activated by including the following block of keywords in the dat file LEFT_TAILS gt START_FINISH here fmin ANd rmax for this tail must be specified gt PARTIAL integer corresponding to the number of a partial mu
10. to obtain the correct shape for the sample background function The correction is subtracted from the experimental data using the external correction file option in PDFGetN for each bank and the banks are merged The procedure involves the following steps 1 Create an atomic configuration based upon atomic positions in the average structure using utility tools supplied with RMCProfile 2 Displace the atoms in this configuration according to random Gaussian distributions with variances corresponding to atomic displacement parameters ADP in the average structure these ADP parameters can be either adopted from Rietveld refinement or assigned arbitrary but sensible values A utility such as supplied as a part of WinNFLP suite can be used to introduce random Gaussian displacements 3 Obtain experimental S x Q for each detector bank using PDFGetN Use any suitable spreadsheet software to convert these Sexp Q to Fexp Q according to Fexp Q bY Sexp Q 1 where b is the mean scattering length for the structure 4 Prepare the RMCProfile dat file and run RMCProfile to fit Fexp Q as the experimental data saving the results and stopping the run after a few cycles Note that a baseline in the calculated S Q represents a realistic shape of the background for uncorrelated atomic motion 5 Convert the output file SQl1 csv into the txt format and store in a folder with the Incoh_subtr exe utility 6 Run Incoh_subtr exe and follow the o
11. A Combined Fit of X ray Neutron Total Scattering EXAFS and Electron Diffuse Scattering in RMCProfile User Manual Victor Krayzman and Igor Levin Ceramics Division National Institute of Standards and Technology Gaithersburg MD 20899 1 General Info Local structure scattering refinements using a simultaneous fit of x ray neutron total scattering EXAFS and diffuse scattering in electron diffraction are implemented as an extension to the RMCProfile software Version 6 Users should refer to the main RMCProfile manual for this version for details regarding RMC refinements using total scattering data alone A user is expected to have a reasonable knowledge of EXAFS phenomena and be experienced in conventional EXAFS local structure refinements Relevant information including tutorials can be found at http cars9 uchicago edu ravel software Likewise a reasonable knowledge of electron diffraction is required The present software enables accurate EXAFS calculations for large atomic configurations with both single and multiple scattering of a photoelectron taken into account The number of datasets is specified in the main input dat file used by the RMCProfile asterisk refers to the stem filename EXAFS data can be fitted either in k or in r space the choice should be specified in the dat file EXAFS signal is calculated for an atomic configuration described in the cfg file All non structural parameters that enter the EXAFS equ
12. ACE Start point for a fit in the r space A 13 gt END_ POINT R_SPACE End point for a fit in the r space A gt R_SPACING Value of the spacing used in the EXAFS fit and the output A gt LOW_R_REGION_LIMIT Optional If specified assigns additional factor to the lower r part contribution to the total misfit This factor must be provided with the subordinate keyword gt LOW_R_WEIGHT gt LOW_R_WEIGHT An additional factor for the lower r part contribution to the total misfit in the case of r space fit gt START_POINT_ K_SPACE Start point of the fit in k space if selected in gt FIT_SPACE or a Fourier transform for a fit in the r space A gt END_POINT_ K_SPACE End point of the fit in k space or a Fourier transform for a fit in the r space A gt K_POWER Specifies the power of n in the weight factor k used to multiply EXAFS signal chi k prior to a Fourier transform gt WEIGHT Parameter to weight the total misfit for the EXAFS data in Monte Carlo simulation gt ENERGY_OFFSET Optional Shift of Eo eV in the experimental spectrum If not included E 0 gt SCALE_FACTOR Optional Scale factor for the experimental spectrum optional If not included scale factor 1 gt NUMBER_OF_TYPES_ OF_ABSORBING_ATOMS Optional Specifies the number of types of absorbing atoms for a given EXAFS dataset If not in
13. The first line is a name of the configuration file The second line is a number of the experimental EXAFS datasets NEXAFS This line is followed by NEXAFS groups of lines The total number of these groups and their order must correspond to the order of the EXAFS groups in the RMCProfile dat file The first line of each group specifies the number of types of absorbers for a given EXAFS dataset NABS This line is followed by one line per absorber In this line the first digit specifies the type of the corresponding absorbing atom This digit is followed by ntypes pairs of real numbers where ntypes is the number of types of atoms in the configuration file The first number in the pair is the maximum distance between the corresponding scattering atoms and the absorbing atoms to be included the list The second number is the maximum scattering angle to search for an intervening atom for the chain scattering that involves these absorbing and scattering types 3 Diffuse scattering in Electron Diffraction 3 1 Diffuse scattering calculations The calculations of diffuse scattering were implemented according to the formalism proposed by Butler and Welberry B D Butler T R Welberry J Appl Cryst 25 391 1992 and later adopted for RMC refinements using electron diffraction by Goodwin et al A L Goodwin R L Withers H B Nguyen J Phys Cond Matter 19 33 335216 2007 According to this formalism the complex total scattering amplit
14. ation such as scattering amplitudes and phase shifts are calculated prior to refinements using the FEFF software http leonardo phys washington edu feff We strongly recommend self consistent calculations of the cluster potential implemented in the FEFF8 version The Artemis package http cars9 uchicago edu ravel software can be used to evaluate photoelectron scattering paths and to perform preliminary fitting of EXAFS data A free version of FEFF included with Artemis does not support self consistent calculations therefore a user needs to import the output files from FEFF8 into Artemis manually Once the EXAFS option is selected in the dat file RMCProfile will calculate an EXAFS signal for each absorber type The calculations are carried out as a sum over signals generated for the single double and triple scattering paths having effective path lengths re lt Rmax During refinements after each atomic move EXAFS is re calculated for all absorbers within the distance Rmax from the moved atom A list of absorbers around each atom in the configuration is generated using the utility SCAT_ABS exe We recommend using Rmax lt 5 A to ensure reasonable computation time This version of the RMCProfile software enables a simultaneous fit of electron and or X ray single crystal diffuse scattering along with x ray neutron total scattering and EXAFS datasets The importance of single crystal diffuse scattering data as obtained using ele
15. cluded the number of types is set to 1 gt TYPE S _OF_ABSORBING _ATOMS A list of types of the absorbing atoms for a given EXAFS dataset LEFT_TAILS RIGHT_TAILS gt START_FINISH min ANd Fmin Values A gt PARTIAL Number of partials to which the restraint is applied gt COEFFICIENTS Coefficients a4 a2 a3 and a in Equation 5 gt WEIGHT Weight of the penalty function due to the tail restraint DIFFUSE_SCATTERING gt FILENAME Filename containing the data gt WEIGHT Parameter to weight the total misfit for the diffuse scattering data in Monte Carlo simulation 14 Appendix Al The Pathsbackup dat file Rmax 6 0000 keep Feff 6L 02 paths 3 05 limit 0 000 heap limit 0 000 Plane wave chi amplitude filter 2 50 000 index nleg degeneracy r 1 98 y Z ipot label rleg 000000 1 980540 4 0 1 9805 000000 0 000000 0 Nb 1 9805 000 index nleg degeneracy r 3 37 y Z ipot label rleg 949350 1 949350 bsr S 3 3764 000000 0 000000 0 Nb 3 3764 000 index nleg degeneracy r 3 38 y Z ipot label rleg 000000 0 000000 4 rO 1 9805 980540 0 000000 4 Or i 2 8009 000000 0 000000 0 Nb 1 9805 000 index nleg degeneracy r 3 89 y Z ipot label rleg 898700 0 000000 3 Al 3 8987 000000 0 000000 0 Nb 3 8987 000 index nleg degeneracy r 3 89 y Z ipot
16. ctron diffraction in local structure refinements is evident from the results obtained by fitting the synthetic data simulated for a cubic perovskite KNbO3 with correlated atomic displacements which is presented in Appendix A4 of this manual A number of electron diffraction patterns that can be included in the fit is limited only by the amount of the available computer RAM and reasonable computation times Appendix A5 describes an effective and robust algorithm for subtraction of incoherent scattering The algorithm is illustrated using the data for a metal hydride but is equally applicable to other systems including nanoparticles 2 EXAFS 2 1 Technical background 2 1 1 Single Scattering Single scattering two leg path contributions to EXAFS for the i absorber and j scatterer are calculated according to a formula given in the FEFF manual o _ SROIE ij kr sin 2kr 26 k lat p at k exp 2r A k 1 where 7 is the amplitude reduction factor K k is the total central atom loss factor rj is the interatomic distance k is the photoelectron wave number F z k F a k exp y k is the complex backscattering amplitude 20 k It is the total scattering phase shift for the absorbing atom and k is the photoelectron mean free path Functions S7 R x 26 k n A K F x k and g z k are calculated by FEFF A utility program EXAFS_INTER exe is used to interpolate these functions to k mesh of the
17. for a triple scattering not chain like process Several nonequivalent paths may exist that include the same types of scatterers Enter the total number of these paths and then the numbers xxxx of the corresponding feffxxxx dat files in the ascending order of the internal angle angle Onij for a triangular path is defined in Fig 1 As the number of the feffxxxx dat file corresponding to the the smallest angle is entered a value of this angle will be displayed Enter the minimum and the maximum values in degrees for the angular range to be sampled The procedure will be repeated for every triple scattering path with the specified scatterers The angle intervals selected for different non equivalent paths involving the same scatterers should not overlap In order to specify the double scattering processes for other types of scatterers select option 5 again 2 5 Creating lists of absorbing and scattering atoms These lists are generated using the utility SCAT_ABS exe and stored in the files absorlist dat Appendix A2 and scattlist dat Appendix A3 For running SCAT_ABS exe copy the initial configuration file cfg into a folder which contains SCAT_ABS exe In the same folder create an input file scat_input txt An example of the input file is shown below SrAINbO3 cfg 2 NEXAFS number of experimental spectra 1 NABS number of types of absorbers for a given spectrum 2 420 0 4 2 0 0 4 2 5 0 4 2 0 0 1 1 420 0 4 0 0 0 4 2 0 0 4 2 0 0
18. he mesh selected by the user nij Section 5 3 and store the resulting data for this type of double scattering paths in the file n mn3s2 The amplitude and phase parameters for the triple scattering paths shown in Figs 2b are stored in the file nsc3 Similar tables for the triple scattering paths shown in the Fig 2c are stored in the file n n n3s2 2 2 The EXAFS files for combined PDF EXAFS refinements Below is a list of files required to run RMCProfile with EXAFS data included in the refinements Filename Path pictogram File Content nscl photoelectron mean free path moduli and O g gt O phases of backscattering amplitudes for the i j single scattering paths amplitude factors and phase corrections for the triple scattering paths 148 c3 e lt 50 i J nyn2n3c2 O effective amplitude factors and phase corrections for the double scattering paths in i j n nearly collinear atomic chains O corrections for the triple scattering paths in n n nn3c3 e gO effective amplitude factors and phase i nearly collinear atomic chains effective amplitude factors and phase j wee Oin corrections for the double scattering paths 18m S having both scattering atoms in the 1 and 2 i On coordination shells around the absorber n 1N 382 n nn3s3 effective amplitude factors and phase _ 7 corrections for the triple scattering paths with Om 1 the two scattering at
19. he averaging is N but using so many configurations would make the computations prohibitively expensive 3 2 Atomic scattering factor calculations The atomic scattering factors for electron diffraction are calculated using the traditional parameterization according to the formula Peng L M Acta Cryst A54 481 1998 fak a exp b k 11 8a ae eo 10 where aj and b are tabulated parameters Peng L M Acta Cryst A54 481 1998 AZ 2 represents the ionic charge the pre factor 0 023934 if k is given in and f k T 252 E is in A The values of a and b are stored in the file FormfactorsTable dat The FormfactorsTable dat consists of three line blocks for each type of atoms in the configuration The first line in a block is a chemical symbol for a given atom type the second line contains five real values of a and the third line contains five real values of bj The order of blocks in the file is not important A user can modify this file using any text editor Ionic charges valences should be specified as real numbers in the dat file after the keyword VALENCE The valences must be listed in the same order as the atoms in the ATOMS line 3 3 Input and output files The input files each containing a distribution of diffuse intensity in a given section of reciprocal space to be included in the fit are produced using the ED exe utility program from the digitized experimental electron d
20. he ideal lattice sites of the cubic perovskite structure The Nb atoms were shifted along 111 directions 0 1V3 A and the O atoms were shifted along 001 direction by 0 1 A to generate positive Nb Nb and negative Nb O displacement correlations along the 001 Nb O Nb lt 001 gt chains the displacements among different chains remained uncorrelated thus yielding the desired 8 site model Figure A4 1 Subsequently all atoms in the configuration were subjected to random Gaussian displacements The total neutron pair distribution function PDF and Bragg profile were calculated for this model configuration and used instead of experimental datasets in the RMC fits Figure A4 1 Probability density distribution functions for Nb and O viewed down 100 directions in the 8 site KNbO3 model A splitting of the atomic positions due to correlated atomic displacements is observed 16 First a combined fit of the neutron PDF and Bragg profile was performed starting from the ideal lattice sites The fit produced discernable negative correlations among the nearest neighbor Nb and O displacements which were evident in the doublet structure of the first peak in the total PDF Despite an excellent agreement between the target and calculated data the magnitude of the Nb O correlations was much smaller compared to the target value More importantly the refined configuration exhibited no Nb Nb and O O correlations but instead featured positive K K correlatio
21. he total scattering and EXAFS data In the present fitting procedure the experimental relative units and calculated intensities are matched using the scale factor and the offset which are adjusted after each RMC move Typically the total scattering amplitude calculated for a single atomic configuration by direct summation 6 is too noisy to be used in the fit In the present software the noise is reduced using the following procedure which relies on the periodic boundary conditions imposed in the RMC refinements The position of an atom in the configuration is described by a sum Ratr mn Therefore the transformation of the atomic coordinates according to the formulae a n 1 X for Lsn lt N an X gt a n 1 N x for Osn lt L b n l1 for l sn lt N bn Von e 85 Yr A 2 10 7 b n l N Xm for Osn lt l e n l Zyn for 1 sn lt N con Z gt ee ae A for O lt n lt l generates the atomic configuration that is equivalent to the original The total scattering amplitude calculated for the new configuration using Equation 6 is somewhat different compared to that calculated for the original configuration whereas the average scattering amplitude remains unchanged According the present procedure the p k calculated after each RMC move is averaged over eight equivalent configurations with 0 N 2 L 0 LN 2 L 0 N 2 The maximum number of equivalent configurations that could be included in t
22. iffraction patterns The procedure for generating these input files is detailed in Section 3 4 The first line of the input file is an integer which specifies a number of the data lines in the file Each following line contains two integer numbers representing the pixel coordinates and three real numbers describing the reciprocal space coordinates of this point in A and the corresponding intensity value Two kinds of output files are produced for each diffraction pattern used in the fit The graphic files exper_diffus_n bmp and calcul_diffus_n bmp facilitate easy visual comparison of the experimental and calculated patterns for the n dataset A digital output is provided in the files diffuse_intensity_inputn dat and diffuse_intensity_outputn dat The diffuse_intensity_inputv dat file contains a diffuse scattering pattern calculated at the start of the RMC run for the original atomic configuration The diffuse_intensity_outputz dat file is saved after a user specified run time along with other output files e g total scattering and or EXAFS The first three lines in this file contain values of the residual a scale factor and an offset for a given dataset These lines are followed by a matrix describing the intensity distribution 3 4 Input file processing Commonly experimental diffraction patterns containing diffuse scattering are recorded on a film In this case the experimental pattern has to be digitized using a suitable scanner or a si
23. label rleg 000000 3 898700 3 ALLI 3 8987 000000 1 980540 4 O 1 9182 000000 0 000000 0 Nb 1 9805 000 index nleg degeneracy r 3 89 y Z ipot label rleg 000000 0 000000 4 VOJ 1 9805 000000 0 000000 3 YAL 1 9182 000000 0 000000 4 Qo ot 1 9182 000000 0 000000 0 Nb 1 9805 T 92 6 xX 0 000000 0 0 000000 0 2 2 8 xX 179493 50 1 0 000000 0 3 3 24 xX 1 980540 0 0 000000 1 0 000000 0 4 2 6 xX 0 000000 3 0 000000 0 5 2 3 12 xX 0 000000 0 0 000000 0 0 000000 0 6 4 6 xX 1 980540 3 898700 1 980540 0 000000 O GOTO O A2 The absorlist dat file 20480 14 10 4097 2 3521 1 10 4098 2 3522 1 8 194 1 14 4609 2 4096 1 total number of lines equal to the total number of atoms in cfg beta 180 0000 180 0000 64 beta 180 0000 180 0000 10 beta 135 0000 135 0000 90 0000 87 beta 180 0000 180 0000 87 beta 180 0000 0 0000 180 0000 87 beta 0 0000 180 0000 0 0000 180 0000 maximal number of absorbers ina line 4609 2 5121 2 56 4610 2 5122 2 56 706 1 1218 1 1730 5057 2 33 2 2049 34 2 2049 1 2242 1 576 1 1480 1 1 2056 1 2050 2754 1 2041 1 2561 1 2617 1 3073 1 1 2562 1 2618 1 3074 1 3266 1 3778 1 T 2056 1 261 7 1 0 O eta 0000 0000 eta 0000 0000 eta 0000 0000 0000 eta 0000 0000 eta 0000 0000 0000 eta 0000 0000 0000 0000 O O O O 15 3521 1 A3 The scattlist dat file 6144 to
24. milar device and stored in the bmp format The processing of the resulting image to produce an input data file for RMCProfile involves the following steps a Define the origin of the co ordinate system for the image and determine it s coordinates b Define two reciprocal space vectors in the image c Mask all the Bragg peaks which will be excluded from the fit d Choose an appropriate quarter of the diffraction pattern to be used in the fit 11 The central spot in experimental electron diffraction patterns is saturated and as such is not suitable for precise determination of the origin Instead the center is found from the coordinates of several Bragg peaks located symmetrically around the central spot The program ED exe prompts the user to select suitable Bragg spots using mouse clicks The program fits each of these peaks with a 2 D Gaussian saturated portions of the peaks if encountered are excluded by the program to find the peak positions The position of the origin is calculated as an average of the Bragg peak positions The two reciprocal space vectors are defined following the on screen prompts by using mouse clicks to select several orders for the two independent reflection families e g 111 222 333 and 100 200 300 and specifying the Akl indexes for each of these peaks The program automatically determines the precise positions of the selected peaks and the length of the corresponding reciprocal space vectors in
25. n screen instructions The output file fix is the background correction file for a given bank 7 Use any spreadsheet software to combine the individual bank fix files into a single fix file that can be plugged into PDFGetN as an external correction file 18 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 Q Ang r Ang Figure A5 1 a Experimental red and calculated blue S Q for the TiZrNiD alloy The experimental data were collected using the NPDF instrument A limited D H exchange reaction was sufficient to induce a significant background due to the incoherent scattering of H in the experimental data The calculated S Q was obtained using RMCProfile for a configuration based on the Rietveld derived model The baseline in the calculated S Q provides a background expected for coherent scattering b S Q for one of the detector banks having its baseline fitted using an analytical function f Q described in the text c S Q before red and after blue subtraction of f Q d G r obtained from S Q before red and after red subtraction of incoherent scattering Note the changes in the low r range For r gt 2 A the effect of incoherent scattering is rather insignificant 19
26. ns which were absent in the target model No noticeable correlations existed beyond 4 A Clearly the local structure obtained using powder total scattering data alone is grossly incorrect even though the 8 site and 2 site splitting was reproduced to some extent for the Nb and O probability density distribution functions respectively The fit also produced reasonable agreement between the calculated and target variances lt u gt for all the atomic positions Unquestionably without a prior knowledge of the structural an incorrect model would have been inferred from RMC refinements using the neutron total scattering data In the second attempt the neutron PDF and Bragg profile were complemented by the two electron diffraction patterns containing diffuse scattering The results of a simultaneous fit of these four datasets are presented in Figure A4 2 G r Intensity 25 30 10 15 20 25 30 Time of flight msec Figure A4 2 Results of a simultaneous fit of the neutron PDF and Bragg profile and electron diffuse scattering two sections a b Experimental blue and calculated red neutron PDF a and Bragg profile b Experimental left and calculated right electron diffuse scattering patterns in the 130 c and 114 d sections of reciprocal space 17 Now the displacement correlations were reproduced in the refined configuration although the correlation strengths were still significantly weaker
27. ompts The reduction factor is the So parameter obtained in the preliminary fit The following menu will appear ex C Documents and Settings Krayzman Wy DocumentsWisual Studio 2005 Projects Console8 Oo x Enter 1 for single scattering fAbs gt Scat gt Abs Enter 2 for triple scattering from the same scatterer fAbs gt Scat 1 gt Abs gt Scat 1 gt Abs Enter 3 for chain like scattering fAbs gt Interv_Scat gt Distant_Scat gt fAbs Abs gt Interv_Scat gt Distant_Scat gt Intery_Scat gt fAbs Enter 4 for non chain double scattering Abs gt Scat 1 gt Scat 2 gt Abs Enter 5 for triple scattering from different scatterers fAbs gt Scat 1 gt Abs gt Scat 2 gt Abs Enter to exit Select the appropriate option s and enter the following information Option 1 Enter a sequence of file numbers xxxx for the feffxxxx dat files corresponding to all single scattering paths An output file n sc1 will be generated Option 2 Enter a sequence of file numbers xxxx for the feffxxxx dat files corresponding to all triple scattering paths which involve one scattering not absorbing atoms and the absorbing atom as the second scatterer An output file n sc3 will be generated Option 3 Enter the types of the distant and intervening scatterers for a double scattering chain like process and the number xxxx of the feffxxxx dat file corresponding to this forward
28. oms located in the 1 J n coordination shell around the absorber and the absorber atom itself acting as a scatterer absorlist dat list of absorber atoms around each atom in the configuration scattlist dat list of all scattering atoms for each absorber In the filenames n stands for the type of the absorbing atom m2 for the type of the distant scatterer and n3 for the type of the intervening scatterer in n nzn3 2 3 files in the files 11m2n382 3 n2 and n3 represent types of the scattering atoms 2 3 Preparation of the EXAFS Data Preliminary analyses of EXAFS data are needed to obtain accurate values of the energy shifts Zo and to subtract the background from the data as following a Use Athena or similar to extract EXAFS from the absorption spectra b For each experimental EXAFS build an appropriate cluster s around the absorbing atom An average structure provides a good staring model Examples of public domain software that can be used to generate these clusters based on the space group and atomic positions include Atoms Artemis For structures with the same absorber species located in non equivalent crystallographic positions separate clusters have to be generated for each of these sites These non equivalent sites must be designated using distinct atom types in the cfg file The contributions of these clusters to the total EXAFS signal are set proportional to the respective site occupancies
29. st be specified gt COEFFICIENTS 4 real numbers describing coefficients a4 a2 a3 and a4 gt WEIGHT weight assigned to the penalty function The restraint for each high r tail to constrained is activated using similar keywords with the major keyword RIGHT_TAILS 5 Major keywords in the dat file EXAFS Introduces a block of data concerning a set of EXAFS data Text can follow the but will be ignored This keyword must be followed by a block of subordinate keywords Each EXAFS spectrum requires a separate keyword and a block of data Do not include if no EXAFS data is fitted LEFT_TAILS RIGHT_TAILS Introduces a block of data concerning restraints on the tails of peaks in partial PDFs This keyword must be followed by a block of subordinate keywords Do not include if no restraints are used DIFFUSE SCATTERING Introduces a block of data concerning electron diffraction pattern Text can follow the but will be ignored This keyword must be followed by a block of subordinate keywords Each diffraction pattern requires a separate keyword and a block of data Do not include if no electron diffraction data is fitted 6 Subordinate keywords in the dat file EXAFS gt FILENAME Filename containing the data gt FIT_SPACE Acceptable values r k case insensitive Specifies whether a real coordinate space or a wave vector space k is used for the EXAFS fit gt START_POINT_ R_SP
30. tal number of lines 26 maximal number of scatterers in a line 26 20491 00 ee 30731 00 20 1811 OO 6901 3 10933 4 7349 3 13493 201494 00 A4 Example of a combined fit of neutron total PDF Bragg profile and electron diffuse scattering The cubic phase of perovskite like KNbO3 is believed to exhibit 8 site displacive disorder associated with random local displacements of Nb along 8 non equivalent 111 directions The displacements are correlated along the Nb O Nb linear chains parallel to 100 directions Similar 8 site disorder is encountered in perovskite BaTiO and AgNbO as well as their solid solutions with other perovskite compounds The correlated displacements are manifested in three orthogonal sets of 100 sheets of diffuse intensity passing through all fundamental reflections the diffuse intensity is extinct through the origin of reciprocal space because the correlated displacement components are directed parallel to the correlation directions In the present example we used synthetic data simulated for a large atomic configuration that mimicked the 8 site disorder for Nb to determine whether the correct displacement correlations can be recovered at least using error free data The simulated data that was used in these analyses included neutron PDF and electron diffuse scattering The structure model used to simulate the data was based on the configuration cell of 64 A x 64 A x 64 A which contained 20 480 atoms located at t
31. ude Ajo k is calculated in the kinematic approach as Aak Dye Kexplik R r 6 where k k ky A i is the diffraction vector Rn anx bny cnz is a vector that describes the origin of the n unit cell fnn mn Ymn Zmn is a Vector that describes the position of the m atom in the n cell f k is the atomic scattering factor a b and c are the lattice parameters N Ny and N specify the number of unit cells along the corresponding axes of the the configuration box N N N N is the total number of the unit cells in the box and M is the number of atoms in the unit cell 0 lt n lt N 1 a E x y Z The average scattering amplitude lt A k gt is calculated as lt Atk gt LF X f exit 0 The amplitude of diffuse scattering Ap k is a difference Ap K A k lt Ak gt y k 8 where the interference function y k is exp ik aN 1 _explik bN 5 ane cN 1 explik a 1 explik p exp ik c 1 vk X explikR 9 The intensity of diffuse scattering is Jp k In Ap k The intensities in experimental electron diffraction patterns are affected by multiple scattering and therefore cannot be reproduced by calculations that rely on the kinematic approximation Therefore only the locus of diffuse scattering which reflects the topology of correlations in real space is fitted the information on the magnitude of correlation parameters can be recovered only to the extent that is encoded in t
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