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XANES Dactyloscope Users Manual and Tutorial

1. Remove current all range e g to restore the default zooming Use the Spectra menu to switch between the loaded spectra change their se quence add or remove spectra access the line properties etc Note that all the properties in the main dialog refer to the current spectrum The current spectrum is also drawn in front of the others When the graph is redrawn the current spectrum blinks In this way you can easily identify the current spectrum when you click in the graph window to redraw it The arrow buttons give access to the corresponding line settings and show to which Y axis left or right the particular line belongs 3 1 Line settings Line Settings x line to edit copy to line f individual settings collective a color ranges 3 spectra Up 3 spectra 3 spectra Down 3 spectra Add 1 t ne Delete selected color range style width spectra lid 3 a inthis 3 iE mins B E OF Cancel collective result etc in loop Replace Apply to all spectra Line colors Select visible spectra eee cunayl20 mu em cunayY1 O mu esse 3 cunayZO0 mu 4 cunay2Z50 mu ees j cunay275 mu ese 6 cunaySO0 mu eee cunayYS30 mu eee cunayYSe0 mu ese 9 cunay400 mu 10 cunay450 mu ese cunayS00 mu 2 cunayYooO mu 3 Cu_nti mu 4 CuOnorm mu ee 15 CuezOfst2 mu The line properties can be set collectively by specifying the color ranges Within each
2. As seen in the list of PC s there are two components with low estimated noise and hence there are two PC s as expected Now switch on the self absorption correc tion again and see that the 3 component in PCA has quite high noise estimation which does not let ne glect it In other words the corrected spectrum represents an independent species which does not fully merge with the transmission spectra Inversely this noise estimation can be taken as the noise level used instead of the experimental noise in the PCA s involving the self absorption corrected fluo rescence spectra of hematite In summarizing this example concentrated references measured in fluorescence must be corrected for self absorption Even being corrected the fluorescence spectra may significantly differ from the trans mission ones and thus introduce new species into the set of principle components 11 4 Recommendations for factor analysis e The reference compounds as they normally are concentrated are better to measure in transmis sion in order to reduce the added uncertainty due to the self absorption correction e All amplitude distortions must be well understood and prevented corrected It always makes sense measuring a calibrated test mixture 12 Fitting by user defined formula The primary usage of this section is doing a linear combination fitting after the factor analysis The fitting formula is typed in by the user It operates the letters
3. use Set reference energy command E 0 000 show reference curve lw show its derivative smooth a A TE times Select visible spectra Select visible spe x cunayl 20 mu eee cunay 0 mu 3 cunay200 mu 4 cunay250 mu f ocunaye 5 mu E cunay300 mu 7 cunayas0 mu 6 cunay360 mu 9 cunay400 mu eee 10 cunay450 mu cunayS00 mu cunayS50 mu 3 Cunt mua see CuOnorm mu suua 15 CueObste mu show full path Cancel Shannen If the absorption spectra are measured in transmission it is a common practice also to simultaneously measure the foil Then the energy axis can be checked for reproducibility and corrected 1f needed If your file format describes the reference curve you can visualize it or its derivative in this section of the main dialog Zoom in the derivative peak as seen on the screenshots below to see this open the project Samples 04 ECalib 0 xpj 0 8 0 6 f i dots left Y Hampie lines right Y metal 0 4 Maximize wiew Extend by 25 H Set reference energy Delete a point Zoom Left Y Axis zoom Right Axis Zoom Both Y Axes 0 0 i 11555 11560 11562 11564 11566 11565 Now select the reference en ergy If your energy mesh around the absorption edge is finely spaced just use maxi mum of reference curve de rivative In the example shown the mesh was rough 0 5 eV Therefore su
4. B B B B Bh Bb B b 0 18 and because of orthogonality of n to B it follows that A A n n Finally if n is solely due to noise the variate y A A e must follow the x distribution law with v r c degrees of freedom Thus the mean value of the squared noise is 2 ATAN The confidence limits Emin and Emax are found in the same way as in PCA 1 e by using the statistical properties of x distribution Notice that we cannot use the target transformation method to determine the decomposition weights b because the expression for the experimental squared target transformation residual A A does not con tain b On the contrary the squared linear fitting residual d gt Bb does contain b whence it can be determined 11 2 2 Questions answered by TT One direct and one inverse question TT1 Given the noise level of a particular spectrum can the spectrum be reproduced by a linear combi nation of the basis spectra TT1 How high must be the noise level of a particular spectrum in order to reproduce it by a linear combination of the basis spectra 11 2 3 Usage of TT in XANES dactyloscope Ii principal component analysis or target transformation spectra to form the space 2 ok target tracking EE To perform TT of a spectrum specify a basis set which does not include the target transformed spec trum the current spectrum Note that in TT all the components must be selected It does not make sense to
5. a through y E stands for energy as independent variable it is internally renamed to z and any usual mathematical operations and func tions A letter can be declared as a fitting parameter or a spectrum loaded by XD In the latter case its energy shift may vary as an additional fitting parameter This capability can be useful when the energy axis is not well reproducible or when mixing data from various beamlines or as in the example below when modeling different spectral features by a single contribution Load the project Samples 12 cefit34 xpj which has a Ce L3 XANES spectrum 2 red fitted by a weighted sum of monovalent 3 and 4 contributions The 3 spectrum was calculated by FEFF spectrum 1 black The 4 contribution is represented by the same calculated spectrum shifted by a fitting value to higher energies 20 Thus the experimental spectrum is fitted by the formula at b c where a and b are the same shifted spectrum 1 the black curve clisa scalar i fitting by user defined formula E alia ana TEE EEE padena formula parameter a I normalize to unity fit C vale function pectrum R 27584529 iter 12 12 Fi E shitt 1 9452e 1 2 0 0100 Statistics Constrain Start formula parameter E formula parameter value function spectrum H f value function spectrum E shite 24088 4 az 00T00 S vaue 25472 1 2 ape 1 0000 The average valence is given in this
6. and Roy S C Physics Reports 140 75 159 1986 Kissel L and Pratt R H Rayleigh Scattering Elastic Photon Scattering by Bound Electrons in Atomic Inner Shell Physics edited by Bernd Crasemann Plenum Publishing New York 1985 http www phys Inl gov Research scattering index html Klementev K V 2001 J Phys D Appl Phys 34 2241 22 Malinowski Edmund R 1977 Anal Chem 49 606 McMaster W H Kerr Del Grande N Mallett J H and Hubbell J H 1969 Compilation of X Ray Cross Sections Lawrence Livermore National Laboratory Report UCRL 50174 Section II Revision I avail able from National Technical Information Services L 3 U S Dept of Commerce http Axs csrri 1it edu database programs mcmaster html http cars9 uchicago edu newville mcbook Pfalzer P Urbach J P Klemm M Horn S denBoer M L Frenkel A I and Kirkland J P 1999 Phys Rev B 60 9335 Pompa M Flank A M Delaunay R Bianconi A and Lagarde P 1995 Physica B 208 amp 209 143 Ressler T Wong J Roos J and Smith I L 2000 Env Sci amp Technol 34 950 Ressler T Wienold J Jentoft R E and Neisius T 2002 J of Catalysis 210 67 Tan Z Budnick J I and Heald S M 1989 Rev Sci Instrum 60 1021 Troger L Arvanitis D Baberschke K Michaelis H Grimm U and Zschech E 1992 Phys Rev B 46 3283 Wasserman S R 1997 J Phys IV France 7 C2 203 23
7. case by 3 4 c 1 c After the automatic fitting has finished press Statistics button You should select the integrated option for the errors 0 s of the fitting parameters See VIPER manual for the description of the other options and the methods behind See VIPER manual for the description of the statistical y and F tests The colored matrix shows the pair correlation coefficients Com pletely red and blue denote 1 and 1 black is 0 The fitting er rors are listed at the left of the correlation matrix Pay attention to the correlation coefficients They should not be close to 1 or 1 or visually much colored or when displayed by the correlation map the yellow black graph diagonally stretched This would aroj a10 5720 Tra ar40 ofo0 5760 Ire mean large fitting errors and frustration for the minimization al GERRUSIEcIMEN SIS Ore Teepe x e N 268 P 3 N P 265 gorithm In this case try to apply constraints to the fitting param Sp ee ens Ddwl Si y 1 1 fe unknown click right mouse a b c eters using the button Constrain Alternatively one can fix a oo ST Ue aa fitting parameter by setting its initial increment to zero 5 e Es y2 test 265 0000000 y and F test Bp i independent A Hel supreme projection a integrated Save cor matrix a priori space sizes Hide Ma reg r O 00000 most probable x gt post 3 00000 pixels mir max x ellipticity param 0 0605 42 exa
8. fluores cence measurements with different positioning of the sample relative to the primary and fluorescence beams An obvious disadvantage of this method is that it 1s solely applicable to polarization indepen dent structures amorphous or of cubic symmetry On the other hand it does not require any theoreti cal tabulation which is the case in the method of lida and Noma 1993 who proposed the background part Uback Uot Hy to be taken as tabulated The advantage of their approach is its applicability to any sample with only one measurement Moreover this method is applicable to samples of general thick ness not only to thick samples as required by the method of Eisebitt et al 1993 It is the method of lida and Noma 1993 which is implemented with some variations in XD The method was re in vented i e published without citing lida and Noma 1993 by Pompa et al 1995 Haskel 1999 and Carboni et al 2005 These three works however were simplified down to infinitely thick limit The correction was extended somewhat by considering a variable escape angle in order to account for the finite not infinitely small detector area only in the synchrotron orbit plane in EXAFS Brewe et al 1994 and also out of plane in EXAFS Pfalzer et al 1999 and XANES Carboni et al 2005 All three works operated in the thick limit To my believe detector pixels are always small in the sense that the self absorption effect can be consider
9. mato mu 10 01 03 11 42 al design of the Load data dialog is old fash mol so52 ru 10 01 03 11 42 E Ok mool 4 10 01 03 11 42 bc ioned the files are always sorted by name magg m I d 002m 10 01 03 11 43 Soe whereas frequently time sorting is more conve re ce Edit file dknots 16 06 03 15 12 Z RR a nient Therefore I recommend drag and drop technique combined with your favorite file commander or Explorer This way is very use ful at a beam time when you quickly add a newly measured file to the already opened ones by simple drag and drop from your time sorted directory I use the Load data dialog mostly to set up new data formats and sometimes to manually select the file format The latter is needed when the same file has transmission and fluorescence signals and one wants to load both In this case one needs two formats described and of course only one of the two will be recognized automatically Important you can load multiple files and do drag and drop only provided your file format is recog nized automatically 1 e when you see the format name updated correctly in the Add spectra dialog after you have clicked a file name The number of the loaded spectra is restricted by your RAM 2 1 File formats Look first at your data file in a common text editor Specify the file header Give one or two sub strings contained in the header format name for automatic recognition If your file is recognized inco
10. range the specified number of ineto edit spectra are evenly spaced in the RGB color space towards E copy to line the next color range If the range is single all the lines of a given kind will be equally colored for each spectrum individual settings collective aA calor ranges Every line of every spectrum can have individual set tings You can decide whether to switch from individual to collective settings or back only for the current spec trum or for all spectra This depends on whether you ac seestediine of curent spectrum SOREN E cess the line settings from the individual arrow buttons S style width result or from the Spectra menu E The dots line style puts dots not equidistantly but at the OK Cancel data points 3 2 Selecting visible spectra The spectra can be selected for viewing in the list of spectra Use Ctrl Shift buttons for multiple selec tion Another way of hiding spectra for clearer view is by using the check button hide all other spectra at the top of the main dialog This option displays Add Add special average rms difference Remove current all range Replace 4ooly to all spectra Line colors only the current spectrum and overrides the selec tion if any in Select visible spectra dialog 4 Energy calibration W E calibration C masimum of mu derivative O masimum of reference curve derivative user defined point
11. remains within noise How to compare with noise Denote the PCA residual A D D ca which must be compared with noise of our data matrix D Consider AVAST ere DDI ee JED D 2 Nee A yi ee J jJj We are interested in knowing d djpc for each spectrum d d d pc F A A 26 4 Ale where e is the i th component of eigenvector e On the other hand d d jo 7 x if we assume that d pca reproduces d within noise individual noise of spectrum d The variate X must follow the x distribution law with v r c M c degrees of freedom The scaling factor c M c is due to the fact that d d pca is given by c M out of c components Finally for the squared noise of spectrum d one gets the mean value Eom didaa NS a A eV Iy 14 The confidence limits and n are given by the x distribution law at selected significance levels In XANES dactyloscope the significance levels are selected to be 2 5 and 97 5 as to give 95 probability that the measurement noise falls within l E nein max if M out of c spectra are lin early independent One can find the global noise by averaging over all i e wa Aye J where the normality of eigenvectors was used XS e ji 1 The last expression is exactly the real er ror RE introduced by Malinowski 1977 However in our derivation we can additionally specify the confidence limits Emnin and Emax 1n the sam
12. remember we are speaking here about thin samples otherwise use the thick option If the physical thickness is known which is usual for foils use the program XAFSmass to calculate urd or Auxd from the sample composition the thickness and density In the example above the edge jump was found from the transmission spectra times y2 because the transmission spectra were measured at normal incidence whereas the fluorescence spectra were taken with the same sample at 45 For future versions of the manual redo this example with simultaneously measured transmission and fluorescence Equation 1s also useful for a correcting the high energy behavior of u This correc 12 tion is especially relevant to samples with low concentra tion of the element being probed or the samples mea a sured in air or at low ener gies In these cases the en ergy dependence of the back ground absorption u and air absorption become impor tant The left picture differs from _ ooo 7200 7300 7400 the right one by added 20 cm 7100 7200 7300 7400 of air The energy dependent u and air absorption should always be opted The option u is constant is meant for illustration and for comparison with other programs 9 Normalization The normalization 1 e dividing the spectrum by a constant such that a particular part of the spectrum equals 1 can be done in three different ways by dividing by 1 the mean value over the specif
13. total weight do integration or peak fitting Been 19980 20000 20020 20040 W base line 10 2 Base line as spline through adjustable knots Zu bead J E ofee subtract The base line is a spline drawn through the manually put knots The knot positions can be adjusted by mouse The knots may be constrained to move only along the u curve declare them as beads to facilitate the manual set up This method can produce more sophisticated shapes of base lines than the smoothing spline method but requires more time for set ting it up to see the example at the left load the project Samples 10 2 moallyl knots xpj After subtraction T ra B 19960 19980 0000 20020 20040 13360 19980 20000 20020 20040 13 11 Factor analysis 11 1 Principal component analysis PCA PCA was described by many authors In the XAFS community the mostly cited papers seem to be by Wasserman 1997 which followed Malinowski 1977 and by Ressler et al 2000 In all the deriva tions known to me there are two major drawbacks 1 The PCA test spectra are compared with the data just by eye without statistical grounds for the comparison Therefore one cannot say how strongly the PCA mismatch may differ from the experi mental noise In other words not only the mean value is needed for the estimation of noise but also the confidence limits 2 The experimental errors of different spectra may obviously differ For instance referenc
14. truncate the sum BY B e e because the basis spectra are supposed to be linearly independent Again load the project Samples 11 1 PCA2 dABCnC xpj which has two independent spectra and a spectrum constructed as the average of the two plus normal noise with o 0 005 For the 3 spectrum active specify the basis set as 1 2 and see the resulting figures under the button target tracking i The experimental noise of the target ii ia obda 1 transformed spectrum here o 0 005 4 175 74328 1 00000 must be within the given noise bounds 065593 0 60 for the question TT1 be answered posi tively If the experimental noise 1s smaller then there are important contri w 1 0 76980 0 56699 0 99247 butions which are not inside the basis v 2 0 06275 0 07393 o 09001 set If it is larger which is unusual then there are some extra correlations between the basis spectra and the target transformed spectrum e g it is artificially con structed by a linear combination of the basis spectra including their noise 95 noise bounds of TTed spectrum 0 00474 0 00535 0 00615 global 95 noise bounds of basis spectra Check also that the noise estimation of the last principle compo nent of the basis set here 0 07393 is much higher than the ex perimental noise otherwise the basis set is bad 1 e internally lin early dependent 20000 20010 20020 20030 20040 200 19 11 3 Pit
15. 040 200 11 2 Target transformation TT You can skip the derivation and go directly to the practical description Section 11 2 2 11 2 1 Derivation of TT based on statistics From c measured basis reference spectra of length r we form an rxc basis matrix B b b b If the basis spectra are linearly independent then the covariance matrix B B is of rank c and then B BY exists The matrix B B B B is an orthogonal projector to the basis space since it is equal to its square B B B B B B B B B B B B B B B B Hence if a spectrum d 1s a linear combination of the basis spectra then B B B B d d and vice versa In practice one checks if B B B B d coincides with d within noise The inverse matrix B B is found through the eigenvalues and eigenvectors of B B as T T BY By d N ee This allows to simultaneously do PCA on the basis set in order to check that the basis spectra are inde pendent Denote the TT residual A d B B BY B d which must be compared with noise of our spectrum d Taking into account the projector property of B B B B we get AT A d 1 B B BY B 1 B B BB B d d 1 B B BY Bd On the other hand we represent the spectrum d by a direct sum of the basis spectra B plus a contribu tion n orthogonal to B d Bb n where b is a c dimensional vector representing the weights of the c basis spectra Because 1
16. 7140 7160 Fal two As seen on the left picture the fluorescence spectra red and green overlapped es sentially differ from the transmission ones light and dark blue overlapped As seen at the right one of the fluorescence spectra green 1s successfully cor rected Notice the EXAFS amplitude and the pre edge peak The parameters for the self absorption correction are seen in the screenshot below It 1s essential to remember about the sample matrix or the supporting agent here PE and to put its chemical formula as well Here the _ weight 83 of PE CH2 was calculated as MppeM Fe203 Mre203 Mpg 80mg160g mol l 1mg14g mol 83 W mu correction t fE from file HE i self absorption correctior show HE compound eg Cu_20 or Fe 5Si0_2 T normalization energy b deg Upis const E dependent fluorescence energy deg thick 0 thin general airen Kaptonjumn T deg tabulation Ag em moll Fel3 99e 4 In order to use equation 1323 54 11 og r si r100 7120 7140 7160 7180 7A for thin samples one must pro vide the sample thickness This could be the physical thick ness then one would need to know the sample density for calculating the linear absorption coefficient in the exponent A more direct way is to use the optical thickness urd or just its jump at the edge which is usually possible directly to measure in transmission spectra
17. Fe K edge Full view of Fe f factor 1 atom Henke et al 1993 SA 3 85592 At 3 37417 fioo F050 F100 F150 200 r250 fat_ 0 s000 10000 15000 20000 25000 200 M 3 56120 af 3 40240 M 3 356120 af 3 40240 Brennan and Cowan 1992 3 G 4 2 fino F050 7100 o 20000 40000 B0000 a000 100C M 3 89920 af 3 4491 2 MP 3 89920 af 3 4491 2 Chantler 1995 15 fioo r050 7100 7150 F200 r250 fat_ 0 20000 40000 0000 S0000 100000 __ 10 PEE af 3 34888 XCOM Hubbell 1977 fioo r050 McMaster et al 1969 fioo r50 M 3 78208 AM s3 30125 F100 F150 r200 r250 eal S 6 4 2 oO 0 7100 7150 r200 r250 Fal CSS eee 40000 20000 3 Fo208 af 3 30125 B0000 S0000 100i 20000 40000 0000 80000 100C XD searches for an absorption edge where the derivative is positive within 250 eV from the specified normalization energy When an edge is found the jump in molar cross section is displayed in XD 8 3 Examples Load the example project Samples 08 fe203_tr_fl xpj It has 4 spectra of Fe2O0 hematite measured in transmission and fluorescence each repeated twice to assure reproducibility The sample is a 13 mm diameter pressed pellet containing 11 mg of hematite mixed with 80 mg of polyethylene PE powder The pellet was wrapped by adhesive Kapton foil g E rog 7180 710 7120
18. XANES dactyloscope A program for quick and rigorous XANES analysis for Windows Users Manual and Tutorial version of manual 1 10 version of program 6 00 2 April 2012 K Klementiev CELLS ALBA Carretera BP 1413 km 3 E 08290 Cerdanyola del Vall s Barcelona SPAIN www cells es Beamlines CLAESS Contents CBG yea TIT Ce CG 1 een ete ee One ee en a ES SSL eR OIE RE RET TaN OSs le NN Tne Rr eee mae Tea Toren 3 Pee Sea sl oa le SUS Cob ol ee ee ee ee ee ee ae ae eee eee er ee eee 3 l2 Systemi regu ire 811 ee ere eee ee ahiak iibahin renee teeter mee eee aaa 3 Dg WN tc cn emaciated arta ia a 3 JPG FANE BGG ACG sisneacesdsaisaissernciovncisnetiebanaelaiielaiiSauicsbaes baseievelassicastdndoessasiebives ures bocelanelSesisedueiumabialeeiNieebi sbi saeeeResEniieaeNS 5 ALT a Oe ee ee ee een 5 Vol Cr OAT 2 i Epe Ig ee ne eee eee a eR eee eet eet eee er ner eee er 6 11 1 4 How the PCA results are related to chemical NI tach ota le te cls 15 11 1 5 Is PCA also applicable to EXAFS cerina aAA EEA a crs 15 LiL reat Average Tis and diference Spelit i siiscissntcsccracesias saci rescevareertesidcsteraea binant essdlistilivensisautberrrnauibaieadeenieeanetaes 21 14 EX POTtin Se data ani savia project Dl issih aisnias dass ces sleires aa vislea dinates vanes dais vaisnitvdaWabdsiiaeexvebsuiebelbaveieesalviniiwessspeasibbdatanvabitoaes 22 A el ARIESO ee PE ENERE EEEE AE NE ee ENADE ESE ET rT T E 22 1 Introduction 1 1 What
19. ary x ray energy E or the fluorescence energy Es ux is the contribution from the edge of inter est 1s the fluorescence quantum yield the probability to create a fluores cence photon from an absorbed photon After integration over z from 0 to d E C Uy a as ee a sin db E u _ ur E url Gn Ocost where the constant C includes all the energy independent factors and is treated as unknown because the actual solid angle is usually unknown and also because it implicitly includes the detector efficiency The total absorption coefficient is decomposed as U Uy U where the background absorption co efficient u is due to all other atoms and other edges of the element of interest The constant C is found by equalizing all u s at a selected energy Enorm normalization energy to the tabulated ones Now the equation can be solved for uy at every energy point E which is the final goal of the self absorption correction When the sample is thick d 0 the exponent factors vanish This thick limit approximation allows finding the ux by simple inversion of without solving the non linear equation and is optional in XD 8 2 Realization in XANES dactyloscope 8 2 1 Extended correction options Some of the options offered by XD are non standard extended 1 The additional term cost in is not quite standard one can also find it in Carboni et al 2005 and Ablett et al 2005 2 Abs
20. ch a cali bration will not improve the energy reproducibility be tween the two spectra try it In this case much better cali bration is given by manual positioning of the reference energy For this use user de fined point and the pop up menu command Set reference energy and put it somewhere close to the peak maximum until you merge the reference curves of all spectra to see this open the project Samples 04 ECalib 1 xpj 1 2 a 2 a dots Feit YO E lines right Y Umetai 0 0 11555 11560 11562 11564 11566 11566 Tip derivative of u is used when the sample is a foil In this case you usually do not put the foil also at the reference position Then you use the derivative of u for the sake of energy calibration but not the derivative of the reference spectrum The correcting energy shift is implemented as constant along the spectrum In contrast to EXAFS XANES spectra are short in energy Therefore the constant energy shift is justified In EXAFS analy sis constant angle and constant lattice shifts are more correct as implemented in the program VIPER and explained in its manual 5 Deconvolution of life time and experimental broadening See Klementev 2001 for the description of the Bayesian deconvolution This procedure is imple mented in VIPER and XANES dactyloscope i deconvolution convolution W apply toil andil i apply to initial spectrum i show cony of decony response e E E pa
21. ct decomposed correlation coefficient 2 442e 1 confidence level 0 393 Stark Save map ETET 13 Creating average rms and difference spectra QS Spec w ho 5 of 10 hide all other spt Average rms and difference spectra can be added via Spectra menu Add 4dd special average rms difference Such spectra called special in XD are updated whenever the original Remove current all range spectra from which the special spectra were constructed have changed Replace Here you can average several repetitions of one spectrum and or sev eral fluorescence spectra measured by a multi pixel detector f average for all spectra ime deviation Cforspecta _ through An rms spectrum is useful for determining the experimental noise diterence between two specta C and C Load the project Samples 11 2 PCA8 dA1I n 10 xpj It has 10 spec OK Cancel tra which are all artificially constructed from a single spectrum with added 10 various realizations of normal noise of nominal o 0 005 Cre r Te eo As Tii ate an rms spectrum and make it active In the description line at the top of the main dialog window find the mean value of the rms spectrum This value can further be used in factor analysis or in calculating the fitting errors 21 14 Exporting data and saving project file The curves visible in the main graph window can be ex save only curent spectrum save all spectra port
22. e individual noise bounds of a the second component when the 3 spectrum is active which means only one component reproducing the 3 spectrum b the third component when the 1 or 2 spectrum is active which means two components reproducing the 1 and 2 spectrum 17 Let us consider another example Samples 11 2 PCA8 dA1I n 10 xpj It has 10 spectra which are all artificially constructed from a single spectrum with added 10 various realizations of normal noise of nominal o 0 005 The individual and global noise estimations correctly give only one principal component and the noise level close to 0 005 The experimental noise level can be found individual 95 noise bounds from averaging see Section 13 as 1 0 78662 o sese1_ 1 01403 2 0 00451 0 00511 0 00589 0 0046 a 0 00441 0 00503 0 00556 h 4 0 00449 0 00517 0 00606 a O 00543 0 00598 0 00476 6 000361 0 00425 0 00518 7 0 00376 0 00453 0 00566 S 000256 0 00315 0 00409 3 000107 0 00137 0 00190 10 0 0007 0 00109 0 00180 global 95 noise bounds 1 0 75674 0 68606 1 01431 2 0 004359 0 00497 0 00574 3 0 00421 0 00481 0 00560 4 O 00402 0 00463 0 00545 5 000384 0 00446 0 00535 6 000366 0 00431 0 00525 7 0 00350 0 00420 0 00524 S 0 00332 0 00408 0 00530 9 000306 0 00391 0 00544 10 000273 0 00381 0 00629 4 20000 20010 20020 20030 20
23. e materials usually have much cleaner spectra than typical diluted samples Therefore the comparison to noise or inversely the estimation of noise should be done individually for each spectrum whereas the standard derivations concern only the global noise The original derivation proposed here is free from the above mentioned drawbacks Those of you who like Winnie the Pooh are bothered by long words formulas go directly to the practical description Section 11 1 3 11 1 1 Notation and basic facts Here capital letters denote matrices bold italic letters denote vectors columns Notice that a b in ner product is a scalar whereas ab outer product is a matrix A symmetric matrix is fully determined by its eigenvalues and eigenvectors Ne a The eigenvectors are orthonormal e 5 Additionally and less trivially amp e e 1 unity matrix 11 1 2 Derivation of PCA based on statistics From c measured spectra of length r we form an rxc data matrix D d d d For the covariance matrix D D find eigenvalues A and eigenvectors e and sort them in descending or der in A s A is the largest Holds always Xe e 1 If only M lt c data vectors are linearly independent this sum can be truncated at j M and still 2 gt e 1 In this case 4 lt 4 V j gt M In practice the sum is truncated until Do Zat DX ee coincides with D within noise or alterna tively the truncated part D 2 _ e
24. e way as for the individual noise 1 e by using the statistical properties of x distribution 11 1 3 Questions answered by PCA Unlike the usual descriptions of PCA the derivation proposed here is capable of answering two direct and two inverse questions PCA1 Given the global average noise level how many spectra are linearly independent PCA 1 How high must be the global noise level in order to have a given number of independent spectra PCA2 Given the noise level of a particular spectrum how many principal components are needed to reproduce the spectrum PCA2 How high must be the noise level of a particular spectrum in order to reproduce it by a speci fied number of principal components As you will see in the example in Section 11 1 6 below the questions PCA1 and PCA2 are not quite the same In order to answer the direct questions PCA1 and PCA2 you must know the experimental noise level How to determine it See Section 13 11 1 4 How the PCA results are related to chemical species A mechanical mixture of chemical species obviously results in a linear combination of the correspond ing spectra However if different species have similar XANES spectra the spectra may be linearly de pendent even for a set of pure chemical species The example in Section 11 3 1 illustrates this case Note therefore that linear dependence of spectra does not necessarily mean mixture of species Inversely 1f some spectra are distor
25. ed as uniform over each single pixel and therefore the correction can be done only for one direction towards the pixel center An interesting approach to correcting the self absorption effect was proposed by Booth and Bridges 2005 who considered another small parameter not the usual exp ud which allowed simplifying the formulas also beyond the thick limit but the treatment was limited to EXAFS Another re invention of the Iida and Noma method with calling it new was presented by Ablett et al 2005 The merit of that work was implementing the method without restriction to the thick limit and providing many application examples and literature references 8 1 Description of self absorption correction The derivation of the fluorescence intensity can be found with different notations in almost all the pa pers cited above Here it is repeated because XD adds some extra factors The standard expression for the fluorescence intensity originated form the layer dz at the depth z is given by the trivial sequence of propagation and absorption with neglected scattering dz Q Pa paomocese ur E z sing dI z E I e u E ad eee sno co 4T primary primary x ray lt x transformed fluorescence x ray flux transmitted to absorbed in layer dz into directed into transmitted to detector depth z due to edge of interest fluorescence solid angle Q from depth z where ur is the total linear absorption coefficient at the prim
26. ed to a column file use Project Make output file own energy for each spectrum initial energy before calibration Another very useful function of XD 1s saving project files A project file has description of data files and all the pro cessing steps The project files Samples xpj have been _ Pests backoround saved in this way E initial mu Important Project files are text file You can edit them po Enn by any common editor A newly created project file has fie name full path references to the data files If you move the data files or if you want to load the project on another com puter you should change the paths accordingly I nor mally keep project files in the same directory with data Then I keep only the file names in a project file and manu ally delete the directory paths by Search Replace com mand in a text editor T 16 04 03 14 26 17 10 09 10 30 17 10 09 12 06 17 10 09 12 07 22 10 09 12 46 22 10 09 12 47 22 10 09 12 46 22 10 09 12 49 22 10 09 12 49 22 10 09 12 50 22 10 09 12 51 17 10 09 10 23 i t t t al t t of m D B a B m B m aa oo oo eo eo l Fa SS 233 p 2zi nnmonmDrt r Cancel References Ablett J M Woicik J C and Kao C C 2005 International Centre for Diffraction Data Advances in X ray Analysis 48 266 Booth C H and Bridges F 2005 Physica Scripta T115 202 Brennan S and Cowan P L 1992 Rev Sci Instrum 63 850 http www bmsc washingto
27. en it is small the solution has rich fine structure when it is big the solution is smooth You can change a and see that very different deconvolution solutions give successful solution checks There is no unique solution 5 1 How to select the regularizer One may try to define an optimal in some sense a In Klementev 2001 I proposed three possible ways for this Unfortunately what I did wrong I did not consider the spectrum length scaling For a full length spectrum the optimal a must be the same as for its shorter piece The third method does not fulfill this It seems that the second method the conservation of S N ratio is reasonable The figures of merit introduced in Klementev 2001 are reported in XD at the bottom of the deconvolution section of the main dialog One can utilize them for non automatized search for an optimum a 6 Transformation to new grid transform to new arid In several cases you need to transform your spectra to a common energy grid For first node dE j A 120 new giid nodes instance you need this for Principal component analysis PCA or for averaging 7 Subtraction of pre edge background pre edge backornd pp polynomial 6 43 2 1f0 1 2 T show subtracted manual correction 7 J The pre edge background is constructed by polynomial interpo lation over the region specified by mouse see the picture on the right The polynomial law is given by the power buttons For instance the screensho
28. es and their changes under processing are visual The visualization is not only a mat ter of convenience it serves for the ultimate quality check of experimental data and processing steps by the program user XD 1s also useful for quick quality check during your beam time at synchrotrons A simple drag and drop action reveals in a second the spectrum quality and reproducibility in E space XD offers the most comprehensive Principal Component Analysis and self absorption correction pro cedures as described below 1 3 System requirements XANES dactyloscope runs on all 32 and 64 bit Windows systems It can run under Linux with Wine The minimum screen resolution is recommended as 1024x768 Originally XANES dactyloscope was a 16 bit program that could not run on 64 bit Windows I thank Roman Chernikov Hasylab at DESY for making the 32 bit build 1 4 About this manual This file describes the program XANES dactyloscope build 5 30 It is essential to unpack the archive with examples The examples xpj can be simply loaded by associating them with XD I have tried to explain all the aspects of the program that may be useful to its user in setting up his or her analysis of XANES spectra 2 Opening data files x You can select multiple files using Ctrl or le name 3 N e Akim WIPERSSAMPLES Hy Shift buttons or by mouse dragging The name ome CER EA e Z of the last opened file is colored by red The T moz 27 11 06 14 55 Pd e
29. falls in factor analysis 11 3 1 Overestimated linear dependence If different species have similar XANES spectra the spectra may be linearly dependent even for a set of pure chemical species To illustrate this load the project Samples 11 3 PCA MoOx xpj which has spectra of 6 molybdenum oxides MoO2 MoO MosOu4 MogO23 M0183052 and MoOs J Wienold T Ressler private communication Ressler et al 2002 As seen there are only 4 or 5 independent spectra out of 6 although each sample has a pure structure as was proven by XRD Another example of overestimated linear dependence is given by PCA applied to EXAFS see Section 11 1 5 EXAFS spectra are usually more linearly dependent than the corresponding spatial structures 11 3 2 Underestimated linear dependence Always remember that spectra may have instrumental distortions due to self absorption non linearity of the fluorescence detector presence of pin holes etc These distortions may break the linear depen dence of spectra even where it would be really expected Consider an example of self absorption from Section 8 3 Load the example project Samples 08 fe2o3_tr_fl xpj It has 4 spectra of Fe O hematite measured in transmission and fluorescence each repeated twice to assure reproducibility To enable PCA transform the energy mesh to a new grid with e g 1 node 7080 eV and dE 0 5 eV Apply this transform to all 4 spectra Switch off the self absorption correction and activate PCA
30. ied post edge region as on the picture at the right 11 the u value at a particular energy and 111 the maximum peak value which was popular some time ago u 0 4 Oe OO sao 11560 11580 11600 11620 11640 11660 1168 10 Base line subtraction A base line 1s needed when considering an absorption peak on a rapidly changing background There are two ways of how to construct the base line e e e W base line 10 1 Base line as smoothing spline a J The base line is a smoothing spline drawn through selected regions of experimental points To make the spline pass under the peak the peak must be excluded from the spline nodes The smoothing pa rameter controls the stiffness of the spline the bigger the stiffer The optimum parameter is found vis ually there is no good strict criterion for it This arbitrariness should not make any problem because 12 normally the smoothing parameter is visually good in a very broad range to see this example load the project Samples 10 1 moallyl sm spline xpj Maximize view Extend by 25 Mende a region into the base line spline Delete a point 0 1 L 1 i 0 1 1 A 1 1 0 1 i i i 18960 19980 20000 20020 20040 18960 19980 20000 20020 20040 18960 19980 20000 20020 20040 0 2 After subtracting the base line with the base ine check box subtract the peak is isolated pm soine 2394 2 _ giis and can be analyzed for its maximum position activate the de rivative for this
31. ious for mats ini files using common text editors re number then the strings properly 2 2 Project files The list of all loaded spectra together with the selected analysis steps can be saved in a project file Project files can be loaded using Project Load project menu or by associating XD with the project files xpj files Several example projects together with the associated data are provided in a separate archive Project Sane oa wae CurOfst mu File format Emu hide all other spectra 15 E min to see this open E max the project E calibration 2al data point i Samples a 03 Cu_NaY14 xpj E bo 7 deconvolution convolution 1 2 oui 1 000 I transform to new grid first node dE 267 mu correction m Fe 20e e 7145 00 45 0 ius is const 5400 00 45 0 p thick m E seal eoem A160 I normalize to unity baze i yia average post edge E principal component analysis or target o4 pre edge backornd pp polynomial 5 4 3 2 10 1 2 M show subtracted 10 manual comection 7 i fitting by user defined formulalE a is FL__ g W mu gni E my a my j The program interface consists of the main dialog and the graph window Use the pop up menu in the graph window to use the most frequent commands integrate mu between ma and o o i s a960 ede S000 3020 g e Add Add special average rms difference
32. is XANES dactyloscope XANES dactyloscope XD is a program for data analysis of XANES spectra It includes e energy calibration e deconvolution of absorption coefficient with monochromator resolution curve and or core hole lifetime broadening curve e transformation to a new equidistant grid e pre edge background subtraction e correction by a user defined function or fluorescence self absorption correction for thick or thin samples e normalization e base line subtraction for analysis of pre edge peaks e principal component analysis or target transformation e fitting by a user defined formula usually a linear combination fitting with advanced error analysis XD does not include ab initio XANES calculation Also XD does not produce publication quality graphs It only exports column files to be loaded by Matplotlib QtiPlot Origin etc Although several ab initio XANES calculation codes have been successful in reproducing some partic ular spectra mostly of metal samples the quantitative treatment of XANES still remains a challeng ing problem For this reason XANES is mostly used for finger print analysis which considers spe cific spectroscopic features finger prints pre edge peaks white lines edge shifts etc for identify ing the chemical states and or local atomic symmetry This explains the name of the program XANES dactyloscope 1 2 What makes XANES dactyloscope special Any time all curv
33. is fact shows that some particular spectra may contain less principal com ponents than the number of independent spectra and that the latter figure may be un derestimated by visual checking of PCA test This example shows also what is the first principal component in this case it is the average spectrum 20000 20010 20020 20030 20040 200 20000 20010 20020 20030 20040 200 The figures nin Emax reported in the pop up menu under the button prin 2 cipal components allow to answer the questions listed in Section 11 1 3 w 1i 269 57526 1 00000 2 0 65615 0 04934 PCA1 Given the global noise level how many spectra are linearly independent 91 0 00228 0 00289 The global 95 noise bounds tell that with 95 of probability the measurement indvidual 95 noise bounds noise must be within the bounds in order to consider the component as unimpor a tant and unselect it from the list of PC s If your experimental noise is lower then 3 0 00248 0 00303 0 00387 i this component must stay selected 1f it is higher then there must be some further sebal 25 noise bounds correlations among the selected components and you should unselect yet more oe E components Finally the number of the selected components gives the number of s o o0ss 0 00433 0 00554 independent spectra Of course you do not have to select unselect the menu Mainowsk sre I xE items Just look at the values where
34. n edu scatter periodic table html ftp ftpa aps anl gov pub cross section_codes Brewe D L Pease D M and Budnick J I 1994 Phys Rev B 50 9025 Carboni R Giovannini S Antonioli G and Boscherini F 2005 Physica Scripta T115 986 Chantler C T 1995 J Phys Chem Ref Data 24 71 http physics nist gov PhysRefData FFast Text cover html http physics nist gov PhysRefData FFast html form html Eisebitt S B ske T Rubensson J E and Eberhardt W 1993 Phys Rev B 47 14103 Goulon J Goulon Ginet C Cortes R and Dubois J M 1982 J Physique 43 539 Haskel D 1999 Computer program FLUO Correcting XANES for self absorption in fluorescence data http www aps anl gov xfd people haskel fluo html Henke B L Gullikson E M and Davis J C 1993 Atomic Data and Nuclear Data Tables 54 181 http www cxro lbl gov optical_constants Hubbell J H 1969 Natl Stand Ref Data Ser 29 Hubbell J H Radiat Res 70 1977 58 81 http physics nist gov PhysRefData Xcom Text XCOM html lida A and Noma T 1993 Jpn J Appl Phys 32 2899 Kissel L Zhou B Roy S C Sen Gupta S K and Pratt R H 1995 Acta Crystallographica A51 271 Pratt R H Kissel L and Bergstrom Jr P M New Relativistic S Matrix Results for Scattering Beyond the Usual Anomalous Factors Beyond Impulse Approximation in Resonant Anomalous X Ray Scat tering edited by G Materlik C J Sparks and K Fischer North Holland Amsterdam 1994 Kane P P Kissel L Pratt R H
35. orption by air and by Kapton foils in front of the sample can be taken into account see the examples below For this the primary flux is multiplied by e7 Hewr 4 40 The similar term at is included into the constant C 3 mis usually taken to be energy independent In XD it is energy dependent 4 One can select among five different tabulations of absorption coefficients actually scattering factors f in XD 8 2 2 How the tables of scattering factors are used In order to use the equation it is prerequisite to know the sample stoichiometry 1 e the molar weighting factors x for each atom type i in the sample Then the linear absorption coefficient is pro portional to the atomic absorption cross section oa Hy XyO and poe Dy x 0 The atomic cross sections in turn are calculated from the tabulated scattering factors f 0 2rychN fU E Since all the tabulations do not contain the partial contributions of each absorption edge of an element but only the combined result of all atomic shells an isolation of ux and the pre edge background is re quired In XD this is done by extrapolating the pre edge region by the Victoreen polynomial The poly nomial coefficients are found over only two pre edge points as the tabulations are usually sparse As illustrated below for each tabulation used the edge jump is the difference between the first post edge value and the extrapolated background tabulation Zoomed around the
36. rrectly try to find other unique sub strings or use button Up to place your format earlier in ry rn ena LURE new f Up the recognition queue Photon Factor f z 7 In the description of the data columns one can use almost any function of Bader consists of I stings variables Coll Col52 For instance one can load several fluorescence consists of strings begining with C ends with last string containing signals il as say Col5 Col6 or better one can load these signals as separate spectra for better visual quality checking unique words in header to recognize this format Ste Jao The internal energy unit is eV Therefore if your energy unit is different data in columns Coll through Col52 you should do a transform like Col4 le 6 For keV unit there is a dedi absolute energy i kel i aes 7 The reference curve is only needed for energy calibration and can be left load 1 colummls as separate spectra from column through empty Usually this is the absorption coefficient of a reference foil placed alae ke between the 2 i1 and the 3 i2 ionization chambers Correspondingly Sata seseean ene it is given by In ColN ColM where ColN and ColM represent 11 and 12 signals cated option The format descriptions are saved in a text file formats ini If you want to transfer it to another com puter just copy it to the directory of the program executable file You can manually merge var
37. scan the x ray energy up the air paths and the s windows become more transparent thus the flux at the sample and the fluores rf ad cence flux grow high This becomes even more pronounced when you normalize by 0 the signal of the 1 ionization chamber its signal goes down at high energy because its gas also becomes more transparent Fi n2 nally the spectrum may look like on the left picture For correcting this select at a least 3 polynomial powers and put an ex tra high energy point The result after sub 7100 7200 7300 o traction is shown at the right 00 00 7200 7300 7400 8 Self absorption correction Many papers have addressed the self absorption effect Most of them provided restricted correction The early papers by Goulon et al 1982 Tan et al 1989 Troger et al 1992 were limited only to the EXAFS case The correction functions there had discontinuity at the edge and thus were not applicable to XANES Moreover those works provided corrections only for infinitely thick samples with an ex ception of Tan et al 1989 where also thin samples were considered but only as pure materials e g single element foils The first self absorption correction for the whole absorption spectra also including XANES was pro posed with two different strategies by Eisebitt et al 1993 and lida and Noma 1993 Eisebitt et al 1993 estimated the two unknowns ho and uy see the notations below from two independent
38. t above shows the modified Vic toreen polynomial aE b where the coefficients are found by the standard least squares method The polynomial is then ex trapolated over the absorption edge For absorption spectra measured in transmission mode usually a Victoreen polynomial aE bE or a modified Victoreen polynomial is implied For absorption spectra measured in fluorescence mode back ground subtraction is frequently not needed unselect all the power buttons More frequently a constant shift is sufficient select button 0 Sometimes the spectra exhibit a net growth with energy which can be approximated by a linear law select buttons 0 and 1 Sometimes a severe background correc tion 1s needed as explained below click amp drag 7 1 Corrections of pre edge background 11400 11500 11600 11700 Some spectra behave strangely they bend up or down which makes the background subtraction diffi cult One can correct such a behavior by introducing more powers into the background and or by adding an extra point at a high energy pre edge backgmnd wp polynomial Checking the manual correction option will put an extra point you position 5 4 3 2 10 ila f sh b d e e Sappi a l showsbiated it by mouse which is additionally considered by XD in the least squares method for finding the polynomial coefficients J e 0 6 ve Consider a fluorescence experiment on a sample inside an in situ cell As you
39. ted due to self absorption non linearity of the fluorescence detec tor presence of pin holes etc linear dependence of spectra may be lost although the samples may re ally represent mixtures Finally this question should be individually explored in every PCA study It also involves careful at tention to experimental details in order to eliminate systematic distortions 11 1 5 Is PCA also applicable to EXAFS Formally yes and some people did it but with very poor logic EXAFS is described by a sum of modu lated sinus functions Sinus functions form a complete set and as such can be linearly combined to repro duce any function Thus it is naturally expected that EXAFS spectra are linearly dependent The bad na ture of the EXAFS kernel can also be seen from another side it 1s impossible if without any regulariza tion scheme to invert the EXAFS equation for getting the radial distribution function The reason 1s the same the degeneracy of the kernel 1 e its low rank when expressed as a matrix of 2k r coordinates Finally the functional shape of EXAFS makes one EXAFS spectrum strongly correlate with another one This correlation happens regardless of spatial structural correlations Doing conclusions on PCA ap plied to EXAFS spectra does not substantiate any conclusions on the number of independent structures Yet finally don t do PCA on EXAFS 15 11 1 6 Usage of PCA in XANES dactyloscope meee ae e U 4 eral nee componen
40. the noise estimations are bigger than the ex 1 956640 0 00000 0 86640 w 2 0 05256 0 05024 0 04277 perimental noise these are the principal components 3 0 00433 0 00353 0 00250 PCA1 How high must be the global noise level in order to have a given number of independent spectra The answer with 95 significance level is in the pop up menu on one line below the given ordinal number PCA2 Given the noise level of a particular spectrum how many principal components are needed to reproduce the spectrum The answer similarly to PCA1 is given by the pop up menu but in the section individual 95 noise bounds Notice that these figures are reported only for the current spectrum and a generally differ from those for another spectrum as shown on the left and right pictures for spectrum 1 for spectrum 3 individual 95 noise bounds individual 95 noise bounds w li 0 76825 0 66522 0 99045 3 0 00248 0 00303 0 00387 a 0 00502 0 00612 0 00753 PCA2 How high must be the noise level of a particular spectrum in order to reproduce it by a speci fied number of principal components The answer is similar to PCA1 but in the individual section The figures refer to the current spectrum In the example above the artificially added normal noise of o 0 005 falls within PCA1 the global noise bounds of the third component which means two principal components PCA2 th
41. ts w The spectra subject to PCA or target transformation must be defined on the same energy grid If the grids are different do the transform Section 6 Specify a set of spectra This is considered either as a data set or as a basis set depending on whether the current spectrum belongs to it Then correspondingly PCA or target transformation is performed Load the project Samples 11 1 PCA2 dABCnC xpj which has two independent spectra and a spectrum constructed as the aver age of the two plus normal noise with nominal o 0 005 The thick curves are data and the thin blue ones are the PCA test curves The components can be selected unselected by pressing the button principal components Unselecting a component means excluding it from the principal ones As seen the test curves reproduce the data exactly when all the components are selected 20000 20010 20020 20030 20040 200 Unselect the last component which is the least important one As seen on the picture at the right the spectra are still well repro duced which is expected as we know that there are two indepen dent spectra and there must be two PC s 20000 20010 20020 20030 20040 200 16 Unselect the second compo nent and see that the first two spectra are reproduced badly hide all other spectra may help in seeing this bet ter left picture whereas the third one can surprisingly be reproduced with only one principal component right picture Th
42. ute 01 56 ak requiarizer Start In ple d J 1 14e 3 R 1 04e 4 Ig det gl 4 35e 3 One can do several deconvolutions one after another the check box apply to initial spectrum must be off for this This makes sense when one first does Instrumental and then lifetime deconvolution The former is typically of Gaussian kernel and is applied to the measured signals ip and i separately The latter is typically of Lorentzian kernel and is applied to u There is a way for how to check the solution after the deconvolution has been found the back convo lution is performed by true integration and the resulting deconvolved convolved u 1 do not know if it is better to say deconvoluted convoluted is displayed in the graph to see this use the previously loaded example project Samples 04 E Calib 1 xpj a Here on the left there are two repetitions red and blue of the same spectrum a On the right the blue one is deconvolved with the pa ae i rameters shown above in i strumental broadening with AE 3 7eV FWHM The brown curve is the solution check Le decon volved convolved u It co incides with the red one which justifies the decon volution You can see this also if you unselect the deconvolution made the initial u and the a solution check must super impose iso nbo nso meo me meo ne fe nso mea neo neo neo n The Bayesian deconvolution depends on a parameter regularizer denoted as a Wh

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