Indian Journa of Pure & Appied Physics Vo. 49, January 0, pp. 5-9 Simpified anaysis of EXAFS data and determination of bond engths A Mishra, N Parsai & B D Shrivastava * Schoo of Physics, Devi Ahiya University, Indore 45 00 * Schoo of Studies in Physics, Vikram University, Uain 456 00 *E-mai: amishra960@yahoo.co.in Received 4 March 00; revised 7 Juy 00; accepted December 00 A simpified anaysis of extended X-ray absorption fine structure (EXAFS) data has been presented for copper and nicke metas. EXAFS data has been generated using standard EXAFS equation empoying the software Mathcad. The phase shift for the backscattered photoeectron wave has been obtained from the experimenta data itsef. The backscattering ampitude taken from the avaiabe tabuations and other parameters taken from crystaographic data have been used as input to the EXAFS equation. The theoretica EXAFS data and its Fourier transform agree we with the experimenta resuts. The bond ength obtained for the first coordination she compares we with the crystaographic vaue. Keywords: EXAFS, Mathcad, Fourier transform, Artemis, Feff, Bond ength Introduction X-ray absorption fine structure (XAFS) refers to moduations in X-ray absorption coefficient ust above an X-ray absorption edge. XAFS is often divided into X-ray absorption near edge structure (XANES), which ies within the first 30 ev of the edge position and extended X-ray absorption fine structure (EXAFS), which ies beyond 30 ev above the absorption edge. The physica origin of EXAFS and XANES is basicay same, i.e., the scattering of a photoeectron by its environment. XAFS is an important probe of materias, since it contains information of the oca atomic structure, i.e., the species of atoms present and their ocations, but extracting this information is often compicated. However, the quantitative anaysis in the EXAFS range is reativey simper. Information avaiabe from EXAFS is the average distance between the absorbing atom and its neighbouring atoms, mean square variation in the distance and coordination number. EXAFS is appicabe to condensed matter (both crystaine and amorphous) and gases. Singe crystas are not required. Appications that immediatey come to mind are compicated bioogica moecues, aoys and amorphous materias, soution chemistry and cataysts. Earier, a simpe and innovative procedure for anaysis of EXAFS data was presented,3. The method was demonstrated to yied satisfactory resuts for Cu (II) isoxezo and Cu (II) pyridine mixed igand compexes,3. In this procedure, the theoretica EXAFS data was generated, empoying computer software Mathcad, for the first coordination she around the absorbing atom, using standard EXAFS equation,4. For this cacuation, the required phase shift was extracted from the experimenta data itsef and the backscattering ampitude was assumed to be equa to one. The atter assumption is over simpification of the rea situation. In the present study, we have incuded the backscattering ampitude aso in the cacuations so that better agreement may be obtained between the theoretica and experimenta spectra and the information obtained from the anaysis about the oca atomic structure may be accurate. In order to standardize the procedure outined in the present work, we thought it proper to appy it to standard systems. Hence, for the present anaysis, we have taken the experimenta EXAFS spectra of copper and nicke meta fois, obtained at room temperature at the synchrotron EXAFS beam ines at Daresbury (U.K.). Methodoogy The attenuation of X-rays by matter generay foows the reation: I = I 0 exp[ µ ( E) x] () where µ(e) is the X-ray absorption coefficient, I 0 is the incident intensity, I is the transmitted intensity and x is the sampe thickness. The EXAFS is defined as the normaized osciatory part of µ(e) and is given by:
6 INDIAN J PURE & APPL PHYS, VOL 49, JANUARY 0 χ ( E) = [ µ ( E) µ ( E)] / µ () 0 0 where µ 0 (E) is the smoothy varying portion of µ(e) past the absorption edge and µ 0 is the edge step. The χ(e) data is converted to data by using the reation: k E E / = [3( 0)] (3) where E 0 is the threshod energy. The EXAFS equation that has become the standard for current work is,4 : 0 kr ( ) ( ) ( ) N S F k χ k = sin[kr + δ ( k)] exp ( σ k ) exp [ R / λ ( k)] (4) The subscript denotes the various scattering paths. N is the number of atoms in the th coordination she, R is the average radia distance to the th atom, σ is mean square deviation about the bond ength. S 0 is the passive eectron reduction factor and accounts for the sight reaxation of the remaining eectrons in the presence of the core-hoe vacated by the photoeectron. S 0 usuay has a vaue between 0.7 and and is different for different eements. The function F (k) is the photoeectron backscattering ampitude and δ (k) is the scattering phase shift for each scattering path. λ(k) is the photoeectron mean free path which is dominated by ifetime of the excited state. The backscattering ampitude is given by 5 : F( k) = ( + )(exp iδ )( ) ik (5) where is the anguar momentum of the fina state and δ (k) are the partia wave phase shifts. The anaysis depends on the argument of the sine term in Eq. (4) as foows: sin[kr + δ ( k)] (6) δ is assumed as inear in k, δ = α k + β (7) Substituting into the argument of sine and rearranging for the first coordination she ( = ), it is convenient to define n by 6 : ( n ) + π = k ( R α ) + β (8) where n = 0,, 4 for maxima and n =, 3, 5 for minima. Using the graphica method outined by Lyte, Sayers and Stern 4 (LSS method), a pot of n versus k for the maxima and minima of the measured EXAFS data determines (R α ) from sope and β from intercept. Once, an EXAFS has been obtained experimentay, its interpretation begins with a Fourier transform of the data. The Fourier transform is taken as 7 : φ w ( R) = k χ( k)exp( ikr) dk kmax w (9) π kmin where w is usuay, or 3, and k min and k max are the minimum and maximum vaues of k, respectivey. The w = 3 transform weights ess the ow-energy portion of, where the undesirabe uncertainties occur, whie it weights most the high-energy portion of. For this reason, we have empoyed φ 3 (R) as Fourier transform in this paper. A Fourier transform of wi have peaks at R=R corresponding to average radia distance (R) of the th atom from the absorbing atom. Thus, the positions of the peaks in the Fourier transform of the EXAFS signa are reated to the distance between the absorbing atom and the neighbouring atoms, and the height is reated to the number of neighbouring atoms at this distance. The distance found in the Fourier transform is about 0.-Å, shorter than the actua distance because of the phase shift δ (k). If this factor was absent, the peak in Fourier transform woud have been a direct measure of R. Hence, to extract the information about the various parameters that can be determined from EXAFS data, the data has to be compared with accuratey known standard, i.e., either theoretica or experimenta standard 8,9. A theoretica standard is a theoreticay simuated spectrum. The crystaographic data can serve as a basis for generating theoretica standard using computer program such as Feff avaiabe in the software Artemis. In Artemis, the parameters of the EXAFS equation come in two sets. First set incudes the terms R, σ, N and S 0. The parameters of this type are the things that may be parameterized in Artemis. The second set of parameters incudes the terms F (k) and δ (k). These are k-dependent functions that have to do with the detais of the atomic
MISHRA et a.: ANALYSIS OF EXAFS DATA 7 species of the absorber and scatterer(s), the number of egs that the scattering path has, and the anges through which the photoeectron scatters as it traverses the path. In Artemis, parameters of this type are computed by Feff and typicay not atered during the course of the fit. That is, Artemis takes the Feff cacuations of the various F (k) and δ (k) functions as true and uses them as the basis for determining the vaues of the first set of parameters. An experimenta standard is an EXAFS spectrum of a known materia. The two functions F (k) and δ (k) can aso be obtained by using experimenta standards 9,0. The ampitude and phase can be extracted from the experimenta EXAFS data of mode compounds, by back-transforming fitered shes. Then these can be used to fit the EXAFS data of the unknown compound to determine the vaues of the first set of parameters. The anaysis of EXAFS data requires expertise and is time-consuming because appropriate theoretica mode has to be obtained by varying the various parameters in the EXAFS equation, even though computer softwares ike Artemis are avaiabe for this purpose. In the present work, we have deveoped a simpified anaysis procedure for extracting bond ength for the first coordination she from the experimenta EXAFS data. The method is simpe and nove because cacuations are done using the computer software Mathcad. The theoretica mode is generated through the standard EXAFS equation given in Eq. (4) for the first she. The vaues of N, R, σ and λ are taken from crystaographic data 4,7. The backscattering ampitude F (k) has been taken from the tabes of McKae as we as of Teo and Lee. The phase shift has been extracted from the experimenta data using Eq. (7) in the foowing manner. From the experimenta versus k pots, the vaues of k corresponding to maxima and minima of have been obtained. The vaues of k thus obtained have been used to pot n versus k curves where n have been defined for Eq. (8). The n versus k curves are given in Fig. for both copper and nicke fois. The vaue of (R α ) and β has been determined respectivey from the sope and the intercept of these pots. These vaues of (R α ) and β have been used to obtain the phase factor, which has been used as input in Eq. (4). The theoreticay generated EXAFS data using Eq. (4), is then Fourier transformed using Eq. (9). The Fourier transform peak for the first she occur at R = R α, where R is the measured distance and R is the true distance. Fig. n versus k curves for copper foi and nicke foi 3 Resuts and Discussion Figure gives the experimenta versus k curve as we as the theoretica curves obtained from Eq. (4) for copper foi. Whie three sets of theoretica curves have been presented in this figure as, and, the same experimenta curve has been reproduced in a the three figures. The theoretica curves reported in Figs and are the resuts of using the backscattering ampitude from the tabes of McKae for these cacuations. In these tabes, McKae has given the theoreticay cacuated vaues of backscattering ampitude for different eements. He has done two sets of cacuations, one using R = 4Ǻ and another using R =.5Ǻ. The backscattering ampitudes, using R = 4Ǻ and R =.5Ǻ, have been used by us in obtaining the theoretica curves reproduced in Figs [ and ], respectivey. Simiary, the theoretica curve in Fig. has been obtained using the vaues of backscattering ampitude from the tabes of Teo and Lee. This has been done in order to ascertain if there is a difference in using
8 INDIAN J PURE & APPL PHYS, VOL 49, JANUARY 0 the two avaiabe tabuations for the backscattering ampitude, i.e., of McKae and Teo and Lee. The tabes of Teo and Lee use pane wave formaism for the scattering of the outgoing photoeectron by the neighbouring atom, whie the tabes of McKae use curved wave formaism. Though the two formaisms have been reported to give simiar vaues of backscattering ampitude for ower Z eements ike copper and nicke, yet we have used both of them in the present work to compare the theoretica curves obtained from both of them. Figures 3(a,b,c) show the Fourier transform of both the experimenta and the theoretica χ( k) versus k curves of Figs (a,b,c). Figures 4 and 5 are simiar figures for nicke foi. It is seen from Figs to 5 that the theoretica curves as we as their Fourier transforms are in good agreement with their experimenta counterparts, Fig. and theoretica versus k curves for copper foi For cacuations, backscattering ampitude has been taken from McKae (vaues for R = 4 Å) McKae (vaues for R =.5 Å) Teo-Lee Fig. 3 of χ (k) versus k curves of Fig. (a, b, c) for copper foi 0. -0. 0 4 6 8 0 4 6 k(å - ) 0. Experimena -0. 0 4 6 8 0 4 6 k(å - ) 0. -0. 0 4 6 8 0 4 6 k(å - ) Fig. 4 and theoretica versus k curves for nicke foi. For cacuations, backscattering ampitude has been taken from McKae (vaues for R = 4 Å) McKae (vaues for R =.5 Å) Teo-Lee
MISHRA et a.: ANALYSIS OF EXAFS DATA 9.5.5.5 Fig. 5 of χ (k) versus k curves of Fig. 4 (a,b,c) for nicke foi showing that the simpified method presented in this work is quite satisfactory. A cose examination of these figures shows that there is hardy any difference in using the tabuations of backscattering ampitude, i.e., of McKae and Teo and Lee. Hence, one can make use of any of these tabes especiay for ower Z eements and for wave vector k >. The vaues of bond ength for the first she in copper and nicke metas obtained from the present anaysis of the EXAFS data are.54 and.47å, respectivey. These vaues are in good agreement with those reported from crystaographic data, i.e.,.556 and.49å, respectivey 3. In the present method, the theoreticay generated data using the standard EXAFS equation has been compared with the experimenta data. Comparison has been done both in the k-space and in the R-space and the agreement between the theoretica and experimenta data has been satisfactory. The resut obtained for bond ength compares we with the crystaographic vaue. In our method, the phase shift has been extracted from the experimenta data itsef and the backscattering ampitude has been taken from the standard theoretica tabuations. 4 Concusions A simpified technique has been presented for the anaysis of extended X-ray absorption fine structure (EXAFS) data and determining the first she bond ength. The method empoyed here, using the Fourier transform technique, is simpe and straightforward, thereby providing a physica picture of the X-ray absorption process. The anaysis uses easiy avaiabe computer program Mathcad. Though, the method outined is simpe, yet it gives adequate resuts, as has been demonstrated in the case of copper and nicke metas. The method can be appied for any pure meta and is quite suitabe for compex systems aso. In the present case, anaysis has been carried out ony for the first she, but it can be extended to other shes aso. References Rehr J J & Abers R C, Rev Mod Phys, 7 (000) 6. Mishra A, Parsai N & Dagonkar N, Indian J Pure & App Phys, 47 (009) 337. 3 Mishra A, Parsai N, Soni N & Awate R, Indian J Pure & App Phys, 48 (00) 8. 4 Lyte F W, Sayers D E & Stern E A, Phys Rev B, (975) 485. 5 Lee P A & Beni G, Phys Rev B, 5 (977) 86. 6 Deshpandey A P, Sapre V B & Mande C, Phys Stat So, 45 (988) 77. 7 Stern E A, Sayers D E & Lyte F W, Phys Rev B, (975) 4836. 8 Frenke A I, Murthy V & Newvie M, J Synchrotron Rad, 8 (00) 669. 9 Stern, E A & Head, S M, Handbook on Synchrotron Radiation, Vo, edited by Koch E E (Esevier Science Ltd, North-Hoand), 983, p. 955. 0 Key S D, Hesterberg D & Rave B, Methods of Soi Anaysis, Part 5, Mineraogica Methods (Soi Science Society of America, Medison), 008, Chap 4. McKae A G, Knapp G S & Chan S K, Phys Rev B, 33 (986) 84. Teo B K & Lee P A, J Amer Chem Soc, 0 (979) 85. 3 Internationa tabes for X-ray crystaography, Vo. III (Kynoch Press, Birmingham, UK), 96, p. 77.