Comparative XAFS studies of some Cobalt complexes of (3-N- phenyl -thiourea-pentanone-2)

XAFS spectroscopy is a useful method for determining the local structure around a specific atom in disordered systems. XAFS study of some cobalt complexes of (3-N-phenyle- thiourea-pentanon-2) is carried out using the latest XAFS analysis software Demeter with Strawberry Perl. The same study is also carried out theoretically using Mathcad software. It is found that the thiourea has significant influence in the spectra and the results obtained experimentally and theoretically are in agreement. Fourier transform of the experimental and theoretically generated XAFS have been taken to obtain first shell radial distance. The values so obtained are in agreement with each other.

modulating part of the absorption coefficient called the extended X-ray absorption fine structure (EXAFS) is described by 2               Where k is the electron wave vector, N j is the number of atoms in the j th coordination shell, R j is the average radial distance to the jth atom, t j (2k) is the back-scattering matrix element encountered by the electrons,  is the mean free path of the electron, the 2 nd exponential containing  j 2 is a Debye-Wallertype term where  j is the rms fluctuations of the atom about R j , and  j (k) is a phase shift. The form of this equation is a sine like scattering from each shell of atoms at R j with the EXAFS signal proportional to the number of atoms surrounding the absorbing atom and inversely proportional to R j 2 .
Each coordination shell contributes a sine like term of period 2kR j . The total result is a summation over all the coordination shells within range of the effect. Several attempts have been made to extract structural information from EXAFS. The most general methods used are fitting procedures [3] and Fourier Transform methods. The Fourier transform method can be applied to structures that are more complicated. From (k) a radial structure function  n (r)can be derived given by where n is usually either 1 or 3, and k min and k max are the minimum and maximum values of k, respectively. The n = 3 transform weights less the low-energy portion of ( ) k  , where the undesirable uncertainties occur, while it weights most the high-energy portion of ( ) k  . For this reason, we will employ 3 ( ) r  as our standard transform in the case. Shells of scattering atoms surrounding the absorbing atom generate the maxima of this function. The positions of the peaks in (r)are shifted compared to true distances due to contribution of the scattering phases that depend on k.
The analysis of Fourier transformation of ) (k k n  into r-space was carried out using the IFEFFIT. This will ensure that the FT gives the correct contribution due to all constituent frequencies in ) (k  .This is important for accurate determination of local structure. The k range for Fourier transform was 2 < k < 9 (Ǻ) -1 .

Results and discussion
The XAFS and magnitude of the Fourier transform of XAFS are shown in figure 1 and figure 2 respectively for five cobalt complexes. The first strong peak at 2.1 Ǻ for [3N3NTU2P] complex in the magnitude of the Fourier transform is due to the sulfur nearest neighbors around the cobalt ions the peaks are shifted towards smaller distances because of the phase shifts. The different Co-S bond distances are described in Table 1. Comparison of bond length to LSS, Lytle, Levy's to the bond length calculated by MathCAD programming and IFEFFIT have been done. The inverse Fourier transform of this peak in k-space gives the contribution to EXAFS from the sulfur nearest neighbors. The method employed for theoretical analysis of EXAFS and verification of various structural parameters using MathCAD programming is simpler than commonly used IFEFFIT technique. [4] In contrast to conventional EXAFS fitting analysis, other kinds of EXAFS analysis computation originated from the Tikhonov regularization method [3][4] is the iterative solution projection method using numerical algorithm [5] of manipulating matrix inversion computation under the ill-posed mathematical problem. The EXAFS spectra obtained using equation (1)

Conclusions
Fourier transform technique provides results with great accuracy. This method is simple and straight forward, thereby providing a physical picture of the X-ray absorption process. This method appears to have a great potential in studying systems such as crystalline and amorphous materials.