The Heisenberg Hamiltonian appropriate to exchange clusters commutes with the square of the total spin ant its third component. Therefore in studying the exchange coupled clusters of medium/high nuclearity the spin quantum number S can be utilized in factoring of large interaction matrices (dimension of which is 104 - 105). Then the blocks of much lower size can be diagonalized using the desktop computers. To this end, the eigenvalues form the partition function Z(T,B) from which all thermodynamic properties, including the magnetization M(B,T0) and the magnetic susceptibility χ(T,B0), can be reconstructed. The matrix elements of the interaction operators in the coupled basis set of spin kets have been generated with the help of the irreducible tensor operators for a loop for S = Smin until S = Smax. In addition to the modelling of energy levels for different topologies, a fitting of magnetic data is exemplified by a number of examples like [Fe6] and [Mn3Cr4] systems
magnetic models of core - mantle boundary and their correlation. J. Geodyn., 45 , 146-153. Prutkin I., Casten U., 2009: Efficient gravity data inversion for 3D topography of a contact surface with application to the Hellenic subduction zone. Comput. & Geosci., 35 , 225-233. Prutkin I., Saleh A., 2009: Gravity and magneticdata inversion for 3D topography of the Moho discontinuity in the northern Red Sea area, Egypt. J. Geodyn., 47 , 237-245. Prutkin I., Vajda P., Tenzer R., Bielik M., 2011: 3D inversion of gravity data by separation of sources and the method of local
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Structural data for fifteen complexes of Fe(III) of a general formula [FeL5X], with pentadentate Schiff-base ligands L5 and unidentate coligands X−, were subjected to a statistical analysis. The multivariate methods such as Pearson correlation, cluster analysis and principal component analysis split the data into two clusters depending upon the low-spin and/or high-spin state of the complex at the temperature of the X-ray experiment. Some of these complexes exhibit a thermally induced spin crossover. The numerical analysis of the magnetic susceptibility and magnetization data for an enlarged set of Fe(III) spin crossover systems yields the enthalpy ΔH and entropy ΔS of the transition along with the transition temperature T1/2 and the solid state cooperativeness. The thermodynamic data show a mutual relationship manifesting itself by linear ΔS vs ΔH and T1/2vs ΔH correlations.
Thieno[3,2-c]pyridine (thpy) has been prepared in a free form and embodied into the [Ni(thpy)2(H2O)2(ac)2] complex as a ligand. The X-ray structure shows a molecular structure of the complex with Ni−O(ac) = 2.059, Ni−OH2 = 2.078, and Ni−N(thpy) = 2.124 Ǻ. Electronically the complex behaves like a compressed tetragonal bipyramid. The molecular units are linked into a complex system of hydrogen bonds. Two units show a π−π stacking of the aromatic rings (3.8 Ǻ). There are planes of tetragons formed of the nickel atom with the in-plane Ni...Ni separation of 7.74 Ǻ and the inter-plane Ni...Ni contacts at a = 9.65 Ǻ. The effective magnetic moment shows a gradual decrease on cooling from the room temperature and an abrupt drop below 20 K typical for the zero-field splitting of S = 1 systems. Above the room temperature the effective magnetic moment shows anomalies – a decrease and then an increase.
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This study presents the results of spectral analysis of magnetic data over Abeokuta area, Southwestern Nigeria, using fast Fourier transform (FFT) in Microsoft Excel. The study deals with the quantitative interpretation of airborne magnetic data (Sheet No. 260), which was conducted by the Nigerian Geological Survey Agency in 2009. In order to minimise aliasing error, the aeromagnetic data was gridded at spacing of 1 km. Spectral analysis technique was used to estimate the magnetic basement depth distributed at two levels. The result of the interpretation shows that the magnetic sources are mainly distributed at two levels. The shallow sources (minimum depth) range in depth from 0.103 to 0.278 km below ground level and are inferred to be due to intrusions within the region. The deeper sources (maximum depth) range in depth from 2.739 to 3.325 km below ground and are attributed to the underlying basement.