Equation For Magnetic Susceptibility Research Articles

Energy spectrum and magnetic susceptibility of the improved Pöschl-Teller potential

This study presents an analytical representation of the internal motion of a diatomic system using the improved Pöschl-Teller potential. The ro-vibrational energy spectrum is derived by solving the radial Schrödinger time independent wave equation (STIWE) under a 2D electromagnetic potential field. Additionally, an explicit equation for magnetic susceptibility is formulated from the internal partition function. The analytical models are used to investigate physical properties of CO (X1∑+), K2 (a3∑u+), BCl (X1∑+), and NaK (c3∑+) molecules. Average percentage absolute deviations (APAD) for the ro-vibrational energy spectrum are calculated as 0.1001 %, 0.5306 %, 1.2070 %, and 0.9779 %, respectively, compared to observed data. Numerical results are consistent with existing literature. Furthermore, the study reveals that the magnetic susceptibility of the system increases with temperature and decreases with an increase in magnetic field intensity, indicating its paramagnetic nature.

Physico-chemical Characterization of Some Metal Complexes Formed by Substituted Thiourea

In view of unique physico-chemical observations affecting the geometry and various properties of the substituted thiourea complexes in literature along with several biological activities, N-(hydroxy)-N,N-diphenyl thiourea was taken up for study. Complexes with geometries of high spin octahedral for iron(II), cobalt(II); tetrahedral & square planar for nickel(II); and dimeric square planar for copper chloride, copper perchlorate, copper acetate and distorted octahedral for copper nitrate were synthesized and characterized based on magnetic moments, visible spectra, diffuse reflectance spectra, electron spin resonance, infrared spectral studies, and thermal analysis.
 Interestingly, the nature of anion influenced the geometry, the complex from copper nitrate salt resulted in a distorted octahedral structure and complexes formed from copper chloride, copper perchlorate, copper acetate exhibited sub-normal magnetic moments, highly insoluble in the most common organic solvents and water. Based on these and spectral data, polymeric or square-planar dimeric geometry with sulfur bridging between copper atoms is proposed. It was confirmed by the application of Bleaney-Bower’s equation for magnetic susceptibility, applicable to dimeric copper complexes.
 The overall thermal behavior of the ligand and complexes were observed and the detailed calculations interestingly lead to confirmation of the above proposed geometrical structures.

Magnetic analysis of a tetranuclear octahedral high-spin cobalt(II) complex based on a newly derived magnetic susceptibility equation.

Here we report a versatile magnetic susceptibility equation for tetranuclear octahedral high-spin cobalt(ii) complexes and a magnetic analysis for a tetranuclear defect cubane cobalt(ii) complex based on this equation. We concluded that the interaction is essentially ferromagnetic despite the decrease in the χT product on cooling from 300 K, and the decrease is due to the spin-orbit coupling.

Spin Susceptibility in High - TC Superconductivity

Spin- current loop fluctuations is proposed as the mechanism of holes pairing in high temperature superconductors using the assumption of the coexistence of short-ranged antiferromagnetism with superconductivity and the Anderson’s superexchange theory. The spin-spin correlation function is calculated using the Kubo-Mori relaxation function and the magnetic susceptibility equation is derived in terms of force correlation. Also a Bardeen –Cooper-Schrieffer (BCS) type of equation is solved for the transition temperature (Tc). KEY WORDS: Superconductivity, cuprates, superexchange, susceptibility.

Crystal structure and magnetic properties of [{Cu(cyclam)}3{Fe(CN)6}2] · 6H2O, a cyano-bridged assembly with a rope-ladder chain structure

The synthesis, crystal structure and magnetic properties of the cyano-bridged complex [{Cu(cyclam)}3{Fe(CN)6}2]·6H2O are reported. Its structure is made up of centrosymmetric S-shaped pentanuclear [{Cu(cyclam}3{Fe(CN)6)}2] units, in which three [Cu(cyclam)]2+ units are alternatively bridged by two trans-CN groups of [Fe(CN)6]3− anions and water molecules. The pentanuclear Fe2Cu3 units are held together by two complementary and very weak Fe–CN⋯Cu1 bonds, forming a rope-ladder chain along the c axis. The compound exhibits a ferromagnetic interaction between the Cu(II) and Fe(III) ions as a consequence of the orthogonality of their magnetic orbitals of σ and π nature, respectively. The magnetic data were fitted to the calculated magnetic susceptibility equation for a pentanuclear model, leading to the following magnetic parameters: J1=9.0(3)cm−1, J2=3.8(4)cm−1, g=2.2, θ=−1.2K. These results show that the interactions through the long Cu–N axial bonds are not so weak as is usually assumed.

Magnetic susceptibility equation for dinuclear high-spin cobalt(II) complexes considering the exchange interaction between two axially distorted octahedral cobalt(II) ions

A new magnetic susceptibility equation has been obtained for dinuclear high-spin cobalt(II) complexes considering the exchange interaction between two axially distorted octahedral cobalt(II) ions. A computational program has been developed, and the temperature dependencies of the magnetic susceptibility have been demonstrated. A characteristic χ A versus T curve due to the zero-field splitting was shown when the distortion parameter v was positive.

Does Cr(CO)3 Complexation Reduce the Aromaticity of Benzene?

Ring currents in (C6H6)Cr(CO)3, 1, (cis-1,3-butadiene)Cr(CO)4 (4), (C6H6)2Cr (5), (C4H4)Fe(CO)3 (6), and (cis-1,3-butadiene)Fe(CO)3 (8) have been assessed by σ−π disected nucleus independent chemical shift (NICS) calculations. Shielding contributions from the C−C(π) orbitals to the NICS values reveal that there is no quenching of ring current in the benzene ring of 1 or in dibenzene chromium 5. The previously reported paratropic ring current for 1 is shown to be a consequence of latent aromaticity in 1,3-butadiene chromium tetracarbonyl 4 (one of the molecules used in the magnetic susceptibility equation). NICS values, a diatropic ring current, and a positive aromatic stabilization energy (ASE) all point to this aromaticity. NICS values for cyclobutadiene iron tricarbonyl, 6, show moderately sized diamagnetic shielding above the plane of the four-membered ring. In addition, 6 has a negative magnetic susceptibility exaltation (MSE) (diatropic ring current), quite opposite from the large paratropic current ...

Magnetic susceptibility of Pr 2- xCe xCuO 4 monocrystals and polycrystals

We measured the temperature dependence of the magnetic susceptibility of Pr 2- x Ce x CuO 4 monocrystals and polycrystals in the composition range x = 0–0.18. For all compositions, the susceptibility curves reveal strong crystal-field effects and are evaluated in terms of Van Vleck's equation for magnetic susceptibility. At temperatures above 100 K, the behavior could be described by a Curie-Weiss-like equation, the parameters of which allow us to characterize the crystal-field interactions. The concentration dependence of these parameters is much stronger in the monocrystals, with the apparent magnetic moment going through a sharp maximum near x = 0.1, the composition of the onset of superconductivity after a reducing anneal. The concentration dependence of the magnetic moment can be qualitatively interpreted as a contribution of charge-carrying spins in localized states, mainly through initiating Cu 2+-Pr 3+ interactions. With increasing Ce, these additional spins can not remain localized, thus the magnetic moment decreases, and a reducing anneal results in superconductivity.

Magnetic exchange between Ti3+ ions in titanium phosphate glass

Magnetic properties of reduced titanium phosphate glasses are reported. Magnetic susceptibility measurements from 1.0° to 400°K indicates behavior typical for amorphous antiferromagnetism. The more reduced glasses show an anomalous field dependence in the susceptibility suggestive of ferromagnetism. A microstructural model for the glasses is developed from physical, chemical and magnetic data. Using the model, a theoretical magnetic susceptibility equation is derived. The equation includes contributions to a total susceptibility from isolated Ti(3+) ions and ion pairs which participate in exchange. From electron spin resonance results, the theoretical susceptibility equation and the experimental Ti(3+) ion concentration in the glasses, a good fit to the experimental magnetic susceptibility data is obtained. Results from the theoretical equation indicates that ferromagnetic and antiferromagnetic interaction between exchange-coupled Ti(3+) ions may occur. At low temperatures a downward curve toward the origin of the inverse susceptibility is predicted which is consistent with the experimental data.