Average Magnetic Susceptibility Research Articles

A comparison of the angular-overlap and crystal-field models in interpreting the magnetic properties of hexakis(pyridine N-oxide)nickel(II) tetrafluoroborate

The angular-overlap model (a.o.m.) has been applied to the title complex where the local metal symmetry is S6. A.o.m. parameters have been obtained which fit the magnetic anisotropy and average magnetic susceptibility and the results are compared with those from a crystal-field model. General expressions are presented which relate the a.o.m. parameters to an ‘effective crystal field’ expressed in terms of coefficents of spherical harmonics. The NiO6 core has almost exact octahedral symmetry and in this case the a.o.m. increases the effective symmetry from S6 to D3. From the X-ray crystal structure, the Ni–O–N angle is 119° and, if one assumes that the oxygen atom is sp2 hybridized, it is possible to obtain values for all the three a.o.m. parameters. These are found to be eσ= 4 393, eπx= 830, and eπy= 1 660 cm–1.

Average magnetic susceptibility of rare earth sesquisulfides

Measurements of the average magnetic susceptibility of Nd 2S 3, Gd 2S 3 and Dy 2S 3 are reported over the temperature range 4–300 K. Paramagnetic Gd 2S 3 becomes ferromagnetic below about 30 K. Magnetic ordering in Nd 2S 3 appears to take place near 60 K. Dy 2S 3 appears to remain paramagnetic to the lowest temperatures investigated. Reasonable agreement has been obtained between a calculation using Van Vleck's theory and the data obtained from these Faraday experiments.

π-Bonding and tetragonality in dchloro- and dibromo-tetrapyridinecobalt(II) and diacetylacetonatodipyridinecobalt(II)

Average and principal magnetic susceptibilities of [Co(py)4Cl2], [Co(py)4Br2], and [Co(acetylacetone)2(py)2] in the temperature range 80–300 K are reported. Interpretation within the low-symmetry angular overlap model, described recently, are characterized by fits describing an approximately linear relationship between the π-bonding parameters. The indeterminacy of absolute eπ parameter values is a consequence of the high symmetry in these molecules, actual or effective. The relative contributions of π-bonding between different ligands and with respect to different directions all appear compatible with otherwise established chemical criteria.

On the calculation of average magnetic susceptibility for anistropic paramagnetic systems

It is shown that the expression x = 1 3 x |+ 2 3 x ⊥ gives fairly incorrect results when used in the saturation region for highly paramagnetic anistropic systems. Explicit expressions for the average magnetic susceptibility in the saturation region are suggested, which besides being extremely accurate, involve computation of the susceptibility only in 3 or 4 fixed directions.

Magnetic properties of polynuclear complexes. Part II. Superexchange in some binuclear cobalt(II) complexes

The average magnetic susceptibilities of six binuclear complexes of cobalt(II) between 80 and 400 K are reported. The compounds studied are Co2(dhph)2X4,nH2O (dhph = 1,4-dihydrazinophthalazine, X = Cl or Br), Co2(dppn)2X4,nH2O [dppn = 3,6-di-(2-pyridyl)pyridazine, X = NO3 or ClO4], Co2(dppn)(SO4)2,5H2O, and Co2(Me2dppn)(NO3)4,2CH3OH [Me2dppn = 3,6-di-(6-methyl-2-pyridyl)pyridazine]. These compounds exhibit weak antiferromagnetic exchange, and the values of the effective isotropic exchange parameter are estimated, making allowance for spin–orbit coupling and the effects of orbital reduction and axial distortion parameters. The values of are compared with those of the analogous nickel complexes reported earlier, and it is concluded that the t2g spin of Co2+ probably makes a ferromagnetic contribution. The exchange interaction is analysed in a one-electron orbital basis, leading to an anisotropic form for the exchange parameter. The average susceptibility data do not distinguish between the isotropic and anisotropic models, however, and the precise identity of the orbitals responsible for the ferromagnetic contribution remains uncertain.

Magnetic Alignment and Diamagnetic Anisotropy of Cholesteric Liquid Crystalline Poly-γ-Ethyl-L-Glutamate

Abstract The axes of the cholesteric structure of liquid crystalline PELG solution in ethyl acetate tend to be perpendicular to a direction of magnetic field, so that the solution becomes anisotropic in the presence of an applied field. The torque exerted on such anisotropic solutions was measured by appling a magnetic field in a different direction from the original field used for alignment of the cholesteric axes. The anisotropy of diamagnetic susceptibility of the cholesteric structure and that of PELG molecule are estimated from the strength of the torque. The latter is larger than 1.64 × 10-8 emu/g. The average magnetic susceptibilities of PBLG, PEDG and PMLG in the solid state were also measured. These values are in good agreement with those calculated using Pascal's additivity rule.

Molecular rotational Zeeman effect in HOF, a comparison with H2O, F2O, and other fluorine containing molecules; and dipole moments of HOF and DOF

The linear and quadratic rotational Zeeman effect in HOF has been observed with a high magnetic field. The magnetic susceptibility anisotropies are 2χaa −χbb −χcc = (−19.6±0.6) × 10−6 erg/G2·mole and 2χbb −χaa −χcc = 12.8±1.2 (the a axis is nearly along the OF bond and the c axis is perpendicular to the molecular plane); the molecular g values are gaa = 0.642±0.001, gbb = −0.119±0.001, and gcc = −0.061±0.001 and the molecular quadrupole moments are Qaa = (0.2±0.4)×10−26 esu · cm2, Qbb = 1.9±0.8, and Qcc = −2.1±1.1. These results are compared with H2O and F2O. The effect of in-plane fluorine substitution on the out-of-plane minus the average in-plane magnetic susceptibility anisotropy, Δχ, is discussed for a number of molecules and additive values are obtained for each successive fluorine substitution for planar molecules. These contributions to Δχ are first fluorine = +4.5±1.2, second F = +2.5±1.1, and third F = +0.6±0.8. These trends are explained in terms of changes in hybridization of the atom to which the fluorine is bonded. These values are used with results on mono- and difluorobenzene to estimate Δχ for benzene and trifluorobenzene. The electric dipole moments were obtained by the Stark effect and are HOF: μa = |0.37|±0.10 and μb = |2.20|±0.10. The total electric dipole moment of HOF is μ = |2.23|±0.10 D. The electronic structure of HOF is discussed in light of these results.

Studies on rare-earth compounds. Part I. The magnetic anisotropy of and crystal field in cerous magnesium nitrate, Ce2Mg3(NO3)12,24H2O

The average magnetic susceptibility and magnetic anisotropy of cerous magnesium nitrate over the temperature range 80–300 K are reported. These results, together with the previously reported g-values, have been interpreted in terms of a point-charge crystal-field model with the inclusion of an orbital reduction parameter k. Values of the radial parameters ρ2, ρ4 and ρ6 for both a 12- and 6-co-ordinate model have been determined. The value of k required by both models is in the range 0·93–0·96. The possible reasons for this parameter being less than unity are discussed.

EVALUATION OF TERRAIN EFFECTS IN GROUND MAGNETIC SURVEYS

Magnetic effects due to terrain can be as much as 1000 gammas in areas of even moderate relief where bedrock contains only a few percent magnetite. These effects may be evaluated simply by subdividing the topography into a series of sloping steps of infinite extent; computation of a theoretical terrain contribution then permits separation of the magnetic effects due to terrain from those due to structural or stratigraphic causes. In areas where terrain effects occur, we can estimate average magnetic susceptibility by comparing observed and computed magnetic profiles.

Paramagnetic Anisotropy, Low Temperature Magnetization, and Electronic Structure of Iron(II) Phthalocyanine

Magnetic anisotropy, magnetization, and average magnetic susceptibility have been measured for iron (II) phthalocyanine. The anisotropy was measured from the room temperature to about 90°K, the average susceptibility from 296 to 1.57°K, and the magnetization was measured at 1.57°K for field strengths between 1100 and 15 000 Oe. The results are interpreted in terms of a B2g3 ground state with a zero-field splitting parameter D = 64 cm−1, and g‖ = g⊥ = 2.74. Iron (II) phthalocyanine is an unusual example in which a large magnetic anisotropy arises entirely from the zero-field splitting. The danger inherent in the existing method of evaluation of ligand-field parameters from the average magnetic susceptibility data has been highlighted, and the advantages of magnetic anisotropy studies in deducing the ligand-field parameters and the electronic structures are discussed. A change of about 70° of the “setting angle” between 290 and 90°K is observed in this crystal when measured with b axis vertical. It is shown that this change is not indicative of a change in the ligand-field parameters with temperature, as generally assumed previously, but depends on the temperature dependence of the ratio of principal susceptibilities.

Paramagnetic Anisotropy, Electronic Structure, and Ferromagnetism in Spin S = 32 Manganese(II) Phthalocyanine

Measurements are reported of magnetization and the average magnetic susceptibility of manganese (II) phthalocyanine in the range 1.7–300°K, which confirm that the Mn(II) atom is in an S = 3 / 2 spin state, and that weak ferromagnetic interactions are present in the crystal, presumably between adjacent molecules. Single crystals of MnPc are moderately anisotropic; the principal magnetic moment μ‖ = 4.0 μB remains constant between 80–300°K while μ⊥ increases from 4.4 μB (300°K) to 5.0 μB (90°K). This magnetic anisotropy is consistent with a A2g4 ground state into which the excited term Eg4 is mixed by spin–orbit coupling. Possible pathways for superexchange are considered.

Molecular Zeeman Effect of Trimethylene Oxide and Trimethylene Sulfide

The rotational Zeeman effect has been observed in trimethylene oxide and trimethylene sulfide. The molecular g values, magnetic susceptibility anisotropies, and molecular quadrupole moments were obtained for both molecules. The a and b axes are in the molecular plane and the a axis bisects the COC or CSC angle. The magnetic susceptibility values are given below in units of 10−6 erg/G2·mole, and the molecular quadrupole moments are in units of 10−26 esu·cm2. The results for trimethylene oxide are: gaa = − 0.0073 ± 0.0005, gbb = − 0.0429 ± 0.0007, and gcc = − 0.0747 ± 0.0005; 2χaa − χbb − χcc = − 20.1 ± 0.5 and − χaa + 2χbb − χcc = − 13.5 ± 0.8; Qaa = − 4.9 ± 0.5, Qbb = + 2.3 ± 0.7, and Qcc = + 2.6 ± 1.0. A reliable value of the average magnetic susceptibility in ethylene oxide is also given. The results for trimethylene sulfide are: gaa = − 0.0148 ± 0.0010, gbb = − 0.0169 ± 0.0006, gcc = − 0.0554 ± 0.0005; 2χaa − χbb − χcc = − 20.9 ± 1.0 and − χaa + 2χbb − χcc = − 24.6 ± 1.0; Qaa = − 2.7 ± 1.0, Qbb = + 3.2 ± 1.0, and Qcc = − 0.5 ± 1.6. Due to the large vibration–rotation interaction in trimethylene sulfide, it was found that consistent g values could be obtained only when this interaction was included in the analysis. The results are compared with previously measured oxygen- and sulfur-containing molecules.

Molecular g Values, Magnetic Susceptibility Anisotropies, Diamagnetic and Paramagnetic Susceptibilities, Second Moment of the Charge Distribution, and Molecular Quadrupole Moments of H3CCN and H3CNC

The high-field, linear and quadratic Zeeman effect has been observed in methyl cyanide (H3CCN) and methyl isocyanide (H3CNC). Both spectra are complicated by the presence of the 14N nuclear quadrupole coupling. The H3CNC system leads to uncoupled spectra in high fields, and the H3CCN system does not exhibit fully uncoupled spectra even at fields of 25 000–30 000 G. In the numbers given below, c = b is perpendicular to the C3 or a axis. The perpendicular g values in H3CC14N and D3CC14N are g⊥ = − 0.0338 ± 0.0008 and g⊥ = − 0.0315 ± 0.0008, respectively. The sign of the electric dipole moment is +H3CCN–. The average magnetic susceptibility anisotropy from the above isotopic molecules is χ⊥ − χ‖ = (10.2 ± 1.0) × 10−6erg/G2·mole. Assuming g‖ = 0.310 from other similar systems gives the molecular quadrupole moment of Q‖ = −(1.8 ± 1.2) × 10−26esu·cm2. Using the known molecular structure and above g values allows a determination of the paramagnetic susceptibilities which are χ⊥p = (145.3 ± 1.0) × 10−6erg/G2·mole and χ‖p = (9.6 ± 0.5) × 10−6erg/G2·mole. Combining the above experimental magnetic susceptibility anisotropy with the known bulk magnetic susceptibility gives the total and diamagnetic terms, χ⊥ = −(24.1 ± 0.4), χ⊥d = −(169.4 ± 1.1), χ‖ = −(34.6 ± 0.5), and χ‖d = −(44.2 ± 1.0), all in units of 10−6erg/G2·mole. The individual elements in the tensor describing the second moment of the electronic charge distribution are 〈c2〉 = 5.2 ± 0.3 and 〈a2〉 = 34.7 ± 0.4 in units of 10−16 cm2. The Zeeman spectra of H3CC15N was also observed to confirm the above results with the 14N isotope. The molecular g value in H3CC15N is g⊥ = − 0.0317 ± 0.0003 and (χ⊥ − χ‖) = (10.5 ± 0.5) × 10−6erg/G2·mole. The perpendicular g value and magnetic susceptibility anisotropy of H3C14NC are g⊥ = − 0.0546 ± 0.0015 and χ⊥ − χ‖ = (13.5 ± 0.7) × 10−6erg/G2·mole. The sign of g⊥ was not determined experimentally; however, an analysis of the molecular quadrupole moment indicates the proper choice of sign. Assuming g‖ = 0.310 from similar systems gives the molecular quadrupole moment of Q‖ = −(2.7 ± 1.6) × 10−26esu·cm2. Using techniques as outlined above give the paramagnetic susceptibilities of χ⊥p = 137.8 ± 0.9 and χ‖p = 9.6 ± 0.6 in units of 10−6 erg/G2·mole. The total and diamagnetic susceptibilities are also estimated. The anisotropy in the second moment of the electronic charge distribution is 〈a2〉 − 〈c2〉 = (27.0 ± 0.5) × 10−16cm2.

Magnetic properties of trigonally distorted octahedral iron(II) complexes

The principal and average magnetic susceptibilities of FeSiF6,6H2O and FeGeF6,6H2O have been measured in the temperature range 300–80 °K. Theoretical magnetic moments have been calculated for a free-ion 5D basis, perturbed by a trigonal crystal-field and spin–orbit coupling. A crystal field (D3d) point-charge calculation was parameterized by the second- and fourth-order radial parameters Cp and Dq, and an angular parameter θ. For Cp > Dq the mixing of the two trigonal 5Eg terms by spin–orbit coupling and the crystal field altered the theoretical principal magnetic moments from those calculated for a 5T2g cubic-field basis set. The low experimental moments of the complexes [as compared to the near tetragonal (NH4)2Fe(SO4)2,6H2O] derives from the sensitivity of the ground-state splitting, Δ, to θ when Cp is large: and this appears to be characteristic of the trigonal nature of the distortion. Assuming λ=kλ0 and Dq= 1000 cm.–1 ambiguous fits with ranges of values of Cp, k, and θ have been found. It was not possible to resolve these ambiguities by use of optical, Mossbauer, or e.s.r. spectra.The magnetic properties of the 5D term perturbed by a tetragonal crystal-field and spin–orbit coupling, have been briefly investigated and susceptibilities of Fe(NH4)2(SO4)2,6H2O discussed.

Theory of a Two-Dimensional Ising Model with Random Impurities. III. Boundary Effects

We study the effects which immobile random impurities may have on magnetic properties and spin-spin correlation functions of a ferromagnetic system properties the Curie temperature. This is done within the context of the model introduced in the first paper of this series by computing the spin correlation functions on the boundary of a half-plane of random Ising spins, where the boundary row is allowed to intereact with a magnetic field $\mathfrak{H}$. We find that as $T\ensuremath{\rightarrow}{T}_{c}\ensuremath{-}$ the average boundary spontaneous magnetization vanishes as ${T}_{c}\ensuremath{-}T$. However, the average boundary magnetic susceptibility is shown not to exist for a finite range of temperature about ${T}_{c}$. Furthermore, at ${T}_{c}$ the average boundary magnetization behaves as $\ensuremath{-}{N}^{\ensuremath{-}1}$ sign $(\mathfrak{H}){[\mathrm{ln} N{\ensuremath{\beta}}_{c}|\mathfrak{H}|]}^{\ensuremath{-}1}$, where ${N}^{\ensuremath{-}1}$ is a measure of the width of the distribution of random bonds. Whenever $T\ensuremath{-}{T}_{c}=O({N}^{\ensuremath{-}2})$, the average spin-spin correlation function for two spins on the boundary is shown to approach its limit at infinite separation as some inverse power of the separation instead of as an exponential. At ${T}_{c}$ this average correlation function behaves asympotically as ${N}^{\ensuremath{-}2} {(\mathrm{ln}m{N}^{\ensuremath{-}2})}^{\ensuremath{-}1}$ when $m$ the separation between boundary spins, is large. Finally, we make the probabilistic nature of the boundary spontaneous magnetization more precise by computing its probability distribution function.

Studies of Chemical Shift Anisotropy in Liquid-Crystal Solvents. II. Theoretical Calculations for the Methyl Halides

Experimentally determined values of the proton chemical-shift anisotropy for the methyl halides have been used to test simple phenomenological theories which have been proposed to account for proton magnetic shielding. It is shown that the frequently used magnetic dipole model predicts that the long-range contribution to the proton shielding anisotropy should largely depend on the average neighbor magnetic susceptibility. Anisotropies calculated from this model are much larger than those measured. Expressions have also been derived relating the proton shielding anisotropy to the electric dipole moment and charge densities of polar substituents. Results of these calculations are not as conclusive as in the magnetic dipole case.

Molecular g Values, Magnetic Susceptibility Anisotropies, and Molecular Quadrupole Moments in Fluorobenzene

The first- and second-order molecular Zeeman effect has been observed in fluorobenzene to give the molecular g values of gaa = − (0.0670 ± 0.0008), gbb = − (0.0397 ± 0.0015), gcc = + (0.0266 ± 0.0017), and the magnetic susceptibility anisotropies of 2χaa − χbb − χcc = + (52.9 ± 0.8) × 10−6erg/G2·mole and 2χbb − χcc − χaa = + (63.6 ± 1.5) × 10−6erg/G2·mole. The a axis passes through the CF bond and the b axis is also in the molecular plane. Only the relative signs of the g values are obtained experimentally. However, by combining our magnetic susceptibility anisotropies with the average magnetic susceptibility we can show that the signs must be as assigned above. The diagonal elements in the total magnetic susceptibility tensor are χaa = − (40.6 ± 0.8) × 10−6, χbb = − (37.1 ± 0.8) × 10−6, and χcc = − (97.2 ± 2.0) × 10−6erg/G2·mole. The diamagnetic and paramagnetic susceptibilities are given as χaad = − (293.3 ± 1.7) × 10−6, χaap = (252.7 ± 0.7) ± 10−6, χbbd = − (509.7 ± 3.6) × 10−6, χbbp = (472.6 ± 2.6) × 10−6, χccd = − (732.4 ± 5.0) × 10−6, and χccp = (635.2 ± 4.0) × 10−6erg/G2·mole. The molecular quadrupole moments are Qaa = − (1.9 ± 0.8) × 10−26, Qbb = + (5.1 ± 1.5) × 10−26, and Qcc = − (3.2 ± 1.5) × 10−26esu·cm2. The values of the second moment of the electronic charge distribution are 〈a2〉 = (111.8 ± 0.7) × 10−16, 〈b2〉 = (60.8 ± 0.7) × 10−16, and 〈c2〉 = (8.4 ± 0.7) × 10−16cm2.

Molecular g Values, Magnetic Susceptibility Anisotropies, and Molecular Quadrupole Moments in Ethylene Oxide

The first- and second-order molecular Zeeman effect has been recorded in ethylene oxide to yield the molecular g values and magnetic susceptibility anisotropies in the molecule. The magnetic susceptibility anisotropies are 2χaa − χbb − χcc = + (18.06 ± 0.58) × 10−6 and 2χbb − χaa − χcc = + (0.78 ± 0.97) × 10−6erg/G2·mole. The b axis bisects the COC angle and the a axis is also in the COC plane. Only the relative signs of the g values are experimentally determined. Arguments are presented which favor one of the two sets of signs giving gaa = − (0.0946 ± 0.0003), gbb = + (0.0189 ± 0.0004), and gcc = +(0.0318 ± 0.0006. The molecular quadrupole moments, with this choice of signs, are Qaa = + (2.5 ± 0.4) × 10−26, Qbb = − (4.3 ± 0.5) × 10−26, and Qcc = + (1.8 ± 0.8) × 10−26esu·cm2. The diagonal elements in the paramagnetic susceptibility tensor are χaap = (60.6 ± 0.3) × 10−6, χbbp = (67.3 ± 0.5) × 10−6, and χccp = (88.3 ± 0.5) × 10−6erg/G2·mole. The known value of the average magnetic susceptibility is combined with our values for the paramagnetic susceptibilities and anisotropies of the total susceptibility to yield the diagonal elements in the total and diamagnetic susceptibility tensors. The total susceptibilities are χaa = − (24.7 ± 0.7) × 10−6, χbb = − (30.4 ± 0.7) × 10−6, and χcc = − (37.0 ± 0.8) × 10−6erg/G2·mole and the diamagnetic susceptibilities are χaad = − (85.4 ± 0.9) × 10−6, χbbd = − (97.7 ± 1.1) × 10−6, and χccd = − (125.4 ± 2.0) × 10−6erg/G2·mole. The second moment of the ground-state electronic charge distribution is 〈a2〉 = (16.3 ± 0.4) × 10−16, 〈b2〉 = (13.3 ± 0.4) × 10−16, and 〈c2〉 = (6.8 ± 0.4) × 10−16cm2.