Description of a procedure for evaluating the induced field contributions from the bulk of the medium

Abstract

Line Shapes in Magnetic Resonance and the Average Static Magnetic Field at a Site: The Role of Discreteness and Continuum within the Material

When there are no time averaged fields (1) to be accounted for, then, within the materials it is the totality of the static fields at every one of the sites [distributed within the material] which manifests in a magnetic resonance spectrum. This essentially implies the spatial distribution of the static magnetic field which contributes to the line shape. Since the discreteness of the contribution from adjacent sites [to be resulting in a summed up total contribution], depends on the nature of material constituents within a small range of distance compared to the macroscopic extent, this contribution can be obtained as a calculated sum for a typical site within the material, [this can be taken to be the Contribution from within Lorentz Sphere (2)] and further considered to be the same for every one of the sites in a homogeneous medium. But the contribution from the remaining bulk of the material could be much more difficult to track and estimate at each site by the methods known till now (3) particularly when the material has such shapes to be causing inhomogeneous induced field distributions even in a homogeneous medium. The methods, used since early days to calculate demagnetization factors, make evident the kind of complications that arise in estimating induced fields within material specimen of arbitrary shapes. All these complications in estimating the induced field distributions and analyzing the observed patterns in spectra, require stringent experimental conditions for implementing certain techniques for their obvious utilities. The case of HR PMR studies in single crystals for determining molecular shielding tensors is such a complication which required invariably making single crystal spheres from single crystals of every organic molecular systems of interest (4). There have been efforts to device rapid computational methods to calculate such induced field distributions within materials (5). It has been possible, since recently, to evolve (6) a simple summation approach to calculate induced fields within a material which can reproduce the known, standard demagnetization factors with comparable accuracy. This method seems capable of simplifying the procedure to estimate the induced fields within the material [and, even outside a magnetized material (7)] and provides a diversion to circumvent the necessities to be considering an “average field” as being represented by the calculated values. This method has been described (8) earlier with an enumeration (9) of the associated advantages. The impact of these results can be effectively enunciated with specific reference to the analysis of line shapes of magnetic resonance spectra of materials.

(1) W.C.Dickinson, Phys. Rev., 81, 717 (1951). (2) S.Aravamudhan, Ind. J. Phys., 88, 985 (2005). (3) G. Mozurkewich, H.I.Ringermacher, and D.I.Bolef, Phys. Rev. B, 20, 33 (1979) (4) http://www.geocities.com/saravamudhan1944/eenc_ampere_lille.html (5) P. Vallabh Sharma, Pure Appl. Geophys., 64, 89 (1966) (6) http://nehuacin.tripod.com/pre_euromar_compilation/id7.html (7) http://saravamudhan.tripod.com/id6.html (8) Poster Sheet_7 to Sheet_10 at http://www.geocities.com/inboxnehu_sa/nmrs2005_icmrbs.html (9) Sheet_11 at http://www.geocities.com/inboxnehu_sa/nmrs2005_icmrbs.html