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The second slide frame below displays several images in succession in the same sequence. When all the images have been displayed, the entire set is repeatedly displayed in the same successive sequence and this is set for a non-stop rotation of the sequence.
Reliable HR PMR measurements made till now- in Solid-State on Single-crystal specimens for the determination of Shielding Tensor parameters which can be extracted from the experimentally measured rotation patterns, required that the specimen be of spherical shape.
If the experiments are carried out on Spherically shaped specimens, then the bulk susceptibility contributions to the Induced fields at the site of the proton become tractable which otherwise inextricably get compounded with the near-neighbourhood contributions and Intramolecular contributions to the shielding at a proton site. The near-neighbourhood contributions can be calculated-out using a magnetic dipole model and lattice summation procedure over a region of 100 A�a radius from the proton site. This contribution from the spherically shaped inner semimicro volume element when calculated out and separated, then from the region outside this sphere the bulk susceptibility contribution would be zero if the macroscopic specimen outer shape is also spherical. This inner volume element which is a hypothetically carved out sphere is referred to as the Lorentz��s sphere. If the material inside the sphere can be considered as non-contributing for any reason, in such contexts this can be effectively considered as a spherical cavity.
The lattice-sum type calculations for Induced field contributions from induced magnetic dipoles within the Lorentz�� sphere is found to result in constant value for the total contribution within a radius of about 100 A�a since contributions included from regions beyond this radius do not add to the total obtained for upto 100 A�a. This if we may call as a trend to converge to a limiting value for a spherical volume element, this has not been considered in any more greater detail than simply stating that at lattice point in Cubic Crystal Lattices, this sum converges to a total of zero value.
Obviously it is the HR PMR measurements which have clearly established the importance of this convergence within the semimicro spherical volume element, identifiable as the limiting intermolecular contributions to the Shielding tensor. Significantly this can be calculated, and corrected for, to obtain reliable intra-molecular shielding tensor values of protons in single crystals of organic molecules and similar systems.
If an ellipsoidal semimicro volume element is considered instead of the spherical element, what could be the type of convergence-trends? What consequence this would have in HR PMR measurements made and can this indicate the trends for arbitrary shapes and not only for the known regular shapes? How much can this lead to a relaxation in the stringency of the required Spherical Macroscopic specimen shape?
The relevance of the materials presented in the poster can be located in the Book by CHARLES KITTEL entitled:'Introduction to Solid State Physics' in the Chapter-12 on "Dielectric Properties" :'Local Electric Field at an Atom'. In the section on 'Field of Dipoles Inside Cavity' the book contains basic equation and the possile computer algorithm. The case of Spherical Symmetry or Cubic surrounding is explained as the simplest case.
H.Mueller, Phys.rev.47,947 (1935);50, 547 (1936); see also L.W.McKeehan, Phys.Rev.43, 1022,1025 (1933)
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