INDUCED FIELDS DUE TO A MAGNETIZED SPECIMEN
S.Aravamudhan
contents of SHEET#1
The contents of this paper are based on the sequence of contributions
at the annual National Symposia in India during the previous 3-4 years including an International Biophysics Congress held
in India in Sept.1999. It is intended to convey here a possible comparitive advantages & limitations, for various experimental
NMR requirements, of the present method and the already known methods for the induced field calculations and hence the demagnetizing
factors also.This contribution would put forward the results in a comprehensive perspective in which it has not been reported
hither to.
This present method resulted when the calculartion of intermolecular contributionmto the shielding tensor values
by a lattice-summing method effectively(1) accounted for the deviations of the experimentally measured tensor parameters and
hence an intensive effort was made to arrive at a possibility for extending it to a summing over the entire extent of the
macroscopic specimen.
(a) This method can be explained as the very simple magnetic-dipole equations and summing over
the large number of contributions where as earlier methodsa required in some form or the other classical electrodynamic considerations
and resulting complications of using difficult integrals to arrive at equations.
(b) Since it is only a summing over
semi-micro volume elements along a radial vector of polar coordinates r,q & j and making a second summation over the different
lengths and polar angles to possibly cover the entire material of the magnetized specimen, this does not require the classical
equations from the electrodynamic considerations and the associated difficult integrals to evaluate.
(c) Because of
this simplicity it becomes easily programmable method for computation and even arbitrary shapes can be included without complications
arising in the already known methods.
(d) In the following presentation of results the demagnetization factors calculated
by the present method are compared with the already reported table of values from the earlier methods to illustrate
the efficacy & reliability of the method used as per the descriptions given here
Reference(1) Multiple-pulse line-narrowing experiments for
High Resolution Proton Magnetic Resonance Spectra and the measurements of proton shielding tensor parameters in single crystals
of PMDA,calcium-,barium-,and lead-formates by the research group of Prof.U.Haeberlen at the Max-planck institute,Abteilung
Molekulare Physik,Heidelberg.
INSTRUCTIONS TO VIEWERS:
A
cursory reading of the sheet 20 even before proceeding from sheet 3 onwards could be helpful.
For necessary
compactness in presenting the contents some of the sheets have the materials reduced to such smaller sizes as is not usual
for reading. These materials in their "un-reduced" sizes are available with the presenter.
contents of SHEET#2
Sheet 1. Title
page with an abstract
Sheet 2. Salient
features of the presentation
Sheet 3. An excerpt from
a project report -An introductory page
Sheet 4. Simplified
equation for the field induced by a dipole originating from a spherical volume element with uniform magnetic susceptibility,
its radius in relation to the distance to the point where the indiced field is relevant. This radius-distance consideration
for packing the spheres along a vector length.And the equation for the number of such dipoles along the close-packing direction.
Sheet 5. Extension of
the above considerations to two and three dimensional expanses to cover the entire material of a macroscopic specimen.
Sheet 6. Equation for
the Shielding constant(induced field analog) s for the contribution from along a vector,two dimensional packing of the vectors
and similar three dimensional depiction.
Sheet 7. Tabulation of
calculated values.
Sheet 8. Results for
the various locations of the center of the inner cavity.
Sheet 9. Results for
the case of ellipsoidal shapes.
Sheet 10. A presentation of
the case of possible application to NMR studies of membrane transport.
Sheet 11. Polar coordinate
definitions and trends of the various factors appearing in the equations.
Sheet 12. ELLIPSOIDS- a pocket
calculator calculation and tabulation of computer calculated values for extended sets of cavity center locationssimilar to
sheet 8.
Sheet 13. Calculation of induced
fields by the same method in regions inside and outside the magnetized specimen.
Sheet 14. Methods based on
bulk susceptibility differences.
Sheet 15. Various sample shapes
in membrane transport context and other NMR situations.
Sheet 16. A typical feasibility
demonstration of simplicity of this procedure to such contexts as in sheet 15.
Sheet 17. Computer program
results of ellipsoids of different a/b ratios for demagnetization factors.
Sheet 18. Similarity of figures
& drawings/plots obtained by this induced field calculations and the reproduced images of objects by NMR imaging.
Sheet 19. Various shapes encountered
in NMR where this procedure of induced field calculation seems to be conveniently applicable.
Sheet 20. Summary and references
contents of SHEET#20
SUMMARY:
The considerations of
possibilities of calculating demagnetization factors(1) by the methods similar to lattice summing provide a possibility to
calculate these factors using even a simple pocket calculator(12) for the standard shapes of homogeneously magnetized specimens.This
enables the calculation of induced magnetic fields inside the specimen at various points conveniently and also how these contributions
at a given point differ depending on the polar and azimuthal angles(5,11) of the contributing elements from within the specimen.There
are experimental situations(10,14,19) where inhomogeneities present in the sample are advantageously used(13,16) for assigning
the NMR signal characteristics from different regions of the sample. It is also being pointed out that these induced field
distributions expressed as field inhomogeneities(13,18) within the sample can be calculated more discretely by the above methods
and can be adding to the methods available for optimizing contrasts in images if necessary with added susceptibility modifying
reagents and these depend on the shapes of the samples and that of the regions considered within the sample. The demagnetization
factors calculated for a few standard shapes are reported(17) for comparison with the standard tabulated values. An effort
is made to depict the pointwise induced field values from the perspectives of image-representations to make it appreciable
that such pictures can be visually indicative18 of the actual modifications required for a given situation to reduce the necessity
for the enormous numerical tabulations(7,17,13) which would render even this simplified calculations relatively tedious.
NUMBERS
OCCURING AS (SUPERSCRIPTS) REFER TO THE SHEET # ON THE POSTER
REFERENCES:
Readings for a better perspective of the
microscopic and macroscopic aspects
1. Local-field Effects
and Effective-medium theory: A Microscopic perspective D.E.Aspnes, American Journal of Physics, 50(8),1982, pages 704 to 708
2. Local
Fields in Solids:microscopic aspects of dielectrics
S.E.Schnatterly and C.Tario,Reviews of Modern Physics, vol 64,1992, pages 619-622.
3. Lattice-sum Methods
for Calculating Electrostatic
Interactions in Molecular Simulations, Brock A.Luty, Ilaro
G.Tironi and Wilfred F.van Gunsteren
Demagnetization Factor Calculations,Induced
Field Effects
1. Effect Of Demagnetization
On Magnetic Resonance Line Shapes In Bulk Samples: Apploication To Tungston , George Mozurkewich, H.I.Ringermacher
and D.I.Bolef, Physical Review B, Vol 20(1), 1979 Pages 33-38.
2. Rapid Computation Of Magnetic Anomalies And Demagnetization
Effects Caused By Bodies Of Arbitrary Shapes, P.Vallabh Sharma, J. Geophysical Research, Vol.64 1966/11, Pages 89-107.
