2. 5/1/2015 5:47:58 AMA summary for the contents in this repository 1 In this slide:- An “abstract” to begin this review This work originated when the measurements of shielding tensor (by HR PMR methods) in Organic Molecular single crystals indicated that at a proton site of a given molecule can have significant induced field contributions from the adjascent molecules particularly when the neighboring molecules contain aromatic rings with high magnetic susceptibilities. The calculations of intermolecular contributions provoked to extend the lattice sum procedure for regions beyond the Inner Spherical Volume element (the conventionally known Lorentz’s sphere) and these considerations resulted in a summation procedure extendable over the entire macroscopic specimen, which is a much more convenient alternative to the usual integration procedures for calculating the demagnetization factors. From Molecule to Materials with HR PMR in Solids S.Aravamudhan, Department of Chemistry, North Eastern Hill University, http://www.nehu.ac.in/ PO NEHU Campus, Mawkynroh Umshing Shillong 793022 Meghalaya INDIA http://www.nehu.ac.in/ http://saravamudhan.tripod.com/ http://nehuacin.tripod.com/ http://aravamudhan-s.ucoz.com http://saravamudhan.tripod.com/http://nehuacin.tripod.com/http://aravamudhan-s.ucoz.com Total of 51 slides and Show time= 50mins

3. 5/1/2015 5:47:58 AMA summary for the contents in this repository 2 Bulk Susceptibility Effects In HR PMR Liquids D a = - 4  /3 D b = 2  /3 SOLIDS Single crystal arbitray shape Single Crystal Spherical Shape Induced Fields at the Molecular Site Lorentz Sphere cavity

4. 5/1/2015 5:47:58 AMA summary for the contents in this repository 3 1. Experimental determination of Shielding tensors by HR PMR techniques in single crystalline solid state, require Spherically Shaped Specimen. The bulk susceptibility contributions to induced fields is zero inside spherically shaped specimen. 2. The above criterion requires that a semi micro spherical volume element is carved out around the site within the specimen and around the specified site this carved out region is a cavity which is called the Lorentz Cavity. Provided the Lorentz cavity is spherical and the outer specimen shape is also spherical, then the criterion 1 is valid. 3. In actuality the carving out of a cavity is only hypothetical and the carved out portion contains the atoms/molecules at the lattice sites in this region as well. The distinction made by this hypothetical boundary is that all the materials outside the boundary is treated as a continuum. For matters of induced field contributions the materials inside the Lorentz sphere must be considered as making discrete contributions. Illustration in next slide depicts pictorially the above sequence http://nehuacin.tripod.com/pre_euromar_compilation/index.html

5. 5/1/2015 5:47:58 AMA summary for the contents in this repository 4 PROTON I II Molecular σ M + Region I σ I + Region II σ II Lorentz Sphere Contribution Bulk Susceptibility Effects SHIELDING σ exp H igh R esolution P roton M agnetic R esonance Experiment 1. Contributions to Induced Fields at a POINT within the Magnetized Material. σ exp = σ I + σ M +σ II Sphere σ II =0 Calculate σ I and subtract from σ exp - σ I = σ I ≡ σ inter Only isotropic bulk susceptibility is implied in this presentation

6. 5/1/2015 5:47:58 AMA summary for the contents in this repository 5 The Outer Continuum in the Magnetized Material Specified Proton Site Lorentz Sphere The Outer Continuum in the Magnetized Material Lorentz Sphere of Lorentz Cavity Outer surface D out Inner Cavity surface D in D out = - D in Hence D out + D in =0 The various demarcations in an Organic Molecular Single Crystalline Spherical specimen required to Calculate the Contributions to the induced Fields at the specified site. D out/in values stand for the corresponding Demagnetization Factors In the NEXT Slide : Calculation Using Magnetic Dipole Model & Equation: 1. Contributions to Induced Fields at a POINT within the Magnetized Material.

7. 5/1/2015 5:47:58 AMA summary for the contents in this repository 6 Equation 1 Equation 2 In equation 1 above E Loc on the Left Hand Side of the equation, obviously depends on the value of P for estimation. And, in equation 2, the value for to is to be estimated from the value of E Loc. If P is related to E mac (instead of to E Loc in equation-2) which is the applied field, then the paradoxical situation would not be posed. The paradox is that E Loc is a field which is a value including the effect of P, and hence to know E Loc for equation 2 the value of P must have been known already. http://nehuacin.tripod.com/id5.html EUROMAR2008

8. 5/1/2015 5:47:58 AMA summary for the contents in this repository 7 C.Kittel, book on Solid State Physics Pages 405-409 Lorentz Relation: E loc = E 0 +E 1 + E 2 +E 3 E 3 = intermolecular E 2 = N inner x P E 1 =N outer x P E 3 is the discrete sum at the center of the spherical cavity; does not depend upon macroscopic specimen shape. (Lorentz field) E 2 is usually for only a spherical Inner Cavity; with Demagnetization factor=0.33 ; E 2 = [N INNER or D INNER ] x P : E 1 is the contribution assuming the uniform bulk susceptibility and depend upon outer shape E 1 =[N OUTER or D OUTER ] x P : E 0 is the externally applied field EUROMAR2008 http://nehuacin.tripod.com/id5.html

9. 5/1/2015 5:47:58 AMA summary for the contents in this repository 8 Magnetic Field {χ M. (1-3.COS 2 θ)}/ (R M ) 3 6.0E-08 Benzene Molecule & Its magnetic moment Each moment contributes to induced field 2 A ˚ equal spacing

10. 5/1/2015 5:47:58 AMA summary for the contents in this repository 9 Magnetic Field {χ M. (1-3.COS 2 θ)}/ (R M ) 3 Benzene Molecule & Its magnetic moment Each moment contributes to induced field 2 A ˚ equal spacing Induced field varies as R -3 Number of molecules in successive shells increase as R 2 Product of above two vary as R -1 The above distance dependences can be depicted graphically Lattice summation Shell by Shell Dashed lines: convergence limit When the R becomes large, the R-1 term contribution becomes smaller and smaller to become insignificant Magnetic field direction -ve zone +ve (1-3.cos 2 θ) term causes +ve & -ve contributing zones See drawing below

11. 5/1/2015 5:47:58 AMA summary for the contents in this repository 10 These are Ellipsoids of Revolution and the three dimensional perspectives are imperative INDUCED FIELDS,DEMAGNETIZATION,SHIELDING Induced Field inside a hypothetical Lorentz’ cavity within a specimen = H`` Shielding Factor =  Demagnetization Factor = D a H`` = - . H 0 = - 4. . (D in - D out ) a. . H 0 out   = 4. . (D in - D out ) a.  When inner & outer shapes are spherical D in = D out Induced Field H`` = 0 polar axis ‘a’ equatorial axis ‘b’ m = a/b Induced Field / 4. . . H 0 = 0.333 - D ellipsoid polar axis ‘b’ equatorial axis ‘a’  = b/a Thus it can be seen that the the ‘D’-factor value depends only on that particular enclosing- surface shape ‘innner’ or ‘outer’ in References to ellipsoids are as per the Known conventions--------  >>>> 

12. 5/1/2015 5:47:58 AMA summary for the contents in this repository 11 Isotropic Susceptibility Tensor = Induced field Calculations using these equations and the magnetic dipole model have been simple enough when the summation procedures were applied as would be described in this presentation. 2. Calculation of induced field with the Magnetic Dipole Model using point dipole approximations. σ1σ1 +σ2+σ2 +σ 3.. σ inter =

13. 5/1/2015 5:47:58 AMA summary for the contents in this repository 12 How to ensure that all the dipoles have been considered whose contributions are signifiicant for the discrete summation ? That is, all the dipoles within the Lorentz sphere have been taken into consideration completely so that what is outside the sphere is only the continuum regime. The summed up contributions from within Lorentz sphere as a function of the radius of the sphere. The sum reaches a Limiting Value at around 50Aº. These are values reported in a M.Sc., Project (1990) submitted to N.E.H.University. T.C. stands for (shielding) Tensor Component Thus as more and more dipoles are considered for the discrete summation, The sum total value reaches a limit and converges. Beyond this, increasing the radius of the Lorentz sphere does not add to the sum significantly

14. 5/1/2015 5:47:58 AMA summary for the contents in this repository 13 Within Cubic Lattice; Spherical Lorentz region ::Lattice Constant Varied 10-9.5 Eventhough the Variation of Convergence value seems widely different as it appears on Y-axis, these are within ±1.5E-08 & hence practically no field at the Centre "http://aravamudhan-s.ucoz.com/amudhan_nehu/graphpresent.html "

15. 5/1/2015 5:47:58 AMA summary for the contents in this repository 14 YES a b Outer a/b=1 outer a/b=0.25 Demagf=0.33 Demagf=0.708 inner a/b=1 Demagf=-0.33 Demagf=-0.33 0.33-0.33=0 0.708-0.33=0.378 conventional combinations of shapes Fig.5[a] Conventional cases Current propositions of combinations Outer a/b=1 outer a/b=0.25 Demagf=0.33 Demagf=0.708 inner a/b=0.25 Demagf=-0.708 0.33-0.708=-0.378 0.708-0.708=0 Fig.5[b] Would it be possible to Calculate such trends for summing within Lorentz Ellipsoids ? 3 rd Alpine Conference on SSNMR (Chamonix) poster contents Sept 2003. Till now the convergence characteristics were reported for Lorentz Spheres, that is the inner semi micro volume element was always spherical, within which the discrete summations were calculated. Even if the outer macro shape of the specimen were non-spherical (ellipsoidal) it has been conventional only to consider inner Lorentz sphere while calculating shape dependent demagnetization factors.

16. 5/1/2015 5:47:58 AMA summary for the contents in this repository 15 The shape of the inner volume element was replaced with that of an Ellipsoid and a similar plot with radius was made as would be depicted Zero Field Convergence Within Cubic Lattice; Ellipsoidal Lorentz region ::Lattice Constant Varied 10-9.5 "http://aravamudhan-s.ucoz.com/amudhan_nehu/graphpresent.html "

17. 5/1/2015 5:47:58 AMA summary for the contents in this repository 16 RECAPITULATION on TOPICS in SOLID STATE Defining what is Conventionally known as “Lorentz Sphere” It becomes necessary to define an Inner Volume Element [I.V.E] in most of the contexts to distinguish the nearest neighbours (Discrete Region) of a specified site in solids, from the farther elements which can be clubbed in to be a continuum. The shape of the I.V.E. had always been preferentially (Lorentz) sphere. But, in the contexts to be addressed hence forth the I.V.E. need not be invariably a sphere. Even ellipsoidal I.V.E. or any general shape has to be considered and for the sake of continuity of terms used it may be referred to as Lorentz Ellipsoids / Lorentz Volume Elements. It has to be preferred to refer to hence forth as I.V.E. ( Volume element inside the solid material : small compared to macroscopic sizes and large enough compared to molecular sizes and intermolecular distances). Lorentz Spheres Spherical For outer shapes ellipsoidal cubical arbitrary Conventional Currently: The Discrete Region I.V.E. Shapes other than spherical I.V.E. need not be invariably a sphere general shape OR For any given shape

18. 5/1/2015 5:47:58 AMA summary for the contents in this repository 17  v = Volume Susceptibility V = Volume = (4/3)  r s 3 rsrs r 1 2  v = -2.855 x 10 -7 r s /r = 45.8602=‘C’  1 =  2 = 2.4 x 10 -11 for  =0 2. Calculation of induced field with the Magnetic Dipole Model using point dipole approximations

19. 5/1/2015 5:47:58 AMA summary for the contents in this repository 18 3 rd Alpine Conference On SSNMR : results from Poster "http://aravamudhan-s.ucoz.com/amudhan_nehu/3rd_Alpine_SSNMR_Aram.html"

20. 5/1/2015 5:47:58 AMA summary for the contents in this repository 19 σ exp – σ inter = σ intra Discrete Summation Converges in Lorentz Sphere to σ inter Bulk Susceptibility Contribution = 0 Bulk Susceptibility Contribution = 0 Similar to the spherical case. And, for the inner ellipsoid convergent σ inter is the same as above σ exp (ellipsoid) should be = σ exp (sphere) HR PMR Results independent of shape for the above two shapes !!

21. 5/1/2015 5:47:58 AMA summary for the contents in this repository 20 The questions which arise at this stage 1. How and Why the inner ellipsoidal element has the same convergent value as for a spherical inner element? 2. If the result is the same for a ellipsoidal sample and a spherical sample, can this lead to the further possibility for any other regular macroscopic shape, the HR PMR results can become shape independent ? This requires the considerations on: The Criteria for Uniform Magnetization depending on the shape regularities. If the resulting magnetization is Inhomogeneous, how to set a criterian for zero induced field at a point within on the basis of the Outer specimen shape and the comparative inner cavity shape?

22. 5/1/2015 5:47:58 AMA summary for the contents in this repository 21 The reason for considering the Spherical Specimen preferably or at the most the ellipsoidal shape in the case of magnetized sample is that only for these regular spheroids, the magnetization of (the induced fields inside) the specimen are uniform. This homogeneous magnetization of the material, when the sample has uniformly the same Susceptibility value, makes it possible to evaluate the Induced field at any point within the specimen which would be the same anywhere else within the specimen. For shapes other than the two mentioned, the resulting magnetization of the specimen would not be homogeneous even if the material has uniformly the same susceptibity through out the specimen. Calculating induced fields within the specimen requires evaluation of complicated integrals, even for the regular spheroid shapes (sphere and ellipsoid) of specimen

23. 5/1/2015 5:47:58 AMA summary for the contents in this repository 22 In fact, the effort towards this step wise inquiry began with the realization of the simple summation procedure for calculating demagnetization factor values. Thus if one has to proceed further to inquire into the field distributions inside regular shapes for which the magnetization is not homogeneous, then there must be simpler procedure for calculating induced fields within the specimen, at any given point within the specimen since the field varies from point to point, there would be no possibility to calculate at one representative point and use this value for all the points in the sample. A rapid and simple calculation procedure [slides # 22 to 28] could be evolved and as a testing ground, it was found to reproduce the demagnetization factor values with good accuracy which compared well with the tabulated values available in the literature. Results presented at the 2 nd Alpine Conference on SSNMR, Sept. 2001 http://saravamudhan.tripod.com/ http://saravamudhan.tripod.com/

24. 5/1/2015 5:47:58 AMA summary for the contents in this repository 23 Induced field Calculations using these equations and the magnetic dipole model have been simple enough when the summation procedures were applied as described in the previous presentations and expositions. Isotropic Susceptibility Tensor = 2. Calculation of induced field with the Magnetic Dipole Model using point dipole approximations.

25. 5/1/2015 5:47:58 AMA summary for the contents in this repository 24 For the Point Dipole Approximation to be valid practical criteria had been that the ratio r : r S = 10:1 R i : r i = 10 : 1 or even better and the ratio R i / r i = ‘C’ can be kept constant for all the ‘n’ spheres along the line (radial vector) ‘n’ th 1st  i will be the same for all ‘i’, i= 1,n and the value of ‘n’ can be obtained from the equation below With “C= R i / r i, i=1,n” 2. Calculation of induced field with the Magnetic Dipole Model using point dipole approximations 3. Summation procedure for Induced Field Contribution within the specimen from the bulk of the sample.

26. 5/1/2015 5:47:58 AMA summary for the contents in this repository 25 Description of a Procedure for Evaluating the Induced Field Contributions from the Bulk of the Medium Radia l Vector with polar coordinates: r, θ, φ. (Details to find in 4 th Alpine Conference on SSNMR presentation Sheets 6-8) http://nehuacin.tripod.com/id1.html http://nehuacin.tripod.com/id1.html

27. 5/1/2015 5:47:58 AMA summary for the contents in this repository 26 For a given  and , R n and R 1 are to be calculated and using the formula “n” along that vector can be calculated with a set constant “C” and the equation below indicates for a given  and  this ‘ n ,  ’ multiplied by the ‘  i  ’ {  being the same for all  }would give the total cotribution from that direction =  i    =  i = 1,n ,   i  = n ,  x  i 

28. 5/1/2015 5:47:58 AMA summary for the contents in this repository 27

29. 5/1/2015 5:47:58 AMA summary for the contents in this repository 28

30. 5/1/2015 5:47:58 AMA summary for the contents in this repository 29 "http://aravamudhan-s.ucoz.com/inboxnehu_sa/nmrs2005_icmrbs.html"

31. 5/1/2015 5:47:58 AMA summary for the contents in this repository 30 A spherical sample is to have a homogeneously zero induced field within the specimen. Because of the convenience with which the summation procedure can be applied to find the value of induced field not only at the center but also at any point within the specimen, it has been possible to calculate the trend for the variation of induced field from the centre to the near-surface points. There is parabolic trend observable and this seems to be the possible trend in most of the cases of inhomogeneous field distributions as well except for the values of the parabola describing this trend. It seems possible to derive parabolic parameter values depending on the shape factors in the case of inhomogeneous field distributions in the non-ellipsoidal shapes. This would greatly reduce the necessity to do the summing over all the θ and φ values. This possiblility has been illustrate (in anticipation of the verification of the trends) in the remaining presentation in particular the last four slides.

32. 5/1/2015 5:47:58 AMA summary for the contents in this repository 31 Using the Summation Procedure induced fields within specimen of TOP (Spindle) shape and Cylindrical shape could be calculated at various points and the trends of the inhomogeneous distribution of induced fields could be ascertained. Zero ind. Field Points Poster Contribution at the 17thEENC/32ndAmpere, Lille, France, Sept. 2004 Graphical plot of the Results of Such Calculation would be on display

33. 5/1/2015 5:47:58 AMA summary for the contents in this repository 32 The top or a Spindle Shaped object comes under the category of Shapes within which the Induced field distribution would be Inhomogeneous even if the Susceptibility is uniformly the same over the entire sample NMR Line for only Intra molecular Shielding Added intermolecular Contribultions causes a shift downfield or upfield homogeneous Inhomogeneous Magnetization can Cause Line shape alterations 4. The case of Shape dependence for homogeneously magnetized sample, and consideration of in-homogeneously magnetized material.

34. 5/1/2015 5:47:58 AMA summary for the contents in this repository 33 The induced field distribution in materials which inherently possess large internal magnetic fields, or in materials which get magnetized when placed in large external Magnetic Fields, is of importance to material scientists to adequately categorize the material for its possible uses. It addresses to the questions pertaining to the structure of the material in the given state of matter by inquiring into the details of the mechanisms by which the materials acquire the property of magnetism. To arrive at the required structural information ultimately, the beginning is made by studying the distribution of the magnetic field distributions within the material (essentially magnetization characteristics) so that the field distribution in the neighborhood of the magnetized (magnetic) material becomes tractable. The consequences external to the material due the internal magnetization is the prime concern in finding the utilization priorities for that material. In the materials known conventionally as the magnetic materials, the internal fields are of large magnitude. To know the magnetic field inducing mechanisms to a greater detail it may be advantageous to study the trends and patterns with a more sensitive situation of the smaller variations in the already small values of induced fields can be studied and the Nuclear Magnetic Resonance Technique turns out to be a technique, which seems suitable for such studies. When the magnetization is homogeneous through out the specimen, it is a simple matter to associate a demagnetization factor for that specimen with a given shape-determining factor. When the magnetized (magnetic) material is in-homogeneously magnetized, then a single demagnetization factor for the entire specimen would not be attributable but only point wise values. Then can an average demagnetization factor be of any avail and how can such average demagnetization factor be defined and calculated.It is a tedious task to evaluate the demagnetization factor for homogeneously magnetized, spherical (ellipsoidal) shapes. An alternative convenient mathematical procedure could be evolved which reproduces the already available tables of values with good accuracy. With this method the questions pertaining to induced field calculations and the inferences become more relevant because of the feasibility of approaches to find answers.

35. 5/1/2015 5:47:58 AMA summary for the contents in this repository 34 Calculation of the Induced Field Distribution in the region outside the magnetized spherical specimen Correlating ‘r’ and ‘r -3’

36. 5/1/2015 5:47:58 AMA summary for the contents in this repository 35

37. 5/1/2015 5:47:58 AMA summary for the contents in this repository 36 http://aravamudhan-s.ucoz.com/amudhan20012000/ismar_ca98.html

38. 5/1/2015 5:47:58 AM 37 A summary for the contents in this repository

39. 5/1/2015 5:47:58 AMA summary for the contents in this repository 38 Advantages of the summation method described in the previous sheets: (An alternative method for demagnetization factor calculation): Also at http://www.geocities.com/inboxnehu_sa/nmrs2005_icmrbs.html http://www.geocities.com/inboxnehu_sa/nmrs2005_icmrbs.html 1. First and Foremost, it was a very simple effort to reproduce the demagnetization factor values, which were obtained and tabulated in very early works on magnetic materials. Those Calculations which could yield such Tables of demagnetization factor values were rather complicated and required setting up elliptic integrals which had to be evaluated. 2. Secondly, the principle involved is simply the convenient point dipole approximation of the magnetic dipole. And, the method requires hypothetically dividing the sample to be consisting of closely spaced spheres and the radii of these magnetized spheres are made to hold a convenient fixed ratio with their respective distances from the specified site at which point the induced fields are calculated. This fixed ratio is chosen such that for all the spheres the point dipole approximation would be valid while calculating the magnetic dipole field distribution. 3. The demagnetization factors have been tabulated only for such shapes and shape factors for which the magnetization of the sample in the external magnetic field is uniform when the magnetic susceptibility of the material is the same homogeneously through out the sample. This restricts the tabulation to only to the shapes, which are ellipsoids of rotation. Where as, if the magnetization is not homogeneous through out the sample, then, there were no such methods possible for getting the induced field values at a point or the field distribution pattern over the entire specimen. The present method provides a greatly simplified approach to obtain such distributions. 4. It seems it is also a simple matter, because of the present method, to calculate the contributions at a given site only from a part of the sample and account for this portion as an independent part from the remaining part without having to physically cause any such demarcations. This also makes it possible to calculate the field contribution from one part of the sample, which is within itself a part with homogeneously, magnetized part and the remaining part being another homogeneously magnetized part with different magnetization values. Hence a single specimen which is inherently in two distinguishable part can each be considered independently and their independent contribution can be added. For the point 1 mentioned above view http://saravamudhan.tripod.com/ Calculation of Induced Fileds Outside the specimen http://nehuacin.tripod.com/id3.html

40. 5/1/2015 5:47:58 AMA summary for the contents in this repository 39 O O O O O O H H Proton Site with σ intra Organic Molecular single crystal : a specimen of arbitrary shape 4 point star indicates the molecule at a central location. Structure of a typical molecule on the right Induced field calculation by discrete summation σ inter Added σ inter Shifts the line position single sharp line Inner Volume Element I.V.E I.V.E. Cavity I.V.E Sphere σMσM σ IVE(S ) Discrete Continuum The task would be to calculate the induced field inside the cavity σ cavity In-homogeneity can cause line shape alterations: not simply shifts only σ intra / σ M σ IVE = σ inter + σ M σ cavit y = σ Bulk + σ M MRSFall2006

41. 5/1/2015 5:47:58 AMA summary for the contents in this repository 40 A cylinder shaped specimen (Blue line in the plot below) Zero ind. Field Points Not to be discussed in this presentation The points on the Blue line would be specified and at these Calculated field values an NMR line would be placed after adding the sum total of intra and intermolecular contributions to induced fields. Calculations at 9 points along the axis Distance along the axis MRSFall2006 http://nehuacin.tripod.com/id1.html http://nehuacin.tripod.com/id1.html

42. 5/1/2015 5:47:58 AMA summary for the contents in this repository 41 No intra molecular Value; inter- molecular value (in I.V.E) set=0 in subsequent plots; only cavity field is used to generate line shapes Cylinder By Calculation Trend line interpolation 7-2.87E-07-2.9E-07 6-1.9E-07 5-1.87E-07-1E-07 43.25E-08-2.8E-08 32.8E-08 26.45E-086.8E-08 19.2E-08 09.35E-081E-07 9.2E-08 -26.45E-086.8E-08 -32.8E-08 -43.25E-08-2.8E-08 -5-1.87E-07-1E-07 -6-1.9E-07 -7-2.87E-07-2.9E-07 Only inter molecular value 5.80E-07 can be set = 0 “Only” inter-molecular value 5.80E-07 was added and the line shape was plotted with those values : NEXT GRAPHICAL PLOT A Graph of the data in table Lines at interpolat ed values Overlapping last three lines Add to all Values down the column

43. 5/1/2015 5:47:58 AMA summary for the contents in this repository 42 Same graph as displayed in previous slide Gradual increase of component lines broadens the lines and can cause the change in the appearance of overall shape. Illustration with 4 different width values Same width as above Width twice that of red Width twice that of blue 10 times that of red Width 2.5 times that of green

44. 5/1/2015 5:47:58 AMA summary for the contents in this repository 43 Line at σ IVE

45. 5/1/2015 5:47:58 AMA summary for the contents in this repository 44 1.Reason for the conevergence value of the Lorentz sphere and ellipsoids being the same. 2.Calculation of induced fields within magnetized specimen of regular shapes. (includes other-than sphere and ellipsoid cases as well) 3. Induced field calculations indicate that the point within the specimen should be specified with relative coordinate values. The independent of the actual macroscopic measurements, the specified point has the same induced field value provided for that shape the point is located relative to the standardized dimension of the specimen. Which means it is only the ratios are important and not the actual magnitudes of distances. These two points would have the same induced field values (both midpoints) These two points would have the same induced field values (both at ¼) Lorentz cavity The two coinciding points of macroscopic specimen and the cavity are in the respective same relative coordinates. Hence the net induced field at this point can be zero Further illustrations in next slide Added Results to be discussed at 4 th Alpine Conference http://nehuacin.tripod.com/id3.html

46. 5/1/2015 5:47:58 AMA summary for the contents in this repository 45 Symbols for Located points Inside the cavity Points in the macroscopic specimen Relative coordinate of the cavity point and the Bulk specimen point are the same. Hence net induced field can be zero In the cavity the cavity point is relatively at the midpoint of cavity. The point in bulk specimen is relatively at the relative ¼ length. Hence the induced field contributions cannot be equal and of opposite sign Applying the criterion of equal magnitude demagnetization factor and opposite sign ⅛ specimen length ⅛ cavity length This type of situation as depicted in these figures for the location of site within the cavity at an off-symmetry position, raises certain questions for the discrete summation and the sum values. This is considered in the next slide

47. 5/1/2015 5:47:58 AMA summary for the contents in this repository 46 In all the above inner cavities, the field was calculated at a point which is centrally placed in the inner cavity. Hence the discrete summation could be carried out about this point of symmetry. For a spherical and ellipsoidal inner cavity, the induced field calculations were carried out at a point which is a center of the cavity. If the point is not the point of symmetry, then around this off-symmetry position the discrete summation has to be calculated. The consequence of such discrete summation may not be the same as what was reported in 3 rd Alpine conference for ellipsoidal cavities, but centrally placed points. This is the aspect which will have to be investigated from this juncture onwards after the presentation at the 4 th Alpine Conference. The case of anisotropic bulk susceptibility can be figured out without doing much calculations further afterwards.

48. 5/1/2015 5:47:58 AMA summary for the contents in this repository 47 This stage of the Report was possible because of the beginning made as early as 1979-80 to be concerned with the Induced field distributions inside the specimen in connection with the HR PMR in Single Crystal solids. A careful consideration of the demagnetization Calculations the results of which had been reported in the form of documented tables revealed that a pattern can be setup with a simplified form but the question was how to translate this criteria in the form of a concrete mathematical equations. An intense effort (which could have elicited a comment as a futile effort from active researchers in the related area) did result in a form for the equation, the derivation of which turned out to be requiring only four to five elementary steps. Equipped with this formulation and equation in hand it did not take any more than half an hour to one hour to arrive at the Zero Induced field value at the centre of the Lorentz Cavity in a spherically shaped magnetized specimen. Then it was a question of arriving at the reported numerical values for the ellipsoids of different shape-factor ratios the 'm' and the 'µ' (reciprocal of 'm'). It took about one month to incorporate the ellipsoidal equation criteria and get a few reported demagnetization factors. All this could be achieved by simple hand calculations - not even a pocket calculator to use. http://nehuacin.tripod.com/pre_euromar_compilation/id5.html http://nehuacin.tripod.com/pre_euromar_compilation/id5.html This was the result in hand as early as 1984. Afterwards,since there were not many who would have wanted to know about these ( because the demagnetization factors were already available in Tables since long before), the results were stored as they were in a scribbling pad filled with numbers due to the hand calculations. By that time all the references which have been gathered (these are all listed out in the website http://saravamudhan.tripod.com, in the page for the '2nd Alpine conference on SSNMR'; CLICK on this pane to display the webpage)indicated that a reference(# 17) in the Physical review publication from authors from Washington, St Louis Missourie,USA had some what similar effort reported.

49. 5/1/2015 5:47:58 AMA summary for the contents in this repository 48 What was referred to before is a publication by an Indian author who worked and submitted a dissertation at E.T.H., Zurich, Switzerland. This work had been also published in Pure and Applied Geophysics. I had tried to get the referred issue from the Geophysical Research Institute at Hyderabad and I mentioned about this to Dr.A.C.Kunwar at IICT, Hyderabad, as early as 1995-96. By that time I had been at the North Eastern Hill University, shillong as Lecturer in Chemistry and as excercises to M.Sc., students I had suggested these simple equations and susceptibility induced fields in magnetized specimen to work for their 6-months project report successively for about 4-5 years. This resulted in a computer program to calculate these induced field contributions and 6 project reports consisted of consecutive materials. There was not much interest from any to these equations and results, presumably, even at that time in my opinion which could be because all the demagnetization factors are well reported and, whether now it is simplified calculation or not,it is merely a question of simplification but the possible values were already well documented.After about two years in 1998 I received by POST the reprint of the publication by P.V.Sharma (in Geophysical Research journal) from Dr.A.C. Kunwar. This paper contained a rapid computation method for such calculations and my considerations were even simpler. And hence from the NMRS symposium at Dehradun in 1999, I have been presenting my consideration by way of Poster/oral presentations and the support I had for presenting them has resulted in this kind of a activity requiring them to be reported in International Conferences. During the period till now these efforts had encouragements from the NMRS, ISMAR and the Congress Ampere and occasional finacial support from these organizers and the Funding agencies CSIR, INSA have gone a long way in pusrsuing the efforts with the possible provisions at the North Eastern Hills University, which is gratefully acknowledged

50. 5/1/2015 5:47:58 AMA summary for the contents in this repository 49 IBS Meeting : Symposium at BHU, 2010 Prof. S. Aravamudhan, receiving a memento after Chairing a technical session From Prof. P.C.Mishra Convener, IBS 2010

51. 5/1/2015 5:47:58 AMA summary for the contents in this repository 50 S.Aravamudhan and K.Akasaka IBS Meeting 2002, CBMR, SGPGIMS, Lucknow International Biophysics Conference IUPAB. At Buenos Aires, Argentina April- May 2002 NR Krishana Amitabha Chattopadhyaya A generous grant from the WELCOME TRUST UK enabled the participation of Dr.S.Aravamudhan in the International Biophysics Conference at Buenos Aires, Argentina which is gratefully acknowledged.

52. 5/1/2015 5:47:58 AMA summary for the contents in this repository 51 End of Presentation Questions & Comments If there is an Internet Browser installed with an Internet Connection on this computer, then Click Below on the URL: http://aravamudhan-s.ucoz.com/amudhan_nehu/graphpresent.html http://www.ugc-inno-nehu.com/isc2009nehu.html http://nehuacin.tripod.com/ Events during January-March 2011 have been recorded at URL http://www.ugc-inno-nehu.com/crsi_13nsc_nmrs2011.html