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NMRS2004 Presentation: Specimen Sample-Shape for Single-Crystal HR PMR Studies

This presentation explores the consequences of inhomogeneities in single-crystal HR PMR studies and the effects of bulk susceptibility on induced fields. It also discusses the calculation of demagnetization factors and the influence of specimen shape on the resulting magnetic field.

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NMRS2004 Presentation: Specimen Sample-Shape for Single-Crystal HR PMR Studies

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  1. Right-Click the mouse and exercise the FULL SCREEN viewing option even at the very beginning Instructions for Viewers The”NMRS2004” presentation is from slide # 2 onwards to # 15 Click At any instant during the viewing, the display can be advanced to the NEXT SLIDE/or the Next frame within the same slide by a simple mouse-click. After each mouse-click carefully watch for the change to the next display. Do not make too many Clicks at one instant. When you encounter a HYPERLINK (a green text box with faintblue font color with an underlining) a link-cursor(not an arrow) would appear on placing the cursor over the link and a mouse-click would display the linked slide. Then look for a return link to display again the source slide. CLICK HERE for MR Symposia 2003 PresentationNMRS2003 from slide#16-31 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  2. NMRS 2004 Presentation 20th February 2004 • Concerning the Specimen Sample-shape • for the Single-Crystal HR PMR Studies • S.Aravamudhan • Department of Chemistry • North Eastern Hill University • Shillong (Meghalaya) 793022 • INDIA NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  3. A recapitualisation from the NMRS2003 presentation Slides 1-6 Bulk Susceptibility Effects In HR PMR Once this question could be adequately answered, the next question was to find the consequences of inhomogeneities arising within the sample. Since even if the bulk susceptibility is the same through out the sample, the resulting induced field distributions will not be homogeneous within the samplefor shapes other than sphere and ellipsoid. The conclusions earlier had been to find answer to the following questions: 1. Should the Lorentz Sphere be Spherical? For this a study of the convergence characteristics for summing over the lattice (cubic and noncubic) for ellipsoidal inner volume element (counter Lorentz “sphere”) SOLIDS Liquids This was the material at 3rd Alpine Conference Poster Induced Fields at the Molecular Site Single Crystal Spherical Shape Single crystal arbitray shape Da= - 4/3 Db= 2/3 Sphere Lorentz cavity NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  4. A link to a Web Site containing Features of Demagnetzation Factors Calculations A detailed exposition of this tensor equation Appears in the next slide #3 i=ii /R3i [1-(3.RRi /R5i)] Demagnetization Effects Size of the Cavity and the choice of its location in the Specimen can be varied to sample the induced field over the extent of the specimen Magnetic Field -4/3 + 4/3 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  5. 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. For example, an insight into the induced fields and demagnetization could be gained as depicted in the next slide which otherwise would have been hard to realize and prove so effctively. Isotropic Susceptibility Tensor = NMRS 2004 : S.Aravamudhan: 20th feb 2004:

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  7. These results could be dated back to the year 2000-2001 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  8. for a cubic parameter value of 9:9:9 the inner volume element was given an ellipsoidal shape with varying ellipsoidal shape parameters CZ BY and AX. In most of the cases BY= AX . In the plot referred to here CZ = 1.0 and BY was varied from1.0 to 0.8. This corresponds to the prolate case for the shape of ellipsoid as in the figure . as the shape becomes more ellipsoidal there seems a lot of deviation occurs in the radius range from 18 to 234 units. Some Results of the 3rd Alpine POSTER at France in Sept.2003 are summarized in the next three Slides 7-9 OR NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  9. Compression of the scale on the Y-axis to 1 division= 1 x 10-4 units from the value of 2 x 10-9 units in the lower plot make the cubic case (spherical inner element) value to be all along the zero line !Monotonically increasing deviations from zero line (on the positive side) with increase in ellipticity!! The convergence value does not depend upon the ellipticity of the inner volume element. When the lattice is of cubic type A=B=C , then for all ellipticity including the limiting case of a sphere , the convergence of the lattice sum occurs to zero value. OR NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  10. Non-Cubic Cases: With a difference of 3 units in lattice parameters, for the two extreme cases of cubic lattices the summation leads to zero value all through for the various radius values. When the C= 10 and C=7 the convergence values range is far away from zero and the values are from -6 x 10-3 to +4 x 10-3 . Lower trace the same cubic/noncubic values with ellipsoidal shape 1:0.7 . Trends of variation in the x-axis regions of 100 units to 224 units indicate an increased deviation with ellipticity. As noted earlier for the cubic cases the convergence values are independent of the ellipticity even for non-cubic cases. Qualitatively, when the ellipticity ratio changes by 0.1, the convergence value changes at the rate of 4.5 x 10-4 per 0.1 value change in the ratio. OR After the CUBIC Case... NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  11. Results of Claculations made for this presentation at NMRS2004 CYLINDER TOP SHAPE (0,7) (0,0) Equatorial NMRS 2004 : S.Aravamudhan: 20th feb 2004:

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  15. END OF Presentation Questions & Comments To End this SHOW make a right-click and clickfurther on theEnd Showoption in the prop-up box. NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  16. Click HERE for visiting the NMRS2003 Web Site Right-Click the mouse and exercise the FULL SCREEN viewing option even at the very beginning Instructions for ViewersMR Symposia 2003 Presentation Click At any instant during the viewing, the display can be advanced to the NEXT SLIDE/or the Next frame within the same slide by a simple mouse-click. After each mouse-click carefully watch for the change to the next display. Do not make too many Clicks at one instant. When you encounter a HYPERLINK (a green text box with faintblue font color with an underlining) a link-cursor(not an arrow) would appear on placing the cursor over the link and a mouse-click would display the linked slide. Then look for a return link to display again the source slide. Test linkHERE and RETURN to NMRS2004 first slide NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  17. MR Symposia 2003 Presentation 5th February 2003 S.ARAVAMUDHAN Department of chemistry North Eastern Hill University , Shillong Can HR PMR Provide a Further Insight Concerning the Requirement of the Spherical Shape of Lorentz Cavity? Text of Abstract: CLICK here for hyperlink to slides 13 &14 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  18. Bulk Susceptibility Effects In HR PMR SOLIDS Liquids Induced Fields at the Molecular Site Single Crystal Spherical Shape Single crystal arbitray shape Da= - 4/3 Db= 2/3 Sphere Lorentz cavity NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  19. A link to a Web Site containing Features of Demagnetzation Factors Calculations Click Herefor the consideration of Variety of possibilities for the lattices and site symmetries i=ii /R3i [1-(3.RRi /R5i)] LINK to Graph Demagnetization Effects Size of the Cavity and the choice of its location in the Specimen can be varied to sample the induced field over the extent of the specimen Magnetic Field -4/3 + 4/3 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

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  23. It may be necessary to calculate the intermolecular contributions inside the Spherical samples with an elliptical shape of the lorentz sphere and find the conveniences of calculating. (Link for details / CLICK option) If it is possible to obtain some well defined shape(not necessarily Spherical) specimen of the single crystal samples on which HR PMR studies have well established results, then the experiments can be made with such shapes by orienting them in 3 independnt rotation axes and try to simulate that shape with the same ratios of the sides and faces but at the range of the Lorentz sphere (about 100 A° ) and calculate the intermolecular lorentz type contributions with the Demagnetizing field type calculation and retrieve the intra molecular contribution as it was done with the spherical samples and reproduce those values. CLICK HERE For a glimpse of Crystal systems as well The Simpler method (Details to be viewed optionally from other slides)of calculating Demagnetizing fields makes it possible to consider different combinations of Macroscopic sample Shape with appropriate hypothetical Cavity shapes to increase the utility of HR PMR measurements in Solids Various Specimen shapes with the variety of Cavity shapes NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  24. END OF Presentation Questions & Comments To End this SHOW make a right-click and clickfurther on theEnd Showoption in the prop-up box. NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  25. Return display to slide 4 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  26. Click to reach for the Web Site LINKS Return display to slide 7 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  27. Link to Internet Web Sites Link #1 for details of Calculations of Induced Fields and Demagnetization Factors Link #2 Link #3 Link #4 http://geocities.com/amudhan20012000/Confview.html NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  28. Abstract for the MR Symposia 2003, IISc., Bangalore, Feb. 2-6,2003 CAN HR-PMR PROVIDE A FURTHER INSIGHT CONCERNING THE SPHERICAL SHAPE OF LORENTZ CAVITY? S.Aravamudhan Department of Chemistry North Eastern Hill University Shillong 793022 Meghalaya India a The Lorentz Cavity, a hypothetical void carved out inside a material medium while considering the demagnetizing fields at a point (site) inside the material-specimen, is conveniently described to have a spherical shape since the demagnetization factor value for spherical external shape is obtained by the spherical symmetry requirement for such shapes in the homogeneously magnetized materials. For the case when the external shape is spherical and if, the carved out cavity also is spherically shaped , then for the inside void one can have the same numerical value, but negative in sign, as for the spherical outer shape which encompasses a spherically filled material specimen. This can result in the required zero Induced fields at the sites inside the material medium.Then for an ellipsoidal outer shape, it would be possible to get induced field values by using the demagnetization factor values for ellipsoidal outer shape and the already eastablished value for the hypothetically carved out spherical lorentz cavity. Click for continuation Abstract in the next slide Email:saravamudhan@nehu.ac.in Web Site:http://saravamudhan.tripod.com NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  29. In the previous reports (1) on ‘Calculation of Induced Fields by Simple Summing Procedures’ and thus, the calculation of Demagnetization Factors, it is mentioned that the requirement of zero induced field in case of the spherical outer shape for the specimen has been calculated by this procedure as well. It is being contended here that the Calculated Induced Field inside a Ellipsoidally shaped specimen can be equal to zero if the carved out cavity inside the specimen also has the same ellipsoidal shape since the demagnetization factor for the inner cavity shape and the outer Specimen shape should be equal in magnitude and opposite sign. HR PMR in solids, as it would be explained in the presentation, seem to provide a unique context to acquire a better insight into the necessity for a spherically shaped specimens for obtaining only the intramolecular symmetry determined shielding tensors. An inquiry as to ‘what the shape of the Lorentz cavity can also be’ becomes possible by being sensitive enough for the intermolecular contributions to Shielding tensors from the neighbouring molecules and groups around a given particular proton site which can be calculated by the recently reported simple procedure(for even the hitherto unreported shapes) and, by considering these aspects by the experimental determination of the proton shielding tensors in single crystals and supplemented with the necessary calculated (anisotropic) induced fields at the site which should take the considerations of shape dependences of such fields appropriately. Ref: (1) Web Site: http://saravamudhan.tripod.comand the HOTLINKS at andfrom http://geocities.com/amudhan_nehu/nehu_link.html CLICK HERE to return display to sd #1 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  30. Spin Precession Animation “DEMO” Precession Starts Automatically Return to(#1) first slide Nuclear Spin NMRS 2004 : S.Aravamudhan: 20th feb 2004:

  31. Crystal Systems CLICKto Return to slide#4 CLICKto Return to slide#8 NMRS 2004 : S.Aravamudhan: 20th feb 2004:

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