1. PRESENTATION FILE: CMDAYS2011 Gauhati University: August 24-26th 2011
CONDENSED MATTER DAYS 2011
PROGRAMME
16 Aug 2011
S.Aravamudhan CMDAYS2011

2. NORTH ESATERN HILL UNIVERSITY, SHILLONG
"When a Magnetic Moment is Subdivided, do the Fragmented Moments Interact with Each Other?"
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S.ARAVAMUDHAN
NORTH ESATERN HILL UNIVERSITY, SHILLONG
Chemistry Department
CMDAYS 2011
Gauhati University
Aug 24-26, 2011
Additional materials for this presentation:
16 Aug 2011
S.Aravamudhan CMDAYS2011

3. Additional materials for this presentation:
E3 is the discrete sum at the center of the spherical cavity; does not depend upon macroscopic specimen shape. (Lorentz field) E2 is usually for only a spherical Inner Cavity; with Demagnetization factor=0.33 ; E2 = [NINNER or DINNER] P E1 is the contribution assuming the uniform bulk susceptibility and depend upon outer shape E1 =[NOUTER or DOUTER]P E0 is the externally applied field
Discrete summation
Additional materials for this presentation:
E3= intermolecular
E2 = Ninner x P
E1=Nouter x P
C.Kittel,
book on
Solid State Physics
Pages
Lorentz Relation: Eloc = E0 +E1 + E2 +E3
17 Aug 2011
S.Aravamudhan CMDAYS2011

4. Evaluation requires solving integrals set up for appropriate shapes
INDUCED FIELDS,DEMAGNETIZATION,SHIELDING
Induced Field inside a hypothetical Lorentz’ cavity within a specimen = H`` 
Shielding Factor =  Demagnetization Factor = Da 
H`` = -  . H0 =  . (Din- Dout)a .  . H0
out
These are Ellipsoids of Revolution and the three dimensional perspectives are imperative 
0.333 in
 = 4 .  . (Din- Dout)a . 
When inner & outer shapes are spherical
N +
S -
Field: Lines of Force
Moment direction
polar axis ‘a’
Din = Dout
m = a/b
Induced Field H`` = 0
equatorial axis ‘b’
Induced Field / 4 .  .  . H0 = Dellipsoid
Thus it can be seen that the the ‘D’-factor value depends only on that particular enclosing-surface shape ‘innner’ or ‘outer’
polar axis ‘b’
 = b/a
Discrete summation
References to ellipsoids are as per the Known conventions >>>>
equatorial axis ‘a’
17 Aug 2011
S.Aravamudhan CMDAYS2011

5. H`` = -  . H0 = - 4 .  . (Din- Dout)a .  . H0
 is the susceptibility which is inherent characteristic of the electronic structure of molecules/materials. Magnetization Mp arising due to the interaction of the material at the Spot with the externally applied magnetic field of strength H0
2-dimensional lattice
When the induced field, due to such native moments, at a distant point is to be calculated, would it be of any consequence to know whether the native moments interact with each other? Would such an interaction if it is present alter the generic field (local filed) value at a site within the specimen?
Each point is
occupied by a molecule with susceptibility p
Magnetization Mp = p H0
Molecular to molar or volume susceptibility  requires appropriate summation over the number of molecules.
Till now no interaction or induced fields due to the Mp has been considered (the native property).
Induced Field inside a hypothetical Lorentz’ cavity within a specimen = H`` 
Shielding Factor =  Demagnetization Factor = Da 
H`` = -  . H0 =  . (Din- Dout)a .  . H0
The native corrective filed due to the molecular susceptibility arises due to Mp and should be equal to Mp · H0 = H”p
(Only) shape dependent value of the Demagnetization factor D arises due to the induced field from all the other molecules.
The bulk property H” is then given by H” = 4π D (corrective field derived from native values)
17 Aug 2011
S.Aravamudhan CMDAYS2011

6. Do these moments interact with each other?
Indfld vs distance
χ|| =-90 x 10-6 [cgs units (molar)]
Per molecule would be
The above value divided by Avagadro number: x 1023
= x = x 10-30
At a distance of 2 Angstrom from this moment (per unit field= χ|| x 1G)
The secondary field value would be x / (2 x 10-8 )3
= x 10-5
For χ|| = -100 x ; Secondary field would be x 10-5
6.0E-08
Indfld vs distance
2 A˚ equal spacing
Indfld vs distance
Benzene
Molecule &
Its magnetic
moment
{χM . (1-3.COS2θ)}/(RM)3
Indfld vs distance
17 Aug 2011
S.Aravamudhan CMDAYS2011

7. It is precisely at this point of knowing the microscopic matter as it prevails, the Proton Magnetic Resonance seems to be answering to the details on the paradoxical situation: THE MICRO-MACRO PARADOX !
The shielding parameter measured by the proton magnetic resonance spectroscopy is a measure of the (native) local field at the nuclear site within a molecule. This shielding has contributions from the neighboring moments present, and in favorable cases these can become significant contributions to alter the pattern of the spectra obtained. How are these significant changes to the spectral patterns also become significant in the net macroscopic field distributions within the magnetized material: it is a matter of numerical values of induced fields at the neighboring moments compared to the native moment induced by the interaction with the externally applied (possibly) strong magnetic fields.
18 Aug 2011
S.Aravamudhan CMDAYS2011

8. H0
These neighbor moment contributions are of the order of ppm of the strength the external fields as much as the native moments are.
The (χv susceptibility values are ppm cgs units) molecular susceptibility values (χmolecular = χv / no. molecular units within volume ‘V’ ) are of order of CGS units to be multiplied by the external filed strength to arrive at the natively induced moments. Thus the native moments μ are themselves of the order of CGS units. If these moments are to induce secondary fields at a neighboring point, (~ μ /R3) which is of the order of ppm, this induced secondary field would add to the native moment only insignificantly in comparison. Thus the interaction of the native moments would not be much consequence for the induced filed values at any location from all the other locations. μ R
Same
10-30
10-42
These estimates have been possible since the validity of point dipole approximation has been assumed
10-37
10-36
THE MICRO-MACRO PARADOX IN INDUCED FIELD CALCULATIONS AND THE ROLE OF HR SOLID STATE NMR
18 Aug 2011
S.Aravamudhan CMDAYS2011

9. Vector map: Slide#4 of 0_2_12Aug2011.ppt
Line defined by Polar angle θ / direction of radial vector
When the magnetic moment is divided then, the divided elements are not molecular moments as considered in the previous slide. The magnetic moments of the divided elemental volumes are semi-micro magnitudes, each element comprising of several molecules. The magnitude of the moments is also larger and hence the induced fields at the neighboring element may also be more, depending on the element to element distance being larger in comparison to intermolecular distances. When the induced field is calculated at a farther point than the neighboring element, how much would be the inter-element contributions to alter the originally divided moment-magnitudes?
It is to be pointed out at this juncture, the total induced field at a point values within the spheroidal specimen results only in a shape (and not the size) dependent pre-multiplying factor to the value of the induced moment (generated by the interaction with external field). It would be true that the individual elemental moments interact among each other but what matters is the effective total interaction. It is only in a spectroscopic analysis as for the Proton Magnetic Resonance Spectroscopy, it is possible to demarcate the intra molecular versus the intermolecular around a particular site and distinguish the strengths and significance of the long-range & short-range interaction scales. And, disentangle the microscopic and macroscopic consequences and observe the effects distinctly as if these are two different physical quantities even though it is all induced fields.
Vector map: Slide#4 of 0_2_12Aug2011.ppt
18 Aug 2011
S.Aravamudhan CMDAYS2011

10. The numerical net value at the center amounts to nearly zero.
This favorable numerical result indicates that the close packing criterion and the associated distances can be applied to know the actualities of contributions besides the afortiori reasons.
16 Aug 2011
S.Aravamudhan CMDAYS2011

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22 Aug 2011
S.Aravamudhan CMDAYS2011