Right-Click the mouse and exercise the FULL SCREEN viewing option even at the very beginning
Instructions for Viewers
Clickis from slide # 2 onwards to # 15
The”NMRS2004” presentation
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
7/28/2016 1:35:16 AM
for MR Symposia 2003 Presentation
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
1
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
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
2
Bulk Susceptibility
A recapitualisation
fromEffects
the NMRS2003
In HR PMRSlides 1-6
presentation
Once this question could
The
conclusions
earlier
Liquidsanswered,
be adequately
had
beenquestion
to find answer
the next
was to to
the
questions:
findfollowing
the consequences
of
SOLIDS
This was the material
Induced Fields
at 3rd Alpine
atConference
the Molecular
Site
Poster
inhomogeneities
arising
1. Should the Lorentz
within
sample.
Spherethe
be Spherical?
Since
if theofbulk
For
thiseven
a study
the
susceptibility
convergence is the same
Single
Crystal
Single
crystal
through
sample,
Daout
= - the
4/3
characteristics
for
Spherical Shape
the
resulting
induced
field arbitray shape
summing
over
the lattice
distributions
will notfor
be
(cubic and
Db=noncubic)
2/3
Sphere
homogeneous
the
ellipsoidal innerwithin
volume
Lorentz
samplefor
shapes
other
cavity
element (counter Lorentz
than
sphere
and ellipsoid.
“sphere”)
7/28/2016 1:35:16
AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
3
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
7/28/2016 1:35:16 AM
Magnetic
Field
-4/3 + 4/3
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
4
Induced field Calculations using these equations and the
  ~
magnetic
dipole
model have been simple enough when the

~
 3  RR  
~
summation
  - procedures were applied as described in the previous
3
5
r
r
presentations and expositions.








xx
xy
xz


 xx
 xx
xy
xz 
xy
xz 







3   yx yy yz   

 
yx
yy
yz
yx
yy
yz 



 




zx
zy
zz

 

 
 xx
xy
xz    zx  zy  zz 
zx
zy
zz 





 
yy
yz 
 yx
r3
r5


 
zy
zz 
 zx
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
~ =


0

0

0

0
0

0

 

R r
  1- 3 cos2  

3  r 2  cos2   

 zz    
5
3
r
r
r3
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
5
Inner ellipsoid
a/b=0.25
demgf= 0.697
Outer ellipsoid
a/b=0.25
demagf= 0.708
Ellipsoid
Outer a/b=0.25
Inner a/b=0.25
demagf=0.333
Outer sphere
Inner sphere
a/b=1
demagf=0.333
From the standard tables demagnetization factor for a/b=0.2: =0.750484
for a/b=0.3: =0.661350
interpolation yields for 0.25: = 0.705
417
It is only conventional in material physics consideration to have a
spherical (Lorentz) cavity while calculating the demagnetization factors
for regular outer shapes of the magnetized specimen. By the procedures
used in this work,it is a matter of simple alteration in sequence in which
certain equations defining the shpes and forms are considered which
makes it possible,without any resulting complications in the calculation,to
get values for Facotrs, based on the definition of demagnetization
factors,as reported above by applying the shapes inside out . This seems
to be very favourable for studying shapes, with added susceptibility
reagents in membrane-media, by spin-echo NMR techniques.The details
are deferred to future presentations.
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
6
Variation of Induced Field at centre of Lorentz' Cavity with centre
position for different cavity sizes
0
-0.5
-1
Induced Field values
-1.5
-2
-2.5
-3
-3.5
-4
-4.5
-5
1.25
1.00
0.75
0.50
0.25
0.00
-0.25 -0.50 -0.75 -1.00 -1.25
Cavity Centre location with respect to the Centre of the Macroscopic Sphere
cav ra1.25
cav ra1.50
cav ra1.75
cav ra2.0
cav ra2.25
These results
could be dated
back to the year
2000-2001
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
7
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.
OR
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
Some Results of the
3rd Alpine POSTER
at France in
Sept.2003 are
summarized in the
next three Slides 7-9
8
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
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
9
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...
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
10
Results of Claculations made for this presentation at
NMRS2004
CYLINDER
TOP SHAPE
(0,7)
(0,0)
Equatorial
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
11
Indcd Field at the Center of a 'TOP"
8.00E-07
Indcd Fields at center
6.00E-07
4.00E-07
2.00E-07
0.00E+00
-2.00E-07
-4.00E-07
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1.0
-2.0
-3.0
-4.0
-5.0
-6.0
-7.0
-6.00E-07
Dist 'Y' from Center 'Ind
0 'field Cntre x=16 y=8
Indcd ield at the Center x=y=8
ind Field Cylinder x=y=8
IndField Cylinder x=4 y=8
Cylinder x=16 y=8
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
12
Cylinder &TOPSHAPED specim ens: Ind Field at Center
6.00E-07
Induced fields at Center
4.00E-07
2.00E-07
0.00E+00
-2.00E-07
-4.00E-07
-6.00E-07
-8.00E-07
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
radius for fixed length=16
7/28/2016 1:35:16 AM
Ind Field Cylinder l=16 & r=3-25
Ind Field TOPSHAPE l=16 & r=2,24
Slope Line Cylinder
Slope line TOPSHAPE
Cylinder offcenter (1,0)
Slopeline for Cylinder(1,0)
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
13
Demagnetization Factors for shapes with circular equatorial cross
section
Deamgnatization factor/shape
factor
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Radius equatorial cross section
Demag factor at Center of Top shaper
Demag Factor at Cylinder Center
Demag Factor at (0,7) of Cylinder
Shape measure factor :Half axial length/equatorial radius
demagnetization factor prolate ellipsoid
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
14
END OF Presentation
Questions & Comments
To End this SHOW make a right-click and click
further on the End Show option in the prop-up box.
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
15
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
Click for Viewers
MR Symposia 2003 Presentation
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 link HERE and RETURN to this first slide
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
16
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
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
17
Bulk Susceptibility Effects
In HR PMR
SOLIDS
Liquids
Induced Fields
at the Molecular Site
Da= - 4/3
Single
Crystal
Single crystal
Spherical Shape
arbitray shape
Db= 2/3
Sphere
Lorentz
7/28/2016 1:35:16 AM
cavity
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
18
A link to a Web Site containing Features of Demagnetzation
Factors Calculations
Click Here for the
consideration of Variety of
possibilities for the lattices and
site symmetries
i=ii /R3i [1-(3.RRi /R5i)]
LINK to
Demagnetization Effects
Graph
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
7/28/2016 1:35:16 AM
Magnetic
Field
-4/3 + 4/3
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
19
INDUCED FIELDS,DEMAGNETIZATION,SHIELDING
Induced Field inside a hypothetical Lorentz’ cavity within a specimen = H``
Shielding Factor = 
Demagnetization Factor = Da
in
out
When
H`` = - inner
 . H0&=outer
- 4 . shapes
. (D - are
D spherical
) a .  . H0
in
out
D = D
Induced
Field H`` = 0

in
polar axis a
out
 = 4 .  . (D - D
)a . 
For
out a spherical shape D-factor = 0.333
equatorial axis b
m = a/b

in
Induced
Field / 4 .  .  . H0 = 0.333 - Dellipsoid
When inner & outer shapes are spherical
in
out
D = D
polar axis b
Induced Field H`` = 0
polar axis a
equatorial axis a
 = b/a
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
20
In the above case of two different shapes the example chosen is such that for the entire
specimen the Magnetic moment induced due to the magnetization of the sample is the same in
both cases of the shapes as indicated by the length of the arrow. If this point dipole is at the
center of the specimen in both cases, then the field sistribution around the specimen outside
the specimen would be the same.
Even if the total moment is subdivided into amaller values and paced distributively at different
points, because of the essential spherical symmetry of the first specimen,the calculation may
not indicate much difference in the field patterns outside.
In the case of an elongated ellipsoid a redistribution would require more number of subdivided
dipoles along the length than the width which means a necessary difference in the field
distribution outside the specimen. Hence more than the quantitative aspects the qualitative
patterns for field distributions outside can be indicative of the shape of the specimen.
If one obtains a field pattern for the outside of the specimen by appropriate experiments fitting
the few field values obtained for poits outside the specimen consistently with the values
obtained for tose field values by the present approach (which seems simple enough)then it
may be possible to get informations about the shapes more definitely. By altering the extents
of magnetization by added susceptibility reagents, devicing appropriate experiments and
predetermining favourable values for the experimental parameters would be much more
amenable and tractable for reliable interpretations from the trends.
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
21
Inner ellipsoid
a/b=0.25
demgf= 0.697
Outer ellipsoid
a/b=0.25
demagf= 0.708
Ellipsoid
Outer a/b=0.25
Inner a/b=0.25
demagf=0.333
Outer sphere
Inner sphere
a/b=1
demagf=0.333
From the standard tables demagnetization factor for a/b=0.2: =0.750484
for a/b=0.3: =0.661350
interpolation yields for 0.25: = 0.705
417
It is only conventional in material physics consideration to have a
spherical (Lorentz) cavity while calculating the demagnetization factors
for regular outer shapes of the magnetized specimen. By the procedures
used in this work,it is a matter of simple alteration in sequence in which
certain equations defining the shpes and forms are considered which
makes it possible,without any resulting complications in the calculation,to
get values for Facotrs, based on the definition of demagnetization
factors,as reported above by applying the shapes inside out . This seems
to be very favourable for studying shapes, with added susceptibility
reagents in membrane-media, by spin-echo NMR techniques.The details
are deferred to future presentations.
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
22
It may be necessary to calculate the intermolecular
contributions inside the Spherical samples with an
elliptical shape of the lorentz sphere and find the
CLICK HERE
For a glimpse of
Crystal systems
as well
The Simpler method (Details to be viewed
(Link
for details / CLICK
option)
optionally
from
other slides)of calculating
Demagnetizing fields makes it possible to
If it is possible to obtain some well defined shape(not necessarily Spherical)
consider
different
combinations
of
specimen of the single crystal samples on which HR PMR studies have well
established
results, then the
experiments
can be made
Macroscopic
sample
Shape
withwith such shapes by
orienting them in 3 independnt rotation axes and try to simulate that shape
hypothetical
Cavity
shapes
to
withappropriate
the same ratios of the
sides
and
faces
but
at
the
range
of
the
Lorentz
Various Specimen
sphere
(about 100 A°
calculate
intermolecular
increase
the) and
utility
oftheHR
PMR lorentz type
shapes
with
the
contributions with the Demagnetizing field type calculation and retrieve the
variety
of Cavity
in
intrameasurements
molecular contribution
as itSolids
was
done with the spherical samples and
conveniences of calculating.
reproduce those values. shapes
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
23
END OF Presentation
Questions & Comments
To End this SHOW make a right-click and click
further on the End Show option in the prop-up box.
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
24
Variation of Induced Field at centre of Lorentz' Cavity with centre
position for different cavity sizes
0
-0.5
-1
Induced Field values
-1.5
-2
-2.5
-3
-3.5
-4
-4.5
-5
1.25
1.00
0.75
0.50
0.25
0.00
-0.25 -0.50 -0.75 -1.00 -1.25
Cavity Centre location with respect to the Centre of the Macroscopic Sphere
cav ra1.25
cav ra1.50
cav ra1.75
cav ra2.0
cav ra2.25
Return
display to
slide 4
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
25
Return
display to
slide 7
7/28/2016 1:35:16 AM
Click to
reach
for the
Web
Site
LINKS
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
26
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
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
27
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
Email:
saravamudhan@nehu.ac.in
Web Site: http://saravamudhan.tripod.com
The Lorentz Cavity, a hypothetical void carved out inside a material medium
while considering the demagnetizing fields at a point (site) inside the materialspecimen, 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
cavity.
Click
for continuation
7/28/2016lorentz
1:35:16 AM
NMRS 2004
: S.Aravamudhan:
20thAbstract in the next slide
28
feb 2004:
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.com and the HOTLINKS at
and from http://geocities.com/amudhan_nehu/nehu_link.html
7/28/2016 1:35:16 AM
CLICK HERE to
NMRS 2004 : S.Aravamudhan: 20th
return display to sd
feb 2004:
#2
29
Spin Precession Animation
“DEMO”
Precession Starts
Automatically
Return to(#1) first
slide
Nuclear Spin
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
30
Crystal Systems
CLICK to Return to slide#4
CLICK to Return to slide#8
7/28/2016 1:35:16 AM
NMRS 2004 : S.Aravamudhan: 20th
feb 2004:
31