Magnetic Field

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Magnetic Field
http://www.worldofteaching.com/
FT NMR WORKSHOP/===/ S.A.I.F./===/ NEHU/==/ Shillong
INTRODUCTORY LECTURE
S.ARAVAMUDHAN
Slide # 2
Spin ensemble and Longitudinal Spin alignments Slide #3
Thermal equilibrium: Transverse plane dephasing Slide # 4
An animated elaboration of the Single spin Interactions
Spin transitions: Longitudinal Magnetization Build up for thermal equilibrium:
Concluding Slide for the Detection of N.M.R.
Slide # 5
Slide # 6
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Spin and Magnetic moment:
Illustration:
Nucleus rotates about an axis
within itself, which is referred to
as the spinning of nuclei.
Spin axis
The spinning object has an angular momentum
Nucleus has electrical Charge. Thus a rotating
charge has associated magnetic moment.
Spin Angular
momentum
The NUCLEI thus possess angular momentum; and the
angular momentum in atomic system are quantized. Due to
this quantization, the angular momentum component in any
chosen direction can take only specified discrete values.
NOTE: that the
single spin is
invariably
associated with
an XY component
perpendicular to
the magnetic field
direction
Ih
+1/2ħ
For protons: Spin
quantum number=1/2
The angular momentum
and magnetic moment
are in the same direction
because of the positive
charge of the nucleus
In the quantized
orientations the spins
experience a torque due
to which they must be
precessing (Larmor
precession)
±1/2
-1/2ħ
Ih
Magnetic Field
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Electromagnetic
radiation causes
the spin flipping
2
At thermal equilibrium Magnetization is
built up in a spin ensemble in a magnetic
field. And, the established magnetization
responds to the electro magnetic
radiation to cause the magnetic
resonance to occur.
How can we describe this
The term
MAGNETIZATION is
Introduced
ensemble picture with the
single spin description of
previous slide?
Spins align
Moment
Ih
Magnetic
Field
Z
Magnetization
Magnetization
External
Magnetic
Field
Y
Chemical substance
Spin ensemble
X
Sample would
be placed in
the field
NET
Magnetization
Moments
Above single spin situation
random NOTE
orientation
of
can be generalized for XYThe
that the XY
moment
the spins
ordered and
components
are gets
components
are
several spins
not zero, the
randomlyof
disposed;
aligned
in presence
resultant
net
value in XY
hence resultant
external magnetic
field would
plane is zero
Oriented randomly
be zero
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Magnetization ONLY
along Z-direction.
NO Magnetization
in the XY plane.
3
at “Thermal equilibrium”
Z- Magnetization
Z- Magnetization
brought to xy
plane
±1/2
Random phase for xy
components
Above motion of xy
components at time
scales small compared
to transverse relaxation
time
Thermal equilibrium
“time scales much greater
than T2”
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Spin ensemble
random
No external magnetic field. The
energy levels are degenerate
-1/2
+1/2
The ensemble of spins,
have equally distributed
population between the two
levels for the spin ½ protons
No net magnetization
On the application of field…..
Splitting is instantaneous & population
redistribution requires more time called the
relaxation time
-1/2
No radiations
are present
-1/2
+1/2
Not stimulated
transitions: but
spontaneous
relaxation transitions
Magnetic field
+1/2
Degeneracy
removed/Energy levels split
‘h ν = g β H’ is the magnetic resonance condition
Net magnetization
Thermal equilibrium
Boltzmann distribution
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Experimental Detection of the
Magnetic Resonance signal requires
setting up a non-equilibrium state Moment vs
+1/2ħ
What is the thermal equilibrium available to
start with?
The spin system, the ensemble, has a time
independent Net Magnetization along the z-direction
(the direction of the magnetic field)
Magnetization
What
difference
does it make?
Detect the XY component
No XY component
Z
Magnetic
field
Bring to Non-equilibrium
Tilt the
Y
magnetization away
from the z-direction
X
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