Transcript A Thumb rule to work out Electron Spin Resonance Frequency [and

A Thumb rule to work out Electron Spin Resonance Frequency [and
the corresponding Proton NMR frequency] is as follows:
since hν=gβH is the relation governing resonance condition, by
knowing the relevant constants from available data tables, it should
be verified that the following equation closely approximates the
resonance frequency-field criterion for ESR.
1 Gauss = 2.8 MHz for a free electron spin with g=2
For proton NMR
1 Gauss = 4.2 KHz
Therefore if one can detect the oscillator levels using an oscillatordetector, and , if the frequencies of the oscillations are in the range
of 8-32 MHz, then using the above equation the corresponding
1.9
resonance field can be calculated. 2.9 – 11.5 Gauss for ESR.
Further a simple Helmholtz coil can be designed to obtain these
Magnetic Field Strengths by providing a suitably designed current
sources which may be available even commercially.
– 7.6
K Gauss
for PMR
Then a Block Diagram of the type shown in the next slide can be
appropriate for constructing and assembling a esr detection system.
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Oscillation Level reduced when there is ESR absorption
Oscillation Level at fixed frequency ‘ν’ When No ESR
Detected DC Level No ESR
2
Oscillator
Φ
Oscillation
Level Detector
1
Reduced DC On
ESR Absorption
Shifter
hν=gβH
0
No oscillations
The role of a phase Φ shifter in
the diagram would be
explained in the succeeding
slides
If the Current is increased from 0 to beyond resonance field,
then, the field [ Ht ] increases with time and causes
resonance at resonance field value
Ht
hν=gβH
2
Current Source
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2
Z - Magnetization along
the Field
XY - Magnetization induces
RF signal in the receiver coil
Z
Defocusing
and signal
decay
Y
X
Output from receiver
coil - FID
RF Pulse : π/2 pulse to
flips the magnetization
into xy plane
amplitude arb units
CW
Oscillator
0.50
1.50
GATE
1.00
0.00
Receiverdetector
RF Pulse
-0.50
-1.00
0
2
4
6
8
10 12
14 16 18 20
22 24 26 28
DC Pulse generator
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Tim e
Probe
38
In Magnet
30 32 34 36
Display
Monitor
FID oRecorder
n
FID with
o ffset
reso nance
40 42 44
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46 48 50
3
Sinusoidal Functional Form and Its SHM Perspective
Digitization
Illustrated
COSINE
CURVE
10.0
10.0
15
Amplitude
10
0
8.1
8.1
5
3.1
3.1
0
0
1-5
2
1
2
3
3
4
4
5
-3.1
5
6
6
7
7
-10
-8.1
-8.1
-15
time
-10.0
8
9
8
9
-3.1
10
10
data
•Digitized
This binary
cosine
curvetime
would
Ampl.
now be represented
a
001 as01010
consequence of a 010 01000
36
synchronized
constant011 00110
72
amplitude- vectorrotation.This leads to the
108
perspective for the simple
100 11001
harmonic motion
144
associated
with the
180
101
10111
sinusoidal functional
10101
110
forms.
cos((pi/5)t)
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Animated Illustration of Digitization of an
ANALOG Function. Numbers in Decimals can be Binary
1.2
Indicators of DIGITIZER
Timings Show up in
sequence
1
1.0
0.8
0.6
0.7
0.4
0.4
0.2
0.3
0.2
0.1
0.1
0
0
4
8
12
16
20
24
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Digitizing Analog Signals and Processing Digital Data in
DIGITAL COMPUTERS
Set to transit to slide 7
1.2
0
1
1
1
0.846482
2
0.716531
3
1.0 4 0.606531
0.513417
0.513417
1.20
5
0.434598
6
0.367879
7
0.311403
1.00
8
0.263597
0.263597
9
0.22313
0.800.188876
10
11
0.15988
12
0.135335
0.135335
f(t)13
0.600.114559
14 0.5
0.096972
15
0.400.082085
16
0.069483
0.069483
17
0.058816
18
0.200.049787
19
0.042144
0.3
20
0.035674
0.03567
0.000.030197
21
0.1
22
0.025562
0
4
8 12 16 20 24
0.1
23
0.021637
0.0 0.0
24
0.018316time
0.018316
't'
25
0.015504
exponential
1
0.8
0.6
Animated
0.4
0.2
0
0
On the L.H.S appears the
On
L.H.S the
table of values of e-t/8 as a
plotted
functionof function
the time ‘t’ is
t

8
f(t)  e
At
these equally
spaced
•The
Digitization
of
the
function
at
This digitzation
process
sequence
of
specified
times, thewould
times 0,4,8…….24
can be displayed for
times
equal
result inat
the
values
column
exponential
curve
is in
sampled
illustration
as it would be
3its
in the
table
for
amplitude
valueup
and
intervals
show
animated herein
displayed
2 4 6 8 10 12 14 16 18 20 22 24
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After Digitization?
Store Digitized Binary Data in
the Computer memory
Input these DATA into a
PROGRAM, run and get the
required output
001 1010
010 1000
output
011 0110
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next slide
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A program in
Fortran for
“Fast
Fourier
Transform”
1
11
Digitized FID
Signal
13
Digital Computer
---------------------------------------------------------------------------------------------------
FFT Program
run
OUTPUT
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10
20
30
dimension A(50),B(50),Y(50),X(50)
K=32
open (unit=1, file="output")
Print 10,K
DO 11 N=1,K
X(N)=(N-1)*3.5/K
X(N)=EXP(-1.0*X(N))
Y(N)=X(N)*(COS(2*3.14*(N-1)*10.0/K)+
COS(2*3.14*(N-1)*4.0/K))
write (1,20) N,Y(N)
DO 12 M=1,K
A(M)=0
B(M)=0
DO 13 N=1,K-1
A(M)=A(M)+Y(N)*COS(2*3.14*(M-1)*(N-1)/K)
B(M)=B(M)+Y(N)*SIN(2*3.14*(M-1)*(N-1)/K)
A(M)=A(M)/K
B(M)=B(M)/K
M2=M/2
write (1,30) M2,A(M2),B(M2)
FORMAT(1x,I2)
FORMAT(1x,I2,2x,F10.5)
FORMAT(1x,I2,2x,F10.5,2x,F10.5)
close (unit=1)
STOP
END
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0.2
Real
0.15
0.1
0.05
0
-0.05
imaginary
-0.1
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
2 4 6 8 10 12 14 16
OUTPUT from the FFT Program: Time domain FID and the
Frequency domain two line NMR spectrum
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Spectrometer operating
frequency decreases
Distance of separation between the multiplets
varies with the field
Field=
H
Separation within the multiplets remain
unchanged with the field
H/2
H/4
H/6.6
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Field
Frequency
Lock
Probe
RF CW Oscillator
Voltage Controlled
Oscillator: VCO
Receiver /
Detector
Correction
signal
ERROR
amplifier
+ve error
signal
Zero error
output
Desired
setting
-ve error
signal
Exact resonance
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High Gain RF
Amplifier
Input to
amplifier
Feedback
RF output
Receiver
Detector
RF frequency component in the noise will be
regeneratively amplified (+ve feedback only at NMR
frequency) and it is an NMR feedback oscillator
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It is possible to apply field gradients
to be able to define spacially
resolvable pixels and measure the
varying frequenies. If water
contents also differ from one pixel
to another, the intensity variations
can produce a phantom image of the
object.
A well defined
Linear field
gradient is
applied. Hence
the sample
location would
be indicated by
its resonance
frequency
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Field
In a homogeneous Field as above the entire object will experience a single
magnetic field and all the material contents will resonate at a single
frequency giving a sharp line
F1 F2 F3
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Distance inside the pole
faces
14