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Transcript of 1 Nuclear Magnetic Resonance ANIMATED ILLUSTRATIONS MS Powerpoint Presentation Files Uses Animation...
1
Nuclear Magnetic ResonanceANIMATED ILLUSTRATIONS
MS Powerpoint Presentation Files
Uses Animation Schemes as available in MS XP or MS
2003 versionsA class room educational material
PULSED FT NMR
http://ugc-inno-nehu.com/links_from_web.html
Video Conversion Using
“WONDERSHARE PPT to WMV” Conversion Software
Dr. S. ARAVAMUDHAN
Automatic Timing: CLICK on “show” and wait and watch all the 13 slides which automatically transit one slide to the next.
2
A steady Uniform Magnetic Field of 9.34 Tesla is applied (find in Slide #3)
Experimental sample is placed in the magnetic field (as in slide#3)
Magnetization Builds up due to Relaxation process in Time T1 (slide#3 & Slide#10)
A rectangular pulse of 400 MHz RF frequency is applied to bring the magnetization to XY Plane (slide #3, 4, &5 and others)
z
xy
Magnetization decay due to T2 process. Free Induction Decay F.I.D. acquired (as in slides # 5, & 10) FID is digitized (slide#6)
FID Fourier Transformed to obtain Spectrum (slide #6)
Obtaining FT NMRElaboration on the even more basic Single spin Magnetic moment situation in a steady applied Magnetic field and the Consequent Magnetization can be viewed at YOUTUBE.COM
http://www.youtube.com/aram1121944/
Uploaded files
1_NMR and 2_NMR
3
P-Xπ/2
At t =0, the end of pulse
External Magnetic Field
Chemical substance Spin ensemble
Z
X
Y
Magnetization
Z
X
Y
x,y-axes Rotating about Lab Z-axis; frequemcy same as the precession frequency
Z
XY A rotating RF magnetic
field results on application of RF at resonance frequency
X
Y
The rotating magnetic field tilts the magentization away from z-axis by 90º for a π/2 pulse
Viewed from within the rotating frame the RF field appears stationary
Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency.
Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame
XY
Induced NMR signal at receiver (RF 300 MHz )
Phase Sensitive detector
Reference in phase at NMR (400MHz) frequency
Output (‘0’ freq)
Reference in phase; offset from NMR frequency (400±0.004 MHz)
Phase Sensitive detector
Output at offset frequency (audio range) ~4KHz
D.C.
A depiction of the Induced RF signal Characteristics would appear………
After the pulse: at t>0
Transverse Relaxation and magnetization decay in XY plane is not depicted.
No more CLICKs. This show has automatic timings
from this stage. Free Induction NMR Signal
NO F.I.D. yet!
Right CLICK mouse
And CLICK on option “PREVIOUS”
OR………….
CLICK toTransit.
Rotating x,y axes :rotation about Lab z-axis
Apply the 90º,
-X pulse now, P-Xπ/2
A BLUE line for z-Axis indicates the view from within the rotating coordinate system.
XY
Rotating system viewed from within that system: STATIONARY
X
Y
Z
X
Y
ZZ
Y
4
For a π/2 pulse the value of ‘ω1 t ‘=90º;
ω1=γH1
The impulse on…
x,y-axes Rotating about Lab Z-axis; frequency same as the precession frequency
Z
XY
X
Y
XY
Rotating system viewed from within that system: STATIONARY
X
Y
Z
A rotating RF magnetic field results on application of RF at resonance frequency
Viewed from within the rotating frame the RF field appears stationary
Z = unit vector along z-axis
Rotation about z-axis= e-iφ Z Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed.
Rotation about z-axis= e-i ω t Z
An equation representing this rotation would be displayed
In terms of Angular momenta, Iz replaces ‘z’; for rotation
about z-axis= e-iφ Iz
Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed.
Rotation about z-axis= e-i ω t Iz
RF source/ transmitterConnected to coil.Linearly oscillating field along the coil axis (X-axis)
The linearly oscillating field can be resolved into two counter rotating components
Only one of the rotating component is effective in causing resonance
2 H1 I-x cos(ωt) = H1 e-iI-xωt H1 e+iI-xωt
http://www.geocities.com/sankarampadi/eulexp.html
A Pulse lasts only for a few μ Secs.
For proton NMR a H1 of ~25Gauss along ‘-x’ , pulse widths are approximately 10-15μs
+
The impulse off…
RF field is along –X in the XY plane, the effect caused would be rotation about X-axis, unlike the precession about z-axis
To repeat the animated RF depictions “right click” and choose option: ‘previous’
Click to end this slide
CLICK ! CLICK !
CLICK !
CLICK !
CLICK !
Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK!
5
Apply the 90º,
-X pulse now, P-Xπ/2
X
Y
Z
Viewed from within the rotating frame the RF field appears stationary
Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency.
XYAfter the
pulse: at t>0
Rotating x,y axes :rotation about Lab z-axis
A BLUE line for z-Axis indicates the view from within the rotating coordinate system.
Z
Y
Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame
X
Y
ZWhen the XY magnetization decays with transverse relaxation time T2,
immediately after the pulse……
When PSD reference is in phase off set from Resonance frequency; NMR signal at receiver (RF 400 MHz )
If No T2……..
Free Induction Decay Signal
No More Clicks ! This show has automatic timings
The F.I.D.
When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 400 MHz )
Tilting of magnetizationDescribed in rotating frame: Rotation about the X-axis
I(tp) =e-iI-
xφ Iz e+iI-xφ with φ=90º &
tp is pulse duration
At the end of pulse, time for F.I.D. begins with t=0
tp
t=0
Acquisition time ~5T2
FID
CLICK to Transit
Induced NMR signal at receiver (RF 400 MHz )
6
PULSED NMR Acquire F.I.D.
Free Induction DecayNMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation
F.I.D.DIGITIZE
Analogue to Digital Converter
A.D.C.
Address Contents
1 0000
15
1111
2 0001
14
1110
3 0010
13
1101
4 0011
11
1011
5 0100
8
1000
6 0101
4
0100
7
0110
1
0001
8
0111
0
0000
--------- ---------
Computer memory
Time domain
15
0
11
FFT from FID
Computer input
Frequency Domain Spectrum
Computer outputThis one-
dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum
Acquisition is automatically in the digitized form
Next Slide
7
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)+ 1 COS(2*3.14*(N-1)*4.0/K)) 11 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) 13 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 12 write (1,30) M2,A(M2),B(M2) 10 FORMAT(1x,I2) 20 FORMAT(1x,I2,2x,F10.5) 30 FORMAT(1x,I2,2x,F10.5,2x,F10.5) close (unit=1) STOP
END
A program in
Fortran for “Fast Fourier Transform”
Digitized FID Signal
Digital Computer
---------------------------------------------------------------------- ---------------------- ------------ -
FFT Program run
OUTPUT
8
Time domain FID data: 32 points
Real Imaginary 16 data 16data points points
Frequency domain spectrum
9
cosine Sine arbitrary phae sinuous
COS Real Imaginary
F.T
RealImaginaryF.T
SIN
Real Imaginary
F.T
Arbitrary Phase
Provision is made in the data processing system, for routinely applying phase corrections
t=0
+1
0
Value between +1 & 0
fc cos(2πνt) + fs sin (2πνt)
with fc2 +fs
2 =1
10
No net magnetization
CLICK !
Magnetization
Sample: Ensemble of spins
Magnetization
Magnetization Builds up exponentially
t
Magnetization
T1
I0 ItExternal Magnetic Field
To repeat the above events: Right Click & Select option ‘previous”
Z
X
Y
Initially, before the external magnetization is applied, the spins are randomly oriented
When the magnetic field is turned on, the spins align at the characteristic longitudinal relaxation time T1
CLICK !
+1/2
-1/2
Magnetic field
+1/2
-1/2No radiations
are present
Not stimulated transitions: but spontaneous relaxation transitions
Degeneracy removed/Energy levels split
On the application of field…..
Splitting is instantaneous & population redistribution requires more time called the relaxation time
Thermal equilibrium Boltzmann distribution
Net magnetization along Z-direction & ZERO XY component
random
(1-e-t/ )T1I0 =It
CLICK for….
CLICK !
It
CLICK for….... On-set of Longitudinal Relaxation
11
In XY plane precessing magnetization
X
YSolenoidal
sample coil axis
Axis- Y
Precessing magnetization induces rf
voltage: NMR signal
Pulse applied
Z
Z
Y
The above picture is for time scales small compared to relaxation time T2
When relaxation process is effective, the relaxation leads to the decay of the transverse magnetization of XY plane
This decay of magnetization due to the transverse relaxation time is because of the defocusing of the magnetization isochromats in XY plane
12
Randomization in XY plane: Magnetization Decays
I h NET Magnetization
Transverse T2
Relaxation
Longitudinal T1 Relaxation
Relaxation Longitudinal and transverse
Magnetic field
A π/2 pulse flips the z-magnetization to xy-plane
CLICK !
Random…Alignment…..
t
13
This Video Movie was made by Dr. S. Aravamudhan
For the occasion of the WORKSHOP on FT NMR
At S.A.I.F , North Eastern Hill University, Shillong
The Sound Tracks ( playeable audio ) are from the album “ARZOO: Nirvana in six strings” and the Album “Elements: Water” of Shiv Kumar Sharma
November 2009
Video Conversion Using
“WONDERSHARE PPT to WMV” Conversion Software