1. Nuclear Magnetic Resonance
ANIMATED ILLUSTRATIONS
MS Powerpoint Presentation Files
Uses Animation Schemes as available in MS XP or MS 2003 versions
A class room educational material
File-12 1hr_lecture; PULSED NMR
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan

2. 'PULSED NMR' by Dr.S.Aravamudhan
External Magnetic Field
Rotating x,y axes :rotation about Lab z-axis Z X Y
Viewed from within the rotating frame the RF field appears stationary
A BLUE line for z-Axis indicates the view from within the rotating coordinate system.
Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency.
Magnetization X Y Z
After the pulse: at t>0
Chemical substance Spin ensemble X Y Z Y
Induced NMR signal at receiver (RF 300 MHz )
Apply the 90º, X pulse now, P-Xπ/2
P-Xπ/2
At t =0, the end of pulse
Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame Z
No more CLICKs This show has automatic timings from this stage. X Y X Y Z X Y
A depiction of the Induced RF signal Characteristics would appear………
A rotating RF magnetic field results on application of RF at resonance frequency
Phase Sensitive detector
Reference in phase at NMR (300MHz) frequency
Output (‘0’ freq)
Free Induction NMR Signal
x,y-axes Rotating about Lab Z-axis; frequemcy same as the precession frequency
The rotating magnetic field tilts the magentization away from z-axis by 90º for a π/2 pulse X Y Z X Y
D.C.
Reference in phase; offset from NMR frequency (300±0.003 MHz)
Phase Sensitive detector
Output at offset frequency (audio range) ~3KHz
Rotating system viewed from within that system: STATIONARY
Transverse Relaxation and magnetization decay in XY plane is not depicted.
CLICK toTransit.
Right CLICK mouse
And CLICK on option “PREVIOUS”
OR………….
NO F.I.D. yet!
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan

3. 'PULSED NMR' by Dr.S.Aravamudhan
External Magnetic Field
Sample: Ensemble of spins
Magnetization
Magnetization
Magnetization I0 It T1
CLICK ! t It
Magnetization Builds up exponentially
(1-e-t/ ) T1 I0 = It Z X Y
To repeat the above events: Right Click & Select option ‘previous”
When the magnetic field is turned on, the spins align at the characteristic longitudinal relaxation time T1
Initially, before the external magnetization is applied, the spins are randomly oriented
On the application of field…..
CLICK !
Splitting is instantaneous & population redistribution requires more time called the relaxation time
CLICK for….... On-set of Longitudinal Relaxation
-1/2
No radiations
are present
CLICK !
-1/2
+1/2
Not stimulated transitions: but spontaneous relaxation transitions
No net magnetization
CLICK for….
random
Magnetic field
Net magnetization along Z-direction & ZERO XY component
+1/2
Degeneracy removed/Energy levels split
Thermal equilibrium Boltzmann distribution
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan

4. 'PULSED NMR' by Dr.S.Aravamudhan
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
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
Viewed from within the rotating frame the RF field appears stationary
RF field is along –X in the XY plane, the effect caused would be rotation about X-axis, unlike the precession about z-axis X Y Z
An equation representing this rotation would be displayed
Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK!
CLICK !
CLICK ! Z
CLICK !
Click to end this slide
To repeat the animated RF depictions “right click” and choose option: ‘previous’ X Y X Y
A rotating RF magnetic field results on application of RF at resonance frequency
x,y-axes Rotating about Lab Z-axis; frequency same as the precession frequency
For a π/2 pulse the value of ‘ω1 t ‘=90º; ω1=γH1
The impulse on…
The impulse off…
CLICK ! X Y
H1 e-iI-xωt
2 H1 I-x cos(ωt) = +
H1 e+iI-xωt
A Pulse lasts only for a few μ Secs.
For proton NMR a H1 of ~25Gauss along ‘-x’ , pulse widths are approximately 10-15μs
Only one of the rotating component is effective in causing resonance
Rotating system viewed from within that system: STATIONARY
RF source/ transmitter
Connected to coil.
Linearly oscillating field along the coil axis (X-axis)
The linearly oscillating field can be resolved into two counter rotating components
CLICK !
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan

5. The F.I.D. No More Clicks ! This show has automatic timings
Viewed from within the rotating frame the RF field appears stationary
A BLUE line for z-Axis indicates the view from within the rotating coordinate system.
Rotating x,y axes :rotation about Lab z-axis
No More Clicks ! This show has automatic timings
Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. X Y Z X Y Z
After the pulse: at t>0 Y
If No T2……..
The F.I.D.
Tilting of magnetization
Apply the 90º, X pulse now, P-Xπ/2
At the end of pulse, time for F.I.D. begins with t=0
Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame
Described in rotating frame: Rotation about the X-axis I(tp) =e-iI-xφ Iz e+iI-xφ with φ=90º & tp is pulse duration X Y Z
When 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 300 MHz )
Induced NMR signal at receiver (RF 300 MHz )
When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 300 MHz )
CLICK to Transit tp
t=0
Acquisition time ~5T2
FID
Free Induction Decay Signal
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan

6. 'PULSED NMR' by Dr.S.Aravamudhan
Relaxation Longitudinal and transverse
Magnetic field
I h
NET Magnetization
Alignment…..
Random…
CLICK !
Longitudinal T1 Relaxation
Transverse T2 Relaxation
Randomization in XY plane: Magnetization Decays t
A π/2 pulse flips the z-magnetization to xy-plane
5/4/2019 1:03:21 AM
'PULSED NMR' by Dr.S.Aravamudhan