1. FT NMR WORKSHOP/===/ S.A.I.F./===/ NEHU/==/ Shillong
FT NMR WORKSHOP/===/ S.A.I.F./===/ NEHU/==/ Shillong
INTRODUCTORY LECTURE
S.ARAVAMUDHAN
An animated elaboration of the Single spin Interactions
Spin ensemble and Longitudinal Spin alignments
Thermal equilibrium: Transverse plane dephasing
Spin transitions: Longitudinal Magnetization Build up for thermal equilibrium:
Concluding Slide for the Detection of N.M.R.
"Wondershare PPT to WMV" conversion Softwatre

2. The spinning object has an angular momentum
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
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
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.
In the quantized orientations the spins experience a torque due to which they must be precessing (Larmor precession)
NOTE: that the single spin is invariably associated with an XY component perpendicular to the magnetic field direction
I h
+1/2ħ
±1/2
I h
-1/2ħ
Electromagnetic radiation causes the spin flipping
Magnetic Field

3. Vector diagramatic description
Spin=1/2
Energy
Field
+1/2
-1/2
A single spin description cannot be complete without the associated XY component
The Larmor precession frequency depends on the strength of external field
hν=gβH
+1/2 ħ
For proton spin of ½, there are two allowed orientations so that the component along z-axis is either +1/2 or -1/2
hν=gβH
Quantized
Energy level description
If a rotating magnetic field of relatively small magnitude is present in the perpendicular plane at frequency ν , then the resonance occurs and the spin undergoes a flipping transition to another orientation.
+1/2 ħ
Lower energy
Vector diagramatic description
-1/2 ħ
Upper energy
Photon energy absorbed; transition occurs
hν=gβH
-1/2 ħ
+1/2 ħ
Radiation
Induced Transition or stimulaed transition

4. A definition:
Magnetic Resonance Phenomenon is a manifestation due to the presence of INTRINSIC SPIN angular momentum and the associated Magnetic Moment characteristically in electrons and Nuclei
Single line NMR spectrum
When the experimental conditions are set for the NUCLEI to resonate, then it is the Nuclear Magnetic Resonance.
NMR spectrum of a sample of spin ensemble……..
0 ppm TMS
10ppm
PMR spectrum

5. "Wondershare PPT to WMV" conversion Softwatre
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.
Magnetization
External Magnetic Field Z X Y
Magnetization
Chemical substance Spin ensemble
How can we describe this ensemble picture with the single spin description ?
The term MAGNETIZATION is Introduced
Sample would be placed in the field
I h
Moment
Spins align
NET Magnetization
Magnetic Field
Moments
Above single spin situation can be generalized for several spins
The random orientation of the spins gets ordered and aligned in presence of external magnetic field
NOTE that the XY components are randomly disposed; hence resultant would be zero
Magnetization ONLY along Z-direction. NO Magnetization in the XY plane.
XY moment components are not zero, the resultant net value in XY plane is zero
Oriented randomly
"Wondershare PPT to WMV" conversion Softwatre
at “Thermal equilibrium”

6. A steady Uniform Magnetic Field of 9.34 Tesla is applied
Elaboration 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
url OF ‘My Channel: at YOUTUBE
Obtaining FT NMR
A steady Uniform Magnetic Field of 9.34 Tesla is applied
Experimental sample is placed in the magnetic field
Uploaded files
1_NMR and 2_NMR
Magnetization Builds up due to Relaxation process in Time T1 z x y
A rectangular pulse of 400 MHz RF frequency is applied to bring the magnetization to XY Plane
Magnetization decay due to T2 process. Free Induction Decay F.I.D. acquired (as in slides # 5, & 10)
FID is digitized
FID Fourier Transformed to obtain Spectrum

7. Defocusing and signal decay
PULSED NMR experiment
XY - Magnetization induces
RF signal in the receiver coil
Z - Magnetization along the Field Z X Y
Defocusing and signal decay
Output from receiver coil - FID
RF Pulse : π/2 pulse to flips the magnetization into xy plane
CW Oscillator
GATE
Receiver- detector
Display Monitor Recorder
RF Pulse
Probe In Magnet
DC Pulse generator

8. Free Induction Decay Signal
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 400 MHz )
Induced NMR signal at receiver (RF 400 MHz )
CLICK to Transit
When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 400 MHz ) tp
t=0
Acquisition time ~5T2
FID
Free Induction Decay Signal

9. "Wondershare PPT to WMV" conversion Softwatre
Z- Magnetization
Z- Magnetization brought to xy plane
±1/2
Random phase for xy components
Thermal equilibrium “time scales much greater than T2”
Above motion of xy components at time scales small compared to transverse relaxation time
"Wondershare PPT to WMV" conversion Softwatre

10. Frequency Domain Spectrum
PULSED NMR
Acquire F.I.D.
Free Induction Decay
NMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation
Acquisition is automatically in the digitized form
Computer memory
Address
Contents 15
1111 14
1110 8
1000 4
0100 7
0110 1
0001
0111
0000
Time domain 15 11
DIGITIZE
Analogue to Digital Converter A.D.C.
F.I.D.
Frequency Domain Spectrum
Computer output
This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum
Next Slide
FFT from FID
Computer input

11. Time domain FID data: 32 points
Real Imaginary 16 data data points points Frequency domain spectrum

12. t=0 +1
Value between +1 & 0
Provision is made in the data processing system, for routinely applying phase corrections
COS
Real
Imaginary
F.T
Real
Imaginary
F.T
SIN
Real
Imaginary
F.T
Arbitrary Phase
fc cos(2πνt) + fs sin (2πνt)
with fc2 +fs2 =1

13. Degeneracy removed/Energy levels split
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

14. Longitudinal T1 Relaxation
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

15. Preparation pulse: facilitates the following……..
Free evolution of spin system
Free evolution of spin system
FFT
Spectrum
Spin Echo Fourier Transform Spectroscopy x z y
Preparation pulse (π/2-pulse)
Echo x z y
Τ secs
Τ secs
Refocussing (Mixing?) pulse
Inverting pulse (π-pulse)
180° pulse
90° pulse
F.I.D
Refocus
Defocus t2
acquisition
The refocus period is somewhat similar to the Mixing Time in the pulse sequences for dimensional NMR Spectra. However the Mixing period is held fixed while varying the t1 period for 2D, as described in the next slide.
Rotating x,y axes :rotation about Lab z-axis
Preparation pulse: facilitates the following…….. Z X Y
Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame X Y X Y Z
Rotating system viewed from within that system: STATIONARY X Y
The description above of the spin echo spin system evolution was with the magnetization vectors in a rotating coordinate system
Transforming to Rotating coordinate system