nuclear magnetic resonance

04/19/23 09:13 PM 'PULSED NMR' by Dr.S.Aravamudhan

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Nuclear Magnetic ResonanceANIMATED ILLUSTRATIONS

MS Powerpoint Presentation Files

Uses Animation Schemes as available in MS XP or MS

2003 versionsA class room educational material

File-12 1hr_lecture; PULSED NMR

http://ugc-inno-nehu.com/links_from_web.html




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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 (300MHz) frequency

Output (‘0’ freq)

Reference in phase; offset from NMR frequency (300±0.003 MHz)

Phase Sensitive detector

Output at offset frequency (audio range) ~3KHz

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


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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


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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


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!

http://www.geocities.com/sankarampadi/eulexp.html


5

Apply the 90º,

-X pulse now, P-Xπ/2

X

Y

Z


Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency.

XYAfter the

pulse: at t>0

Induced NMR signal at receiver (RF 300 MHz )

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 300 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 300 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


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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

nuclear magnetic resonance

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