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Nuclear Magnetic Resonance

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Nuclear Magnetic Resonance

ANIMATED ILLUSTRATIONS

MS Powerpoint Presentation Files

Uses Animation Schemesas available in MS XP or MS 2003 versions

A 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.

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

http://www.youtube.com/aram1121944/

z

y

x

Obtaining FT NMR

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)

Uploaded files

1_NMR and2_NMR

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)

Magnetization decay due to T2 process. Free Induction DecayF.I.D.acquired (as in slides # 5, & 10)

FID is digitized (slide#6)

FID Fourier Transformed to obtain Spectrum (slide #6)

Z

Z

External Magnetic Field

Y

Y

Z

Z

X

X

Y

Y

At t =0, the end of pulse

Reference in phase at NMR (400MHz) frequency

Phase Sensitive detector

P-Xπ/2

X

X

Magnetization

Y

Y

Y

Y

Chemical substance Spin ensemble

X

X

X

X

Output (‘0’ freq)

Phase Sensitive detector

Reference in phase; offset from NMR frequency (400±0.004 MHz)

Output at offset frequency (audio range) ~4KHz

Rotating x,y axes :rotation about Lab z-axis

A BLUE line for z-Axis indicates the view from within the rotating coordinate system.

Viewed from within the rotating frame the RF field appears stationary

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

Z

After the pulse: at t>0

Y

Induced NMR signal at receiver (RF 300 MHz )

Apply the 90º, -X pulse now, P-Xπ/2

Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame

No moreCLICKs.This show has automatic timings from this stage.

Z

A depiction of the Induced RF signal Characteristics would appear………

A rotating RF magnetic field results on application of RF at resonance frequency

Free Induction NMR Signal

x,y-axes Rotating about Lab Z-axis; frequemcy same as the precession frequency

The rotating magnetic field tilts the magentizationaway from z-axis by 90º for a π/2 pulse

D.C.

Transverse Relaxation and magnetization decay in XY plane is not depicted.

Rotating system viewed from within that system: STATIONARY

Right CLICK mouse

And CLICK on option “PREVIOUS”

OR………….

CLICK toTransit.

NOF.I.D.yet!

Z

Y

X

Y

Y

Y

X

X

X

In terms of Angular momenta, Izreplaces‘z’;forrotationabout z-axis= e-iφIz

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 tIz

Viewed from within the rotating frame the RF field appears stationary

Z= unit vector along z-axis

Rotation about z-axis= e-iφZ

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 tZ

RF field is along –X in the XY plane, the effect caused would be rotation about X-axis,unlike the precession about z-axis

An equation representing this rotation would be displayed

Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK!

CLICK !

CLICK !

CLICK !

Z

To repeatthe animated RF depictions “right click” and choose option:‘previous’

Click to end this slide

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 impulseoff…

The impulseon…

CLICK !

H1e-iI-xωt

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

+

2 H1I-x cos(ωt) =

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 !

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

Z

Z

Y

Y

X

X

Y

X

t=0

FID

tp

Acquisition time ~5T2

Rotating x,y axes :rotation about Lab z-axis

A BLUE line for z-Axis indicates the view from within the rotating coordinate system.

Viewed from within the rotating frame the RF field appears stationary

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

No More Clicks ! This show has automatic timings

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

Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame

At the end of pulse, time for F.I.D. begins with t=0

Described in rotating frame: Rotation about the X-axis I(tp) =e-iI-xφIz e+iI-xφwithφ=90º & tp is pulse duration

When the XY magnetizationdecays 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 )

FreeInductionDecay Signal

Computer memory

Time domain

DIGITIZE

15

Analogue to Digital Converter A.D.C.

11

0

Computer output

FFT from FID

Next Slide

Frequency Domain Spectrum

Computer input

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

F.I.D.

This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum

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

Time domain FID data: 32 points

Real Imaginary 16 data16datapoints points Frequency domainspectrum

Value between +1 & 0

0

+1

F.T

F.T

COS

Real

SIN

Imaginary

Imaginary

Real

F.T

Arbitrary Phase

Real

Imaginary

t=0

Provision is made in the data processing system, for routinely applying phase corrections

fc cos(2πνt) + fssin (2πνt)

with fc2 +fs2 =1

Z

External Magnetic Field

Y

X

T1

(1-e-t/ )

I0

T1

It

=

-1/2

Magnetization

Magnetization

Magnetization

+1/2

random

Sample: Ensemble of spins

I0

It

CLICK !

t

It

Magnetization Builds up exponentially

To repeat the above events:Right Click & Select option ‘previous”

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

On the application of field…..

CLICK !

Splitting is instantaneous & population redistribution requires more time called the relaxation time

-1/2

CLICK for….... On-set of Longitudinal Relaxation

No radiations

are present

CLICK !

Not stimulated transitions: but spontaneous relaxation transitions

No net magnetization

CLICK for….

Magnetic field

Net magnetization along Z-direction & ZERO XY component

+1/2

Degeneracy removed/Energy levels split

Thermal equilibrium Boltzmann distribution

Z

Pulse applied

In XY plane precessing magnetization

Y

Solenoidal sample coil axis

Axis- Y

Y

Precessing magnetization induces rf voltage: NMR signal

X

Z

When relaxation process is effective, the relaxation leads to the decay of the transverse magnetization of XY plane

The above picture is for time scales small compared to relaxation time T2

This decay of magnetization due to the transverse relaxation time is because of the defocusing of the magnetization isochromats in XY plane

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

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

November 2009

The Sound Tracks ( playeable audio ) are from the album “ARZOO: Nirvana in six strings” and the Album “Elements: Water” of Shiv Kumar Sharma

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