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