3 L Rotating Frame

8/11/2019 3 L Rotating Frame

1/17

Rotating frame of reference


2/17

Sample

Magnetization

Response

Data

A conceptual block diagram of the pulsed Fourier

transform NMR experiment

Spectrum

Storage

Magnet

Perturbation

Detection

Fourier Transformation


3/17

If the magnetization can be moved away from its equilibrium position , thenprecession occurs and a signal may be detected.

The displacement of the magnetization from equilibrium or excitation isproduced by the second magnetic field B1(with frequency 1)

When frequency 1= 0= B0 , magnetization moves towards the xy plane.

The final position of magnetization will depend upon the length of the timefor which the radiofrequency is applied. The angle through which themagnetization is tipped from the z axis (flip angle or tip angle) is

= B1tp

We measure the magnetization in the xy-plane, looking along the x-axis,

there will ideally be a sinusoidal variation in intensity with pulse width. The

signal will be a maximum for a tip angle of /2, a null at when the

magnetization is along tha z, a negative maximum at 3 /2 and null at 2 .


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z

Absence of magnetic field

mI=+1/2

mI=-1/2

b

az, B

0M

0

Presence of magnetic field

Phases of spins are random

LL 2

0


5/17


6/17

The Nature of Linear and Circularly Polarised

Fields

leftright linear

The linear field as sum of counter rotating circularly polarised

components


7/17

The Rotating Frame

linear field:1

( ) cosx rf

B t B t

+

BR(t)

BL(t)

B1(t)

only the component that rotates in

the same senseas the Larmor

precession of the spins is retained!

The other is hundreds of MHz

off-resonance

and will be ignored!

j

i

)sincos(2

)( 1 tjtiBtBfrfrR

)sincos(2

)( 1 tjtiB

tBfrfrL


8/17

L

0

z, B0

)( 1Brf

)( 1Brf

x

timmel.chem.ox.ac.uk


9/17

x

y

z

B0

B1(t)

B(t)

We have two fields

Move into rotating frame (sit on the carousel)

y

x

y

z

B0?

B1

B?



10/17

L

0

z, B0

)( 1Brf



11/17

L

0

z, B0

)(1

Brf Lrf B )( 1


12/17

01)( Brf

z, B0

//)( 00 rfrf BB

rf 0


13/17

x

y

z

B0

B1(t)

B(t)

x

y

z

B1

B

We have two fields

Move into rotating frame

B0 rf/


14/17

The Rotating Frame of reference

View NMR experiment in rotating frame

which rotates about z-axis with angular frequency rf,radiofrequency field B1 now appears static; B1 pulse is

simply a temporarily applied field orthogonal to B0

x

z

x

y

z

before pulse

Maligned along z-axis of rotating

frame

during pulse

M precesses about the B1field along

thex-axis (onto y axis)

yB1

M


15/17

Pulsesx

y

z

angular frequency of precession(nutation frequency)

11 B

angle through which Mrotates pt1 length of pulse

x

y

z

900-degree pulse

transverse magnetisation

populations equalised

x

y

z

1800-degree pulse

inversion of equilibrium

magnetisation


16/17

IBT03AUTUMN2014@ googlegroups.com

[email protected]


17/17

IBT03AUTUMN2014@ googlegroups.com

[email protected]

Rotating frame of reference

3 L Rotating Frame

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