3 L Rotating Frame
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Transcript of 3 L Rotating Frame
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Rotating frame of reference
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Sample
Magnetization
Response
Data
A conceptual block diagram of the pulsed Fourier
transform NMR experiment
Spectrum
Storage
Magnet
Perturbation
Detection
Fourier Transformation
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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
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The Nature of Linear and Circularly Polarised
Fields
leftright linear
The linear field as sum of counter rotating circularly polarised
components
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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
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L
0
z, B0
)( 1Brf
)( 1Brf
x
timmel.chem.ox.ac.uk
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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?
timmel.chem.ox.ac.uk
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L
0
z, B0
)( 1Brf
timmel.chem.ox.ac.uk
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L
0
z, B0
)(1
Brf Lrf B )( 1
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01)( Brf
z, B0
//)( 00 rfrf BB
rf 0
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x
y
z
B0
B1(t)
B(t)
x
y
z
B1
B
We have two fields
Move into rotating frame
B0 rf/
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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
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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
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IBT03AUTUMN2014@ googlegroups.com
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IBT03AUTUMN2014@ googlegroups.com
Rotating frame of reference