This document discusses the principles of nuclear magnetic resonance (NMR) and how it can be used to characterize samples. NMR uses magnetic fields to manipulate the magnetic moments of nuclei in a sample. It describes how free induction decay (FID) signals can identify the elemental composition of a sample using Fourier analysis. Spin echoes can revive decaying FID signals by flipping the magnetic moments. The document also discusses how Carr-Purcell and spin-lattice relaxation time methods can obtain information about a sample's physical properties by measuring characteristic relaxation times. These methods allow distinguishing between ice and a mixture of corn starch and water.

1. Spin
Echoes
&
the
Principles
of
NMR
Frank
Odom
III
Department
of
Physics
&
Astronomy
University
of
the
South:
Sewanee
Overview
Nuclear
MagneEc
Resonance
is
widely
used
in
the
fields
of
biology,
chemistry,
and
medicine
as
a
non-­‐
destrucEve
imaging
method.
NMR
can
obtain
valuable
informaEon
about
a
given
sample
by
manipulaEng
the
magneEc
moments
of
its
nuclei.
I
have
conducted
NMR
experiments
using
Earth’s
magneEc
field
(about
39
μT)
as
my
primary,
external
magneEc
field.
Figure
2.
FID
signal.
Elemental
ComposiEon
We
can
easily
obtain
informaEon
about
the
elements
within
a
sample
from
an
FID
signal.
Any
nucleus
with
a
net
magneEc
moment
will
precess
at
a
characterisEc
frequency,
called
the
Larmor
frequency.
Fourier
analysis
can
easily
idenEfy
the
consEtuent
elements.
Figure
1.
Equipment
from
TeachSpin
Spin
Flips
&
Spin
Echoes
Our
FID
signal
decays
primarily
due
to
field
inhomogeneiEes;
however,
we
could
revive
the
signal
by
“flipping”
our
magneEc
moments
(a
spin
flip),
causing
them
to
precess
in
the
opposite
direcEon.
The
revived
signal
is
called
a
spin
echo.
Figure
3.
Spin
Echo
signal
Electronics
We
will
try
to
excite
a
spin
flip
using
radio
waves.
So,
our
electronic
circuit
must
be
able
to
provide
the
following:
• Time
delay
of
about
0.5
s
• Sine
wave
output
pulse
of
easily
controlled
magnitude
and
duraEon
Figure
4.
Electronic
circuit.
Quantum
Mechanics
Using
Schrödinger’s
equaEon
as
well
as
Eme-­‐dependent
perturbaEon
theory,
the
probability
of
a
spin
flip
is:
0.5 1.0 1.5
»Vosc» HVL
0.5
1.0
1.5
2.0
Spin Echo HVL
10 20 30 40
Number of Cycles
0.5
1.0
1.5
2.0
2.5
Spin Echo HVL
1500 1600 1700 1800 1900 2000
fosc HHzL
0.5
1.0
1.5
2.0
2.5
Spin Echo HVL
Carr-­‐Purcell
Method
We
can
determine
the
characterisEc
relaxaEon
Eme
for
a
given
sample.
This
is
called
the
spin-­‐spin
relaxaEon
Eme.
Figure
5.
Carr-­‐Purcell
method.
Spin-­‐Labce
RelaxaEon
Time
AddiEonal
valuable
informaEon
can
be
obtained
from
the
spin-­‐labce
relaxaEon
Eme.
This
is
more
easily
thought
of
as
the
“polarizaEon
Eme”
for
a
given
sample.
5 10 15
Time HsL
1
2
3
4
5
6
7
FID Signal HVL
Figure
6.
Spin-­‐Labce
RelaxaEon
Time.
Characterizing
a
Sample
We
can
use
these
two
methods
of
imaging
to
determine
the
physical
characterisEcs
of
samples–
namely,
ice
and
a
mixture
of
corn
starch
and
water.
1 2 3 4 5 6
Time HsL
5
10
15
20
FID Signal HVL
Figure
7.
Spin-­‐Labce
RelaxaEon
Emes
for
ice
and
mixture
of
water
and
corn
starch.
Acknowledgements
• TeachSpin
• Dr.
Peterson
• Sewanee
Physics
Dept.
The
mixture
of
corn
starch
and
water
behaves
much
more
like
ice–
a
crystalline
solid–
than
a
liquid.
Without
any
addiEonal
informaEon,
it
would
be
much
easier
to
disEnguish
the
mixture
from
water.