I want you to close your eyes for a second.
We're going to take a trip. OK, I'm with.
You We are leaving Earth behind. We're traveling about, what, 140
million miles outward through the vacuum of space to a place
that is cold, desolate and covered in a fine, rusty dust.
We're on Mars. We are standing on the surface
of Mars. It is a haunting image, isn't
it? That endless red dust covering
everything. The silence, the the thin
atmosphere. It is.
And reeling through that dust, let's imagine one of the NASA
Rovers, maybe Spirit or Opportunity.
We always picture them taking those incredible panoramic
photos, you know, or drilling into rocks with those mechanical
arms. The classic Mars postcard shots.
Exactly. But there was an instrument on
those Rovers, a specific piece of technology that was doing
something that frankly sounds like magic.
It does. It wasn't just looking at the
rocks. It was interrogating the atomic
nuclei inside the rocks to sniff out the history of water on the
planet. That's right.
And to do that it was using a technique that bridges 2 worlds
that you know, they usually ignore each other.
Nuclear physics and geology. Today we are doing a deep dive
into that technique. It's called Mussbauer
spectroscopy. And look, I know the name sounds
a bit intimidating. Oh, it really does.
It sounds like something you'd fail a test on in grad school.
It definitely has that reputation, but it is genuinely
one of the most elegant, precise concepts in all of physics.
Once you get past the name, the mechanism is it's just
beautiful. And that is our mission today.
We're going to unpack this. We've got a stack of research
papers, lecture notes, and diagrams here, and we are going
to figure out how probing the tiny, dense nucleus of an atom
can tell us about the chemistry happening on the outside.
Right, the electrons. How the nucleus tells you about
the electrons? It's a story about radioactive
decay, relativity, quantum mechanics, and a tuning fork.
A tuning fork is actually the perfect place to start.
It's the best analogy we have for the core phenomenon.
OK, so let's set the stage. The year is 1957.
Who is the hero of our story? Our hero is a German physicist
named Rudolf Musbauer. He was quite young at the time,
actually working on his doctoral thesis in Heidelberg.
So this was a PhD project. This was his PhD project, and
like many great discoveries, he stumbled onto something that
broke the existing rules, or at least the rules as people
understood them. At the time.
He was looking at a phenomenon called nuclear resonance.
Nuclear Resonance? That sounds like the title of a
Tom Clancy novel. It really does.
But let's break that down. I know what resonance is in
music. If I have two guitar strings
tuned to the same note and I pluck one, the other one starts
vibrating. Exactly.
Or think of two identical tuning forks.
If you strike one, let's say it's an A note at 440 Hertz, it
sends out sound waves. If you bring a second identical
tuning fork close to it, that second fork will catch those
sound waves. And it starts to hum.
It absorbs the energy and starts to sing.
That's resonance. Because they match the key fits
the lock. Precisely.
Now, physicists knew this happened with sound.
They also knew it happened with light and atoms.
If you shine a specific color of light at an atom, the electrons
can absorb that light and jump to a higher energy level.
Right, that's standard spectroscopy.
That's how we know what stars are made of.
It is. That's how neon signs work.
Essentially energy goes in, light comes out, or vice versa.
OK. But Mussbauer was interested in
the nucleus. He wanted to know, can we do
this with the core of the atom? Can one nucleus emit a particle
of light, A photon, and have another nucleus of the same type
catch it? A nuclear tuning fork.
So instead of electrons jumping between their shells, we are
talking about the nucleus itself jumping between its own energy
levels. Yes, and this is a crucial
distinction you have to appreciate.
The energy scales here are vastly different.
How different? Well, when electrons jump
around, they release visible light or maybe UV light X-rays
if you're hitting the core electrons.
But when a nucleus jumps, when it rearranges its protons and
neutrons, it releases gamma rays.
Gamma rays. That's Hulk territory.
That's high energy. Extremely high energy.
We are talking about transitions that are thousands, even
millions of times more energetic than visible light.
So the theoretical idea was simple enough.
Nucleus A is excited. It's in a high energy state.
It drops to a lower energy state and shoots out a gamma ray.
Nucleus B is sitting there in its ground state.
It should catch that gamma ray and jump up to the excited
state. Simple catch and release.
If the nuclei are identical, say they're both atoms of iron, the
frequency should match perfectly.
The tuning forks are tuned to the same note.
That that was the theory. That's what everyone thought
should happen. But for decades, nobody could
get it to work in a practical, consistent way.
What would happen? They would fire gamma rays from
a source at a target of the same material and nothing.
The gamma rays would just pass right through, no resonance.
The second tuning fork stayed silent.
Why? I mean, if they were the same
element, shouldn't the key fit the lock?
It feels like it should be automatic it.
Feels like it, but it comes down to a fundamental law of physics,
the conservation of momentum. Or, as we need to discuss it
here, recoil. Recoil like firing a gun.
Exactly like firing a gun. Imagine you are standing on a
perfectly frictionless skateboard and you are holding a
very heavy medicine. Goal.
Yeah, I'm picturing it. I'm on the skateboard.
No, you want to throw that ball to a friend who is also on a
skateboard forward a few yards away.
You heave the ball forward with all your might.
What happens to you? I roll backward.
For every action there is an equal and opposite reaction.
I recoil. Right, you recoil.
Now here's the problem. You put energy into that throw.
You wanted all that energy to go into the ball so it would reach
your friend with maximum speed. But it didn't, no.
Yeah, because you recoiled. You stole some of that energy.
The kinetic energy of your backward motion creates A
deficit. The ball leaves your hands
moving slightly slower than it theoretically should have.
So the bullet is underpowered. Yes, the gamma ray has slightly
less energy than the transition inside the nucleus actually,
provided. We call this recoil energy or E
sub R. So the emitted photon has the
transition energy minus ER. OK, so I throw a weak ball, but
what about my friend who is trying to catch it?
Your. Friend has the same problem,
just in reverse. If they are on their skateboard
and they try to catch that heavy ball flying at them, what
happens on impact? They get pushed backward.
They recoil too. Exactly.
And to absorb that impact and stop the ball, they need to
expend energy. Essentially, for the nucleus to
absorb the gamma ray, it needs the full transition energy, plus
a little extra to account for the fact that it's going to get
kicked backward by the photon. Oh, I see the gap now.
There's a double whammy. The emitter is shooting low
energy minus recoil. The absorber has a high bar to
clear energy plus recoil. And in the world of nuclear
physics, where the energy levels are incredibly sharp, that gap
is twice the recoil. Energy to ER is a chasm.
It's an insurmountable gap. So the photon arrives at the
target nucleus and the nucleus says sorry this isn't enough
energy, I can't make the jump. Your key is just slightly too
small for my lock. The photon either bounces off or
passes straight through. The resonance fails.
And this is what was happening in those early experiments.
Yes, because they were often using gases or liquids where the
atoms are just, you know, floating around, free to move.
So they were all on tiny little skateboard.
They were all on tiny skateboards.
If the atom is free to move, it recoils.
If it recoils, you lose the resonance.
So how did Rudolf Musbauer fix this?
How do you stop an atom from recoiling?
You can't exactly hold it down with tweezers.
No, you can't. But you can change its
environment. This was Musbauer's Nobel Prize
winning insight. He realized that if you lock the
atom inside a solid rigid crystal lattice, everything
changes. Because it's chemically bonded
to all of its neighbors. Exactly.
It's handcuffed to the atoms next to it, which are handcuffed
to the atoms next to them, and so on for the entire crystal.
So now when the nucleus tries to kick back after emitting the
gamma ray, it can't just move the single atom.
It has to try to move the entire crystal.
The entire crystal. I see where this is going.
It's the difference between throwing that medicine ball
while standing on a skateboard versus throwing it while bracing
yourself against a brick wall. That is the perfect analogy.
If you are braced against a building, you don't move, you
don't recoil. All the energy goes into the
ball. The ball flies at full speed.
And your friend, who's also braced against a wall can catch
it without getting knocked over. And physically, this works
because of the mass, right? The formula for recoil energy
has mass little M in the denominator.
If M is the mass of one single atom, the recoil energy is
significant. But if the atom is part of a
crystal, the effective mass becomes the mass of the entire
lattice. That number is huge, billions
and billions of times larger. So if you divide by a
practically infinite number, the recoil energy drops to 0.
Effectively 0. It's not truly 0, but it's so
small it becomes negligible. We call this recoiless nuclear
resonance. By freezing the atoms in a
solid, the emission line and the absorption line now overlap
perfectly. The key fits the lock.
The second tuning fork. That is, it's a physics magic
trick. You're using the collective
stiffness of a crystal to enable a nuclear measurement.
And that is the Mussbauer effect.
It opened the door to some of the most precise measurements in
the history of physics. It turned a theoretical
impossibility into a practical, powerful tool.
OK, so we have the method. We have this this recoilless
trick to make nuclei talk to each other, but we aren't just
doing this for the sake of physics.
We want to learn something about the stuff we are studying.
We want to do chemistry. We want to do chemistry, and to
do that we need a specific element.
The outline mentions iron. Is iron the only one this works
for? It's not the only one.
There are, I think over 40 elements where this effect has
been observed. Things like tin, europium, gold,
nickel, but iron specifically the isotope Iron 57 is the
absolute superstar. The king of Mussbauer.
Absolutely. I'd say 90%, maybe even more, of
all Mussbauer publications are on iron.
Why? Is it just because iron is
common? That helped.
I mean, it's everywhere in geology, biology, and industry.
Corrosion, Hemoglobin Magnets. Mars.
It's everywhere. It is, but physically Iron 57
just happens to have the Goldilocks properties.
The energy levels are just right.
The lifetime of the excited state is convenient for
measurements, and, crucially, it works reasonably well at room
temperature. So it's practical.
It's very practical. Many other elements require you
to cool your sample down to near absolute zero temperatures to
get a strong enough effect, which is, you know, a hassle and
expensive. OK, so Iron 57 is our player,
but here's a detail from the notes that confused me
initially. To study iron, we don't start
with iron, we start with cobalt. Right.
This is about how we generate the gamma rays.
You can't just buy a bag of excited iron nuclei.
Excited states decay very, very quickly.
So you need a generator. You need a parent isotope that
decays into the thing you want, conveniently leaving it in that
excited state for you. So cobalt is the parent.
Yes, Cobalt 57, it's radioactive and it has a half life of about
270 days. That's a nice half life.
Not too hot, not too cold. It's great.
It means you can buy a force from a supplier and it will be
useful in your lab for a year or two before it gets too weak.
And what does this Cobalt 57 do? It undergoes a process called
electron capture. What is that?
It's exactly what it sounds like.
The nucleus, which is positively charged, reaches out and grabs
one of its own inner electrons from the K shell.
Usually it pulls that electron in a proton plus an electron
becomes a neutron. So the atomic number drops by 1.
The atomic number drops by 1. Cobalt is element 27.
It captures an electron. A proton becomes a neutron, and
now it has 26 protons. It's iron.
Alchemy in action. Indeed.
But the iron nucleus it creates is born in a highly excited
state. It's vibrating with excess
energy. It wants to calm down.
So it sheds that energy. It cascades down first.
It drops from a very high spin state of 52 down to a lower
excited state of 32. In doing so, it emits A136KV
gamma ray, which we don't care about.
We just filter that one out. Noise.
It's noise, but now it's sitting in that 32 excited state, which
has a lifetime of about 100 nanoseconds.
And then it makes the final drop.
It drops from the 32 state to the ground state, which is 12.
And that final drop is the money shot.
That's the one. That specific transition
releases a gamma ray with a very precise energy of 14.4 qv. 14
point 4K electron volts. I'm guessing that number is
burned into the brain of every Musbauer spectroscopist.
It is the sacred number that is our probe, that is our perfectly
tuned key. That gamma ray flies out of the
cobalt source, travels towards our sample, and if everything is
right, it gets absorbed. So let's visualize the machine.
We have the source which is the Cobalt 57 embedded in some kind
of matrix. Usually a rhodium foil, yeah.
OK, so the cobalt source, then we have the absorber, which is
our sample, let's say a piece of that Martian rock.
And behind the rock, we have a detector.
Correct. It's a transmission experiment,
just like an X-ray at the doctor's office.
You're looking for the shadow. You are counting the gamma rays
that don't get through. So if the iron in the rock
absorbs the gamma rays, the detector sees a dip in the count
rate. It sees a shadow.
Exactly. You get a plot of gamma ray
transmission versus something else and you look for the dips.
But wait. We have a problem if we have the
perfect resonance we just talked about, no recoil, wouldn't we
just see a total blackout? If the source is emitting from
an iron 57 nucleus and the sample is also iron 57,
shouldn't they always match perfectly?
Now that is the billion dollar question, and the answer is what
makes this technique useful? If every iron atom in the
universe were identical and floating in a vacuum, yes you
would see one single strong absorption line.
But. But.
They're not. Atoms aren't in a vacuum.
They're in molecules. They are in crystals.
They are surrounded by electrons.
Chemistry gets in the way. So chemistry messes with the
nucleus. Chemistry gets in the way, and
this is the whole point of the deep dive.
The chemical environment, the oxidation state, the atoms it's
bonded to, the whole cloud of electrons whizzing around the
nucleus actually affects the nucleus itself.
It subtly shifts the nuclear energy levels.
So the lock in the sample is slightly jammed or slightly
modified compared to the key from the source.
Exactly. The source nucleus is in a nice
clean, symmetric rhodium metal environment.
The sample nucleus might be in a rusty, distorted, messy mineral.
Their energy levels are no longer a perfect match.
So the resonance is lost again. The gamma rays just pass right
through, correct? So we broke it.
We did all this work to get recoil, this resonance, and that
chemistry has come along and broken it.
We didn't break it, we made it sensitive.
We've turned a bug into a feature.
Now to find the resonance again, we have to tune our gamma ray.
We have to slightly change its energy to match the new
chemically shifted requirement of the sample.
How do you tune a gamma ray? You can't just turn a knob on
the nucleus. No, but you can move the source.
We use the Doppler effect the. Train whistle effect the Neos as
it passes by. The very same If a train moves
towards you, the sound waves get squashed, the frequency goes up
and the pitch sounds higher. If it moves away, the waves
stretch out and the pitch goes down.
We do the exact same thing with the gamma ray source.
So you physically move the radioactive source.
We mount the radioactive cobalt source on a motor, a high
precision linear motor, and we vibrate the source back and
forth very smoothly. You're kidding.
Not at all. When the source moves toward the
sample, the gamma ray gets a tiny boost of energy, a blue
shift. When it moves away from the
sample, the gamma ray leases a tiny bit of energy, a red shift.
This seems incredibly primitive and incredibly high tech at the
same time. We are mechanically moving a
radioactive rock to tune a quantum nuclear transition.
That's a great description of it.
How fast does this motor have to move?
I'm imagining something blurring back and.
Forth. That's the best part, and this
speaks to the insane precision of the effect.
To shift the energy enough to scan through all the typical
chemical changes, we don't need to move at the speed of light or
even the speed of a car. We need to move it millimeters
per second. Millimeters per second, like
snail speed. Literally snail speed.
The typical range for scanning iron compounds is usually
between -10mm per second and plus 10mm per second and.
That creates enough of an energy shift to matter.
Yes, the nuclear resonance is so incredibly sharp, so exquisitely
tuned, that a tiny Doppler shift is more than enough to scan
across the entire absorption line.
That's why when you look at a Mussbauer spectrum, the X axis
isn't labeled in joules or frequency, it's labeled in
velocity. Is wild.
You're plotting transmission against the speed of a snail.
So we are looking for a dip in the grab a shadow at a specific
speed, maybe at plus .2mm the detector count suddenly drops.
Exactly. And that velocity where the dip
occurs tells us exactly how much the energy levels in the sample
have shifted relative to our source.
And that brings us to our first major data point, the first
piece of chemical information we can extract, the isomer shift.
OK, let's decode this. The isomer shift which is given
the Greek letter delta. I see what is physically
happening in the atom to 'cause this shift.
What is chemistry doing to the nucleus?
It comes down to something that seems very strange at first.
It's about the size of the nucleus.
We usually think of the nucleus as a hard little point, like a
marble, but it's not rigid. When a nucleus gets excited by
absorbing A gamma ray, it actually changes its radius.
It puffs up or it shrinks. For some isotopes it gets
bigger. For others it gets smaller.
For our hero Iron 57, the excited state is actually
smaller in radius than the ground state.
The nucleus physically shrinks a tiny bit when it gets excited.
OK, that's a weird concept to wrap my head around, but I'm
with you. The nucleus changes size.
How does chemistry connect to that?
The connection is the electrons. The nucleus is surrounded by
electrons. But remember your orbital shapes
from high school chemistry SPDF. Vaguely S orbitals are spheres,
P orbals are dumbbells, D orbals are like clovers.
Perfect. The key here is that only the S
electrons, the spherical ones, have a non 0 probability of
being found inside the nucleus. Inside, I thought electrons
orbited around the nucleus like planets.
In the old Bohr model, yes. But in quantum mechanics,
electrons are clouds of probability.
Their wave functions describe where they are likely to be, and
the spherical wave function of an S electron actually
penetrates the nuclear volume. It spends a tiny fraction of its
time literally sitting on top of the protons and neutrons.
So the P&D electrons stay outside, but the S electrons get
in. That's the crucial point.
The nucleus feels the presence of these S electrons.
It's in direct contact with them, and because the nucleus
changes size during the transition from ground to
excited state, the electrostatic interaction between the nucleus
and that S electron density changes.
And that changes the energy levels.
It shifts them. The energy of the ground state
and the excited state are both shifted by this interaction, but
by slightly different amounts because their radii are
different. This creates a change in the
transition energy. This creates the isomer shift.
So if I change the chemical bonding around an atom, I change
its overall electron configuration, which changes the
S electron density, which changes the shift.
Precisely, you've got it. Let's look at the tin example
from your notes. Tin 119.
It's a classic and a great way to visualize oxidation states.
Tin Tin We have two common oxidation states, tin 2 and tin
3. Right, a neutral tin atom has an
electron configuration ending in five shellers, 5 P $2.00, two
airs electrons, 2P electrons and it's outer shell.
Got it? Now consider tin 3 the stanic
ions 7 plus dollars to become four plus thera it.
Loses those 4 outer electrons or it forms bonds where they are
shared so strongly they are basically pulled away.
So the S electron density at the nucleus is lower.
OK, low density for tin 3. Now look at tin 2, the Stannis
ion 70 plus dollar. When tin forms A2 plus ion, it's
energetically favorable to lose the electrons first.
So it loses the five PT 2 electrons, but it keeps the five
PT 2 pair as a lone pair. So TIN 2 has this big fat cloud
of selectrons sitting right on the nucleus.
Exactly. It has a much higher electron
density at the nucleus compared to tin four, and because the
nucleus interacts with that density, the nuclear energy
levels shift by different amounts.
In the case of TIN, this means TIN compounds show up at a much
higher positive velocity than TIN compounds.
So you can just look at the chart.
If the dip is way out of plus 3mm you can say with confidence
that's tin 2. If it's down near 0 you say
that's 10 four. You are reading the oxidation
state directly from the nucleus. You are.
It's an incredibly powerful fingerprint for oxidation state,
and it gets even more subtle. We can see the effect of the
neighbors, the ligands that the atom is bonded to.
The notes mentioned fluorine versus chlorine bonded to tin.
Right, this is all about electronegativity.
Remember that from chemistry and atoms greed for electrons.
Chlorine is the greediest of all.
Fluorine is the bully of the periodic table.
It wants electrons more than anyone else.
So if you bond 10 to 4 fluorine atoms to make 7F4 hills, the
fluorine atoms pull the bonding electrons violently away from
the tin. So the two nucleus is left
naked? Electronically speaking, yeah.
Relatively speaking, yes, it has very low electron density around
it and therefore a very low electron density at the nucleus.
This results in a very low, even negative isomer shift.
The data shows Maddio .47mm for that compound.
OK, now what if we swap the fluorine for chlorine?
We make SNCL 4 SU dollars. Chlorine is also very greedy,
but it's not as greedy as fluorine.
It pulls on the electrons, but it lets the tin keep a little
bit more of the electron density for itself.
So the S electron density at the nucleus goes up and the shift
goes up. Correct.
The isomer shift for SNCL 4 three is +85 millimeters.
That's a huge difference in this world.
It's a completely different part of the spectrum.
I love this because it's so tangible.
You are using a nuclear interaction that's happening on
a femtometer scale to measure how greedy A neighboring atom
is. It is a nuclear spy in the
chemical camp. It's reporting back on the
nature of the chemical bonds. So that's the isomer shift, the
side to side movement of the peak.
But looking at these Martian Spectra, the graphs aren't
always just single dips. Sometimes they look like, well,
they're split in two, or they look like a comb mountain range.
Yes, the single absorption line we've been talking about can
split into multiple lines. This is where we get into the
other hyperfine interactions. The isomer shift is 1, but there
are others. The first one in the outline is
quadrupole splitting. That sounds like a leg exercise
at the gym. What is a quadrupole?
It refers to the shape of the electric charge distribution in
the nucleus. We like to imagine nuclei as
perfect little spheres, like basketballs.
In that case, the chart is distributed symmetrically.
But it's not always like that. For many isotopes, including
Iron 57 in its excited state, the nucleus is deformed.
It's not a sphere. It's shaped more like a rugby
ball or an American football. We call that prolate.
Or it could be flattened like an M&M, which we call oblique.
OK, so we have an asymmetrical nucleus, A football shaped
nucleus. Now imagine you put that
asymmetrical nucleus into an asymmetrical electric field.
What would create an asymmetrical field?
The electrons, if the electrons in the chemical bonds around the
atom aren't distributed evenly in a nice symmetrical way like a
cube or a sphere, they create what's called an electric field
gradient. There's more negative charge in
One Direction than another. Got it?
So you have a non spherical nucleus in a non spherical
electric field. The nucleus experiences a
torque. It tries to align itself, but
quantum mechanics says it can't just point anywhere.
The energy levels split. So instead of 1 jump from the
ground state to the excited state, there are now 2 possible
jumps with slightly different energies.
Exactly. And because there are two
possible transition energies, the single absorption line
splits into a doublet 2 distinct line side by side.
And what does that tell the chemist?
What's the take away from seeing a doublet instead of a singlet?
It tells you about symmetry. If you see a single line, it
means your iron atom is sitting in a very symmetric local
environment. Maybe it's at the center of a
perfect cube of oxygen atoms, or a perfect octahedron.
But if you see that splitting that doublet, you know the
environment is distorted. So if you squash that cube, or
if you replace one of the neighboring oxygen atoms with a
nitrogen atom, you break the symmetry.
You break the symmetry, you create an electric field
gradient, and the quadruple splitting appears.
It's a geometry detector. It tells you if the Adam's house
is perfectly built or if it's a bit lopsided.
That's a great way of putting it.
And then we have the big one, the one that was so important
for Mars, magnetic splitting. Yes, this is also known as the
nuclear Zeeman effect. This is what makes Iron 57 so
incredibly powerful for geology and material science.
So what's the principle here? The nucleus itself, because of
the spin of its protons and neutrons, acts like a tiny bar
magnet. It has a magnetic moment.
A tiny compass needle. Tiny compass needle.
Now, if there is a magnetic field present where that nucleus
is sitting, that compass needle will try to align with it.
And just like with the quadrupole effect, quantum
mechanics says it can only align in a few specific, quantized
ways. This splits the nuclear energy
levels apart dramatically. And this magnetic field, does it
have to be from a big external magnet?
It can be, but often for materials like iron, metal or
iron oxides, the material generates its own incredibly
strong internal magnetic field. OK, so the material itself is
magnetic. How many lines do we get from
this splitting? For Iron 57, due to the specific
spin states of the ground and excited levels, the levels split
in such a way that you get 6 allowed transitions.
So the single line splits into a sex stat A.
Sex Stat 6 lines. 6 lines. It looks like a six fingered
comb, usually with a characteristic 3 to 2 to 1
intensity ratio for the pairs of peaks.
And this is the fingerprint. This is the definitive
fingerprint. Different magnetic iron minerals
have different magnetic strengths and structures.
Magnetite fee three O 4 Chore 3 creates a very wide splitting
pattern. Chemotite from how the main
component of rust has a different very distinct pattern.
Another common iron mineral is different again.
So when the Rover on Mars looked at one of those little spherical
rocks, the blueberries and its must power spectrometer saw a
sextet with a specific spacing and a specific isomer shift.
It knew with 100% certainty that is hematite.
No other mineral gives that exact signal.
And why do we care about hematite on Mars?
Because on Earth, that specific form of hematite almost always
forms in the presence of large amounts of standing liquid
water. Finding those specific magnetic
fingerprints was the smoking gun.
It was the absolute proof that Mars had a wet past.
That is incredible. We found the ghost of an ancient
ocean on another planet by jiggling a radioactive source at
the speed of a snail. It puts it in perspective,
doesn't it? The scales are just mind
boggling. There is one last technical
hurdle I want to touch on because it seems important for
actually doing these experiments.
The notes mentioned temperature and liquid nitrogen.
We talked about how the crystal needs to be solid to absorb the
recoil. Does temperature affect that?
Hugely. Even in a solid crystal, atoms
aren't perfectly still. They vibrate.
They have thermal energy. In solid-state physics, we
describe these collective vibrations as phonons.
Like sound particles. Essentially, yes, quantized
lattice vibrations. Now, if the atom is vibrating
too violently, if the crystal is too hot, the probability of a
purely recoilus event drops. Why?
Because the atom has another way to deal with the recoil energy.
Instead of transferring the momentum to the entire crystal,
it can just absorb the kick. By increasing its own vibration,
it can create a phonon. And if it creates A vibration,
it uses up some of the energy and we lose the perfect energy
match. Exactly.
The recoil free fraction, which has the technical name of the
West Waller factor, goes down as temperature goes up.
If your sample is made of atoms that are weakly bonded, if the
crystal is soft, or if it's too hot, the signal just disappears
into the noise. You get no absorption.
So that's why you see photos of these with giant steaming metal
flasks, doers of liquid nitrogen.
They are freezing the sample. They're freezing the sample to
make the crystal lattice as stiff and rigid as possible.
They're trying to maximize that recoil free fraction.
To quiet down the thermal vibrations.
Exactly. For many isotopes you absolutely
need to go down to 77 Kelvin, which is the temperature of
liquid nitrogen, or for some even more difficult cases, down
to 4 Kelvin with liquid helium to see anything at all.
But Iron 57 works at room temperature, you said?
Iron 57 is robust enough. The bonds in typical iron
compounds are strong enough that we can get a decent signal at
room temperature. The signal gets much sharper and
stronger if you cool it down, but you can do it at 300 Kelvin.
And that's why we could send it to Mars.
That's why you definitely do not want to try and haul a Dewar of
liquid helium 140 million miles to Mars.
No, that seems like a logistical nightmare.
A definite non starter for a Rover mission.
So let's wrap our heads around this entire journey.
It really is a synthesis of so many different fields of
science. It truly is.
We start with the deepest physics, the nucleus.
Radioactive decay, high energy gamma rays, even special
relativity comes into play with some of the temperature effects.
Then we move to solid-state physics.
The crystal lattice phonons the whole idea of the collective
solid absorbing the recoil. Then we use the Doppler effect,
which is pure classical mechanics, the physics of trains
and sound waves, to tune the energy.
And finally, we interpret the data using pure chemistry,
Oxidation states, electronegativity of ligands,
molecular geometry, symmetry. It's a tool that ignores
boundaries. It doesn't care if you call it
physics or chemistry or geology or material science.
And that's. Why it's so powerful?
It allows us to see the local environment of Ecific atom in a
way that other techniques can't always do.
Exactly. Something like X-ray diffraction
is great for finding the long range average structure of a
crystal where the atoms are in the unit cell, but Mussbauer
tells you what that one specific iron atom is feeling.
Is it magnetic? Is it in a distorted site?
Is it you would to or you would to?
Is it giving up its electrons to a greedy neighbor?
It's like interviewing every atom individually instead of
just taking a census of the crowd.
That's a beautiful way to put it.
It gives you that local atom specific perspective.
I want to leave our listener with that thought about
precision. We talked about how we are
moving the source of millimeters per second, but the precision of
the measurement itself is just. It's hard to comprehend.
Let me try to give you a comparison.
The sharpness of the 14.4 KV line in iron 57 is such that we
are detecting a change in the energy of a gamma ray of about
one part in 10 to the 12, so one part in a trillion.
One in a trillion. Now to put that in perspective,
if you were to measure the distance from the Earth to the
Sun, which is about 93,000,000 miles, OK, and you wanted that
same level of precision, one part in 10 to the 12, you would
be measuring that distance to within about 15 centimeters,
about 6 inches. You'd be measuring the distance
to the sun with the accuracy of a school ruler.
That is the level of precision we are talking about, and we do
it on a tabletop or on a Rover millions of miles away.
It's just astounding. Sometimes the quietest, slowest
movements really do reveal the deepest truths.
I couldn't agree more. It's a testament to how
interconnected everything is, from the largest scales to the
smallest. That's our deep dive on
Mussbauer spectroscopy, from the rusty dust of Mars to the
quantum dance of the nucleus. Thanks for coming on this
journey with us. It was an absolute pleasure.
And to you, our listener, next time you see a piece of rust on
an old gate or a nail, remember there was a whole Symphony of
nuclear physics happening inside it, just waiting for the right
tuning fork to make it sing. See you next time on the Deep
Dive.