September 23, 2025 • 24 mins
In this episode of Math! Science! History!, Gabrielle uncovers the fascinating story of quasicrystals, once thought impossible, now proven to exist both in the lab and in meteorites from space. Listeners will learn how quasicrystals challenged centuries of crystallography, the math that explains their strange patterns, and the surprising ways they’re used today, from non‑stick coatings to futuristic photonics.
Three Things You’ll Learn
- Why quasicrystals broke the old definition of crystals and forced scientists to rewrite the rules.
- How Penrose tilings and higher‑dimensional geometry reveal the math behind quasiperiodic order.
- Where quasicrystals are used today in technology, industry, and even planetary science.
Resources & Links
- Dan Shechtman’s Nobel Lecture: Nobel Prize 2011 in Chemistry
- Paul J. Steinhardt, The Second Kind of Impossible (2019)
- Marjorie Senechal, Quasicrystals and Geometry (1995)
- Luca Bindi et al., “Natural Quasicrystals,” Science (2009): https://doi.org/10.1126/science.1170827
🔗 Explore more on our website: mathsciencehistory.com
📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:01):
Today, we are exploring quasicrystals.
What they are, how an impossible pattern was found in a lab,
and how it became the catalyst to rewriting textbooks.
And why this exotic order matters for real-world technologies
from wear-resistant coatings to photonics.
(00:23):
I'm Gabrielle Birchak, and this is Math Science History.
Imagine holding a metal that seems to obey rules that nature once forbid.
You shine an electron beam through it, and on the detector,
a perfect ring of 10 bright dots appear.
(00:44):
Tenfold symmetry, crisp and clean.
For more than a century, crystallography said that symmetry was impossible in a crystal.
Yet, there it is, staring back at you.
It is order without repetition, and a pattern that never tiles
by marching the same unit cell across space.
This is a quasicrystal.
(01:06):
So what exactly is a quasicrystal?
Well, when most people think of crystals, they picture something like salt or quartz.
It's neat, geometric, and orderly.
That's because traditional crystals are built from tiny repeating patterns,
like perfectly placed tiles on a bathroom floor.
This repeating unit, called a unit cell,
(01:29):
fits together over and over in all directions to fill the space.
These crystals follow strict symmetry rules.
So imagine rotating a snowflake.
It still looks the same at every 60-degree angle.
That is called six-fold symmetry.
Salt crystals, for example, can have four-fold symmetry.
(01:50):
And diamonds follow a three-fold pattern.
These regular symmetries leave a signature when scientists shine x-rays through them.
They create sharp, clear patterns, much like a fingerprint of repetition.
Quasicrystals are different.
They are ordered, but not periodic.
Their atoms sit in a coordinated arrangement that exhibits long-range order.
(02:14):
Yet the pattern never repeats by simple translation.
In reciprocal space, quasicrystals still show sharp peaks.
These are signatures of long-range order.
But those peaks arrange themselves in forbidden symmetries,
such as five-fold, eight-fold, ten-fold, or even twelve-fold.
And since I have Taylor Swift on the brain,
(02:37):
they got engaged.
I'm going to give it a literary perspective.
Periodic crystals repeat, but quasicrystals rhyme.
If you want a mental picture, imagine a penrose tiling,
the famous kite and dart pattern that covers a plane with no repeating wallpaper motive.
Yet it contains a hidden hierarchical order.
(03:00):
I'm going to post an image of that at masssciencehistory.com
that you can find under the link called Transcriptorium.
That's the blog page.
And oh, hey, while you're there at Mass Science History,
don't forget to click on that coffee button and make a donation to Mass Science History
because every donation you make helps to keep the podcast up and running.
(03:21):
So, penrose tiles were groundbreaking because they revealed two key ideas.
First, non-repeating order is possible.
Second, the golden ratio appears again and again in the spacings of motives.
But with quasicrystal structures,
the distances between atomic clusters often occur in phi-related ratios.
(03:42):
Yeah, that wasn't a flub-up.
I said phi-related ratios.
Okay, so what is a phi-related ratio and what is phi?
Okay, well, phi is a Greek letter.
You've probably heard of that.
And it looks like a lowercase O with a line through it,
kind of like a backward-facing P stuck toward a forward-facing P.
(04:03):
And like the Greek letter pi, phi has a value, which is about 1.618.
I'm going to put the math up at Mass Science History
so that you can see the representation of phi
and how it is mathematically defined if you are interested in that.
So, here's an audio analogy.
Okay, clap every two beats with one hand and every three beats with the other.
(04:29):
The composite rhythm never exactly repeats, but it isn't random.
It is structured.
Quasicrystals are like that, except the beats are vectors in space
and the interference creates a tapestry of order that never loops.
Another important point of quasicrystals is that they are definitional.
(04:50):
The International Union of Crystallography eventually reframed the term crystal
to emphasize diffraction, stating that a crystal is any solid
that yields an essentially discrete diffraction pattern.
That moves us away from a, quote, must-have-a-unit-cell, unquote,
and toward a, quote, must-exhibit-long-range-order, quote,
(05:15):
which is a definition quasicrystals satisfy perfectly.
So, instead of insisting that a material must repeat the same tiny building block over and over,
like tiles that all match, scientists began to focus on something broader.
They focused on material that has an overall structure
(05:35):
that stays consistent across large distances.
That's what we call long-range order.
And while quasicrystals don't repeat like normal crystals,
they still have this deep, elegant order, just without the strict repetition.
In fact, quasicrystals are the perfect example of long-range order without periodocity.
(05:57):
So, they don't have that spatial repetition that we would see in regular crystals,
like salt or quartz, where the atoms repeat in a very strict grid-like pattern.
That, in regular crystals, is called periodic spatial order.
In quasicrystals, atoms are arranged in a way that is ordered but doesn't repeat.
(06:18):
They still follow the mathematical rules and exhibit long-range order,
but you won't find repeating tiles for a repeating unit cell.
So, on to the discovery that should not have happened.
It was a spring morning in 1982.
In a quiet lab at the National Bureau of Standards in Maryland,
which is now known as the National Institute of Standards and Technology,
(06:41):
material scientist Dan Schechtman was alone at his electron microscope,
analyzing a rapidly cooled aluminum manganese alloy.
He wasn't expecting a revolution.
He was studying alloys like he had countless times before.
Routine, repetitive, predictable.
But what he saw next changed everything.
(07:04):
The diffraction pattern staring back at him showed tenfold rotational symmetry,
like a decagon etched in atomic light.
That was impossible.
According to the study of crystallography,
you simply couldn't have a crystal with tenfold symmetry.
The laws were clear.
Only twofold, threefold, fourfold, and sixfold symmetries were allowed.
(07:28):
Anything else was forbidden.
Then, Schechtman blinked, recalibrated, took another look.
It was still there.
He scribbled in his notebook,
tenfold with a bunch of question marks.
Was it an error?
A twinned crystal playing tricks?
He checked again and again.
The pattern held.
In a 2011 interview,
(07:50):
he told the story of how his colleagues reacted to his discovery.
When Schechtman shared the data with his colleagues,
the response wasn't celebration.
It was disbelief.
One colleague reportedly said,
go read the textbook.
Another insisted he was wrong.
Finally, his group leader told him,
Danny, you are a disgrace to my group,
(08:12):
and I want you to leave my group.
I don't want to be associated with this.
And so, Dr. Schechtman was removed from his research group.
I'm going to post the link to this interview
on the Math Science History website.
It's a really interesting read
because Dr. Schechtman doesn't take it too personally,
even though he felt rejected.
He says it wasn't a traumatic period.
(08:34):
He just said the reception was everything between encouragement and rejection.
But, when he was removed,
though he didn't feel good about it,
he states that he just became a scientific orphan
and then found another group leader who would adopt him.
Still, the vitriol continued,
even from none other than Linus Pauling.
Pauling, at a conference,
(08:55):
announced that, quote,
Danny Schechtman is talking nonsense.
There are no quasi-crystals,
only quasi-scientists.
But, Schechtman persevered,
and he kept doing his research,
and he ignored the critics.
Schechtman stood his ground quietly.
Methodically, he gathered more evidence,
and two years later, in 1984,
(09:16):
he published a paper with colleagues
Elon Bleck, Dennis Gratias,
and John W. Kahn in Physical Review Letters.
The title was called
Metallic Phase with Long-Range Orientational Order
and No Translational Symmetry.
This paper defined a quasi-crystal.
It took years for the community to accept the idea.
(09:37):
But, eventually, it did.
And, in 2011, Dan Schechtman
received the Nobel Prize in Chemistry
for discovering a new form of solid matter.
It was an acknowledgement
that quasi-crystals had not only
widened the map of crystallography,
but also reshaped its borders.
We'll be right back after a quick word
(09:57):
from my advertisers.
Dan Schechtman's discovery in 1982
may have been the spark,
but the kindling for that fire
had been gathering for centuries.
So, let's travel back to the 1600s.
The great astronomer and mathematician
Johannes Kepler was obsessed
with patterns in nature.
(10:19):
He marveled at five-pointed stars
and the geometry of regular solids.
He sketched intricate tilings
with pentagons, elegant, mesmerizing,
but never quite able to fit together
perfectly without gaps.
It was beautiful,
but it was forbidden in the language
of periodic repetition.
So, now, when we fast forward
(10:41):
to the 20th century,
the crystallographic restriction theorem
had become gospel.
Only certain symmetries,
two-fold, three-fold, four-fold,
or six-fold, were allowed
in a crystal that repeated in space.
Five-fold was considered impossible.
And as for icosahedral symmetry,
like you find in a soccer ball
(11:02):
or a virus shell,
that couldn't fill space
with a repeating unit cell either.
But then, in the 1970s,
mathematical physicist Roger Penrose
introduced something radical.
He introduced tilings that never repeated,
yet still had structure.
His aperiodic tilings
looked chaotic at first glance,
(11:23):
but they followed strict rules,
like a melody that never loops
but always harmonizes.
Soon after that, physicist Alan McKay
ran a simulation of X-ray diffraction
on a Penrose tiling,
and he found sharp diffraction spots
with five-fold symmetry.
This was clear evidence of order
without repetition.
(11:44):
So, by the time Schechtman saw
that forbidden ten-fold pattern
in a rapidly cooled aluminum-manganese alloy,
the groundwork had already been laid.
Some theorists scrambled to explain it.
Some looked beyond our three dimensions,
proposing quasi-periodosity.
This was patterns that come from slicing
(12:05):
through a higher-dimensional crystal
and projecting the points into our world,
kind of like casting a shadow
of a four-dimensional object.
What had once been mathematical musings
and impossible geometries
were suddenly staring back
through the microscope,
not as abstract art,
but as reality.
(12:27):
For a while, it seemed,
quasicrystals were lab-born oddities,
fragile phases coaxed into existence
by rapid quenching.
Then, in 2009,
researchers reported natural icosahedral
and decagonal quasicrystals
in microscopic grains
from a meteorite
collected in Chukotka
(12:47):
in the Russian Far East.
Their compositions were aluminum-copper-ion,
and they matched known lab phases.
And the diffraction patterns
were unmistakable.
This implied that the extreme conditions of space
shock, high pressure, rapid cooling
can drive matter into a quasi-periodic order.
(13:09):
Shock can also come from human technology.
Quasicrystals weren't just found in a lab.
They also showed up in one of the most
violent human experiments in history.
When scientists later examined
the glassy debris left behind
by the very first nuclear bomb test
in the mid-20th century,
they discovered tiny quasicrystals
(13:29):
hidden inside.
The blast had melted
and then instantly cooled
the surrounding sand and metal.
And in that split second of extreme heat
and rapid cooling,
quasicrystals formed.
That discovery proved something remarkable.
Quasicrystals aren't necessarily
fragile lab creations.
They can emerge even in the most chaotic environments.
(13:51):
So from that point on,
quasicrystals were no longer dismissed
as man-made oddities.
They earned their place as genuine members
of nature's own library of materials.
And even though quasicrystals
were now cemented into reality,
there were still many myths and misconceptions
that surrounded this discovery.
Some people stated that quasicrystals
(14:12):
are just disordered crystals,
but they aren't.
The sharp Bragg peaks mean
that there is a long-range order.
The order is quasiperiodic,
not random.
Furthermore, scientists believe that
this forbidden symmetry broke the rules.
But it didn't.
It revised our definition.
Once we defined the crystals
by diffraction rather than
(14:34):
by translational periodocity,
these 5, 8, 10, and 12-fold symmetries
became legitimate.
Many material scientists believed
they were too brittle to use.
However, bulk brittleness is real.
But coatings, composites, approximates,
and patterned metamaterials
are already practical.
(14:56):
So what do quasicrystals
feel like to engineers?
Well, if you handle quasicrystalline materials,
which are most often as coatings
or fine-grained composites,
a distinctive engineering profile emerges.
Quasicrystals possess a unique set of properties
that make them stand out
from ordinary metals and alloys.
(15:16):
Their complex atomic tilings
give them exceptional hardness
and wear resistance
because the structure prevents dislocations
from moving easily
and suppresses plastic deformation.
As a result, quasicrystals perform superbly
as thin protective wear layers.
They also exhibit low friction
and low surface energy.
(15:38):
Their surfaces resist wetting
by molten metals, oils,
and even some adhesives,
which is why tribology tests
often show them sliding
with unusually low friction.
And if you're interested to know
what tribology is, please come visit
Math Science History.
Click on the Transcriptorium link
and dig through the archives.
(15:59):
I do a podcast on that one, too.
So back to quasicrystals.
In addition, aluminum-rich quasicrystals
offer excellent corrosion resistance
by forming stable oxide skins
that protect the metal beneath,
a feature especially valuable
when applied to steel or aluminum.
Unlike most metals,
(16:19):
quasicrystals also show
low thermal and electrical conductivity,
which makes them useful
as thermal barriers
or for reducing eddy currents.
Admittedly, bulk quasicrystals
can be brittle at room temperature,
but this drawback is often
mitigated by design.
Large approximate crystals
(16:40):
can be tougher,
and composites that embed
quasicrystalline particles
in more ductile matrices
can achieve practical durability.
Finally, their unusual
phase-on effects,
which are subtle atomic rearrangements
unique to quasiperiodic order,
mean that careful processing,
(17:00):
such as annealing
to reduce phase-on strain,
can significantly sharpen
their mechanical and corrosion performance.
In the early days,
quasicrystals were really tricky to create.
Scientists had to cool down
molten metal extremely fast,
so fast that the atoms
couldn't arrange themselves
(17:22):
into the usual repeating crystal patterns.
Instead, they froze
into the unusual,
almost but not quite regular
patterns we call quasicrystals.
And later, researchers learned
that by carefully reheating
these materials,
a process called annealing,
they could turn unstable forms
(17:43):
into more stable quasicrystals
or related structures.
And this also helped smooth out
flaws and release internal stresses.
Today, scientists have new ways
to work with quasicrystals.
Instead of just casting metals,
they can make fine metal powders
and press or fuse them together
using special high-heat methods.
(18:03):
Even though solid blocks
of quasicrystals are still brittle,
this powder approach lets engineers
mix tiny quasicrystal particles
into stronger materials,
giving them useful toughness.
At the same time,
techniques like thermal spraying,
vapor coating, and even 3D printing
can spread thin layers
of quasicrystals onto surfaces.
(18:26):
That means quasicrystal coatings
can now protect tools,
valves, or pump parts
anywhere you need
extra durability,
resistance to corrosion,
or strength in high heat.
With these processing advances,
quasicrystals have moved from
chalkboards to shop floors
and even into the realm of metamaterials.
(18:48):
Their low surface energy
and high hardness make them
ideal for wear and corrosion-resistant
coatings that reduce
friction, combat galling,
and extend the life of industrial
components. Their ability to
stay non-stick at high temperatures
has led to specialized applications
in bakeware, release
surfaces, and molds
(19:08):
where conventional fluoropolymers
would degrade.
Quasicrystals don't just look unusual,
they also behave in unusual ways.
Their surfaces can act a bit
like built-in catalysts,
helping certain chemical reactions
run more smoothly and with less
wear. Some quasicrystals even
play well with hydrogen, which makes
(19:29):
scientists curious about whether
they could be used in the future for things
like purifying gases or
building better membranes.
And because quasicrystals don't carry
heat very well, they are being
studied as materials for things like
heat-resistant coatings and
energy devices that turn waste heat
into electricity.
(19:49):
Quasicrystals have even inspired
engineers to create special
patterned materials that
can shape light and sound
in surprising ways.
Yeah, this is really cool.
Okay, so imagine printing a design
based on a quasicrystal
geometry into glass or
plastic. Suddenly, you can
bend, scatter, or block
(20:11):
light in ways that ordinary materials
can't. For optics,
that means clearer images
in telescopes and microscopes where
tiny distortions can blur
what you see. It also means
better performance in everyday
eyeglasses or camera lenses
where quasicrystal-inspired
coatings can reduce glare
and control how light
(20:33):
passes through. These same
patterns can even scatter sound
more evenly, which is useful
in technologies like ultrasound
imaging or noise reduction.
Quasicrystals aren't just
about metals and coatings.
They can also shape
sound. Acoustic
quasicrystals guide sound waves
(20:53):
more smoothly, which makes them
useful for things like clearer
imaging devices or controlling
unwanted noise. In mechanics,
engineers are even
3D-printing quasicrystal-
inspired patterns into
metals and plastics. These
unusual structures spread
out stress in surprising ways,
(21:13):
helping to stop cracks from
growing. That means we can
design lighter crash-absorbing
materials for cars or
even medical implants that
mimic the natural stiffness of the
bone. In short, the ability
to process quasicrystals
into metamaterials has turned
them from fragile laboratory
curiosities into versatile
(21:35):
high-performance tools,
materials that not only withstand
harsh environments, but
also shape light, sound,
heat, and stress in ways that
conventional crystals never could.
Dan
Schechtman's story is more than a
tale about an unusual pattern
of atoms. It is a lesson
(21:55):
in scientific courage. He
faced ridicule, isolation,
and even expulsion
from his research group. Yet
he trusted the evidence before
his eyes. Decades
later, the world validated
his perseverance with the highest honor
in science, the Nobel Prize in
Chemistry. His journey reminds
us that discovery often
(22:17):
begins at the edge of what
others say is impossible.
No doubt, science changes
and science advances when
someone is stubborn about
the truth. So today,
the forbidden symmetries that
once got him laughed out of the lab
are helping us build the future.
Quasi-crystals are finding
(22:37):
their way into durable coatings,
cleaner catalysts, hydrogen technologies,
heat barriers, optics,
acoustics, and even lightweight
structures that mimic the resilience
of a bone. From the lens of
a telescope to the surface of a
jet engine, quasi-crystals
are no longer curiosities.
They are tools.
So, when we think of Schechtman
(22:58):
peering into his microscope on that
spring morning in 1982,
seeing tenfold symmetries
sparkle where none should exist,
we are reminded of the power
of persistence. Because sometimes
it takes one person
refusing to look away from the evidence
to reveal an entirely new
order in nature and
open doors to innovations that can
(23:20):
shape our world for generations to
come. Science
is a living language. We
refine our definitions as our
measurements teach us new grammar.
Quasi-crystals remind
us that nature doesn't read
our textbooks.
So, when a tenfold pattern
appeared on a screen in a small
lab, it asked a simple
(23:42):
question, will you trust your
eyes? Thank you for listening
to Math Science History, and
until next time, Carpe Diem.
Thank you
for tuning in to Math Science History.
If you enjoyed today's
episode, please leave a quick rating
and review. They really help the podcast.
(24:02):
You can find our transcripts
at mathsciencehistory.com,
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donate supports a portion of our
production costs and keeps our
educational website free.
Again, thank you for tuning in
and until next time, Carpe Diem.
Today, we are exploring quasicrystals.
What they are, how an impossible pattern was found in a lab,
and how it became the catalyst to rewriting textbooks.
And why this exotic order matters for real-world technologies
from wear-resistant coatings to photonics.
(00:23):
I'm Gabrielle Birchak, and this is Math Science History.
Imagine holding a metal that seems to obey rules that nature once forbid.
You shine an electron beam through it, and on the detector,
a perfect ring of 10 bright dots appear.
(00:44):
Tenfold symmetry, crisp and clean.
For more than a century, crystallography said that symmetry was impossible in a crystal.
Yet, there it is, staring back at you.
It is order without repetition, and a pattern that never tiles
by marching the same unit cell across space.
This is a quasicrystal.
(01:06):
So what exactly is a quasicrystal?
Well, when most people think of crystals, they picture something like salt or quartz.
It's neat, geometric, and orderly.
That's because traditional crystals are built from tiny repeating patterns,
like perfectly placed tiles on a bathroom floor.
This repeating unit, called a unit cell,
(01:29):
fits together over and over in all directions to fill the space.
These crystals follow strict symmetry rules.
So imagine rotating a snowflake.
It still looks the same at every 60-degree angle.
That is called six-fold symmetry.
Salt crystals, for example, can have four-fold symmetry.
(01:50):
And diamonds follow a three-fold pattern.
These regular symmetries leave a signature when scientists shine x-rays through them.
They create sharp, clear patterns, much like a fingerprint of repetition.
Quasicrystals are different.
They are ordered, but not periodic.
Their atoms sit in a coordinated arrangement that exhibits long-range order.
(02:14):
Yet the pattern never repeats by simple translation.
In reciprocal space, quasicrystals still show sharp peaks.
These are signatures of long-range order.
But those peaks arrange themselves in forbidden symmetries,
such as five-fold, eight-fold, ten-fold, or even twelve-fold.
And since I have Taylor Swift on the brain,
(02:37):
they got engaged.
I'm going to give it a literary perspective.
Periodic crystals repeat, but quasicrystals rhyme.
If you want a mental picture, imagine a penrose tiling,
the famous kite and dart pattern that covers a plane with no repeating wallpaper motive.
Yet it contains a hidden hierarchical order.
(03:00):
I'm going to post an image of that at masssciencehistory.com
that you can find under the link called Transcriptorium.
That's the blog page.
And oh, hey, while you're there at Mass Science History,
don't forget to click on that coffee button and make a donation to Mass Science History
because every donation you make helps to keep the podcast up and running.
(03:21):
So, penrose tiles were groundbreaking because they revealed two key ideas.
First, non-repeating order is possible.
Second, the golden ratio appears again and again in the spacings of motives.
But with quasicrystal structures,
the distances between atomic clusters often occur in phi-related ratios.
(03:42):
Yeah, that wasn't a flub-up.
I said phi-related ratios.
Okay, so what is a phi-related ratio and what is phi?
Okay, well, phi is a Greek letter.
You've probably heard of that.
And it looks like a lowercase O with a line through it,
kind of like a backward-facing P stuck toward a forward-facing P.
(04:03):
And like the Greek letter pi, phi has a value, which is about 1.618.
I'm going to put the math up at Mass Science History
so that you can see the representation of phi
and how it is mathematically defined if you are interested in that.
So, here's an audio analogy.
Okay, clap every two beats with one hand and every three beats with the other.
(04:29):
The composite rhythm never exactly repeats, but it isn't random.
It is structured.
Quasicrystals are like that, except the beats are vectors in space
and the interference creates a tapestry of order that never loops.
Another important point of quasicrystals is that they are definitional.
(04:50):
The International Union of Crystallography eventually reframed the term crystal
to emphasize diffraction, stating that a crystal is any solid
that yields an essentially discrete diffraction pattern.
That moves us away from a, quote, must-have-a-unit-cell, unquote,
and toward a, quote, must-exhibit-long-range-order, quote,
(05:15):
which is a definition quasicrystals satisfy perfectly.
So, instead of insisting that a material must repeat the same tiny building block over and over,
like tiles that all match, scientists began to focus on something broader.
They focused on material that has an overall structure
(05:35):
that stays consistent across large distances.
That's what we call long-range order.
And while quasicrystals don't repeat like normal crystals,
they still have this deep, elegant order, just without the strict repetition.
In fact, quasicrystals are the perfect example of long-range order without periodocity.
(05:57):
So, they don't have that spatial repetition that we would see in regular crystals,
like salt or quartz, where the atoms repeat in a very strict grid-like pattern.
That, in regular crystals, is called periodic spatial order.
In quasicrystals, atoms are arranged in a way that is ordered but doesn't repeat.
(06:18):
They still follow the mathematical rules and exhibit long-range order,
but you won't find repeating tiles for a repeating unit cell.
So, on to the discovery that should not have happened.
It was a spring morning in 1982.
In a quiet lab at the National Bureau of Standards in Maryland,
which is now known as the National Institute of Standards and Technology,
(06:41):
material scientist Dan Schechtman was alone at his electron microscope,
analyzing a rapidly cooled aluminum manganese alloy.
He wasn't expecting a revolution.
He was studying alloys like he had countless times before.
Routine, repetitive, predictable.
But what he saw next changed everything.
(07:04):
The diffraction pattern staring back at him showed tenfold rotational symmetry,
like a decagon etched in atomic light.
That was impossible.
According to the study of crystallography,
you simply couldn't have a crystal with tenfold symmetry.
The laws were clear.
Only twofold, threefold, fourfold, and sixfold symmetries were allowed.
(07:28):
Anything else was forbidden.
Then, Schechtman blinked, recalibrated, took another look.
It was still there.
He scribbled in his notebook,
tenfold with a bunch of question marks.
Was it an error?
A twinned crystal playing tricks?
He checked again and again.
The pattern held.
In a 2011 interview,
(07:50):
he told the story of how his colleagues reacted to his discovery.
When Schechtman shared the data with his colleagues,
the response wasn't celebration.
It was disbelief.
One colleague reportedly said,
go read the textbook.
Another insisted he was wrong.
Finally, his group leader told him,
Danny, you are a disgrace to my group,
(08:12):
and I want you to leave my group.
I don't want to be associated with this.
And so, Dr. Schechtman was removed from his research group.
I'm going to post the link to this interview
on the Math Science History website.
It's a really interesting read
because Dr. Schechtman doesn't take it too personally,
even though he felt rejected.
He says it wasn't a traumatic period.
(08:34):
He just said the reception was everything between encouragement and rejection.
But, when he was removed,
though he didn't feel good about it,
he states that he just became a scientific orphan
and then found another group leader who would adopt him.
Still, the vitriol continued,
even from none other than Linus Pauling.
Pauling, at a conference,
(08:55):
announced that, quote,
Danny Schechtman is talking nonsense.
There are no quasi-crystals,
only quasi-scientists.
But, Schechtman persevered,
and he kept doing his research,
and he ignored the critics.
Schechtman stood his ground quietly.
Methodically, he gathered more evidence,
and two years later, in 1984,
(09:16):
he published a paper with colleagues
Elon Bleck, Dennis Gratias,
and John W. Kahn in Physical Review Letters.
The title was called
Metallic Phase with Long-Range Orientational Order
and No Translational Symmetry.
This paper defined a quasi-crystal.
It took years for the community to accept the idea.
(09:37):
But, eventually, it did.
And, in 2011, Dan Schechtman
received the Nobel Prize in Chemistry
for discovering a new form of solid matter.
It was an acknowledgement
that quasi-crystals had not only
widened the map of crystallography,
but also reshaped its borders.
We'll be right back after a quick word
(09:57):
from my advertisers.
Dan Schechtman's discovery in 1982
may have been the spark,
but the kindling for that fire
had been gathering for centuries.
So, let's travel back to the 1600s.
The great astronomer and mathematician
Johannes Kepler was obsessed
with patterns in nature.
(10:19):
He marveled at five-pointed stars
and the geometry of regular solids.
He sketched intricate tilings
with pentagons, elegant, mesmerizing,
but never quite able to fit together
perfectly without gaps.
It was beautiful,
but it was forbidden in the language
of periodic repetition.
So, now, when we fast forward
(10:41):
to the 20th century,
the crystallographic restriction theorem
had become gospel.
Only certain symmetries,
two-fold, three-fold, four-fold,
or six-fold, were allowed
in a crystal that repeated in space.
Five-fold was considered impossible.
And as for icosahedral symmetry,
like you find in a soccer ball
(11:02):
or a virus shell,
that couldn't fill space
with a repeating unit cell either.
But then, in the 1970s,
mathematical physicist Roger Penrose
introduced something radical.
He introduced tilings that never repeated,
yet still had structure.
His aperiodic tilings
looked chaotic at first glance,
(11:23):
but they followed strict rules,
like a melody that never loops
but always harmonizes.
Soon after that, physicist Alan McKay
ran a simulation of X-ray diffraction
on a Penrose tiling,
and he found sharp diffraction spots
with five-fold symmetry.
This was clear evidence of order
without repetition.
(11:44):
So, by the time Schechtman saw
that forbidden ten-fold pattern
in a rapidly cooled aluminum-manganese alloy,
the groundwork had already been laid.
Some theorists scrambled to explain it.
Some looked beyond our three dimensions,
proposing quasi-periodosity.
This was patterns that come from slicing
(12:05):
through a higher-dimensional crystal
and projecting the points into our world,
kind of like casting a shadow
of a four-dimensional object.
What had once been mathematical musings
and impossible geometries
were suddenly staring back
through the microscope,
not as abstract art,
but as reality.
(12:27):
For a while, it seemed,
quasicrystals were lab-born oddities,
fragile phases coaxed into existence
by rapid quenching.
Then, in 2009,
researchers reported natural icosahedral
and decagonal quasicrystals
in microscopic grains
from a meteorite
collected in Chukotka
(12:47):
in the Russian Far East.
Their compositions were aluminum-copper-ion,
and they matched known lab phases.
And the diffraction patterns
were unmistakable.
This implied that the extreme conditions of space
shock, high pressure, rapid cooling
can drive matter into a quasi-periodic order.
(13:09):
Shock can also come from human technology.
Quasicrystals weren't just found in a lab.
They also showed up in one of the most
violent human experiments in history.
When scientists later examined
the glassy debris left behind
by the very first nuclear bomb test
in the mid-20th century,
they discovered tiny quasicrystals
(13:29):
hidden inside.
The blast had melted
and then instantly cooled
the surrounding sand and metal.
And in that split second of extreme heat
and rapid cooling,
quasicrystals formed.
That discovery proved something remarkable.
Quasicrystals aren't necessarily
fragile lab creations.
They can emerge even in the most chaotic environments.
(13:51):
So from that point on,
quasicrystals were no longer dismissed
as man-made oddities.
They earned their place as genuine members
of nature's own library of materials.
And even though quasicrystals
were now cemented into reality,
there were still many myths and misconceptions
that surrounded this discovery.
Some people stated that quasicrystals
(14:12):
are just disordered crystals,
but they aren't.
The sharp Bragg peaks mean
that there is a long-range order.
The order is quasiperiodic,
not random.
Furthermore, scientists believe that
this forbidden symmetry broke the rules.
But it didn't.
It revised our definition.
Once we defined the crystals
by diffraction rather than
(14:34):
by translational periodocity,
these 5, 8, 10, and 12-fold symmetries
became legitimate.
Many material scientists believed
they were too brittle to use.
However, bulk brittleness is real.
But coatings, composites, approximates,
and patterned metamaterials
are already practical.
(14:56):
So what do quasicrystals
feel like to engineers?
Well, if you handle quasicrystalline materials,
which are most often as coatings
or fine-grained composites,
a distinctive engineering profile emerges.
Quasicrystals possess a unique set of properties
that make them stand out
from ordinary metals and alloys.
(15:16):
Their complex atomic tilings
give them exceptional hardness
and wear resistance
because the structure prevents dislocations
from moving easily
and suppresses plastic deformation.
As a result, quasicrystals perform superbly
as thin protective wear layers.
They also exhibit low friction
and low surface energy.
(15:38):
Their surfaces resist wetting
by molten metals, oils,
and even some adhesives,
which is why tribology tests
often show them sliding
with unusually low friction.
And if you're interested to know
what tribology is, please come visit
Math Science History.
Click on the Transcriptorium link
and dig through the archives.
(15:59):
I do a podcast on that one, too.
So back to quasicrystals.
In addition, aluminum-rich quasicrystals
offer excellent corrosion resistance
by forming stable oxide skins
that protect the metal beneath,
a feature especially valuable
when applied to steel or aluminum.
Unlike most metals,
(16:19):
quasicrystals also show
low thermal and electrical conductivity,
which makes them useful
as thermal barriers
or for reducing eddy currents.
Admittedly, bulk quasicrystals
can be brittle at room temperature,
but this drawback is often
mitigated by design.
Large approximate crystals
(16:40):
can be tougher,
and composites that embed
quasicrystalline particles
in more ductile matrices
can achieve practical durability.
Finally, their unusual
phase-on effects,
which are subtle atomic rearrangements
unique to quasiperiodic order,
mean that careful processing,
(17:00):
such as annealing
to reduce phase-on strain,
can significantly sharpen
their mechanical and corrosion performance.
In the early days,
quasicrystals were really tricky to create.
Scientists had to cool down
molten metal extremely fast,
so fast that the atoms
couldn't arrange themselves
(17:22):
into the usual repeating crystal patterns.
Instead, they froze
into the unusual,
almost but not quite regular
patterns we call quasicrystals.
And later, researchers learned
that by carefully reheating
these materials,
a process called annealing,
they could turn unstable forms
(17:43):
into more stable quasicrystals
or related structures.
And this also helped smooth out
flaws and release internal stresses.
Today, scientists have new ways
to work with quasicrystals.
Instead of just casting metals,
they can make fine metal powders
and press or fuse them together
using special high-heat methods.
(18:03):
Even though solid blocks
of quasicrystals are still brittle,
this powder approach lets engineers
mix tiny quasicrystal particles
into stronger materials,
giving them useful toughness.
At the same time,
techniques like thermal spraying,
vapor coating, and even 3D printing
can spread thin layers
of quasicrystals onto surfaces.
(18:26):
That means quasicrystal coatings
can now protect tools,
valves, or pump parts
anywhere you need
extra durability,
resistance to corrosion,
or strength in high heat.
With these processing advances,
quasicrystals have moved from
chalkboards to shop floors
and even into the realm of metamaterials.
(18:48):
Their low surface energy
and high hardness make them
ideal for wear and corrosion-resistant
coatings that reduce
friction, combat galling,
and extend the life of industrial
components. Their ability to
stay non-stick at high temperatures
has led to specialized applications
in bakeware, release
surfaces, and molds
(19:08):
where conventional fluoropolymers
would degrade.
Quasicrystals don't just look unusual,
they also behave in unusual ways.
Their surfaces can act a bit
like built-in catalysts,
helping certain chemical reactions
run more smoothly and with less
wear. Some quasicrystals even
play well with hydrogen, which makes
(19:29):
scientists curious about whether
they could be used in the future for things
like purifying gases or
building better membranes.
And because quasicrystals don't carry
heat very well, they are being
studied as materials for things like
heat-resistant coatings and
energy devices that turn waste heat
into electricity.
(19:49):
Quasicrystals have even inspired
engineers to create special
patterned materials that
can shape light and sound
in surprising ways.
Yeah, this is really cool.
Okay, so imagine printing a design
based on a quasicrystal
geometry into glass or
plastic. Suddenly, you can
bend, scatter, or block
(20:11):
light in ways that ordinary materials
can't. For optics,
that means clearer images
in telescopes and microscopes where
tiny distortions can blur
what you see. It also means
better performance in everyday
eyeglasses or camera lenses
where quasicrystal-inspired
coatings can reduce glare
and control how light
(20:33):
passes through. These same
patterns can even scatter sound
more evenly, which is useful
in technologies like ultrasound
imaging or noise reduction.
Quasicrystals aren't just
about metals and coatings.
They can also shape
sound. Acoustic
quasicrystals guide sound waves
(20:53):
more smoothly, which makes them
useful for things like clearer
imaging devices or controlling
unwanted noise. In mechanics,
engineers are even
3D-printing quasicrystal-
inspired patterns into
metals and plastics. These
unusual structures spread
out stress in surprising ways,
(21:13):
helping to stop cracks from
growing. That means we can
design lighter crash-absorbing
materials for cars or
even medical implants that
mimic the natural stiffness of the
bone. In short, the ability
to process quasicrystals
into metamaterials has turned
them from fragile laboratory
curiosities into versatile
(21:35):
high-performance tools,
materials that not only withstand
harsh environments, but
also shape light, sound,
heat, and stress in ways that
conventional crystals never could.
Dan
Schechtman's story is more than a
tale about an unusual pattern
of atoms. It is a lesson
(21:55):
in scientific courage. He
faced ridicule, isolation,
and even expulsion
from his research group. Yet
he trusted the evidence before
his eyes. Decades
later, the world validated
his perseverance with the highest honor
in science, the Nobel Prize in
Chemistry. His journey reminds
us that discovery often
(22:17):
begins at the edge of what
others say is impossible.
No doubt, science changes
and science advances when
someone is stubborn about
the truth. So today,
the forbidden symmetries that
once got him laughed out of the lab
are helping us build the future.
Quasi-crystals are finding
(22:37):
their way into durable coatings,
cleaner catalysts, hydrogen technologies,
heat barriers, optics,
acoustics, and even lightweight
structures that mimic the resilience
of a bone. From the lens of
a telescope to the surface of a
jet engine, quasi-crystals
are no longer curiosities.
They are tools.
So, when we think of Schechtman
(22:58):
peering into his microscope on that
spring morning in 1982,
seeing tenfold symmetries
sparkle where none should exist,
we are reminded of the power
of persistence. Because sometimes
it takes one person
refusing to look away from the evidence
to reveal an entirely new
order in nature and
open doors to innovations that can
(23:20):
shape our world for generations to
come. Science
is a living language. We
refine our definitions as our
measurements teach us new grammar.
Quasi-crystals remind
us that nature doesn't read
our textbooks.
So, when a tenfold pattern
appeared on a screen in a small
lab, it asked a simple
(23:42):
question, will you trust your
eyes? Thank you for listening
to Math Science History, and
until next time, Carpe Diem.
Thank you
for tuning in to Math Science History.
If you enjoyed today's
episode, please leave a quick rating
and review. They really help the podcast.
(24:02):
You can find our transcripts
at mathsciencehistory.com,
and while you're there, remember to click on that
coffee button because every dollar you
donate supports a portion of our
production costs and keeps our
educational website free.
Again, thank you for tuning in
and until next time, Carpe Diem.
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