Master class with Sharon Glotzer

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Master class with Sharon Glotzer
Soft matter quasicrystals
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Quasiperiodic crystals with long range rotational symmetry but no translational repeat unit have been known in metallic alloys since they were first reported in 1984. Yet only in the past ten years have such complex structures been reported in soft materials, comprised of, e.g., polymers, macromolecules, nanoparticles and colloids. In nearly all of these soft matter systems, quasiperiodicity is entropically stabilized, and any interactions are essentially short range. Interestingly, despite the fact that most metallic quasicrystals exhibit icosahedral symmetry, no icosahedral quasicrystals have been reported for soft matter systems. Instead, primarily 12-fold rotational symmetries are found, with recent, occasional reports of 8-fold, 10-fold, 18-fold, and even 24-fold planar quasicrystals. In this talk, we discuss common features and unifying principles for the self-assembly of soft matter quasicrystals, and we present results for the first icosahedral quasicrystal to be thermodynamically self-assembled in a computer simulation. This icosahedral quasicrystal is robust over a range of parameters, and is obtained from a single particle type interacting via a short-ranged, oscillatory pair potential that may be achievable in systems of colloidal spheres. The icosahedral quasicrystal we report is surrounded in parameter space by clathrates, important for deep sea methane storage, and other new crystal structures never before reported in a one-component system.
Keywords matter quasicrystals
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kyodo doing sewer money
machine boxer I'm a professor at the University of Michigan farm but I actually am I teach chemical engineering and materials science but but actually card-carrying physicist I got my bachelor's degree in physics at the University California Los Angeles my grew up in alley California and then I got my a PhD are at Boston University in physics studying statistical mechanics and critical phenomena and spent 8 years at a national out called the National Institute of Standards and Technology in Gaithersburg Maryland arm which is a fundamental science lab that can works with industry and them and then at Tulane University Michigan so I have a pretty large group about 30 PhD students post oxen research scientists were we study Soft Matter and armed and self-assembly and anything that involves the emergence of patents I'm obsessed with patents and so that's how I got into sending a cause crystals right so ominous talk about some sort matter by crystals so if if if you're someone who's traditionally the soft matter community you don't usually hear about or talk about why the crystals and if you are not in the closet crystal the die-hard classic crystal community chances are your metallurgist and you don't even think about soft matter and has it's like completely irrelevant to your world OMB and so the Jets
imposition of the 2 is something that I think is really interesting is something that's really only come about I'm in the last decade or so of the 1st mentioned that an initial also
some results from from our group and and the students public Dharmasena Michael angle on Mayor Haji of Bari Chris at the bell at the hearing keys in hand and Carolyn Phillips contributes to To during all of the worst missionary in all indicate but who's done what I'm in there so this picture here In the background was something we're hoping to get on the cover of Nature materials but failed in January of you never know whether the picture cover once I lost out and really awesome picture of a twisted now ribbon to a tiny whiny premium bird is like like this that was more interesting anyway US Michael angle upheld Masino Carolyn Phillips and and I had to have a paper that amid talk about at the end because it's illustrative a sort of where we are right now in understanding on plastic crystals and what we can learn from them so let's stop by and by talking Alcott was a crystals are so back in
1982 91 1982 but Dan Chapman was really said I have no pointer anything but that's OK so Dan Shechtman I and his and his colleagues at noon mostly down Danny we're
doing on experiments on these are all metallurgists and they were doing doing experiments on aluminum of manatees and
looking at the metallic solids looking looking for crystals and and he found something that he couldn't understand did make sense spent a couple years trying to understand it I'm John Connor is a very
famous on materials scientists who is retired now on helped him to figure out a sort of what was going what was going on and and he his
metallic solid and found that had long-range orientation water but something that was inconsistent with lattice translations so what does that mean it means that if you eat a few have
a regardless of how complex you crystal ears
the atoms arranged in a periodic array you can find some units sell some repeat unit that he translated around you can reproduce the entire crystals In this structure there was no
such thing could not find the repeat unit but
instead you can see that had it there was something order about it and will go through and see what was what was ordered about and what is what's so this
paper was was published and visible and I should say that this all this work was done then it was ,comma national beer standards but it but then but when I was there much much later it was called the National Institute of Standards and Technology and I I did I worked with John Connor within shipment of but but there's a lot history in hallways and so what's really interesting about this discovery is that unlike most discoveries in science can really be pinpointed to an
exact date and time on also realize that I have no
quicker so I have to think of how I can most easily thing so
but so there's a notebook that shows his arm but
when he found this was it was April 8th 1982 Thursday morning in the ACP electron microscope you out on she was elected indentured minutes what the expert electron microscopic and he was on on on sabbatical at at the
National Beer standards and to work to do some experiments and so he looked at this and rapidly solidified metal alloy arm of aluminum and
manganese something that should form some kind of complex crystal alloy and they were interested in Altus .period alloys for aerospace
applications on which is an interesting because 14 % manganese which is what they're working for is actually on brittle which is which is unusual for an aerospace applications so so they were setting as any found this thing and and and so this is a picture of his notebook I have like I know a
dozen of these green books in my basement but they all contain anywhere in having anywhere near as interesting I'm from that time so so she was she had a
scattering power and make it look like this and so so when when you see Dan Shechtman give a talk on the but that's the way he says it is to looked at the scattering pattern and he started counting down 1
2 3 4 5 6 7 8 9 10 camping 1 2 3 4 5 6 7 8 9 10 campaign he started counting the
starts around and said that this is inconsistent with crystallography this is not something that's that's allowed crystal graphically but clearly you look at this new seem sharp diffraction peaks right it's not diffuse there's clearly scattering going on on and there's definitely some water to this pattern so on and so there he is indexing this and you could see appear he says he
rates tenfold ?question mark ?question mark ?question mark so so
again the reason why this is interesting is because it until that point anybody who is
studying was doing any crystallography was studying crystals like sodium chloride would be a very simple example of a crystal arm where you would have thought of a diffraction pattern that that looks like this where you can index all the peaks and and everything reconciles makes sense from McChrystal graphic point of view but what they found was something really different I'm speaking
moving his only way so they found
something that has that has a cost he order to it and so they grew up crystal and and if
you if you mention that there Adams said each with these vertices and it makes up this big I cut the hinges and this is a fivefold direction there's a twofold direction and a threefold direction fans so here it is so
6 5 10 threefold and 15 to 4 fold Accies that's characteristic of of a costly symmetry and this was the 1st time that anything like this had been and we may not seem but at least you don't notice to airmen in question and
bomb and they try to figure this out and so there was a lot of excitement at that time and trying to figure this out writing of this paper but at the same time so this could have paper was published in 1984 on
and end at the time Linus Pauling who is 1 of the most famous chemist ever
on I was very up discouraging of the work and gave the whole team a very very hard time there's a famous quote from him and that the American equivalent of the meeting that were at now they PS meeting which is held every March in 1987 that Sierra actually saw grad school there is a "quotation mark Ebenezer Dan Agnes talking nonsense
there are no plans a crystals only cause the scientists so that Obama was minus polling says that about your work I
and and so he had some he gave some explanations of why what was going on
but at the same time in the physics community because to the chemistry community than met the crystallography community
they were like this is complete nonsense but this is the completely wrong interpretation
when applying it but at the same time it was important theoretical work that was going on but completely in parallel with that so so earlier even in and Alan
McKay but published a paper on call crystallography in the Penrose Pattern where he on his her discovered this kind of a patent theoretically arm and said that it has local 5 axes represents a structure outside the formalism of classical crystallography and might be designated acquire the lattice so this work wasn't wasn't known to the nastiness of it
was published and was published in physical arm but but there was already there the laying of the foundation for theoretical foundation for these interesting kinds of patents and don't Levine who was at the time a graduate student Paul Steinhardt who's now Princeton and they were apparent and wilderness at the Technion in Israel now on the double
meaning for his PhD thesis I had the idea knew about McKay's work and said You know what if what if you could actually
have not just to the patterns like McKay was talking about but in 3 dimensions and you could have but this kind of a structure where you had no long-range translational order no repeat unit but long-range orientation of order and he called it the cold acquires a crystals and will Paul Steinhardt tells the story of she says that she was teasing dug about it and said they got the name because they called it because Paul said 1 of queasy Cuesta let so Colored queasy "quotation mark crystals director of public plaza crystals because quasi queasy crystal sounds weird OK so that's where the words and hats were got its name from Bulgaria of and so you can say I'd consequences that extension of the notion of a crucial to structures with quasiperiodic rather than periodic translational work here in a class by better synergy and rotation and it showed that many disallowed crystal cemeteries are allowed Kwanza crystal cemeteries they do they they for the 1st time the analytically computed with the diffraction pattern of the ideal Kwanza crystal might be and they compare it they say that we
we show that the recently observed electron diffraction pattern of aluminum manganese alloy and they're referring to to the nest
work is closely related to that of an icon Hugel cause a crystal and so the physics community of was much more receptive I would say to them and then my understanding as registered investment or actually a high school student no yeah anyway OK so why requires a crystals not discover before 1982 Tom they're actually not
rare they're there they you see them alive in the laboratory they are and they had been thought for a long time maybe toward stable but they are a stable very stable and actually really on me pretty straightforward and to make and this is about crystal this is 10 mm here the scale Bobbitt aluminum palladium on manganese because Hugel classic crystal from biased a newish I'm just to show you how you can actually get a really robust hunk of
of Kwanza crystal and want to go into the details of what is
acquires a crystal how you get it had you characterize it in a minute but I'll mention it since the 1984 publications the bid over
10 thousand papers on Plaza crystals arm it's it's seen as means in materials science 1st of all it
changed it changed crystallography so that there the International whatever skull comedian crystallography had to change the definition of a core of a crystal because of the recognition that you could have these for any kind of quasiperiodic crystals and they have interesting properties in terms of friction hardness and he connectivity all there it gave rise to new synthesis methods in physics there's an interesting things about
stabilization of classic crystals that will talk about entropy verses energy arm will moment don't talk about the possible electronic properties and photonic properties on and the appearance of matter which is what we're going to focus on in mathematics there's all this
diffraction theory in Tieling topology work that alarm that grew because of our cause a crystals in geology there's a natural so sodas and another great story Paul Steinhardt tells that really they should make it into a movie and she casts Harrison Ford as as Paul Steinhardt which is that he beat Dave date this is greater if they'd they found on a tiny little pieces In a museum in Florence that they thought but that was because you cause a crystal that the track to the contractor mountains in within Russia somewhere that they thought was a naturally occurring in the
1st and only naturally occurring naturally
found cause christening not made in the lab but it it turns out that it came from media because the direct
to on the search for naturally occurring classic crystal but if you
go back to 11th and 14th century tiling you see these things everywhere
said this is an image of him from a shrine in Aron from 1453 see that of that shows these kinds of quasiperiodic tiling seen you can you can see them all over if you look at these on these old shines in and temples it's something that would when when making mosaic tiles and other artists knew about these interesting symmetries that they can make the really interesting patterns that we were more challenging to the eye that were
somehow interesting and in different from your usual periodic kinds of Thailand's and so as as I'm sure you know didn't Shechtman and won the
Nobel Prize in chemistry in 2001 and for the discovery some of the love of
classic crystals and not true that the chemists were so thrilled about it because it's not necessarily chemistry peseta natural sciences physics is whatever it is but I think it's been in it's not necessary because closet crystals are so important as the substance of the material that you'd wanna make they are interesting video technological applications but it was more about how it just flew in the face of everything that we understood up into that time about crystals and crystallography and how complex matter could be arm and change the way that we that we thought about things so so let's talk a little bit about about symmetry and details behind cause a crystal so I only think about so so it's all it's all about symmetries we think about the suit you look at these lattices here the a lattice of triangles of squares and hexagons and each 1 of them has the property that they tile the plain meaning you could push him altogether no gaps and distilled two-dimensional Euclidean space just fine and here each of these has on it's Tennessee from
the colors in the back at each of these has 2 different colors Ahmed so this 1 there's a there's a threefold rotational symmetry around any
vertex this 1 has a fourfold symmetry meaning you have to turn it 1 2 3 4 times to get back to the original picture because there's 2 colors and hearing of sixfold rotational symmetry because of the different colors that you have to turn it 6 times right through whenever that is
30 degrees 60 degrees sixfold to get back to where you where you started from a peck
on and these are examples of I of hirelings with simple cemeteries in the plan but when you look at on the Pentagon's Pentagon's are an example of a shape that doesn't tile two-dimensional space you cannot fit them together so that there are no gaps and this is study of Monte-Carlo simulation of her Pentagon's it was done by a tiny Schilling when she worked with Don Frankel I think when they were here in it at our mall come and they looked at how was that what was that the best way to pay and this is the best way Tupac handguns at the dentist you could possibly packed them but there's another way
that you can order that you could arrange Pentagon's in a plane on and and that is related to something called the golden mean and he has heard the golden mean before the golden ratio or whatever so it's a number it's 1 plus the square 5 over 2 0 which is 1 . 6 1 8 0 3 below and that this number it's this it's his magic ratio that they find in not knowing in them like the
Greek and what sort of like an auditorium forms
when they have a certain ratio of the full side of an ellipse that was esthetically pleasing to the eye and these ratio there's there's always these ratios of of Lead scales throughout art and architecture but if you look at the ratios you somehow come up
with this number the golden me I and the golden mean is that great is is so so the golden mean is defined as
if you have the option to line segments together 1 of late a 1 of B and the whole thing is of course a plus B if the ratio of a plus B over aim is the same as the ratio so the whole thing over a is the same as the ratio of 8 over B that particular ratio which just 1 way to do it 5 is is they shivered Talbots the golden mean OK so if you make if you drive at the Pentagon so that the ratio of the sides To that to this sorry to this I'm laying here is the golden mean and then you can do the following things so you can take a Pentagon the Pentagon with upward with the particular size ratio of lands the golden mean and you take a Pentagon any proposed 5 Pentagon's around it like that and that makes a new Pentagon and then you take that Pentagon and put 5 Pentagon like it around it so you start with this 1 and we flipped over the need for 5 more rounded and now you have this extra space which he fell in with another Pentagon I'm Justice just because you have this open space and you trying to get a denser packing and then you can take that thing and do it again and keep going and this is something that's example of what's called a Penrose tiles that was discovered in the seventies but by Roger Penrose and and eventually you can you can build this thing and you see all kinds
of pentagonal order and this is what was referred to as "quotation mark period to because again in this pattern you cannot find a repeat unit but you look at any simple clearly there's or some kind of water and that pattern is not a random pattern right and so on and so
make a wrote about these patterns on them as well this is the pen rose Pentagon I'm tiling and McKay did some work on the pentagonal on Snowflake and was that so another thing that comes up in Kwanza crystals is the Fibonacci series too the Fibonacci series so the Fibonacci series is this is a is a sequence of numbers that starts with 1 and then you add the previous number to the current number to get the next summer to share with 1 1 and 0 is 1 1 and 1 is 2 2 and 1 history 3 into his 5 you keep going on and see you get this you get this series
so here's here's a series here so that is doing it with numbers and then you get these numbers of but you can also apply that to arm to Tieling and so for example if you up so this this is an experiment
that was done by the beckoned your group in 2008 they took a flat plain and and they took colloidal particles that on their own would want to self assemble into a hexagonal packing in 2 dimensions to sleep the tightest packing that you get a ball bearings on the surface arm but instead of letting them do that they show they shined fire laser beams to create a fivefold symmetric intention was meant to pack and the college wanted to go with or whether it might with a light was Win interference patterns were and so they ended up getting up acquires a crystal structure by doing that and and 1 of the ways to analyze their this this structure is that they have these cut they found these kind of Thailand's were 1 colloidal particles would sit on every vertex like this and if you look at the time things you arm another sold the maker of Fibonacci series is that you you have a rule that wherever you see see have the short the short so this is it said this is a entirely motif with all these triangles squares triangles and this is what we call 1 motif which is another row of squares and another of triangles and you can make a Kwanzaa crystal by taking this motif the blue line and this motif agreement and putting them together in just the right order and if you put it together in this order some of where you so ever see start with I say with a short while and then the next 1 and if you see short the next 1 is a long 1 and if you see along when you place a buy along 1 and a short 1 and there's a pattern that you follow that pattern is the Fibonacci series and so a Fibonacci series it turns out is a 1 has is is one-dimensional quasiperiodic example 1 the cause across all in 1 dimension so that something come it'll come up later will restart allies some of our crystals of is that 1 of things you look for is this Fibonacci series of spacings between neighboring particles the between small motifs of neighboring particles OK so what is all this have to do with soft matter this is the last place I was different because that was the last thing you do is lost .period so you can mean not periodic and indeed random or follow some other sort of raw so the Fibonacci series that that follows a particular rule that it's not it's not periodic but it's generated by rule right and so we call a quasiperiodic or a periodic is another way of saying it which is different than something that's just random meaning it is random there's no underlying ruled that's generating it other than something stochastic but it is a deterministic rule to generate something that's it but it's still not periodic then you can call that a periodical quasiperiodic and that's the situation cause a crystals yes it was important what the president of the United this you go so that is a great question how form in talk about that later how in the hell in the world do these things do these things for yeah I so when you make 1 when you build 1 by hand yeah there's a starting point you put something down to to Connella spilled off from there following some roles the only way now and in fact will talk about is that there's there's it then they're not necessarily unique Thailand's there's different ways of generating acquires a crystal and even from 1 set of diffraction data you couldn't principle match different quasiperiodic tightening diffraction but will get that and the questions OK so so we so wears off matter command so until I'm like 19 until the early 2000 the only Plaza crystals that were known about anybody talked about or metals metal alloys at least 2 components Moses 103 components and most cause a crystals work had this icon the Hugel cemetery which will talk more about cut in and win what that means is that it is that it's it's it's on so unaccustomed was a crystal is 80 periodical quasiperiodic in all 3 Euclidean directions took at the other cause a crystals that are not the only periodic into dimensions and and to talk about that but so what is it that we get to soft matter so on stage we take a quick aggression on soft matter 1 of the common motifs and soft materials are myself so my cells are what you'd get if you have
say but a small molecules like it's cold call the surfactant with their head group and a tail
group better chemically different from each other maybe 1 is loving and the other water-loving we throw them into water and the oil about water-loving part of the molecule is very happy the way loving not part of the of the molecule is very unhappy and water and so on we will naturally start to see these molecules was necessary to self assemble in such a way that it reduces the exposure of the water heating parts to the water and increases the exposure of the water-loving parts the water because that lowers the overall free energy and of the system I it's always in in materials cause a crystals as well as staff matters systems were trying to always system is always trying to minimize the free energy and so this is
an example here of some surfactant in water say with an oil loving tail and water-loving had groups depending on the concentration of these surfactants in water
and you can get different kinds of structures of the of the molecules and you can get something that like this
which is just some would call the myself which basically you have enough that it can form a closed shell expel all the water from the inside the tail groups on the inside a very happy because they don't have any water and and the whole thing is like a closed essentially spherical objects that's a myself on if you
are you could also with higher concentrations are depending on the geometry of the architecture of Europe molecules you can get by later sheets you can get these things called the zones which inverted my cells which it's like a buyer later she racked up on itself so that you have all of the above the water like loving head gives on the outside and the inside to get water inside here water outside here but still look state oil loading held observer are the middle so surfactant system detergents soaps this is what is going on in those kinds of complex fluid systems arm that is it more like a ubiquitous example of a Meisel type forming on system but you could also have this in block a polymer systems where you have to long chain polymers that are chemically different but they're bound together covalently at 1 point so they have to stay together and 1 of them may like this all 1 of them will not like the solvent and so again don't act like a surfactant system only now it's that the length scale is a little larger because now you have to wonder chain molecules once you get this objects this kind
of a myself it turns out that in all the soft matter
requires a crystals that'd be reported experimentally what except for 1 inch 4 explained and they're all made it myself whether the my cells act like an adult
so instead of having an aluminum ore manganese Adam at all
these different points and making up acquires a crystal you have entire myself replacing an Adam so that is completely unexpected kind counterintuitive and so
there's media few dozen papers I think there are fewer than a dozen reported experimental observations of causing
crystals that are metals the very
first one was from Unger at all this is from Virgil projects on at Penn on and this is also from I think purchase group attend pencil publishes and Science and Nature 2003 2004 on because it was so it was so unexpected they're they're working with dangerous
years Sowetan tumors judges are said tenderers are these kind of fractal molecules were you have a generation you come out with arms than you have and 2 more say 2 or 3 more arms coming up from the charm more coming up from more arms and everything we do that it's another generation to get this kind it could spoil things it military and if you go on out
there basically spherical objects
and there are and what they found is that these gentlemen molecules begin acted like Adams and forms so
each 1 of these blondes here is a dangerous and they found their range and in a really funky pattern that at the time they said this looks like a acquires a crystal wine because they look at this and recounted 1 2 through 4 5 6 7 8 9 10 11 12 they said this 1 isn't isn't
tenfold symmetric tenfold symmetric like the 1 that check found Binford 12
fold symmetric and so the city have these particles at 12 12 neighbors around them so bowls 1 those were the 1st
reports on and those are the only ones for for a while and then I this is 1 from Frank betas group that was published in Science in 2000 and tend to get see how rare these things are to be published so-called higher impact glossy journals because there
there's it's so surprising finest so they were working with tribal copolymers were 1 of the blocks collapsed and they form these kinds of myself and end years of at the bigger picture I think this is a form of the tedium image quality and image where you can see these dots here those are my myself and around them are a bunch of other myself and they makers they make this kind of pattern and here they're trying to drive Tylenol splendor that tiling in a minute or and so this is another example where will these kinds of structures had not ever been seen in Denver systems for my cell and economize solar systems unit no 1 ever saw construction for a block or Palmer system began in the difference to tune in to mediate
between the 2 is very minor and that they're both it whatever the start with they make their made of Michael's the ranging
themselves a pattern and then this 1 was published by Fisher at all all the impunity as in 2011 where they they have hydrogen bonding they have a block a polymer but 1 block is is hydrogen-bonding but it collapses in water into basically by myself again what what's amazing about
their myself as they actually that they're my sources that they actually of assembled not
only in the 12 fold saying a 12 fold on at the start the quasiperiodic structure with 12 full rotational symmetry
but also the very 1st 18 fold potential Cemetery which was unheard of raping could find something like that but the diffraction data which is hot it's kind of hard to see here the diffraction data was was good enough to the plausible that you could do that we actually did some further analysis to show that it looked like they were that that it was really was 18 fold on samachar and so so those myself phases I wanna go back a mention this 1 thing here to Dmitry Taliban and and Chris Murray in 2009 published what I think is the 1st on example of cause a crystal structures obtained from nanoparticle self-assembly reduction in working with Chris Morris group since then and they found lots and lots more classic crystals that were analyzing for them and and and and writing about on but this is an example so few here they have big particles and smaller particles 2 3 4 5 6 7 get some sevenfold and fivefold kinds of objects there but the ISI's so-so and in many cases that the samples are very big to it's really hard to do large-scale analysis could you don't know but if I just what bigger would it be when I find a repeat unit OK
so just to give examples of how this works so we actually had done a study to try to understand why are these wider these my solar cause a crystals form on and missed interest this simulation of but
about the head group this just this 1 B on the top and detail on where the tales are attractive to each other and the head groups are not
simply throw them in a simulation box and you molecular-dynamics simulations of simulations
or whatever and you call the system down or denser fiber system then at
some point in order to minimize the Pharaonic free energy of the system it will have to the the the deal will have
to itself symbol in agony into some sort of structure and so on so the time shows an example of what they do so they form these myself and actually tender for myself that some of them around but they're not always round sometimes a little oblong sometimes you get a double 1 that splits into 2 and in principle in equilibrium these myself are alive and their swiveling and they're moving around in the
system In the Brownian sort of way and and it equilibrium the particles will leave individual mountains will leave while my Meisel good another my myself and you can have equilibrium enough in that way so this is an
image of what we saw in our in our simulation box and again these are these are very big simulations the simulations go because you need something
like I say 30 to 40 molecules to self assemble into 1 myself and each purple blob here is a
myself and each 1 of these molecules is represented by 2 like 10 12 the city multiplied together
becomes a fairly large simulation so now we can do much bigger but that we
did best this was sort of the size you can get and we were seeing the same kind of patents that that Unger and and saying we're seeing from Penn exact same kinds of as they saw In their on in the dental the kind of system that we did another simulation of different architecture so here's 1
with 2 tenders 1 either side it's like a try local parliament where the middle blockers collapsed on hand and so they did the green block here is attractive is in is a poor solvents so wants to go on the inside and the purple tether wants to be on the outside just just to make a different architecture just to make it a little bit more complicated to make it more like the 1 at Frank Bates was looking at but he is in his heart trouble copolymers system and again you see the same kind of
pattern to each 1 of these green blobs is a myself of but
30 to 40 molecules and inside of it OK and you see
again this kind of pattern emerging so the question is why these patterns emerge while any patterns emerge and why do you get these particular patents yes the president of the
Islamic conditions on this issue yes if the loss of the yeah that's a great question so whatever we do the simulation some animosity later or not to praying bounding conditions but for sure the Perry boundary chitchat conditions can affect if you're trying to form ordered structure where the delay the scale of the order exceeds that of your simulation box Spinnaker matter so when we do simulations where we have objects that are bordering on a larger scale we always let the box and change its sighs fluctuate in size change its arms the angles between the box edges to the achieve any symmetry any crystal symmetry that you want that's what's important to you do diplomatic better conditions as long as you let your boundaries fluctuate and accommodate any crystal symmetry that might want to grow so that's the kind of thing we do in some of the simulations another thing you can do because letting the boundaries fluctuate like that in accommodate any Chris looking kid that wants to be is expensive so I even do is just keep it in a QB box and go bigger and bigger and bigger and and make sure that the pattern scene is affected by the size of your box or by the you know that you but the period this year that the period is he doesn't change as you change the size of box that's another way of doing it in simulations were such later is a simulation work we do appear advantages but we start from a gas the whole thing collapses animals you know enough to worry about the period beneficial but that's always an
issue and it always comes up especially in something like a classic crystal where you wanna claim that something is cause appear a periodic and there's no repeat unit but you've impose a
repeat units it's the box size rate so then the question is also had you map the materiality and then you have to do different kinds of things like make it build bigger bigger bigger allow it to be indifferent cemeteries arm and look for strain in the box and then you could also do things like scale symmetry which helped which I'll show you more inflation's images were always so OK this is collection and this is a list of the soft
manner and and then a particle they also say so but when I think about nanoparticles assembly I call that soft
manner because when nanoparticles self assemble there's the you know that the the now particle itself might not be example of a soft matter system and its electronic properties applies money properties and not something that I would consider a soft matter problem but when nanoparticle self assemble based on electrostatic Savannah walls interactions or hide you mining between the league the coating them or whatever in solution better maritime problem because you can apply the rules of statistical mechanics of the minarets understand the Assemblies of the nanoparticles forming sigh ,comma most of that time so
you'll notice that almost all of them were 12 fold there's some there's a tenfold 1 and then there's that 18 fold 1 that I mentioned here by Forster's group that was found in 2011 but but there's no icon Seagal cause a crystals at all and there all these
planar axial "quotation mark the crystal so this is this is what
a donor can Korzhakov's looks like said this is hard to see can this the individual particles unlike 4 minutes so this year but In a molecular-dynamics simulation of particles interacting with the pair potential that will talk about a minute from so
you start out with a fluid and to cool it down and all of a sudden itself audits itself assembles into this into the structure so this
is a big three-dimensional bulk sample and every 1 of these particles these red things is a particle and if you see there's all centers and there's 12 around them and the 12 around America like 1 is from what is back on his front lawn is back so that is a classic example of a Doda candle cause a christening 12 full rotational symmetry it's cause a crystal and in this plane but coming out of the screen its periodic thanks to the so it'd take a different class acquires a crystal the call a
player cause a crystals axial but quite the crystals there almost always seen In
metals mostly binary internally and metallic alloys and things like chromium nickel vanadium nickel vanadium nickel silicon tantalum to learn classic
systems that make these 12 fold I am going to Chile word on the cause crystals and 1 of the ways
that you that you quantify they characterized the acquires a crystal you have some pattern think I think is acquires a crystal 1 of things you can do is make a Tieling City you go to the centers of all of these rings and you draw a line from the center of warning to the center of the name of the neighboring Maine underlined to a neighboring procedures Cinema Center a new draft whatever whatever neighbors you have you go to the 1st new neighbor that is center again of 1 of the strings the and then when you
do that you end up with this tiling
and you see that the different kind the tiles there's lots and lots of square tiles and triangle tiles and that's the predominant
once they're also these things called shields and there is an example of much of tile
called wall OK so in some kinds of Thailand's implies a crystals those are a part of the timing on typically in Doda can acquires a crystals if it's perfect you have a bunch of square and Triangle tiles and they come together in just the right way an analyst that so
let's talk about some terminology for singers who hears that this is another image of that cause so we're just looking at In this treaty box and here's the tiling that would that would put on it and so there's different kinds of crystal lattices that you can get better seen in both and soft matter my solar systems sometimes but mostly in atomic systems and metals this was
how the a 15 days busy phase and the significance there just arrangements of Adams or particles or myself whatever is here building elementary building block and in a 15 days it's of this this is the pattern and there were these rings interlocking rings and if you connect the centers of all the rings to make a town it just square so this 15 phase which is also called the the tungsten face is that this is a is a square then there's the triangle tiling called the the face and again you can see that there there always these rings around the center ring known as there always is interlocking rings interlocking because the neighboring ring share a couple of these Adams please see that kind of small look at this 1 27 the triangle tiling and this is a signal missing with phase is a mixture of busy phase and 15 face it's a mixture of the 2 kinds of track of tiles triangles and squares and In the 2nd phase they come together in a perfectly ordered arrangement where you can find a repeat unit of squares and triangles and say that's my opinion it copied it and that's called the Sigma face and in fact if you go back to this To this faith here it
turns out that that's so I rode up
the approximate it turns out that so this this picture's sheared but if you're on sharing duties very nice triangle and square tiles and if you take all these rings me connect all these
when you then that is with the perfect signal a perfect ordered arrangement of triangle and square tiles and it turns out that the signatories is what's called the 1st 2 water
approximate to do together requires a crystal meaning that the donor down acquires a crystal is this
8 periodic arrangement of the square and and triangle tiles but if I took that square in Triangle tiles and rearrange them into something bordered with all the units which might be big but some repeat unit that I made an approximate meaning it approximates the classic a crystal but but it's periodic entered a period K so that's often
seen in these kinds of systems you see instead of acquires a crystal you'll see the signal that sort of the donor can was a crystal you see significance
every quarter Crystal has some kind of an approximate and they have higher order approximates so all
Austria constructors and couple
OK so why things here so I'm so these are the basic on tiles and I don't think crystals and their periodic approximates are examples of water called Frank Caspar structures but so Frank Caspar structures are the
structures like crystals which can be period agreed period crystals that are locally Polly touching he job but you will see little touches he draw all over the place if you look at arrangements of particles and what
that means is on something of a few takers sphere and you and you
want and you see what is that what is the best packing spheres Ramos here 12 Sears will come around of the same size right arm and they will they will 12 spheres will come around a centrist here and that's the best you can Pappas fear was that you compact 12 12 years around central sphere locally yes systems were driven by wanting to packed densely like that they would just keep going but they can't because if you pack in this I cast huge away so so basically we packed the 12 spheres around an inner sphere you make a little across and if you keep adding to that at some point you end up with these big gaps and it's frustrated in three-dimensional including space so that's why we don't have Icaza Hugel I'm structures all all over the place and instead the next best thing they can do is make a the and cubic crystals but in freight Caspar phases and things like these classic crystals that
were talking not you see a lot of these local arrangements this once called the 12 which is so every hill particle or myself or
whatever and every 1 of these vertices that custody during you could also have 14 or 15 the 14 so 14 Adams from
15 Adams are essential but if you look you see all these local Polly that took pot Tejeda structures Republicans there's multiple such regional structure so we need that terminology of OK so if we want to answer this question of why do these myself
form means is whether acquires a crystal or its periodic approximately 1 a white why would they do that anyway it actually goes back to parliament
was posed by Calvin Back in that whenever 1600 when Calvin and it's really does something called the Calvin problem and so the common problem cult Calvin pose
this problem is he said What is the space of I have a bunch of cells and I were pretty cells together which is a bunch of of of
cells the Shipley Polly he what is that of what is the densest arrangement that is totally
space-filling that minimizes the surface area but the whole structure so mechanical phone structure began yeah or you can
become a border like construction or something like that so I take these things and I said What if I want to just take three-dimensional space on carving up into identical cells that stance based and I want the surface area of those cells to be the minimum possible that was the Kelvin problem and common said Oh that's the body 100 cubic structure and I later
where and Salen millennia later where and failing show that actually 815 face the square tiling phase but that's actually has a but surface area has a smaller surface area than the BCC fix OK what in
the world does this have to do with my myself so when you have a myself so here's an example of the day held you might imagine a danger arm myself these muscles a packing together they have these they may have their or even if they're not gender myself there any
kind of myself they have they have stuff on the outside and that stuff on the outside is getting pressed together OK so and so typically you
form in my sells non close-packed structures because of that
soft interaction so were actually get to the soul of a later but when you so that the at the typical crystal configuration for steers his face and in Cuba for hard spheres work harder actions that 3 typically get give Lennard-Jones fears you get FCC so this is the most common crystal structure that if you soften the pair potential between Spears eventually seven-inning facing a CU you get bodies and Cuba when you have these my sells their fuzzy like this there's a lot of entropy in there and so if they get too close together they have to pay a larger Tropic penalty so they would be more open then face energy back and so they you
Tennessee a lot of of of BCC and a 815 face there really similar in free energy by Bridget calculations like there really similar free energy and so if you have this kind of fuzzy objects that are packing in space it's
it's not so surprising that you might it's to open structures like the BCC earned 15 face OK and that's exactly
what items are hurl and and Connie in I'm at 10 proposed in in you know that they were looking at these kind of my solar systems and they said I that the BCC 15 structures which is the Calvin and where fail structures that that explains a lot of the faces that
had been seen at times but it didn't explain the acquires a crystals it in explaining that the winding you should lose this long-range arms translation order OK so now
what's on explaining why I think that these things form
of white Mai-Mai cells will adopt these kinds of phases and what we learn about that In terms of entropy said if
you have a pair potential the city of appear potential that looks like this but without this so I just make a pair potential human achievement in the more soldiers stratosphere here so let's say I have a lot
of the service Maine class too I'll go through it 15 workers there we go over the back so let's make a pair potential between the 2 objects to spheres whatever Of the look something like that so this looks like a winner Jones pair potential 1 of Nevada the 6th 1 of our the top is 1 of our the 6 so if you something like that then then with has this well that's similar story to this shape but but without the strength of that says that there is a preferred distance between the neighbors and then that 1st well tends to promote local politics residual water in Union systems of .period particles which fears if you place if you if you now add an art a solitary nature to it an atom bomb and then there is 0 then if you place than worried so this is now a penalty so any 2 particles that are separated by this distance are penalized energetically later raises the potential energy the system so they're not going to want you not gonna wanna have particles separated by that distance In your system and so what this does then is if you if this if you place this boss right where urine and 2nd neighbor would be fewer FCC then it inhibits FCC the tells the system so so if if the pair potential look like there's only it might prefer FCC but if you add this bomb and put this where the 2nd neighbor would go which is no SEC is bad so it puts frustration into the system this is a potential that all of this is suspended until the Taft came up with an early the nineties called the distributor of potential on because it was the 1st simple kind of potential that could generate these data gathered in a plaza crystal right so you can get
cause a crystal you can get approximates out of this and in fact good the simulation
nite that I showed you of the Doda catalog was a crystal the red picture with the tiling that was that was made by simulating molecular-dynamics simulations of a bunch of particles interacting with despair potential so the
ground stated this is actually FCC if you get cold enough With just loses and it forms of FCC but if you have high if you're high enough
temperatures then and then you end up getting these these kinds of acquires a crystalline phases so this potential is
a nice called the mermaid potential David Nelson pointed out to me because it's attractive but has all along repulsive tale OK so in that system that took a tougher liquidity and this graph that it's color something going on here and you could see it but the winner just potential that I sketched over there it is shown on top of this state the superimposed the duke it out potential so can see that the kind of and then and then they deviate from 1 another because that bomb and what happens is that in the Lennard-Jones fluid you will tend to have these local politics Jaeger structures
but they become longer lives more pronounced could grow larger when you have this extra bar that says don't form FCC reached a peak of that I'm under give you an energetic penalty if you do that then allow it to form or more politic treated structures that was the brilliance and to be tougher coming up with this with this potential existed before the simplest thing I can do that will inhibit the standard FCC ACP from forming and so these are
a bunch of other examples of what somebody's politic Cheadle structures look like in the fluid to take considered a potentially do molecular-dynamics
simulation equal it down and it is very cold fluid you trying to solidify and you'll see all these kinds of structures forming none of which if they grew larger larger would be sustainable in three-dimensional space has just buried there there's all this frustration on but these are examples of of these Polly a politician took courses that you get and these are the politicians who clusters that are also seen in In inquiry crystals In atomic and these molecular systems so what we think is going on is the following
that essentially in these mice solar systems so has said so this this potential is the simplest pair potential I the gives at work or approximates there out there the other ones where you can just you can do this he can make a hard
here square while calling call that and then put about pump like this make a really simple was squares and that that that works too but essentially this kind of thing where 1 well on this 1 but that is the thing the simplest thing they were bustling robustly gives you data-gathering posit crystal every time and so on there must be some physics in that so if I look at the myself system I can say way is there some What is
the physics and Meisel system that somehow is giving me effectively as tho I have .period particles of this pair potential and so what we think is going on is that you've got these my cells and and the 1st and and then they're they're trying to locally order so there's always this tendency for spherical objects to have this local
Polly Tetra Hugel arm ordering but it wants to make this open structure because of this there is the squishy they're not like hard spheres the squishy things and so there's a lot of entropy and so if you're if they're too close packed the new page huge entropic penalties to the 1 1 be a little bit open case so that's enough to give me BCC 15 phases but then there
has to be something else going on in the systems because we see that this alone is not enough to have something more and that something more is we think to support that you have to do something to suppress the close packing at least that's what exhibit of potential does so what is the meaning is my solar systems 1 way to suppress close packing so here if you have
entropy if you if you have them if the system wants to do like tell them and when and what Calvin and where steady work the if they want to form these these open structures they can still form close structure but you need something else to suppress this close packing to push them off of that Of the preferred
neighbors that would have formed say FCC or even BCC and so on we tested this idea by I am making these model will myself so should
use simulation myself before where we we we just through bunch molecules in the box they of similar myself the myself self assembled into a dough together repositories alike structure so now I said
OK let's start with the myself themselves because that's
much faster simulation into and just put a bunch of Circle muscles in a box and play around with how much entropy ,comma to wiggle room is in the outer corona of the myself with the tip of the superstitious something super floppies and see what that does to the overall structure of the Of the myself and so this
is where our little myself look like swimming this rigid Cape Cajun trip we catch little beads with Springs occasionally he just
tune that spring constant they could suppress staffers the super floppy I what that showed us is that so depending on how
stiff that that was we can get different kinds of structures OK so if we maintain that spring
constant very still but we always got an SEC structure as soon as you start to make it more floppy then you get BCC and then you get a 15 and waterways ways that we can see this
is so this plot here shows good decreasing stiffness so increasing flopping to the right of the site groups and this shows that relative free energy difference compared the FCC goes ATP so whenever you want to study on of the stability of a structure you always have so you can you can
you can do all kinds of simulations and get things out that self assemble but you don't know that's the free energy minima not don't know if it's their manically stable or matters stable relative to some other if you have other candidate structures reminding you can compare the free energies of 2 structures on by doing some kind of anemic integration which is what what we do here on where you
basically calculate the work that it would take to go
from some perfect Einstein like crystal to the crystal that you have and forensic crystal to the other candidate crystal and you could subtract the tissue and many of the difference in the free energies between here structured some other candidate structure which ever is lowest for energy wins so here were calculating the free
energy difference further increase mobility and increased sloppiness and down here it's really step but the the springs are really steps and the thing with the lowest free energy on those blue triangles and the pink triangles and that's the standard cubic and hexagonal close-packed research almost the same in Trinity but if this is just
a teeny bit lower and free energy knows something that Don Frankel showed some years ago so when the
things a superstar the free energy tells us that yeah SCH PCP is stable but then you see that as we start to make them
more floppy myself sells more quickly then all of a sudden the call structures become the lower free energy and therefore more stable and that the 15 B C C &
a Doda cattle cause a crystal OK so those structures have a lower for energy so it's possible to
calculate rigorously the free energy and show How the crossover occurs as you end and all we're doing is adding a little more entropy in the by making that does this spring's less staff anything more wiggling yet is loaded the use of so so we
did simulation with the potential with the bump and we got a deck and a classic result would still be tougher had already showed so we were
able to reproduce the data can request a crystal now are taking a system we have no pair potential which is throwing in surfactants in this case from building these my cells were throwing them in a box and letting them interact will by there so they're just hot particles like sorry you're my cells and you have a little beads and beta connected to the myself but there's no interaction of 1 myself with another other than they can they just excluded volume so there's no exhibit potential and that's what we're trying to do is understand How the essential features Of the duke it out potential which gives us a dedicated requires a crystal Our manifested In a software system of myself Britain were not putting the potential in explosively we're trying to see on the beaches just naturally inherent to these my solar systems that I could point to and say Oh that's giving me an effective the 1st well into the top and that is giving me the effect of the bump into the talks if I can find those 2 things then I understand why my cell systems are always forming these please do again
requested crystals that makes sense to go home that's not doing OK so this playing so should this is important so this thing right here all spherical muscles material the mobility and we got we were able to go from the FCC to these more open structures we got a lot of these colleagues had to Haeju local structures but on its own but couldn't self assemble classic herself if we set it up as
a classic crystal and calculate the free energy difference compared to something else in that if this spring was floppy than it was a lower free energy but just letting them I still suffer some on their own it we could get so we need something else we went back and an asshole so remember the finally clear right here so we can the
simulations were we just threw the molecules in there and make aggregated themselves and the myself before the myself ordered we look at there this furor city of myself we saw that there were a lot of most muscles were basically spherical but once a number not spherical and that happens in both cases in either case so there and there's no reason to expect that muscles always perfectly spherical anathema Namik system not at 0 temperature radio fluctuations you could have some muscles spherical To said well
maybe that's what's providing this this the effect this bond to inhibit close packing so we went and did look at this simulation we should 1 of which is mixed together a bunch of hard spheres and hard diners until we start with fears that we just throw-ins diners throw some more threats more severe like oblong as soon as they do throw
oblong ones then SEC is not amenable to form like the circular example amenable to form and because when the mess up the lattice spacing which is not the work and so we did that and then we again calculated now the free energy difference in such a system as a fraction versus the 4 minute faction dimers if we had known diners and all they're just fears and of course will comes out as SEC in but as we start to throw more more more diverse what comes out is the the 815 phase and the dough together "quotation mark a crystal become lower free energy but again they offer some on their own but if we put it together if we throw together a spherical myself With floppy floppy Corona
and some may submit some 80 spherical myself every time out comes the stood account all like ordering of aquatic resources so if you go back to
the farm To the danger in case of project at all and you go back to Frank Bates's case of tribal copolymers into Fischer's case of block upon which hegemonic there are instances where the myself are perfectly circle the muscles can be summed up in 1 and that messes up the local packing so this is 2 things you've got you've got this the fuzzy across all those cases they're trying to give you more open packing and you've got this other feature of their 9th Cir nature something that pushes off a lattice spacing says even the species that In a 15 is bad and then you have enough frustration that outcomes this this was a crystal structure like
so that's why that's what we think is going on on and it seems like this is something that you don't have to design your my solar system special which is if you have any
software system that tends to form myself you always have these 2 things that my soul is a floppy objects and the myself or at all perfectly round at the same time and that's all you need to get this Doda counterparts so for us the question is not why do we see Doda can quality pistols and my cells is why would they not seen all the time they should be always be there and in fact they they probably are but they were recognized as such because they can look messy unless you have a big sample and you can see this big pattern and you know we're looking for a handout and also
because it may not be the long-time stable face maybe something not so that it's and there is a noticeable face so a before we break the main point that I want to make is that software requires a
crystals all of them so far that I know of are entropic we stabilize this is not typically the case for regular closet crystals made of metals entropy can play a role In those systems but in these mice sewer systems it seems to be the whole ball game that you have a lot entropy In these myself and and so they're all intricately stabilized so when we come back from break will talk more detail about what is entropy why is it so important in the systems worse coming from and how can we understand that to build more
complex system entropy is typically taught as something that could colloquially be the thought of his disorder but that's a really bad way to think about and entropy and
instead entropy she really thought about options as as options so this is a Boltzmann expression for
entity where but if the if W it's say a the number of ways or the number of Mike estates in the system 0 Ezell when when I say micro-states so every possible instantiated of system so in this room every possible microstate might be every possible arrangement of you guys in your chairs that might be 1 that being so this is 1 microstate interview to switch that's another microstate device which that's another microstate so there's a touch volleys of Formica states then you can imagine Mike estates of will the cheers were there but the cheers were over here you can think about all those all those trips to the meeting that all degrees of freedom in the system every possible and stanch Asian that is the amicably allowed is a microstate of the system and so if W is the number of micro-states in the system if all microstate are equally likely then the entropy is is equal to that so all like estates equally likely then then it's a cable to the time-slot W so what when do you have all states equal all microstate equally likely if they all have the same energy In what we call Michael canonical ensemble of you have a completely closed utterly isolated system where nothing can go in and out no energy notification particle number nothing completely isolate closed system all Microsystems are equally likely and the entropy will tend to be too to maximize the system and essence is just KB times the log of the number of possible arrangements for a number micro-states that the same thing as if you are a because and heads and tails and flip about bunch coins every possible sequence of heads and tails is equally likely because there's nothing there's no more information in the system there's no bias saying of the system to 1 microstate another talking more generally we have the Gibbs entropy lawyer order gives entropy role word entropy is on minus the sum Over all micro-states the probability of microstate times a log of the probability of microstate Sibiu had a situation like in a thermal system where your system stays in contact with the heat back on and so he can flow back and forth to have seen at cannot a conical ensemble a and ensemble then the probability of a microstate depends on energy of the microstate come and our and so did so so piece of new is something that it depends on the Balsam factory the miners data energy the mike estate but divided by a constant the partition function but in the case for war they were all Mike acidic equally likely then on of them in the piece of new it's just 1 over she said is just 1 over W the probability of anyone might receive is just 1 over the number might estates that I have if they're all equally likely right and so that if I substitute 1 over W in here I have minus the sum over new 1 over W log of 1 over W which is then sold the minus some of what we 1 W cancel each other so I won over W. W times some overall micro-states but there's W. like estates so that councils so this should be overcame the T K B and so on this sense of giving as was KB throughout W so gives entropy formula is the most general expression that there is for entropy estimate Acadia outfits right that because it's enduring constant that we have because of the classiest clap Bryna remember cool introduced at constant on but when you want to make connections of entropy to information saying information theory that Wilson constant isn't there anyway this is the most general this is like the 1st thing that you might always write down for entropy and depending on the situation in might simplify OK regardless how you think about it entropy is a concept that on it is often harder to To quantify than other types of forces because it's like a statistical emergent forced the reason why entropy is interesting and why thinking about entropy is disorder is not the right way of thinking about it is that entropy can order stuff if
there's more ways of being ordered then there are the disorder survivors system who's
who's what would the system tends to maximize the entropy maximizing the entropy means
maximizing the number of possible like estates in the system and in there more Mike estates available to the system in which the objects are ordered then disorder the the system to maximize the entropy then that's not usually the way we think about on systems it's it's in in in many systems that's not the case that that the more ordered things are the higher the
entropy it often and the other the other way around but it's not that this comes up a lot
and 1 in the 1st place is this comes out of is work that was done by on saga on liquid crystals back in 1949 who recognize that if you have a bunch of rods whose aspect ratio is long enough being bigger and longer than 6 3 2 1 arm and they're hard rides and you put no interaction energy in the system whatsoever there just hard particles they just can't overlap and you can and this is a set of Monte Carlo simulation were just randomly moving translating and rotating the particles over time when they're red their disorder relative to their neighbors and we color them green as soon as the summer kind of net alignment with its neighbors and so you see that as you indicate that you run the simulation started wholly disordered if the concentration is high enough in the box of brides it'll spontaneously order you go from dis you go from isotropic too in the 2 nomadic systems face arm of a liquid liquid-crystal spent this is and this is the reason why this happens in service showed is that the system the gets so close that they realize that if they if they want to keep but the rotational symmetry they can only packed so close so that system gives up a tational symmetry in order to
gain more translational degrees of freedom gives a petition to gain translations and because there are more micro-states available to the system and so the selected this 1 the summer's Alderfer Mike estates all the 4 ways you can do this then if the view that they have the full degree of rotation then I'll get jammed up and that's that's all the physics there is beat the
behind an isotropic cinematic transition it's a completely tropical during transition so that's not so weird we think about rides we get it pushing together they think they can't line up so 1 of men they have more than makes sense but it's also true of of of spheres and that was something that was proposed by the chemist Kirkwood back in the fifties and then his stint at the time Bernie all their working with rain right to the very 1st molecular-dynamics simulations and of hot particles ever and 57 and Kirk with other student would be the 1st Monte-Carlo simulation ever of the exact same system and both of them so that if you just put hard spheres in a box just like on fares rise but now the spheres there's no interaction energy additional pair potential there just hot particles as soon as you get to 50 % packing fraction they go from being a disordered too being and when the green that shows local SEC ordering and you could see it starts a decree in the whole boxes green and that's because but there are more microstate available system where the particles look like with the woman look like this that seems totally counterintuitive but that's
because I take this year a move a little this way Lewis was loosely defined as the Formica state but it's still consistent with a crystal so these particles are moving around their call Lloyd's insolvent they're moving around the Bryans fears moving around and they can move a lot and still be consistent with the crystal so it turns out that if you
don't if the Sears don't water then they'll pick a random coast packing transition and I think something like 63 per cent success particularly covering they cannot have any denser the care that they kill just built this jail but if you all of a sudden arrange them guess you can actually packed them the 74 . 0 5 per cent so there's a time more room in the system you get to this point and it's like the stock and they say Oh criminal not won't let organize you you get all this extra room in the system at all that extra free volume in the system means more possible microstate
more places to put the particles so that's so counterintuitive that it for decades it was something argued vehemently according conferences and throughout the physics and chemistry community saying that just makes no sense such as crazy Of course was you my computer simulation but back then that was not enough to convince everybody and so it took until I think sometime in the 80's and for Pewsey handshake and others to actually do the experiment and show that hard here crystallized
so before we ever got some of the 1st time ever start thinking up crystals
on was completely by accident because we were studying hard teacher he
dropped so this territory usually shaped objects through box
just like the hard sphere simulation to Monte-Carlo
simulation of hard-to-treat Yeager and Al came something that look like there's this about 13 thousand particles and we said OK will that looks like something and we didn't know
what it was so we sliced and diced it looked a different ways and if
you more to so few call this you put in some Accies xyz on orthogonal Accies and then you turn it and you look at it down on the XY plane then it looks like this but I still couldn't see anything so I ask students to make them translucent so I could see through the whole box set but if there's some kind water that somehow these education all lined up and so suddenly is a mail like this so you have you can start to see the edges are lining up in start to see these wheels and it turns out that that this thing has 12 fold petition of symmetry and that was a
big surprise but because until we done this study hard to Draeger were not known or thought to self assemble just to entropy into anything but it turned out that they form this very complicated structure if he turned on its side remember we said that the Doda can cause a crystals quasiperiodic in a plane the periodic in the 3rd direction sold from the side what this actually looks like it is all a bunch
of pet pentagonal some died pyramids so 5 of these animals 5 of them touching Judd together in a little wheels and then 12 of them
ups up down up down up down and make a rating contended that permits entering then there's another pentagonal the pyramid another rain keeps going and each 1 of these logs is 1 of those
things so these logs that you see here are the are the 12 member rings up down up down the go around and then in between each of these plays hard to see is 1 of these little caps the five-member little contended permanent starts up completely destroyed the fluid 50 percent packing fraction sit there do my simulation just randomly choose a particle tried rotator
translated if they overlap you reject the move it doesn't overlap you accept the move that's it and out comes
this this complicated so they form these lines in the logs tilt little like this but because
it turns out that they have orange appear that way I'm and then diners of 2 due to come in and fill in interstitial This is the most complicated structure and ever seen in my life this is
what this bill scanning pattern called upon the diagram of flexible so the 1st thing was which argued the scattering pattern and we started counting 1 2 3 4 5 6 7 8 9 10 11 12 and every 1 of these ratings as another 12 spots another 12 spots so that confirmed this suspicion that yet this is some sort of 12 fold on coordinated thing and then this is that looking at it from that of the periodic directions and you see that you don't have this week period is repository to stay on in the other direction these things at the top of me is that a alive in our analysis on the called Bondurant diagrams and I'll show you some of the images of ponder diagrams all they need is you stand on a particle so for us when we stand a particle we stand on the center of mass particle and don't
care about with the corners are to stand in center massive attaches dress and then you look for the other centers mosques and the other 2 changes in your 1st neighbor shell and then you Our draft spot on the unit's fear and that's a 4 into you can't you can project the 1st name shell onto the surface of units fear you can also do secondary there never shells and so if the system is completely random and there's no orientation core on tissue order between the particles no no correlation between the the positions of particles then you just see white noise on your share instead of you see
pattern tells you that there's some supporters in the system so this is what the pattern looks like for a Dedekind cause a crystal on the fish sharpened up a little you sir see these stocks but at the time that was that that was the best we can do but that's like a really quickie quick and dirty way of seeing if you have some order the system so
you do that for every single particle in your system and then you just superimposed all year on bonded did all that statistics for all the little spheres onto sphere that idea so and so this is what the whole image looks
like completely see-through I think that's cool with extinguished and this is what the the structure looks like this is looking at it from the top down and these the pentagonal that pyramids and those of the the on of the 12 member the ratings and so as far as we know this is the 1st it's the 1st example of a dedicated
cause a crystal for heart for purely hard particles and protect your future this is an example of
this is that same simulation just to show you I I'm just I'm I'm I'm not showing you all the Hatcher he that Dole would in the end come together in 1 lot just agency but they're all over the place there's a ton of motion in the system it's only 50 per cent of boxes full 50 presented and the and you could see how far they In that moving and images pages formless is for directions the correct there's nothing it's just entropy so that
simulation there is what got me obsessed with entropy and convince me that I did not understand the way that I wanted and needed to understand entropy and because this shows you that entropy is coming and it's clear that so this is saying in the key simulation in
in an NTT system a
canonical ISO thermal system that the Helmholtz free energy and is equal to potential energy modesty times at end of the system is going to minimize F but now I don't have any pair potential it's if it's if I do I just don't allow any interaction so now it is always so all I have is this so from the minimize the free energy I have to maximize the entropy and so there's nothing else going on in the system if we go back to the case of the myself at the end of the day those my cells once the myself there's all kinds of interactions in these in the normal intermolecular interactions in the between the double copolymers of surfactants water or whatever but at the end of the day you end up you end up with these myself and the myself my cell interactions are very weak all the interactions have inside to make myself the myself themselves the outer parts the Meisel certain good solvent they're happy like that so it's it's it's like they're hard particles but not hard maybe soft and we saw that the kind of squishy particles so entropy is in the end of the day with ordering those myself too so this is just like stripped down to its bare essence just put particles fears rods treachery Yeager on whatever whatever shapes in a box so I'm sure so of 1 of the leading groups and In the Netherlands Maryland group are you guys in the group half of the their the leading group doing in these kinds simulations and in the Netherlands so are you talks as you honesty like hard
particles of different shapes up assembling into into different crystal structures there's just there's no between you and your group in our group and a few other groups we've we've studied thousands of shapes now and then and seen when entropy can order part things like this but so far with purely hardships not found anything more complicated than this
crazy .period again cause a crystal and it turns out that our cause the crystal is His ISO structural To the tantalum tellurium "quotation mark a crystal which is a chalcogenide so this is an experiment that was published in 1990 8 of the 10 elements intuitive system this is where the talent to L'Oreal Adams also set an interview with you connect all the dots connect all the atoms you end up with something like this this is what their soups a few This is the scattering panicked this is the scanning pattern I rotated so that we can line up with ours and we see that that peak for peak for peak that they all the president of 1 of 2 we actually have a favor to the gaggle cause a crystal and if you did the tiling still these rings interconnected rings all over the place than you connect the dots make the tiles to see this square Triangle square triangle over the public's right and so you can see it's a it's a similar type of thing now I mentioned that the dough together cause a crystals always described by the square triangle tile tiles but there's a lot of different ways you can decorate books will decorate the timeline decorate Gladys see could also community that was a wall I usually in the ECO at Michigan in this round
auditorium this old amphitheater round auditorium and standing there while introducing me I'm in the long only with the walls door it was open knows about anyway you can actually
decorate these timing sinking at these go together
because a crystals can get crazy crazy crazy complicated but still at the end the day the described by tied the tiling like this so here is our
Tetra he drew acquires a crystal and still looking down on the In this sort of it in a dual representation and then connecting the dots and we can see this kind of tiling and this is what makes up the tiles so underlying the
tiling are particles from and so here's the pentagonal determining these 12 member rings and then there's other ones that I said by mentioned that there's other ways of Philip interested she should just go there because that's the way to maximize the entropy of structure and so there is this is the Triangle Tyre and and that's
the square tile and those things are basically arranged randomly in this system it's also cool about this particular and plans crystal is that some additional being made up of all these with square Triangle tiles
pilings if you like To look at a lot new take one-touch region and you go out you come out but there's a there's a spiral attaches he looks like this so
here's a teacher hillocks and here's another 1 and here's another 1 and so too number 6 French expression of Lincoln Logs Lincoln monster like these their logs with cutouts me
off that together make a cabin but anyway the whole system is made up of these interconnected Tetreault cities so if you come out of so you have these logs these logs are defined by the 12 member rings actually have 12 teacher helices coming out and going through every line every log every particle is part of that 1 or more touches you Alex so goes right-handed and left-handed right-handed left-handed so the whole thing overall is in Cairo but there's all
kinds of amazing structure in here that's all figured out that's all a result of entropy maximization so I mentioned
before these periodic approximate I said if you
could separate the tiles and put it back together In ordered way then make what's called an approximate to cause a crystal so this is an
example of the simplest for the 1st order approximate to our today can acquire the crystal is to take on the tiles and put together like this so you can see that here's a square so by it but to connect the dots between the centers of contended that pyramid there's a square tiles and here's a triangle tile here there's another square title on and she could see a concerted drawn entirely sofa overlay like that so there's the Thailand's superimposed on top so you know you see the triangle and squared triangle and square and it's called 3 4 3 2 4 hour comedian tiling so they go around the Cook said pick up this vertex for a here and the triangle square triangle triangle square so that triangle is 3 squares for 2 threes were 3 square in another form so argument Thailand's there's all 11 marking Thailand's are
timings that spans space for which there's only 1 kind of attacks so I could square grid is not it's just each Vertex's Square Square Square Square just 4 2 4 and this 1
is the 3 4 3 2 4 hour meantime which is also the significance mission .period out before the Sigma phase is about 3 to 4 3 4 3 2 4 Parkmead tiling so what's important about this is it's a completely different symmetry today it's it's it's got fourfold rotational symmetry as soon as you make the significance to can see it
want to get the diffraction pattern it looks similar very similar to the costs he outside to the debtor can cause a crystal but you can see that fourfold symmetry of 12 fold symmetry as soon as you get the approximate so if you have good enough data which is really hard to get in experiments on soft manner systems because you need so many myself on the system is noisy so we have to do is really big simulations in order to get enough statistics to get so many rings with such clarity that we can actually tell the difference between fourfold magic and Torvalds magic in that scary part but that
you can and an and then so you can see that there's this difference and what's interesting is that the nearest periodic approximate has 82 particles in the units so the top of the approximate has a lower free energy then the was crystal
Blood it takes so long for this is in order because the 82 particle units of the whole thing would have to organized and so kinetically it's very hard to see the equilibration into the into the approximate
tours with the 2 different timings look like so this is the time when I was just showing you where it's of it's every vertex is identical and here's a random here's the tiling for the cause a crystal and the other thing you notice is that the ratio of triangles Square Thailand's is different just we're only scratching out of sight the ratio of Triangle Square Times is different in the closet crystal to an approximate so that's another thing you can do on your system if you
have a system he said Is this a classic crystal I don't know you could start making your tiling he said to count how many different kinds of vertices dynamic timing harmony triangle tiles have Britain was ratio of Triangle to square tiles and if it's closer to then
you probably have a Sigma faced it's closer to . 4 then you may actually have acquired crystal so in addition to looking at things in the Bonda diagram the
diffraction patterns you can do a lot a real space analysis to see what it is that you have as long as you have clinical data now it turns out that so when we talk about ground states In any any kind of says we talk about a ground state usually mean like the distilling the ground like 0 temperature ground state of the system and and before not adhere temperature at some finer temperature than when the system is that so if we just have a liquid or something like that are for any kind of a solitaire crystal and we say we're at
some temperature and so were not in the ground state which has what's the ground state structure versus the structure than that at some finite temperature for entropy made play more of a role and sometimes there the structure of the
abyss of having crystal at non-zero temperatures is the same as the grounds a crystal structure and sometimes it's different in these hot particle systems the equivalent to the ground state structure instead of Chico 0 it's the it's the infinite pressures structure it's the dentist packing limit structure that's the thing that minimizes the Gibbs free energy is the densest possible structure and so will we asked What's the ground state equivalent we see what events packing and turns
out that the densest packing of torture he drove is not the cause a crystal and not the approximate although we thought so for like a month Back in November October 2009 until this paper came out by Kallis Elsa and gravel on the archive that showed that a much simpler arrangement of teacher he just farm where took to territory put on like that and have dimer kneejerk another
diamond because the antisymmetric impolite that that units itself that's it 4 partly in itself so they constructed this and showed
that you could actually packet to a density of 85 . 4 6 with them the densest we were able to pack our approximate was something like 80 for something so this was denser so that means that the ground state structure now it turns out that they they had almost right but not quite right they had the big had the unit-cell right but the but the end but the symmetry the lattice wasn't quite right and soon we we found that out instead of their at the cemetery just tweak a little bit and you have actually get a denser structure that packs at 85 6 4 for 7 per cent and that is the densest packing so if you ever on like other of jeopardy or some game showed some nasty with the dense you could possibly Pak hard-to-treat your box you 85 . 6 3 4 7 per cent OK so but some sober but basically looks like that's so that means that that the
Internet pressure limit that's the feminine chemically favorite structure I mean impermeable self-assembly but I know that that's at them anemic ground state of the system so let's say I build my system like that and then I started to expand the box and let there be a little more than a little bit more room it's like it's like going up in temperature for and crystal sensor to give it more room that you what happens that structure what we do is we don't start from the dense structure and expand the box we just start from a dance fluid of particles and let it as similar to whatever once and never ever
does a symbol that thing it always assembles the cause so
then you can answer questions so what does that mean that the closet crystal or its approximate is the manically favorite at the densities were added and leader there should be a fairly transition to this thing for are the state's Medus stable and always wants to be us but kinetically just can't figure it out although then why would like to form the fact that the factory conformance something his nearest periodic approximate his 82 particles in the unit-cell itself seems to me harder then to make this thing with 4 particles in the unit-cell itself
so you can do you can you can calculate the free energy
arm of the systems and and you can look for example at all but the packing fraction as a function of the pressure so if you look at that top curve that equation of state it said if I by system is so every point along that estimate chemically equilibrated to say at this packing fashion with the pressure and I increase the packing fraction new pressure increase when Watson pressure and so you make a make all those curves on and and the blue R is the direct result of the red is the approximate which we always have to build his will get an assimilation and acquires a crystal we always get over over simulation and then the blow up there so conceded that part right there is blown up and that's where the phase transition is that through the Mets were goes from fluid to cause a crystal and and then OK so and many state so then you see the top part so but if you look so OK here this takes the free energy difference between the Kwanza crystal and the dimer across all as a function of pressure and what it shows is that which will assist this is dealt you so this must be some the Daimler minus cause a crystal so this says that the a crystal or its approximate is the manically stable at at all pressures up to here and
then the Dow McChrystal becomes the mannequin more stable but if I look at that pressure and I look up
there and they say Oh that's a really high pressure what is the packing fraction have to be To get that pressure it has to be nine-percent packing fraction so that's why we never ever see it because it's just not the relatively stable at packing fractions below 80 per cent and we would never be able to equilibrate on something beyond the 75 per cent 70 75 % packing fraction it just you have to just wait for ever and I don't think that that's
just sheer simulation attitude of of an experiment and call on hard part particle collagen in solution as well if you have it so densely packed that it's like 75 80 per cent 85 % work here in this case 84 %
packing fraction the kinetics are so slow you just never see order but this shows you how How you go belly can you get a sister if you you you do
simulation itself as almost something and the Wow is that is that this directly stable state you can never know for sure that it's the medically stable you can know that it's not because you what you want to watch it and paying it changes something else you all was meant stable but it has never changed anything all you can know is that it it's persists in its stable and if you have a candidate structure that you can compare the free energy to you can say whether or not it's stable relative to that of the but you don't know whether or not it's unstable relative to something that you haven't tried that's just the way this great state so you know there's certain things that you can think of to try if no 1 had found this time McChrystal we would never have thought we would not have had no 1 would ever thought to try it again something we would know what to try against but at least now that the directors presently try against shows that in principle the touches region phase diagram is really pretty complicated because it goes from the squad's a crystal approximate 10 days to this dynamic crystal so we have this
brilliant idea we said well somehow it all of
these pressures and
packing fractions lower than here the system back
surmises entropy through the plaza crystal rather than the dimer face so what have we reduced some of the degrees of freedom hand favored divers bye take the law teacher he dropped and gluing them together in pairs and just throwing hard diners in the box surely there and that it will suffer similar to the dire McChrystal because we've removed a lot of the entropy we you the still educated dimers but now there's no there's this this happened many particles on the system principle right because we glued all pairs together so we have removed much entropy from the system hand we favored the motifs that the directors 1 but we still can't get the crystal instead we
get back out exactly the same cause a crystal that we got before if you look at it from the point of view of the individual the particles you can't tell the difference between the original Plaza crystal and this 1 made of diners only she
start to look at the damage you see the bacon .period all these different ways so it's a good it's a good agenda requires a crystal critical point you could take your
your territory Geneva take diners appoint them in all sorts of different at different ways of and so that's interesting that they still like this that the squad's a crystal phase which used to be so
hard to see so hard to get seems to be so robust In this kind of system so were still trying to understand why the dedicated show cause a chrysalis preferred intent to redraw clearly we know that I would systems have local Tennessee to its local politician Angel watering they tend to form the core of the crystals like across cluster crystals and data by crystals and since we have teacher he dropped by default when we are promoting locally Tagesspiegel coordination but that still doesn't explain exactly why we see the structure that we get were still trying to understand the main thing that is really also do not very puzzling to me is that there has never been a report of an eye
cost the Hugel cause a crystal and saw that a system that's the
1 that the the crystallography 1st the the cause a crystal guys called Real Quiet a crystal because it's it's quasiperiodic in all 3 directions it's not just a plain and all the other ones eightfold tenfold 18 fold the 12 fold those are all cause a crystal in a plane and periodic in the 3rd direction that passage requires a crystals only all through direction it is also the 1 that's most commonly seen in metal systems if you take alloys you knew most of the time you do get in constitute "quotation mark a crystal so you know why why is
that the other reason why the interesting having a cost you cause a chrysalis if you refuse to talk to "quotation mark a crystal metallurgists there are a lot of theories as to why you get cause a crystals water the interactions between atomic elements that give this to you that's typically thought that you have complex .period
mechanical interactions metallic bonding and all sorts of details like that that make it possible to get these because each requires a crystals and the lack of ever seeing them in any kind of a soft matters system or entropy is really driving things suggests that maybe that is
maybe that's the case they just very much more complex and particle interactions to see it there are there's like this there so many instances of
accosted cause officials found in the lab but they're always interrogated with scattering and so you have also to diffraction patterns but diffraction patterns are unique could you never have infinite resolution so they're not unique and so from a diffraction pattern 1 builds a real space model but there could be a couple real space models that are both consistent with the same diffraction patterns since it's not infinitely resolved parliamentary don't know which is the right real space model so we know many people build
these real space models and and try to understand if there the model of a particular concierge crystal there have been
many attempts to do simulations of you know aluminum manganese or other systems with detailed like embedded Adam tight pair potentials were you have an aluminum alumina interaction you appear potential it's much more of a complicated than this with free oscillations along what you know very long-range interaction that you would expect for a system under gray metallic bonding where they have aluminum limiting these Maine is making these interactions your knowledge of and interactions many people don't simulations of those never produced a classic so instead they build acquires crystal and and then figure out the pair potentials that make it stable but nobody's ever self assembled and constitute cause a chrysalis simulation some
and uh but and 1 and 1 more thing is that I mentioned before that they have a photonic band gaps so this is something that was actually on the fees some like I forgot how they built this thing out but they said this is worked on might Steinhardt and and shaken when they did experimental measurement of photonic properties of an eye constitute cause a crisis we basically built this cause a crystal and scattered off of it and look at that photonic spectra and
saw that has a complete treatment three-dimensional of pro-Taliban all 3 mentions which means a clear gap with 4 bidders were from were certain way litigious forbidden the pass fate and so that's interesting for on optical things if you wanna have like fiber-optics things they don't we wanted traps certain wavelengths inside of wave guide so that's another reason why it would be interesting to
have caused a crystals that are not native Adams cousin was used on
about that he had made of coal with spacing the on the wavelength of light of light a visible light because then you can actually do something interesting with
that so I so we studied this pair potential and so this shows 3 different pair potentials there's B-1 B-2 B-3 they're just slightly shifted from 1 another all of them look like this they have 1 well and the bomb and so you might think that 1st part is likely to be top potential squeezed it then there's another while another another
bomb in another world another ball singing just goes on to take this a Ocilla to appear potential in Indian country afterward and so we so if you look at the Blue only 1 mile 2 wells 3 wells and its covered there an agreement cut down the road once cut there so we have so for all of these 3 pair potentials which are practically the same magistrate's channel that and they all have 1 2 3 wells and the country I'm right here at 0 where the potential is 0
which means that you can you can still see Maggio pointers .period particles interacting with them 1 of those from pair potentials and so you can do this in a big box appeared at boundary conditions
on but anything that you can do it 0 pressure and because of
the nature of the come and it's a long story explained how we got to this but it turns out that these pair potentials given a concierge requires a crystal for the 1st time ever so this just came out this month in this month's nature materials Is this 1 component because it requires a crystal on which is so the
1st time it's been self assembled in the simulation and it's with 1 component just 1 type of particle in 1 interaction between 1 type of so
we're going to play with the actions see how sensitive it is show you several different ones on but it turns out that this pair potential gives you I'm or pair potential that looks like this give you an account supervisor crystal what we found the importance that the ratio of these 2 wells which is what this is with saying this is this is where roughly where I want my
first-ever Shelda Bede and want any particles at that position with peak is or what really headed back and then I'd like my 2nd imbecility somewhere here with the new version of the summer and here the ratio of this distance that distance it is the golden mean so if we had been smart we
would just built this thing it was he who was just below the pair potential that the golden mean and end favors us but we did not win did not but we did not engineer the pair potential as much as I like to say that we did on instead we like and we found it by accident and so on so we need to show you what it looks like so this
is simulation 20 thousand particles in a box molecular-dynamics simulation using GPU code whom the blue to
super-fast arm and the blue-collar indicates that it's on
the outside of the cause it's not it's not crystal yet and everything in Green is is nicely crystal once and then this is showing you on is just starting to connect bonds it into this diesel particles each red 1 is a is a particle and then this is drying bonds between C could start to see a pattern which really cool about about this is that because of the attractive
nature the pair potential unlike with hot particle systems that you would have to have them under pressure but if you always have to confine them to fix the volume otherwise there's no interaction builders fly all part affected which are particles room the fly part to confine them here you have to confine anything so we start with a gas will lower the temperature condensers and then just a girl from the center into this
because acquires crystal so here's what the scanning patterns look like these are experimental quality higher resolution he would make a crystallography four-week
diffraction pattern of along the
fivefold access three-fold axis and the twofold but rotational symmetric axis and you could see you know how sharp these different peaks are this is a reconstruction of where once we figured out what the model was further because each requires a crystal meaning
exactly where all the Adams Adams on which to patrol the other atoms that
we built that I just a look-alike and so that's what that's what the ideal perfect 1 would look like come on
what we did is so I can show you this expression said this pair potentials called what called the oscillating pair potential Mikhail Henley ahem Chris Hanley and Mikhaylovich Chris Hanley said Cornell and they came
up with the empirical oscillation pair potential which just means he said but I just want potential it's oscillating Aldus right went down to empirical and and then we said OK let's modify that a little bit me play around with it and them and so the former deprived pair potential the we and abusing looks like this it's got a 1 over art the 15th to give you this
really steep beginning so that there a hardcore interaction and then it's got 1 over are acute and the end of co-signed term armed with this parameter but K and 5 and so those are the 2 premiers you continue your potential you can you can tune in the selection in next season continues you can tune that way
vector K and you can tune that facial 5 time you do that you're altering the potential little bit you're pulling the wells down your pulling them out like this and if we do that then you can make like the phase diagram where for every 8 instantiated and of fight and it with the face was the face what will we get with the church like again and see that all these different kinds of structures so everything it's pink Indiana are causing crystals to this it's it's really robust and then around the all these other phases so if I shrink it down and now show you all the faces these are all the different structures that we get in addition to the cause a crystal will meet to the pair potentials so in every 1 of these parts the blue curve is the pair potential for that value of k and that fly so that's what the pair potential looks like you see that always has 3 wells but sometimes those who 1st well as higher relative in the 2nd while sometimes it's a little lower
sometimes the width of the of the of the 1st and the 2nd well as little there our sometimes it's a little broader this 1 has a really deep 1st while this 1 has a really deep 1st well compared to 2nd while battling the 1st
well is even deeper than the 2nd well and then and then the 1st will becomes just barely like a little bump here but little that 1st pitch that's what you did to with this 1
privatization as this 1 on expression and these 2 parameters you can tune between all of those things so I mean if you're standing 1 system you wouldn't do that you'd say I want to study this system and you would you would do you would develop the pair potential for that 1 system so this is kind of like a materials design approach Reese a wall imagine that I am I can just like I can vary my system and I received from you for for what pair potential for what shapes appear potential I a really cool structure and then I'll figure out what materials will fit that intermediate structure sits at inverse design kind approach on and so and so
we get all these different kinds of structures clathrates Eastern Conference Silesia clathrates down here on all these are all these very open complex structures with complex unit sells to them and then all in here is this :colon crystal and then wait
there right there separated from this whole stability field of quality crystals With all these other complications surrounding it is the sweet spot for crystal we have no idea why yet this is where it just crossed beautifully every time superfast and the rest of them grow but why it separated from the rest I had
no idea I know I was going to
point out that here we have this 815 phase and is the phase which in those other phases that we saw before which are on
approximates to two-dimensional .period account acquires a crystals those also fall fall out of That's so originally we were trying to come up with a potential all that Our
call Lloyd synthesis friends could bank who said we want again I can't we knew we wanted complex structures we had given up hope of actually finding accustomed to cause a on purpose and we're trying always but we didn't really have a plan but we're trying to make open complex structures From coal Lloyd's where you can imagine using Wiggins or DNA or proteins or other things to set preferred distances so most "quotation mark just look at these pair potentials we can make that 1 well to Wells 3 wells and every time we put 1 well I the otherworldly killing separating interactions it's it's difficult to do so we were hoping to get down to 2 wells where are the areas because we got sidetracked by finding a concierge require herself ,comma but we're trying to
see if 1 can simplify the pair potential and still get these really complex opened phases
so just to show you some analysis of this classic so I mentioned the these there's a stability is never meant they were labeled lt http ID which supposed to stop but only ended we White at 10 o'clock OK official broke with the problem at Penrose tying showing before were you will
take a Pentagon with the golden characters the golden mean any Nissan Pentagon by 5 handguns into that thing and
that is what this is To take a patsy there's a panic said these are all Adams and green when you connect them and then at the Pentagon and then there's the Pentagon's all around it and the new tile those things and if you cut if you take cuts through the gate of Fibonacci sequence of the spacing of the particles and this is another way that you can look for him the safety of aquatic resources to look for self-similarity as you go bigger bigger bigger to see told inflation symmetry to see the same thing and bigger and bigger and bigger scales like that Penrose timing so that's something that we also see here so this is a bigger version of it I think this is for not 20 thousand particles but 100 thousand particles on and if you were to make of 40 filtered image which approximately the high-resolution electron cost pattern this is what you would expect this this is what you would look for for fewer experimentalists trying to get you want to get that to get pattern so I'll say no just 1 more thing
which is so 1 of things that we did major civic and charitable inquiry if you're
interested in finding out more about us in this so with our paper we so in SI can't Bukan click on this link from the Nature paper from management shows paper and get this web interface job script were you can read in our data and you could turn around and come in candy things like you can show the particles a shrink the particles you can show the bonds between the pot of gold and not show the particles the new consent to turn around and look for the different planes cannot plaguing the coal production yet but this is also showing the bond were intentional order diagram that I explained before and in that now you just turning around searching for these different patterns and then down here is the diffraction patterns along whatever direction I'm aligning it so it's calculating them on the fly for you too and also in this nice replied puts an applet and you can also pulled out all the different Plaza crystals some approximations but all these other phases like the clathrate faces read all then which I think is really nice simulators we have so much data and whenever public publish like static pictures I'm hoping that we can do more of this in the future so people can actually see a community making these three-dimensional structures and mean I can't even see it unless I'm like invited on and so this is a way of learning how to handle head of calculate the diffraction patterns honorary diagrams of things OK so that link is it is in the paper for anyone who's interested in let me just finish Atkinson finally late analysts say 1 more thing because the Casper U.S. nonaggression Calligaro had things grow so quickly the
classical mutilation picture of crystal growth
which who knows even write anyway for regular or crystals that still a topic of lot debate is really pretty
simple you take your you have a fluid on a liquid
gas whatever and you quench it too a temperature pressure where that is no longer ceramic stable state the crystals of the relic stable state and the system is is now unstable but were better and its fluctuates fluctuating around in it and it's no it's sampling phase space and it hasn't yet realised but this state if it is not the thematically stable state I am and what
tipped typically has to happen is that the there needs to be of fluctuation in the system of of old all cluster of particles that is an arrangement such that the free energy of that is now lower than the rest of systems of basically describing these 2 terms of long-term Anna and the surface terms and as soon as the volume
terms that lowers the free energy exceeds the surface term that nothing will grow and that's called the critical nuclear so you have all over the place of these fluctuations at some point the nuclease gets big enough and it takes over the whole system and so you go from the fluid you you nuclear something eventually end up with a with a solid and and
so this is a picture of entropic This is a system of hard after he it starts out fluid and this is in the middle of the the nucleases ground that crippling place has been exceeded and now the crystal is growing from a point 2 that's homogeneous nuclear nations meaning that the system that it you don't have to neglected it's all over the place and you're not including from a wall from surface which is starting to grow grows out from 1 1 seat if you if you if you're lucky and then you just want to overtake the whole system just like those fears crystallizing SEC when put them OK
so the quake the point is just so it's not that unlucky it if you want to study homogeneous nuclear nation
then your system it is just the right size and you pick the quench step just right but it doesn't include any everywhere and you could just watch the process cleanly answered typically fear if you do on any kind of transition path sampling umbrella sampling transition Interface Sampling the sampling methods that are designed to sample rare events like the nuclear of the critical Nicklaus that's a rare event you have to wait for that to happen to get over the energy when you're doing that and messes it up if you have more than 1 growing thing in this system no 1 time so that's why interest that's where you'd like to December 1 look at the point is in if you're growing a crystal he indeed growing from inside and so even
here when you when you look at this image here it's there's there's this Crystal that's growing there's a front here it's growing into the fluid
typically if you look at what's happening in the outer particles in the fluid St .period their day template the growing crystals and make the They just aligned with the growing crystals and so you end up with this final crystal structure that's typically the way that it's that crystal growth is is defined of course this is
like a C Chris also there's only 1 particle in itself when you have many particles in the unit itself it's not so simple about how the
particles a template but the point is in a quandary crystal but they they can't just template the growing nuclear because then you get a appear crystal if they just fell into registry you'd get a credit Crystal City must do something
else so placed in Yankees in this study some time ago in this exhibit Osasuna .period particles with this pair potential at what he found was that there is this sort of blow or the fluid and use you can start to see that there's there's patterns in the fluid and these are little I cast huge on these local politician Hugel clusters that that doorway found I showed you they're all over the fluid the forming the breaking of forming breaking you get a little nucleus of the quads a
chrysalis starts to grow and instead of growing outward and subsuming the other Adams 1 by 1 it subsumes hold politics you clusters it just take them in those areas and interest in it suggests it just
being just grow to become part of it I think like the board to no 4
start aboard the Justice similarly all cultures so this is just growing out and the easiest thing to do is to subsume the entire local you it's a it's a it's a nice locally energetically stable configuration so just subsumes like that and I mean that's all we know right now that the
minutes I complete the on exploration it's an observation of of that's what they do and so
there's many many questions remain as to how how these things form so I think that's a good place to start
an online readership as have more questions and things like