 So my research question is about metallic alloys and in particular where do these alloying elements go right at the atomic scale? So most people are familiar with the sort of the atomic scale from high school chemistry class, right? If you think of water where you have the oxygen and two hydrogens But of course for metals, we don't have things just floating around really nilly But it's solid and in particular metals share something in common with diamond and that is that they're both crystalline So that means all of the atoms are sitting on a lattice in two dimensions You can think of a chessboard where each atom is a piece on the board and it sits on a particular square But unlike a very perfect or flawless diamond Not all the atoms in a chunk of metal you see you know in a table or a car are all one perfect crystal It doesn't go on forever, but rather there's groups called a grain that share a lattice and In our chessboard example You can think of sort of cutting a chessboard and cutting another chessboard and sticking them together Then you have the lattice on either side But where these guys meet it's very disorderly and there's not a clear space for the piece or for the atom to sit And so these chunks that are all one lattice are called a grain and these areas in between them are called grain boundaries And these are very important. There's a there's a famous relationship called the whole pet relationship And that says that the smaller of grains you have So the more little areas and the more of these grain boundaries you have in your material the stronger the material it comes We're interested then in knowing if we have alloying elements on this lattice and in this metal How do they interact with these grain boundaries with these areas where the site isn't the perfect crystal lattice site in particular? If it really sits at the grain boundary and it strongly interacts with it It can stabilize it to stop it from moving stop it from growing and this can improve the mechanical properties of our alloy So our primary method is one of simulation So once you're interested in materials at the atomic scale to get atomic resolution It's very difficult and we have ways to do this with with really amazing microscopes But it's quite expensive and so we can use the simulation to Inexpensively look at lots of things that we wouldn't be able to otherwise see easily when you're doing simulations at the atomic scale You have sort of two choices first one is the gold standard And this is to do a full quantum mechanical simulation of your atoms So that means you don't just figure out where the atoms are but you know all about the electron density all around them Unfortunately, if you do a calculation like this for ten atoms and then another one for a hundred atoms Even though you only have ten times more atoms It's a thousand times longer to compute for us because we're interested in these grain boundaries Which have all sorts of chaos and disorder and interesting environments We need lots and lots of atoms in order to capture the full complexity of it. So this isn't an option What we use instead is is classical simulations And so this is a model for the sorts of interactions the atoms have if they're too close together They are Pell if they're sort of nicely in between they like to shake back and forth and if they're too far apart They simply don't see each other anymore And what's nice about this is if you have a hundred atoms it takes only ten times longer than ten atoms So we can build these very large structures The way we go about actually building our grain boundaries is to take a large perfect sphere So all one crystal all this perfect chessboard and another duplicate of it and we choose a shared axis between them Misorient them in opposite directions Now what we do is we choose a cutting plane and we basically cut each of the spheres in half and stick them together And now what we have is two perfect crystals on either side with this green boundary in the middle And by choosing lots and lots of different cutting planes We can explore an entire subspace of the available grain boundaries for this material And once we've done that and we have our grain boundary in place We can start playing around with a little bit So we can take one of the atoms that sits at the grain boundary and replace it with a solid atom And what we're interested in is seeing how happy is that solid atom to be sitting at the grain boundary Compared to being just off in the lattice somewhere This lets us measure and see if we put the solid atom in our alloy How much does it just sit in the bulk and how much does it go to this grain boundary and influence the grain boundary properties? For a long time People modeled the interaction of these solid atoms with the grain boundary with a single parameter with one energy That says how happy is the solute to be at the grain boundary instead of off in the lattice somewhere in the 1970s people introduced a new model that said actually there's not just one energy that describes this But a whole spectrum of energies and this is very easy to justify because we can see in our minds I that if we have this disordered environment where these two lattices meet There's lots of different sites than an atom might find itself Some of those sites are bigger than the lattice some of the sites are smaller than lattice Some have more neighbors or fewer neighbors There's all sorts of arguments you can make for why a solid might prefer one site or another Unfortunately that model came out in the 1970s and computing power wasn't what it is today And so what we've done is we've generated millions of these calculations For each individual site to measure how much it likes to be at the grain boundary compared to the bulk Now one thing that we haven't done is look at the effect of temperature So we just look at the potential energy letting everything roll downhill until it's perfectly happy But there's an entropic consideration So when we have our alloy as we make it hotter and hotter it likes to be a little bit crazier wilder and more entropic And what this means is that being off in the lattice winds up being a much better position because there's lots and lots of different lattice sites So something called configurational entropy Which means that there's lots of places for it to be and so it likes it better Whereas if it's at a grain boundary site, it has to be at that grain boundary site And so what we can do is we can take this distribution We can use actually the same statistics that Fermi and Dirac used So if we know a distribution of how happy the atoms are at these different sites At a given temperature we can predict which of these sites will be occupied by an atom and which ones won't What this lets us do is for a given temperature for a given grain boundary Predict what pretend percentage of the alloying elements will be at a grain boundary and what percentage will be off in the bulk And what we can show is that actually this model with only a single energy is just Qualitatively wrong so it's it's really flat out wrong when you look at it as function temperature And we really need to know about these distributions But of course they're quite expensive to calculate even with our classical simulation And so what we did was we took another step to train the computer using machine learning algorithms to predict Which of these sites the atom will like to be at without ever doing the calculation So having done a million calculations we can now make predictions for for calculations We don't ever do and so we can build these Distributions much more quickly so before we just had you know a handful of cutting planes to build our grain boundaries We can now make predictions for the distributions segregation distributions for lots of different grain boundaries One of the most powerful tools that we've had in metallurgy is the phase diagram So if you go back to high school science again, and we think about water You have a phase diagram there in pressure and temperature So at high temperature you have liquid water right and as you drop the temperature It solidifies into ice and if we then radically drop the pressure it might sublimate into into a gas Now in metallurgy, we'd like to not think of these necessarily in terms of temperature and pressure But very often in terms of temperature and composition And so you know you have your aluminum alloy with some magnesium and you add more and more magnesium And you get different phases and the different phases we get are actually different orderings on the lattice So at very low low magnesium concentration our alloy our aluminum alloy will have just isolated magnesium atoms floating around But if we add more and more magnesium eventually we get some sort of ordered repetition You know aluminum aluminum magnesium aluminum aluminum magnesium And this is important because the different phases have different properties Some might be harder softer more or less brittle etc What we're starting to understand now is that we cannot just build phase diagrams for the bulk phase for the entire material But really for the individual defects in it And so in the context of our our whole patch model where we want more and smaller grains to have a stronger material We can start looking under what conditions does our grain boundary like to have all these solids added? Because we can take the idea of solid segregation and the solid being happier at the grain boundary in Trinidad's head We can think that the grain boundary itself is happier more energetically stable when it has solids there and So understanding the distribution of segregation energies and how we can predict these and generate these quickly for different grain boundaries Different defects we can start to build these diagrams for individual defects and engineer our materials Not just at the bulk scale, but really at the atomic scale The research we've done so far has a couple of limitations We were just doing zero temperature calculations So when we put our atoms there we let them roll downhill until they're perfectly happy We're also only putting one atom in at a time So there's actually been some very nice. I'll work work already by other researchers looking at these distributions in terms of What is the mathematical shape of the distribution you get when you start averaging over more and more grain boundaries and getting this fully defined? People have also started to look at what the interaction is between solid atoms when there's more than one solid atom at the grain boundary close Enough to see each other and my group one of the things we're looking at is to extend this to finite temperatures by looking at the Vibrational impacts when we have the atoms sitting at their lattice sites We know they actually shake and shimmy and vibrate around and how does this impact their preference for different sites? Another thing we're looking at in my group is to keep all of the quantum mechanical accuracy While still having access to these really big length scales one of the tools that's very exciting for that right now Is machine learned potentials so instead of having a classical potential that you fit once put it on the shelf And people use it again forever We really have them be living things that you train to quantum mechanical data and systematically improve until it has the accuracy that you want