 Thanks for the invitation, pleasure to be here. I'd like to tell you a little bit about some works we did a few years ago, actually, while I was still at Bosch. I'm currently at Harvard as of three weeks ago. And I just want to give you one example in thermoelectrics and if I have time, maybe an ionic transport in some effort how we looked at design of materials based on transport properties. Basically, the work that we typically do starts with designing methods for predicting properties of materials. In this case, it's ionic, electronic and thermal transport. And then trying to set up these methods in the way that they're automated easily and can be put on sort of high throughput frameworks and then generate a lot of data and then learn from the data to find some design rules and trends and then design better materials. So in the case of thermoelectrics, we were looking for materials to capture waste heat in automotive systems. So basically something that would go in the exhaust gas, manifold and convert some of that waste heat into useful electricity and feedback into the car. And the principle behind thermoelectric materials is really the seabag effect, which is illustrated here. For metals, nothing fancy, sort of nothing special goes on because the density of states is very high. And the Fermi drug distribution, regardless of how sort of wide it is, regardless of the temperature, it doesn't really shift the chemical potential of the electron, which is very different than the semiconductor where you're very sort of close to the edge of the density of states where depending on your temperature, your Fermi level can shift quite a bit. So this is the seabag effect. And the ratio is the seabag coefficient, which is essentially the main ingredient for a thermoelectric performance. It's not the only ingredient. The other ingredients are for good thermoelectric or of course, electronic conductivity, sigma, so that your material can actually conduct electrons and you can extract the current. There's also electronic thermal conductivity in the denominator here and lattice thermal conductivity. Those you wanna be as low as possible because you don't want the temperature gradients to relax without producing any useful electricity. So this is a figure of merit which we're trying to predict from first principles from ab initio calculations. And we're looking for better materials, obviously. So the materials that we know today are in this diagram here and some of them are good in terms of ZT but they're not stable or they're very expensive. Other materials are better in terms of cost but they're not good in terms of performance. So we were focusing on material class that is good in terms of stability and decent in terms of performance but was particularly bad in terms of cost. So we're trying to optimize the actual cost of the element. So trying to replace the composition with something cheaper. And the way we were approaching the problem is by solving the Boltzmann transport equation for electrons and also for phonons to try to predict the conductivity so that we can then estimate the ZT. And the idea was to try to do it from first principles. And the formalism of Boltzmann transport is been applied many times before for thermoelectrics because some of the properties are easily computed like the band structure, for instance, in this case you could rely on the GW corrected band structure or just a regular LDRGGA. And then you can plug in the velocities for the electrons basically the slopes of the band structure into this equation for the electronic conductivity which comes from the Boltzmann transport equation solutions. And you can do the same for the C-back coefficient and then get something just from the band structure for the C-back coefficient because what happens in that case is that the lifetimes of electrons essentially cancel out the first order. They don't cancel out in the electronic thermal conductivity and the electronic electrical conductivity. And this is a problem, right? So the lifetime of the electron actually enters a proportionality constant in the electronic conductivity. So we actually need to estimate it in order to predict thermal electric performance. And this wasn't done before because it's very difficult to estimate lifetimes of electrons. You need to know the scattering mechanisms that's way beyond just band structure calculations. So this is essentially an issue is that using a commonly sort of assumed constant relaxation time is really not appropriate as we'll show for predicting thermal electric performance. It's okay for C-back, but not okay for electronic conductivity. So the idea was to try to compute it from first principles. And the main transport dominating sort of mechanism at the higher temperature where thermal electrics really operate is electron phonon coupling. So the idea was to try to estimate the lifetimes just from the sort of electron phonon scattering matrix. And then from the Fermi golden rule, you could essentially write down the lifetime as a quantity that depends on actual mode on the electronic state and count all the scattering events and add them all up in this first order of perturbation theory and then try to compute the lifetime. The challenge with this approach is that it's doable in principle, but it's very difficult in practice because you need very fine meshes for electronic and phononic states. So the K and the Q meshes need to be very fine for this to converge. So this approach really has an issue. It's doable for simple materials. So actually it does quite well as I'll show for graphene. This is something that was done by Cholampank a couple of years ago. This is graphene as a function of temperature and doping level. And it's a very simple material with two atoms per unit cell. So you can actually do this electron phonon coupling calculation in a brute force way and integrate these large K and Q meshes. It's really difficult to do for a practical material. So we were trying to find a way to shortcut the calculation to somehow average it in a simplified way so that we can actually access real materials from ab initio to compute lifetimes of electrons in more complex semiconductors. So to go beyond sort of idealized materials like silicon and graphene. And the approach we took was to try to move the integration which is complicated in K and Q space in momentum space and move it into energy domain. So replace some of these KQ dependent quantities like the electron phonon coupling matrix with the one that depends only on the energy. So essentially remove the directionality dependence in a way from the integral. And also replace the phonon dispersions by just sort of simplified model where we have optical bands with some three frequencies that don't depend on the momentum vector which is a good approximation at higher temperatures where your optical phonons really dominate the scattering. So the resulting expression is much simpler because you only have to sort of compute the density of states and this whole momentum space integration becomes much, much easier to do. So you cut the computation cost by four orders of magnitude compared to a more complicated brute force integral with momentum you have to do integration. You're also using Vanier interpolation which is another non-trivial step if you want to scan many materials. So how to get those Vanier functions is still a little bit tedious. So this is a method that allowed us to automate and simplify the whole calculation. And we wanted to check how well it does to the actual fully exact sort of interpolated momentum space integral and it actually turns out to be okay which is a bit surprising and we still don't understand fully sort of the limits of this kind of approximation but it does show that if you look at properties like electronic conductivity for some of these materials and compare the EPW which is the Vanier interpolated momentum space integration scheme with EPA which is this averaged energy scheme that we developed. It does very well especially it does okay compared to experiment at higher temperatures which is encouraging which means that basically you are capturing the correct scattering from the phonons which dominates at high temperatures. You do quite poorly at low temperatures because your defects actually dominate the scattering and you don't expect of course the model to work very well at lower temperatures because of that. So that's fine. And for the Siba coefficient it's all quite in good agreement already again because the lifetime is not a very important factor for the Siba coefficient. So this graph here this set of graphs shows that the electronic lifetime is actually quite sensitive to energy. So this commonly used constant relaxation time approximation where you just assume tau for the electrons is a constant and for sort of a material you don't capture the energy dependence. This is the blue line here basically you assume a constant regardless of energy and also in practice people usually assume the value for this tau to be something typical of a semiconductor something on the order of a femtosecond. It's actually also not the constant as a function of material composition. So for instance here the best fitted tau is about an order of magnitude different from the best fitted tau in this material. These are sort of two different compositions here. So we both don't capture the energy dependence as well as composition dependence which is a problem but with these methods with either EPW or EPA you're able to get a very physically meaningful picture and also notice how this resembles the density of states essentially so that sort of hints at the possibility of having these simplified models for the electronic lifetimes that don't have to actually maybe take into account the entire complexity of scattering but somehow these sort of models largely sort of proportional to the density of states. Okay so we have the scheme right so then for every material what we need to do to optimize thermoelectric performance is to really sweep with respect to the Fermi level because as you get away from the edges from the bend edges your electronic conductivity of course increases because you have more carriers and your C-beck coefficient will die off because of this metallic regime that I showed in the beginning is not good for C-beck. So there's really a trade-off and you really have to optimize this carry concentration to find the sweet spot for thermoelectricity. So for every material that we actually design we have to perform this sweep and this is particularly convenient for the EPA scheme because all you have to do is just change one parameter and out comes the property. So in this case ZT as a function of chemical potential of electrons really peaks at these edges and this is how you find the best optimal point for the thermoelectric performance and we have to do it for every material. So in the end the workflow for ZT optimization starts with phonon calculations, electron calculations looking at the couplings producing electronic and thermal conductivities and then sweeping everything with respect to the chemical potential and find the optimal composition and we started doing this for lots and lots of materials first narrowing down by composition within the half-hoistler family to only select the semi-conducting ones and throw out the metallic ones and then from the pre-screening then we ended up with a set of 28 interesting materials that essentially produced properties like this. So what they say we have for lots of these different alloys and half-hoistler family we have these ab initio predictions of ZT and before I get to the ZTs I'll just mention that the electronic lifetimes you can see here already from this plot you see there are two orders of magnitude variation between different materials so this also tells you that it's very, very important to get the lifetimes right if you want to optimize the thermal electric. So once we have the lifetimes you can also predict the mean-free path of electrons and the mean-free paths are in this plot here and you see that they're not very long actually they're quite short which means that the phonons are very effective at scattering electrons even on the length scales let's say 10 to 100 nanometers. What that means in practice is that it's actually a very good idea to nanostructure these thermal electric materials and this is actually true experimentally because when you nanostructure you can't really go to 10 nanometer grains you usually are like a micron and maybe 100 nanometer, a few 100 nanometer grains so your scattering of electrons already happens within the grains so the grain boundaries don't add any extra significant contribution there but they are very effective at scattering phonons because phonons in these materials happen to be very long propagating modes that are hard to scatter because of the nature of the material so actually these materials benefit quite a bit. As a result you only have to worry about the electronic transport property when you predict better materials in this family so we predicted a bunch of these materials and then a few months later our experimental partners synthesized a few of these in this case this is a new alloy and Iobi, Myron and Simonide which was synthesized and it actually shows better power density than the state-of-the-art half-coistler material that was known until that discovery and the more important thing is that we were able to reduce the cost so from 350 dollars per kilogram it's now about 40 just because the elements of half-human zirconium are not in the composition so you have a much cheaper material and also the turnaround time was under two years for sort of method development screening and then a few months for the experimental synthesis so this is sort of an example of how you could rapidly get better materials if you have some more predictive tools in your toolbox. Just to take this a little bit further and start asking questions, you know what can we do even faster in terms of screening materials? Can we find some descriptors without having to do all this electron phonon coupling, lifetime calculations? Can we find some properties that we can predict easily that correlate with the final material performance that we are interested in? So this is in the domain of sort of finding design rules and descriptors that we can start extracting from the data that was computed and very briefly here what we found is that for all the materials that have computed for all these tens and tens of half-coistler alloys in particular the C-back coefficients at optimum concentration of electron basically at optimal doping they're all pretty much the same so we couldn't really distinguish materials based on the C-back coefficients they're all about 200, say 175. What we did find interesting is that ZT in particular was mostly sensitive to the electron effective mass and later on you could write down sort of parabolic band models and rationalize why that is the case but it's interesting that you can never find a very good material at very heavy electron effective masses of electrons but you can find very good ZTs at very light effective masses so this is not a perfect correlation by any means it's more of a classifier in terms of descriptor language so this is one of those most useful ones we found and we've checked you know band gaps and phonon velocities and so forth and so on this is very simple to compute but at the same time it gives you a filter so if you find a material here that you don't even hope to get a good ZT and if you find a material here then you actually can do more detailed calculations so it's more of a filter and helps you to screen materials much faster than trying to do electron phonon coupling for everything so to summarize I guess the story on thermoelectrics I just want to emphasize that we're getting to a point where these calculations of ab initio transport property especially for electrons and for phonons are getting more predictive and with some simplifications and some sort of practical shortcuts you can now design and study complex materials for practical technological applications and the key really is to find what simplifications to make so that you can access much more complicated systems we also emphasize that the electronic lifetime is quite sensitive to composition and to the energy so you actually need to include explicitly in the calculation of thermoelectric performance and we still don't know how much detail really to put into these calculations it could be that we can get away with much much less work actually to predict at least approximately thermoelectric performance so this question you know how much complexity how much detail is really needed is really an open question at this point so I'll switch to another topic which is more anionic transport just to illustrate some of the ideas there and to give you also a sense of what kind of tools might be useful for designing ionic conductor materials and this is more in the domain of solid state batteries so this is now an energy storage where we're looking for materials to transport ions in a safe way from the anode to the cathode without causing explosions and here we need a solid an inorganic crystal that has very very high ionic conductivity at room temperature this is the design goal here and I'll start with a system that is completely unrelated and just to illustrate some of the interesting concepts that are emerging in this direction this is a model of a anti-ferromagnetic ising model on the triangular lattice which has nothing to do with ionic transport at first glance but it's a very interesting system because of a quantity I guess of a property here called frustration frustration means you can't really find the very well-defined ordered state the system doesn't know what to do locally because of the competing interactions and in this case imagine trying to put anti-ferromagnetic spins in a triangle and you really can't because if you put up here, down here that you don't know if up or down goes here since either way will give you the same energy so you have in the end sort of this indeterminacy, this frustration and if you replace now spin by occupancy by doing sort of a variable transformation you could map it into a lattice gas model and this is sort of the two scenarios equivalent to this one here so basically you can choose whether to put an lithium ion on the side or not and it gives you the same energy so if you look at, in the case of this 2D anti-ferromagnetic triangle ising model if you look at the ground states you immediately see there is a very high degeneracy of the ground state in this case at half filling essentially where you're trying to sort of put up and down spins equivalently but that's not true if you're at one third filling and this is something that's very important to understand in frustrated systems you only have frustration in the sense only at particular carry concentrations here you do have a very well ordered ground state at one third where you actually just put every and every sort of big hexagon you put one lithium ion so you actually have a very nicely low entropy state here this has a very important implication for transport if I show you the electronic conductivity so the slide is gas as a function of temperature this is important to understand what happens is that there are these phase transitions especially at carry concentrations that correspond to the possibility of having these highly ordered states like this one what happens is essentially system freezes as a function of temperature into these readily available low entropy states and it cannot freeze if you're frustrated in fact in this triangular model Gregory Vanier showed before he got into Vanier functions he showed explicitly that in a triangular model anti-framagnetic ising lattice cannot freeze at any finite temperature because of the frustration so this is a suppression of phase transition that actually allows the system to keep sort of some degree of freedom even at zero temperature when you turn on long range interactions that's not long at true but it's still true that system will transport charge much more easily in the system where you have sort of this degree of degeneracy and frustration so we take this to ionic transport and study material which is very complicated it's the garnet one of the sort of best materials today in the oxide family for transporting ions and we try to understand it from this point of view of sort of sub lattice symmetry and frustration to try to explain why certain garnets are good conductors and why certain garnets are not and this emerged as sort of general design rule for ionic conductivity for other materials as well I'll show you this example so the garnets have a complicated crystal structure with all sorts of sites octahedral tetrahedral sites that can be occupied and this material can be tuned in terms of how much lithium it can take in terms of the lithium content by substituting different elements on the other sides so you can go from three to seven lithiums per formula unit in this material just by changing chemical composition and as a result, of course, as you'll see the ionic transport properties are very much affected so first we basically ask a question how do we make this material as frustrated as possible so how do we engineer this high entropy residual sort of residual entropy state that can transport charge easily how do we avoid these irregularly ordered ground states and the idea is to first find those ordered states and for that we use group theory techniques to basically just classify all the subgroups of the prototypical garnet find all the subgroups that can accommodate irregular lattice of lithium at a particular concentration so we go sort of group by group projecting downwards towards lower symmetry cubic into tribunal groups to find all possible orderings that are compact enough so that they can actually be ground states and then we basically hypothesize that those orderings are not good for transport so without even looking into group theory if you just do ionic transport calculations with molecular dynamics you see these kind of features that you already saw in the Ising model basically in this material certain compositions have these dips in other words indicative of phase transition of the sub lattice of lithium and these freezing points actually correspond to a much lower conductivity and they exactly correspond to the situations whereby group theory analysis you find these highly ordered states and they correspond to these integer values of lithium content in the material three, four, six, seven five happens to be degenerates so that you actually can have disorder there so this gave us sort of new materials and recipes for improving in this particular case ionic conductivity by telling our experimental partners to remove lithium and to make material as disordered as possible so this was sort of interesting and taking this further into sort of screening for better materials and looking at all possible oxides that exist that contain lithium we started looking essentially in an automated way using ab initium microdynamics in hundreds of these oxide compositions I'll just jump to the conclusion or I guess the summary of the result here we did find actually in many, many crystal structures that you pull out from ICSD database and you start running microdynamics things don't move exactly because you're sort of ahead of time a priori you already have an order structure so the idea is to make these materials frustrated by extracting lithium by engineering these sort of frustrated carrier concentrations and we do find that in this case you can make 40% of materials that don't even show conductivity you can make them into conductors by applying these modifications to the concentration of the lithium sub lattice so this is sort of a I think a design rule that can be used very effectively in actually screening materials it turns out that the carrier concentration the lithium carrier concentration is one of the most important tuning parameters for ionic conductivity especially if you're working in crystalline solids so I'll just briefly mention the fact that disorder in general in this case frustration was sort of a sub lattice disorder but disorder in general seems to be an interesting tool for engineering high ionic conductivity in organic materials it seems that by far more materials when you make them amorphous they start conducting ions better we don't understand really why there are some hypothesis based on percolation models but you know some materials actually do better some materials do worse but the fact that most materials do better when they're amorphized indicates that disorder in frustration materials is actually an interesting design tool for supraionic conductivity in general so with that I'll just show you a summary of sort of materials we've looked at and patented the few of these using this sort of search techniques and just mention that it's also not the only property to consider when you're designing materials for real applications you also need to consider stability to water stability to carbon dioxide all sorts of sort of environmental issues as well as you know cost of elements and you end up sort of with a matrix like this to give to experimentalists that includes not only the ionic conductivity but also these other properties that can be computed from an issue so yeah so I hope this was sort of useful as two examples of materials where you can apply and issue tools to get to better materials in a quicker way using sort of combinations of models and screening and with that I'll thank you and take any questions