Magneto-structural coupling
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Abrikosov, Igor
Ekholm, M.
Ponomareva, A. V.
A lecture given by Igor Abrikosov, at the Adventures in the Physical Metallurgy of Steels (APMS) conference held in Cambridge University. The emphasis is on how magentic properties play a role in the properties of iron. Ab initio simulations based on the Density Functional Theory (DFT) are known as a useful tool for prediction of materials properties and for their understanding. In this talk we review recent progress in applications of DFT for Fe-based alloys. We underline a necessity to take into account explicitly temperature induced magnetic excitations. We show that magnetic and chemical interaction in Fe-based alloys are deeply interconnected, and strongly affect each other. We start with relatively simple examples, and show that there exists very strong dependence of thermodynamic properties, like elastic constants, structural distortions, and mixing enthalpies, on the underlying magnetic state in Fe alloys with Cr, Mn, Ni, V, Nb, C, and N. We then show that effective chemical interactions in steels can be tuned by its global magnetic state, which opens exciting possibilities for materials synthesis. Using first-principles theory we demonstrate that in Fe-Si system the magnetic disorder at high temperatures favour a formation of cubic Fe2Si phase with B2 crystal structure, which is not present in the alloy phase diagram. The experiment confirms the theoretical predictions, and the B2 Fe2Si alloy is synthesized from Fe-Si mixture using multianvil press.
 Thank you very much. So the next talk is going to be given by Igor Abrikosov, who originally is from Russia, from Mises, which is now called the National University of Science and Technology, but now works in Sweden. And you know, magnetic properties of steels are the essence of steels, and there are so many unsolved problems in the magnetic properties of steel, one of which he has solved. So there's a long way to go. It's a long way to go. Yes. Thank you very much, Hari. So first of all, I would like to thank you for inviting me here. So you told us that you had no problems of generating support for your conference, so basically everybody said yes within a minute. I don't know how difficult it was for you to assemble the audience, but at least in my case, it didn't take more than a minute to convince me to come here when you explain the idea. Thank you very much. Fantastic idea. My presentation is about magnetic properties of steel, and I am doing theory. I am actually doing quantum mechanical calculations. This work was done in a collaboration with Markus Eckholm from Linköping University and Alena Panamareola from Moscow Institute of Steel and Alloys. But of course, I would like to acknowledge our people who were involved in this research, Andrei Rubin, Professor Garnostarov, Dubrovinsky-Dubrovinsky, Levento Vitesh, Yana Valenius and Per Olsen. And I would like to thank my sponsor, the Swedish Foundation for Strategic Research, the Swedish Research Council, and I am doing computation. This is my main tool, so I would like to acknowledge Swedish National Infrastructure for Computing. Let me give a true talk of my presentation, which I submitted to this conference before it was severely cut. And I will be given introduction on Abinishu Simulation of Iron-Based Alloys. I will show that magnetostructural coupling gives a new possibility for steel design. At least this would be one of my provocative statements that is one of the subjects for these conferences. I will try to illustrate the universality of theoretical methods by giving different examples. I will show calculation of mixed-in-anthalipysofironchromium alloys, multi-component ironchromium alloys. I will talk about studies of carbon nitrogen, vanadium and neobium and carbon nitride precipitations in austenite. I will show how magnetism influenced phase transition of iron nickel-free thermalloy. And I will also give an example when we were able to synthesize new material by tuning its magnetic states, by synthesizing B2 phase of iron II silicon. I'll hopefully have time to make a conclusion. The main task for me is to convince this community that theory is a useful thing. The main goal which we have is actually to shorten the time for material design. I think that by using theory we have a great possibility of shortening this time as much as by factor of two. You probably saw these types of graphs many times because if I wanted to do material design, the type of presentations which were given in the previous talk, for example, I want to design steels for nuclear reactors, I obviously cannot do my quantum mechanical calculations at this scale. So the state of the art idea of involving theory is the so-called multiscale approach where I do quantum mechanical calculations for several hundreds of atoms and determine the relevant parameters like energy, elastic properties, and teratomic interaction, and provide it for high-level models like thermodynamic or statistical models where we can simulate phase stability, calculate free energies, and provide further information for even higher level continuous model like phase field simulations where the microstructure can be simulated, et cetera, et cetera up to engineering level where parameters and knowledge generated before is used. And by the way, I just want to point out that my area of research is at this blue arrow which is put here. So I'm working in quantum mechanical calculations and statistical mechanics simulations. This scheme is state of the art, but it's a little bit outdated. What we have realized now that it takes too long time to go with chain because it reflects the traditional idea and traditional vision of material design. Basically you have a property which you need to optimize and you have an idea for the material that you want to create and you test this material in addition to experiment. You can nowadays do theory, but you test this material. You see if it works or not. Most probably it doesn't work when you have to go back and to reiterate and to reiterate and to reiterate this process. The new ways of using theory are given by the so-called high-throughput type of computations where you are able to identify the level of the parameter for your material and then scan theoretically or experimentally all available materials pretty quickly because our codes are now pretty fast to find the best material which optimizes this parameter. The main problem with this approach is that we have to find a good set of parameters to optimize or the so-called descriptor. Not all the parameters can be calculated explicitly. I'll show you for example that a young model or a share model can be calculated very reliably, but hardness, toughness and other things we cannot do too much at this point directly. Even more promising way which we are working now is given by setting up a computational databases. The high-throughput design on the traditional approach has another drawback. It requires the formation of teams between theoreticians and experimentalists. We have to work together so people who know the material, who know problem, have to find a theoretician who can do calculation, etc. The way how we start to think about using carbon issue theory is to create a computational databases of parameters which are relevant for material properties. And how nice could it be for you to Google the young modelers of iron, 10 percent chromium, 5 percent nickel, 3 percent cobalt. And to get these young modelers as a function of temperature, we calculated the quality comparable to experimental accuracy. So this opens a new way for material design because people who know how to design materials, engineers can use parameters calculated by experts in their particular work. So I would say that the goal for theoretical calculation now is to be able to predict and calculate relevant parameters at realistic condition and by realistic condition. I mean that in most calculations so far we use very approximate vision of material because our tool density functional theory and the density functional theory of course was awarded not a prize in 1998 so it's very powerful theory but it allows us strictly speaking to do calculation at zero temperature. So if I calculate elastic properties, most probably I calculate zero temperature elastic properties. If I put it in the database, how nice would be to use this zero temperature elastic constants in estimating the growth and phase transformations and the stresses which are in your material at 1500 Kelvin. So the task for me is now to learn how to calculate these reliable parameters at realistic conditions and the subject of this talk is partly related to these realistic conditions and to magnetism. So density functional theory was formulated in 1965 by Hohenberg and Kohn and Wenbenkoh by Kohn and Schem and as I said it's very powerful theory, a Nobel prize was awarded to it but I think it's 1978 is very important date for theoreticians because at this year Murutsi, Yanuk and Williams published their famous book and in this famous book there was a graph where they show that without any adjustable parameter we were able to accurately calculate atomic volume of Wigner's AIDS radius, cohesive energies and bulk modulus of 3D and 4D transition metals and achieve very nice agreement with experiment. In this graph I underlined a rectangle, I shade a rectangle which includes chromium, manganese, iron, cobalt and nickel. Despite the great success of the calculations by Murutsi, Yanuk and Williams for all other materials results for these elements are obviously not so nice and it was realized from the very beginning that the problem was that these are magnetic elements. All other elements are non-magnetic and theory gave very good results in comparison with experiment but for magnetic elements in this earlier calculation magnetism was not taken into account, the agreement was actually quite poor. And just to show you what we can do much better nowadays with magnetic materials, I show the graph and calculations which were published in this year in collaboration with Ahen group where they calculate young modulus of iron, manganese, alloys with chromium, cobalt, actually it was also nickel and copper in these elements and agreement between theoretical results and calculations which are shown here in open circles for young modulus is a function of composition of chromium and cobalt in iron manganese steels with iron to manganese rate of 2.3 and agreement with another indentation experiment done by our collaborators is actually very, very impressive. So there is a possibility to calculate relevant materials parameters with almost the accuracy as good as one can achieve in experiment. But once again to achieve this quality we need to use realistic condition and in this talk I will concentrate on magnetism. If we look at the body center at cubic iron, BCC iron, we know that it is ferromagnetic but so all magnetic moments in iron are pointed parallel to each other but this nice picture is actually present only at zero Kelvin. If you start to heat the sample, magnetic moments start to disorder first and above the curie temperature all magnetic moments are pointed in different direction. So we go from the ferromagnetic state to paramagnetic state and the difference between this arrangement and this arrangement was often ignored in theoretical simulations. I will show you during this talk that if you take into account this difference you can obtain much more reliable calculated parameters. Now this picture has further simplifications. Now we suffer from the fact that movies were not recommended but it's not only we, it's basically the entire subject suffers from the fact that movies are not recommended because in practice both atoms vibrate and magnetic moments do not sit in their constant positions but they move all the time. So these motions also need to be included in the simulations. I will not talk about it too much today but we have a certain simplification. So I'm going to talk about disordered magnetism. As I said we have paramagnetic state where all the magnetic moments are pointed in different directions and they change all the time. And the model which was extremely successful in describing this disordered magnetism is called the so-called disordered local moment where you substitute this live picture of moving magnetic moments by a static picture of disordered moments pointed up or down in a random fashion. And the model goes back to Harvard and Hassegawa, the rate of reticence and its practical implementation in the field was done by Balazs Jorfi, British physicist who passed away last year unfortunately. I am going to show the applications in calculating, first of all, consider iron chromium alloys. These are, of course, based for very many important industrial steels, particularly where used as cladding materials in the fast neutral reactors. And it is known that low chromium steels with up to 10% of chromium show a lot of nice properties. They are very stable and very good. But the origin of these nice properties of 10% chromium steels was not well understood. There was a lot of simulations carried out for these steels, but I would like to call your attention to the fact how theory can complement available experiment. So this is old figure from Heilgrinburg, which shows mixing enthalpy of iron chromium alloys. Actually it's still alpha phase, so it's BCC iron chromium alloys. And it shows that tendency to demixing, so the mixing enthalpy is positive all the way and it's pretty much symmetric. I would like to underline that this experiment was taken at 1600 Kelvin, so up here at the phase diagram it's shown by the blue line. And it's definitely above the curie temperature for iron, so it is taken in this paramagnetic state. However, the operational temperature for reactors is about 800 Kelvin at Mach, so we are still in the ferromagnetic case. So is it possible to use this mixing enthalpy nice and parabolic for understanding the properties of iron chromium alloys? We can do calculations. Mixing enthalpy can be calculated nowadays. I will not go into details of these calculations. There can be find and papers which are inside here. But to make the long story short, this graph shows the calculated mixing enthalpy as a function of chromium composition and it shows calculations for two cases. Blue color indicates calculations done in the paramagnetic state when all the magnetic moments are disordered. And the red line, red symbols and black symbols indicates calculation done in the ferromagnetic states where all magnetic moments are ordered. So the blue lines can compare with experiments from Halvin, as I said, from Halvin's handbook. And this is a typical accuracy of ab initio calculation. So you can see that nowadays mixing enthalpies can be calculated really, really with very high accuracy. I use electron volt units here, electron volts per atom, which are probably not that familiar for our people. So if you want kilojoules, you have to multiply this number by roughly 100. Anyhow, so we are able to reproduce this nice and parabolic behavior in a paramagnetic state. But in a ferromagnetic state, we see qualitatively different behavior. We see that the mixing enthalpy exhibits very strong deviation from the regular solid solution behavior. And we see that iron chromium alloys are particularly stable at 10% composition. The mixing enthalpy is actually negative. And when we were able to go to experiment and find an indication that it's really true. So this is what about normal things. But we can do with theory more. For the next generation of reactors, people now try to allow it with nickel, manganese and molybdenum. We can do calculation adding with many elements. It's from ab initio point of view. It's definitely not a problem. Go from the binary to multi-component alloys. And we can see how these elements influence the mixing enthalpy. And in particular, we see that this stability is significantly reduced. And the tendency to spinodal decomposition moves to low chromium compositions. Let me give another example of our calculations. Calculations of impurity solution energies for niobium, vanadium, carbon, and nitrogen, which play a very important role in carbonite-red formation. Because we are interested in this system in austenite, which is FCC iron. And FCC iron is paramagnetic. So once again, we are dealing with disordered magnetism. And magnetic moments are alive. So to describe this picture, we had to develop a new model, which is a supercell realization of a disordered local moment model. We consider the system with disordered distribution of magnetic moments. And then we take, say, carbon impurity, put it on an octahedral site, and then go all the entire system putting this carbon atom in different magnetic environments. So it corresponds to the situation that carbon atom experience in real life, that its magnetic environment changes a lot. And calculations show that the energetics are very different depending on the atom's seats. But because these changes are very fast, they have to average over all possible distribution. And in this table, the final results for the impurity solution energies are presented. I would like to call your attention to the green column, which is our best type of calculation. So these are calculations which show how wrong theory can be if we don't include many effects into the account. And then we can compare it to the experiment. And the experiment we find for carbon and for nitrogen, we can see that we can pretty much well represent trends. There is a little difference between the calculated and experimental impurity solution energies. Well how important is this difference is up to engineers to understand. But I want to show, for example, one of the parameters which we were asked to calculate, which is a solubility product for vanadium carbides and vanadium nitride and neobium carbides and neobium nitride in austenite calculated based on these models. And the solubility product represents the maximum product of composition of carbon and nitrogen or vanadium and neobium, which is still dissolved in austenite. So if you exceed this product, you obtain the precipitates. Here are our calculations shown in red line. And the different experiments are shown in blue and green. And you can see we do our calculation up to our best at this point. We are in very good agreement with experiment for vanadium, little bit differences present in neobium. Let me move to the final part of my talk and show that using the magnetism, we can influence interatomic interaction and this gives us an opportunity to design new material. So this is an experimental phase diagram for iron nickel and we are particularly interested in permalyl nickel free iron, which exhibits all the disorder transition at 516 degrees Celsius, which is just 100 degrees Celsius less than magnetic phase transition when the system becomes paramagnetic. So basically, if I want to model the system with completely ordered magnetic moments, I have to do calculation somewhere here at zero temperature for completely disordered model, which I showed you before. I would be here. But my actual transition happens when the magnetic moment just starts to disorder a little bit. Basically, in this situation, so magnetization is reduced by 40%. So I have still 0.6 saturation magnetization present in my system. So here I have, so what I wanted to show, what I do, I want to calculate this phase diagram assuming these three models for my magnetic state. This is part of the answer to your question. So if I assume complete order of magnetic moments, I obtain the right topology of the phase diagram. So this is a nickel rich part of the phase diagram. Red dashed line corresponds to the experiment. But I overshoot my phase transition temperature by 300 degrees. If I assume complete disorder of magnetic moments, I undershoot my order of transition temperature. And the span is actually 500 degrees Kelvin. So taking different types of magnetic order gives 500 Kelvin in simulating over phase diagram. So only taking a right magnetic order, I can reproduce the phase diagram correctly. And theory would not be theory if I cannot do it self-consistently. So for expert, the details are shown in this paper. But self-consistent theoretical temperature can be calculated in good agreement with experiment. So what was important in the example before is that different types of magnetic order obviously influence the phase transition temperature. And because of these, we can try to use magnetism in designing new material. So this is my final example, and I really try to go through it very, very quickly. So I'm going to talk about iron-silicon phase diagram. So we have DO3 structure, iron-free silicon, B19 iron-silicon, iron-2-silicon, the high-temperature hexagonal phase is known. But the B2 type phase was not known at least very well. It is not present at this phase diagram. So we did calculations of mixing enthalpy for this material in the paramagnetic magnetically disordered state. And to our great surprise, we find out that B2 iron-silicon is actually the most stable phase in the paramagnetic state. Of course, it's not stable if you cool the system. The DO3 should be stable as it is. But if we're able to keep our system paramagnetic, Monte Carlo simulations carried out by us showed that the B2 iron-2-silicon phase can be synthesized. Of course, you also have to apply not only high temperature, but high pressure to suppress B19 phase, which we don't want to have in these simulations. So this phase is metastable. Calculation shows that it should decompose in DO3 and iron-5-silicon-free phase. But at least it should be possible to synthesize it if you do synthesis at high temperature where the system is paramagnetic. We went to our experimental colleagues and they were able to synthesize some nice polycrystalline by single phase samples with the composition of iron-2-silicon. And this graph should be read from the bottom to the top. So we can clearly see iron-2-silicon lines on this graph so they're very sharp. And then we only hit the system and decompose to epsilon and other phase as it should. But B2 iron-2-silicon material was synthesized in high pressure, high temperature synthesis by tuning the magnetic state of the system. So now my conclusion that relevant materials parameters can nowadays be calculated abinitio of the accuracy comparable to experiment. But it is essential to carry out simulation at realistic condition. And temperature-induced magnetic excitation in particular are important. And by tuning the magnetic state we can synthesize new materials. Thank you very much. Thank you very much. Can I ask you since we are asking questions about short range order and how that fits into your limit between the disordered local moments and the collinear magnetic ground state. So does your scheme include explicitly short range order at the intermediate temperatures? So the chemical short range order at intermediate temperatures can be included within supercell technique without any big problem. And also in supercell and Monte Carlo calculations which we use, the chemical short range order is explicitly included in simulations. Including in simulation magnetic short range order is still a challenge. There are several walks, for example, Andrew Luban at Royal Institute of Technology has developed new technique which probably is a good one to include in magnetic short range order. But magnetic short range order is still a challenge. So this would require you, for example, to go beyond the single site CPA? We definitely have to go beyond the single site CPA, but we also probably have to go beyond the collinear description of disordered local moment picture. So the full non-collinearity needs to be included. In the case of the iron chromium enthalpy anomaly, is non-collinear magnetism critical? Not in terms of comparison with experiment at 1600 Kelvin, which I presented. So it obviously, disordered local moment, obviously works good. But around the phase transition, magnetic phase transition, it may contribute. So if you need very high quality simulation parameters you need to take into account magnetic short range order. Also, not the short range order, I was talking about the non-collinear magnetism. Non-collinear magnetism, yes. So would determine the enthalpy to some measurable extent? I expect so, because if we go from the situation with the minimum to the fully symmetric situation when we change magnetic order, obviously, our type of magnetic order is going to be important. Yes, I think so. I haven't done this calculation. I was unable to do this calculations yet. The graphs you put up originally showing the disagreement between experiment and theory predicting the bulk modulus. Yes. Are you essentially saying that the assumptions they use to do those calculations don't take account of the magnetic moment, which does have an effect on, I guess, the bonds, different things? Yes. And then later on, obviously, you show that it has an effect on enthalpy. Yes. Not entropy, I guess, because that's statistical entropy that we refer to. Statistical. I mean, I'm just, I'm asking. Yeah. So statistical entropy is obviously not affected by magnetism, except through the interaction between atoms, because you can have different type of chemical short-range order. But you have to include magnetic entropy, which is also very interesting question. There is a very simple model how to include magnetic entropy, and it's unclear how well this model works. Okay. I guess the impression I'm getting here is that we've missed out some of these assumptions when we calculate things like modulus and entropy and enthalpy previously. And this kind of worries me, because I'm wondering if, you know, for example, all the phase diagrams that we're using, which depend on those calculations, are they going to, is that going to have a sort of major effect, or will it be quite minor? It depends. So in CalFET community, the realization of the importance of magnetic entropy is a well-known problem, and magnetic entropy is included in all calculated phase diagram using thermocalc. The question is how well we describe the magnetism. Okay. And that's a task for the theory. Yeah. This is probably a very simple question for you, because I don't understand magnetism at all. But you mentioned in passing spinodal decomposition. Yes. In the ion-chrome system. Yes. So are you suggesting, or is there any evidence that the misability gap in the ion-chrome system is actually due to magnetic perturbations? Oh, yes. Okay. Yes. So the magnetic nature of decomposition in ion-chrome is pretty well understood nowadays, and it is related partly to the frustration of between chromium, but its magnetism is determined. That is fully correct. So the short answer is yes. The long answer probably requires another 20 minutes talk. As a student, Harry told me about this two gamma state, gamma one and gamma two in austenite. It just leads to invoralize. Yes. So going back to your Google's way, how can I develop a new invoralize with your composition instead of using nickel? Is there any way of doing this right now? Yes. So first of all, we have published paper in 1999 in Nature where we actually think that it's not two gamma state. So by including non-colinear states into account, me together with Mark von Schilegard, who is now in London, were able to show that there is an infinite family of states which feel the gap between high spin, high spin ferromagnetic and low spin anti-ferromagnetic state. And with this one contribution of the theory, so we are nowadays able to see what is really going on in the system. In terms of how to use this knowledge for the design of new iron nickel alloys. So at present, there is only one way. So you should talk to experts, say to me or to Mark von Schilegard. Yes. And we can try to do calculations at more realistic conditions. Our dream is, as I said, that we pre-calculate all kind of parameters depending on the magnetic state on this non-colinearity and you are able to go to this database and find them. Thank you. What is the ductility of the FE2SI? Do you know? No, I don't. Good. As I know, industrial alloys on the base of iron and silicon contains no more than 6% of silicon. Could you explain the reasons of your interest to alloys with high concentration of silicon? It was my first question and the second question is, if we are speaking about alloys with properties which doesn't depend on structure, you can predict these properties, you can predict these parameters of these alloys. But if we take the account structure or parameter or smoker structure, for example, what will be your next step to improve your calculations? Thank you very much. These are both very relevant questions. So my interest to iron and silicon system actually came not from metallurgy but from the studies of the Earth core. So in 2003, we published a paper which demonstrates explicitly that pressure-induced phase decomposition in iron and silicon system in the formation of B2 iron silicon at ultra-high pressure, which is relevant for the understanding of the so-called double prime layer at the boundary between the solid, sorry, liquid core and the mantle. So the interest to high concentration iron silicon comes from there. So the work which I presented now was a kind of a side project where we try to understand the influence of magnetism on the phase stability. In terms of influence of microstructure and how to include microstructure in my calculation, I don't think that I can go much beyond this multi-scale modeling scheme, which I started my presentation with, and basically to try to compute parameters for each phase. We can look at the interfaces now, for example, and we can provide these parameters to experts in higher level theories. One cannot do everything yourself. I have this quick. I was possible when you mentioned that the missibility gap is... It's on. It's on. Missibility gap being strongly related to magnetism. Does that mean that you can control through magnetism, spinodal decompositions? That's a very interesting question. I theoretically, yes, but I don't think that you can do it in practice because all the fields which are available at this point are too small at the energy scale of the phase stability. Yes, yes, and phase stability. These are simply very different energy scales. So we have two small fields in our laboratories. Thank you very much, Igor, for an excellent talk. I apologize. Thank you. Thank you.
 Thank you very much.  So the next talk is going to be given by Igor Abrikosov, who originally is from Russia,  from Mises, which is now called the National University of Science and Technology, but now  works in Sweden.  And you know, magnetic properties of steels are the essence of steels, and there are so  many unsolved problems in the magnetic properties of steel, one of which he has solved.  So there's a long way to go.  It's a long way to go.  Yes.  Thank you very much, Hari.  So first of all, I would like to thank you for inviting me here.  So you told us that you had no problems of generating support for your conference, so  basically everybody said yes within a minute.  I don't know how difficult it was for you to assemble the audience, but at least in  my case, it didn't take more than a minute to convince me to come here when you explain  the idea.  Thank you very much.  Fantastic idea.  My presentation is about magnetic properties of steel, and I am doing theory.  I am actually doing quantum mechanical calculations.  This work was done in a collaboration with Markus Eckholm from Linköping University  and Alena Panamareola from Moscow Institute of Steel and Alloys.  But of course, I would like to acknowledge our people who were involved in this research,  Andrei Rubin, Professor Garnostarov, Dubrovinsky-Dubrovinsky, Levento Vitesh, Yana Valenius and Per Olsen.  And I would like to thank my sponsor, the Swedish Foundation for Strategic Research,  the Swedish Research Council, and I am doing computation.  This is my main tool, so I would like to acknowledge Swedish National Infrastructure  for Computing.  Let me give a true talk of my presentation, which I submitted to this conference before  it was severely cut.  And I will be given introduction on Abinishu Simulation of Iron-Based Alloys.  I will show that magnetostructural coupling gives a new possibility for steel design.  At least this would be one of my provocative statements that is one of the subjects for  these conferences.  I will try to illustrate the universality of theoretical methods by giving different  examples.  I will show calculation of mixed-in-anthalipysofironchromium alloys, multi-component ironchromium  alloys.  I will talk about studies of carbon nitrogen, vanadium and neobium and carbon nitride precipitations  in austenite.  I will show how magnetism influenced phase transition of iron nickel-free thermalloy.  And I will also give an example when we were able to synthesize new material by tuning  its magnetic states, by synthesizing B2 phase of iron II silicon.  I'll hopefully have time to make a conclusion.  The main task for me is to convince this community that theory is a useful thing.  The main goal which we have is actually to shorten the time for material design.  I think that by using theory we have a great possibility of shortening this time as much  as by factor of two.  You probably saw these types of graphs many times because if I wanted to do material design,  the type of presentations which were given in the previous talk, for example, I want  to design steels for nuclear reactors, I obviously cannot do my quantum mechanical calculations  at this scale.  So the state of the art idea of involving theory is the so-called multiscale approach  where I do quantum mechanical calculations for several hundreds of atoms and determine  the relevant parameters like energy, elastic properties, and teratomic interaction, and  provide it for high-level models like thermodynamic or statistical models where we can simulate  phase stability, calculate free energies, and provide further information for even higher  level continuous model like phase field simulations where the microstructure can be simulated,  et cetera, et cetera up to engineering level where parameters and knowledge generated before  is used.  And by the way, I just want to point out that my area of research is at this blue arrow  which is put here.  So I'm working in quantum mechanical calculations and statistical mechanics simulations.  This scheme is state of the art, but it's a little bit outdated.  What we have realized now that it takes too long time to go with chain because it reflects  the traditional idea and traditional vision of material design.  Basically you have a property which you need to optimize and you have an idea for the material  that you want to create and you test this material in addition to experiment.  You can nowadays do theory, but you test this material.  You see if it works or not.  Most probably it doesn't work when you have to go back and to reiterate and to reiterate  and to reiterate this process.  The new ways of using theory are given by the so-called high-throughput type of computations  where you are able to identify the level of the parameter for your material and then scan  theoretically or experimentally all available materials pretty quickly because our codes  are now pretty fast to find the best material which optimizes this parameter.  The main problem with this approach is that we have to find a good set of parameters to  optimize or the so-called descriptor.  Not all the parameters can be calculated explicitly.  I'll show you for example that a young model or a share model can be calculated very reliably,  but hardness, toughness and other things we cannot do too much at this point directly.  Even more promising way which we are working now is given by setting up a computational  databases.  The high-throughput design on the traditional approach has another drawback.  It requires the formation of teams between theoreticians and experimentalists.  We have to work together so people who know the material, who know problem, have to find  a theoretician who can do calculation, etc.  The way how we start to think about using carbon issue theory is to create a computational  databases of parameters which are relevant for material properties.  And how nice could it be for you to Google the young modelers of iron, 10 percent chromium,  5 percent nickel, 3 percent cobalt.  And to get these young modelers as a function of temperature, we calculated the quality  comparable to experimental accuracy.  So this opens a new way for material design because people who know how to design materials,  engineers can use parameters calculated by experts in their particular work.  So I would say that the goal for theoretical calculation now is to be able to predict and  calculate relevant parameters at realistic condition and by realistic condition.  I mean that in most calculations so far we use very approximate vision of material because  our tool density functional theory and the density functional theory of course was awarded  not a prize in 1998 so it's very powerful theory but it allows us strictly speaking to  do calculation at zero temperature.  So if I calculate elastic properties, most probably I calculate zero temperature elastic  properties.  If I put it in the database, how nice would be to use this zero temperature elastic constants  in estimating the growth and phase transformations and the stresses which are in your material  at 1500 Kelvin.  So the task for me is now to learn how to calculate these reliable parameters at realistic  conditions and the subject of this talk is partly related to these realistic conditions  and to magnetism.  So density functional theory was formulated in 1965 by Hohenberg and Kohn and Wenbenkoh  by Kohn and Schem and as I said it's very powerful theory, a Nobel prize was awarded  to it but I think it's 1978 is very important date for theoreticians because at this year  Murutsi, Yanuk and Williams published their famous book and in this famous book there  was a graph where they show that without any adjustable parameter we were able to accurately  calculate atomic volume of Wigner's AIDS radius, cohesive energies and bulk modulus  of 3D and 4D transition metals and achieve very nice agreement with experiment.  In this graph I underlined a rectangle, I shade a rectangle which includes chromium,  manganese, iron, cobalt and nickel.  Despite the great success of the calculations by Murutsi, Yanuk and Williams for all other  materials results for these elements are obviously not so nice and it was realized from the very  beginning that the problem was that these are magnetic elements.  All other elements are non-magnetic and theory gave very good results in comparison with  experiment but for magnetic elements in this earlier calculation magnetism was not taken  into account, the agreement was actually quite poor.  And just to show you what we can do much better nowadays with magnetic materials, I show the  graph and calculations which were published in this year in collaboration with Ahen group  where they calculate young modulus of iron, manganese, alloys with chromium, cobalt, actually  it was also nickel and copper in these elements and agreement between theoretical results  and calculations which are shown here in open circles for young modulus is a function of  composition of chromium and cobalt in iron manganese steels with iron to manganese rate  of 2.3 and agreement with another indentation experiment done by our collaborators is actually  very, very impressive.  So there is a possibility to calculate relevant materials parameters with almost the accuracy  as good as one can achieve in experiment.  But once again to achieve this quality we need to use realistic condition and in this  talk I will concentrate on magnetism.  If we look at the body center at cubic iron, BCC iron, we know that it is ferromagnetic  but so all magnetic moments in iron are pointed parallel to each other but this nice picture  is actually present only at zero Kelvin.  If you start to heat the sample, magnetic moments start to disorder first and above  the curie temperature all magnetic moments are pointed in different direction.  So we go from the ferromagnetic state to paramagnetic state and the difference between  this arrangement and this arrangement was often ignored in theoretical simulations.  I will show you during this talk that if you take into account this difference you can  obtain much more reliable calculated parameters.  Now this picture has further simplifications.  Now we suffer from the fact that movies were not recommended but it's not only we,  it's basically the entire subject suffers from the fact that movies are not recommended  because in practice both atoms vibrate and magnetic moments do not sit in their constant  positions but they move all the time.  So these motions also need to be included in the simulations.  I will not talk about it too much today but we have a certain simplification.  So I'm going to talk about disordered magnetism.  As I said we have paramagnetic state where all the magnetic moments are pointed in different  directions and they change all the time.  And the model which was extremely successful in describing this disordered magnetism is  called the so-called disordered local moment where you substitute this live picture of moving  magnetic moments by a static picture of disordered moments pointed up or down in a random fashion.  And the model goes back to Harvard and Hassegawa, the rate of reticence and its practical implementation  in the field was done by Balazs Jorfi, British physicist who passed away last year unfortunately.  I am going to show the applications in calculating, first of all, consider iron chromium alloys.  These are, of course, based for very many important industrial steels, particularly where  used as cladding materials in the fast neutral reactors.  And it is known that low chromium steels with up to 10% of chromium show a lot of nice properties.  They are very stable and very good.  But the origin of these nice properties of 10% chromium steels was not well understood.  There was a lot of simulations carried out for these steels, but I would like to call  your attention to the fact how theory can complement available experiment.  So this is old figure from Heilgrinburg, which shows mixing enthalpy of iron chromium alloys.  Actually it's still alpha phase, so it's BCC iron chromium alloys.  And it shows that tendency to demixing, so the mixing enthalpy is positive all the way  and it's pretty much symmetric.  I would like to underline that this experiment was taken at 1600 Kelvin, so up here at the  phase diagram it's shown by the blue line.  And it's definitely above the curie temperature for iron, so it is taken in this paramagnetic  state.  However, the operational temperature for reactors is about 800 Kelvin at Mach, so we are still  in the ferromagnetic case.  So is it possible to use this mixing enthalpy nice and parabolic for understanding the properties  of iron chromium alloys?  We can do calculations.  Mixing enthalpy can be calculated nowadays.  I will not go into details of these calculations.  There can be find and papers which are inside here.  But to make the long story short, this graph shows the calculated mixing enthalpy as a  function of chromium composition and it shows calculations for two cases.  Blue color indicates calculations done in the paramagnetic state when all the magnetic  moments are disordered.  And the red line, red symbols and black symbols indicates calculation done in the ferromagnetic  states where all magnetic moments are ordered.  So the blue lines can compare with experiments from Halvin, as I said, from Halvin's handbook.  And this is a typical accuracy of ab initio calculation.  So you can see that nowadays mixing enthalpies can be calculated really, really with very  high accuracy.  I use electron volt units here, electron volts per atom, which are probably not that familiar  for our people.  So if you want kilojoules, you have to multiply this number by roughly 100.  Anyhow, so we are able to reproduce this nice and parabolic behavior in a paramagnetic  state.  But in a ferromagnetic state, we see qualitatively different behavior.  We see that the mixing enthalpy exhibits very strong deviation from the regular solid solution  behavior.  And we see that iron chromium alloys are particularly stable at 10% composition.  The mixing enthalpy is actually negative.  And when we were able to go to experiment and find an indication that it's really true.  So this is what about normal things.  But we can do with theory more.  For the next generation of reactors, people now try to allow it with nickel, manganese  and molybdenum.  We can do calculation adding with many elements.  It's from ab initio point of view.  It's definitely not a problem.  Go from the binary to multi-component alloys.  And we can see how these elements influence the mixing enthalpy.  And in particular, we see that this stability is significantly reduced.  And the tendency to spinodal decomposition moves to low chromium compositions.  Let me give another example of our calculations.  Calculations of impurity solution energies for niobium, vanadium, carbon, and nitrogen,  which play a very important role in carbonite-red formation.  Because we are interested in this system in austenite, which is FCC iron.  And FCC iron is paramagnetic.  So once again, we are dealing with disordered magnetism.  And magnetic moments are alive.  So to describe this picture, we had to develop a new model, which is a supercell realization  of a disordered local moment model.  We consider the system with disordered distribution of magnetic moments.  And then we take, say, carbon impurity, put it on an octahedral site, and then go all  the entire system putting this carbon atom in different magnetic environments.  So it corresponds to the situation that carbon atom experience in real life, that its magnetic  environment changes a lot.  And calculations show that the energetics are very different depending on the atom's  seats.  But because these changes are very fast, they have to average over all possible distribution.  And in this table, the final results for the impurity solution energies are presented.  I would like to call your attention to the green column, which is our best type of calculation.  So these are calculations which show how wrong theory can be if we don't include many  effects into the account.  And then we can compare it to the experiment.  And the experiment we find for carbon and for nitrogen, we can see that we can pretty  much well represent trends.  There is a little difference between the calculated and experimental impurity solution energies.  Well how important is this difference is up to engineers to understand.  But I want to show, for example, one of the parameters which we were asked to calculate,  which is a solubility product for vanadium carbides and vanadium nitride and neobium  carbides and neobium nitride in austenite calculated based on these models.  And the solubility product represents the maximum product of composition of carbon and  nitrogen or vanadium and neobium, which is still dissolved in austenite.  So if you exceed this product, you obtain the precipitates.  Here are our calculations shown in red line.  And the different experiments are shown in blue and green.  And you can see we do our calculation up to our best at this point.  We are in very good agreement with experiment for vanadium, little bit differences present  in neobium.  Let me move to the final part of my talk and show that using the magnetism, we can influence  interatomic interaction and this gives us an opportunity to design new material.  So this is an experimental phase diagram for iron nickel and we are particularly interested  in permalyl nickel free iron, which exhibits all the disorder transition at 516 degrees  Celsius, which is just 100 degrees Celsius less than magnetic phase transition when the  system becomes paramagnetic.  So basically, if I want to model the system with completely ordered magnetic moments,  I have to do calculation somewhere here at zero temperature for completely disordered  model, which I showed you before.  I would be here.  But my actual transition happens when the magnetic moment just starts to disorder a  little bit.  Basically, in this situation, so magnetization is reduced by 40%.  So I have still 0.6 saturation magnetization present in my system.  So here I have, so what I wanted to show, what I do, I want to calculate this phase  diagram assuming these three models for my magnetic state.  This is part of the answer to your question.  So if I assume complete order of magnetic moments, I obtain the right topology of the  phase diagram.  So this is a nickel rich part of the phase diagram.  Red dashed line corresponds to the experiment.  But I overshoot my phase transition temperature by 300 degrees.  If I assume complete disorder of magnetic moments, I undershoot my order of transition  temperature.  And the span is actually 500 degrees Kelvin.  So taking different types of magnetic order gives 500 Kelvin in simulating over phase diagram.  So only taking a right magnetic order, I can reproduce the phase diagram correctly.  And theory would not be theory if I cannot do it self-consistently.  So for expert, the details are shown in this paper.  But self-consistent theoretical temperature can be calculated in good agreement with experiment.  So what was important in the example before is that different types of magnetic order  obviously influence the phase transition temperature.  And because of these, we can try to use magnetism in designing new material.  So this is my final example, and I really try to go through it very, very quickly.  So I'm going to talk about iron-silicon phase diagram.  So we have DO3 structure, iron-free silicon, B19 iron-silicon, iron-2-silicon, the high-temperature  hexagonal phase is known.  But the B2 type phase was not known at least very well.  It is not present at this phase diagram.  So we did calculations of mixing enthalpy for this material in the paramagnetic magnetically  disordered state.  And to our great surprise, we find out that B2 iron-silicon is actually the most stable  phase in the paramagnetic state.  Of course, it's not stable if you cool the system.  The DO3 should be stable as it is.  But if we're able to keep our system paramagnetic, Monte Carlo simulations carried out by  us showed that the B2 iron-2-silicon phase can be synthesized.  Of course, you also have to apply not only high temperature, but high pressure to suppress  B19 phase, which we don't want to have in these simulations.  So this phase is metastable.  Calculation shows that it should decompose in DO3 and iron-5-silicon-free phase.  But at least it should be possible to synthesize it if you do synthesis at high temperature  where the system is paramagnetic.  We went to our experimental colleagues and they were able to synthesize some nice polycrystalline  by single phase samples with the composition of iron-2-silicon.  And this graph should be read from the bottom to the top.  So we can clearly see iron-2-silicon lines on this graph so they're very sharp.  And then we only hit the system and decompose to epsilon and other phase as it should.  But B2 iron-2-silicon material was synthesized in high pressure, high temperature synthesis  by tuning the magnetic state of the system.  So now my conclusion that relevant materials parameters can nowadays be calculated abinitio  of the accuracy comparable to experiment.  But it is essential to carry out simulation at realistic condition.  And temperature-induced magnetic excitation in particular are important.  And by tuning the magnetic state we can synthesize new materials.  Thank you very much.  Thank you very much.  Can I ask you since we are asking questions about short range order and how that fits  into your limit between the disordered local moments and the collinear magnetic ground state.  So does your scheme include explicitly short range order at the intermediate temperatures?  So the chemical short range order at intermediate temperatures can be included within supercell  technique without any big problem.  And also in supercell and Monte Carlo calculations which we use, the chemical short range order  is explicitly included in simulations.  Including in simulation magnetic short range order is still a challenge.  There are several walks, for example, Andrew Luban at Royal Institute of Technology has  developed new technique which probably is a good one to include in magnetic short range  order.  But magnetic short range order is still a challenge.  So this would require you, for example, to go beyond the single site CPA?  We definitely have to go beyond the single site CPA, but we also probably have to go  beyond the collinear description of disordered local moment picture.  So the full non-collinearity needs to be included.  In the case of the iron chromium enthalpy anomaly, is non-collinear magnetism critical?  Not in terms of comparison with experiment at 1600 Kelvin, which I presented.  So it obviously, disordered local moment, obviously works good.  But around the phase transition, magnetic phase transition, it may contribute.  So if you need very high quality simulation parameters you need to take into account magnetic  short range order.  Also, not the short range order, I was talking about the non-collinear magnetism.  Non-collinear magnetism, yes.  So would determine the enthalpy to some measurable extent?  I expect so, because if we go from the situation with the minimum to the fully symmetric situation  when we change magnetic order, obviously, our type of magnetic order is going to be important.  Yes, I think so.  I haven't done this calculation.  I was unable to do this calculations yet.  The graphs you put up originally showing the disagreement between experiment and theory  predicting the bulk modulus.  Yes.  Are you essentially saying that the assumptions they use to do those calculations don't take  account of the magnetic moment, which does have an effect on, I guess, the bonds, different  things?  Yes.  And then later on, obviously, you show that it has an effect on enthalpy.  Yes.  Not entropy, I guess, because that's statistical entropy that we refer to.  Statistical.  I mean, I'm just, I'm asking.  Yeah.  So statistical entropy is obviously not affected by magnetism, except through the interaction  between atoms, because you can have different type of chemical short-range order.  But you have to include magnetic entropy, which is also very interesting question.  There is a very simple model how to include magnetic entropy, and it's unclear how well  this model works.  Okay.  I guess the impression I'm getting here is that we've missed out some of these assumptions  when we calculate things like modulus and entropy and enthalpy previously.  And this kind of worries me, because I'm wondering if, you know, for example, all the phase diagrams  that we're using, which depend on those calculations, are they going to, is that going to have a  sort of major effect, or will it be quite minor?  It depends.  So in CalFET community, the realization of the importance of magnetic entropy is a well-known  problem, and magnetic entropy is included in all calculated phase diagram using thermocalc.  The question is how well we describe the magnetism.  Okay.  And that's a task for the theory.  Yeah.  This is probably a very simple question for you, because I don't understand magnetism  at all.  But you mentioned in passing spinodal decomposition.  Yes.  In the ion-chrome system.  Yes.  So are you suggesting, or is there any evidence that the misability gap in the ion-chrome  system is actually due to magnetic perturbations?  Oh, yes.  Okay.  Yes.  So the magnetic nature of decomposition in ion-chrome is pretty well understood nowadays,  and it is related partly to the frustration of between chromium, but its magnetism is  determined.  That is fully correct.  So the short answer is yes.  The long answer probably requires another 20 minutes talk.  As a student, Harry told me about this two gamma state, gamma one and gamma two in austenite.  It just leads to invoralize.  Yes.  So going back to your Google's way, how can I develop a new invoralize with your composition  instead of using nickel?  Is there any way of doing this right now?  Yes.  So first of all, we have published paper in 1999 in Nature where we actually think that  it's not two gamma state.  So by including non-colinear states into account, me together with Mark von Schilegard, who  is now in London, were able to show that there is an infinite family of states which feel  the gap between high spin, high spin ferromagnetic and low spin anti-ferromagnetic state.  And with this one contribution of the theory, so we are nowadays able to see what is really  going on in the system.  In terms of how to use this knowledge for the design of new iron nickel alloys.  So at present, there is only one way.  So you should talk to experts, say to me or to Mark von Schilegard.  Yes.  And we can try to do calculations at more realistic conditions.  Our dream is, as I said, that we pre-calculate all kind of parameters depending on the magnetic  state on this non-colinearity and you are able to go to this database and find them.  Thank you.  What is the ductility of the FE2SI?  Do you know?  No, I don't.  Good.  As I know, industrial alloys on the base of iron and silicon contains no more than 6%  of silicon.  Could you explain the reasons of your interest to alloys with high concentration of silicon?  It was my first question and the second question is, if we are speaking about alloys with properties  which doesn't depend on structure, you can predict these properties, you can predict  these parameters of these alloys.  But if we take the account structure or parameter or smoker structure, for example, what will  be your next step to improve your calculations?  Thank you very much.  These are both very relevant questions.  So my interest to iron and silicon system actually came not from metallurgy but from  the studies of the Earth core.  So in 2003, we published a paper which demonstrates explicitly that pressure-induced phase decomposition  in iron and silicon system in the formation of B2 iron silicon at ultra-high pressure,  which is relevant for the understanding of the so-called double prime layer at the boundary  between the solid, sorry, liquid core and the mantle.  So the interest to high concentration iron silicon comes from there.  So the work which I presented now was a kind of a side project where we try to understand  the influence of magnetism on the phase stability.  In terms of influence of microstructure and how to include microstructure in my calculation,  I don't think that I can go much beyond this multi-scale modeling scheme, which I started  my presentation with, and basically to try to compute parameters for each phase.  We can look at the interfaces now, for example, and we can provide these parameters to experts  in higher level theories.  One cannot do everything yourself.  I have this quick.  I was possible when you mentioned that the missibility gap is...  It's on.  It's on.  Missibility gap being strongly related to magnetism.  Does that mean that you can control through magnetism, spinodal decompositions?  That's a very interesting question.  I theoretically, yes, but I don't think that you can do it in practice because all the fields  which are available at this point are too small at the energy scale of the phase stability.  Yes, yes, and phase stability.  These are simply very different energy scales.  So we have two small fields in our laboratories.  Thank you very much, Igor, for an excellent talk.  I apologize.  Thank you.  Thank you.
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