Reliable ab initio methods

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Reliable ab initio methods
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Reliable first principles calculations for iron: APMS conference
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Paxton, Tony
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A lecture given by Tony Paxton, at the Adventures in the Physical Metallurgy of Steels (APMS) conference held in Cambridge University. Electron theory in the understanding of iron, its magnetic properties and the behaviour of intersitials such as hydrogen and carbon in iron. An argument is made that the well established tight binding approximation to the electronic structure now furnishes us with a reliable theory for the description of the three phases of pure magnetic iron and its principal interstitials, including carbon and hydrogen. This will open the way in the coming five years to fully quantum mechanical atomistic simulations of steel and its embrittlement by hydrogen. Some key questions have recently been answered using density functional theory, namely: what are the equilibrium concentrations of vacancy-carbon and vacany-hydrogen point defects? Can hydrogen dissolve exothermically in ferrite through its binding to defects? Do carbon atoms form "dimer molecules" when bound to vacancies in ferrite? The tight binding theory can also answer these question quantitatively as I shall show, and moreover this is a theory that can be implemented with sufficient speed in a computer to admit molecular dynamics and statics simulations well out of the reach of density functional theory. Soon we will be able to answer questions such as, how do carbides act as traps for hydrogen? How deep are these traps? Are they located at the metal-carbide interface or in the depths of the precipitate? These are questions that are also just beginning to be answered using atom probe tomography, so the theory and experiment are at similar stages of this enquiry.
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the To protect the it take the would time to do it there and and go when you it took the top job at the end of the year and I'm so our 1st speaker Aden a it's Professor Anthony Paxton
from national physics laboratory at King's College London here is going to torturous about reliable energy method saved focus on what he did yes this
my opportunity to embarrass Harry varies slightly by saying thank you very much for the support and encouragement that you've given me
over the years nothing Harry has the same vision that you mother had the notion that at the heart of physical metallurgy lies the election theory and it's very notable that's already there too elections speaking at this symposium which is something that wouldn't have happened 20 years ago 20 years ago no 1 would have to show a couple of slides explaining what is meant by the density functional theory and nowadays it's hardly necessary people seem to know what
it is the point is of course of the year of the electrons the glue
which holds the atoms together in in any case of condensed matter and so that's the nature of the of the city of nature of the situation in both chemistry and physics and physical metallurgy and study of condensed matter 1 has to solve the shredding equation for the
electrons which are holding the nuclei together and ultimately that and possibly what's responsible for the mechanical properties of the material and this is
done through the density functional theory is interesting so because of their own and in 1
Monday he explained that the density functional theory was 1st produced in 1965 interesting that's also the date Jack Christians 1st edition was published and he had a similar visions of 1 of the nature
of the importance of electrons theory officials about the same time you rather he wrote some of the extraordinary difficulty in obtaining a a quantitative theory that that could be used in the design of of metals and
and indeed he was right in the sense that the DFT really took another 20 years or nearly 30 years before it became established that the
2 could be usefully used in the context and that interest us today and my own work over the years has been included in an abstraction of
density functional theory into a model which we call the time finding theory and this has the benefit that it's a great deal more efficient computationally and in some sense also gives greater insight into the nature of the chemical and physical bonding and that's mostly what I want to talk about today and from a technical point of view the tight
binding approximation of instead of constructing a Hambletonian self consistently and have
initiated and which is up the title of this tall and uses an approximation uses a lookup table parametrized matrix elements and so on all
told a little bit about line but what's important and what in my view has created the breakthrough even in these last few years which has not been possible up to now is to is to study and and model :colon in iron which means
that we are now able to study state and I think government has taken this on board at least in in other countries expand society has established a huge 1 or 2 new director it's in the interest of the institute to creates an environment for the model steals and a lot of the work is being done elsewhere in Germany and Sweden in United States there a view that a policy makers I would urge you to consider that the UK now needs also to come to the forefront of this kind of work the the challenge for me to understand
Coburn in line with with was was creating models and an
understanding of the phenomenon which are very well known to namely that that the carbon and is associated with the optic parasites and other limits of the city I looked in the concentrated limited future make the fictitious and FEC phase in the BCC structure than the column would be in touch with me .period and something concentration on 1 unit of of year the system goes over to preferring not to neutral sites with the associated to tribunal distortion on account in modern that's very well meant that the could the common at something rather let what physicists call powder in which there is a type called the force which reorient United agrees and says the company defeated Australia something about shortly and even more unusual amendment striking
is that in most enlightening the SEC face the same thing happens that the :colon occupies
the upheaval sites in the diet limit but if you're going to make an FCC FEC
nonexistent positive beautiful nation it which make that Chrysler would have the sink and structure not the rock salt structures and the cobbler preferred the tactical side know that interstices considerably smaller than the optical sighting of the city and 1 might be tempted to think that the reason for that is that
company like some sort of S P 3 funding environment as a dozen diamond and so it prefers the situation of having 4 neighbors rather than 6 neighbors even those that little bit of the site available is that much smaller than the crystal expands accordingly and when these models nominees from the standard density functional theory describes the situation perfectly well the challenge is to find models of quantum mechanical models of
his time finding modeled to sign hydrogen the similar questions Huygens all the different in the sense that in the BCC structured always occupies technical
sites that at concentrations in the dollar limits and then again we need to have described that I want to start off with the child of us off years
ago which I found quite striking these a density functional calculations
and done by a group of rehire respectability the authors of this paper and they calculated using the density functional theory the formation energies and the configuration and represent a large number all of complexes defect complexes particularly containing other carbon all vacancies and then they plot in this this diagram what would be the concentrations of these defects and threw them at acknowledgment minimization of the energy as a function of carbon concentration this is the 160 degrees centigrade and set around here this is the right hand and 1 has a list the minimum like common high carbon steels and what's striking is that the new would Michael eliminated vacancy is centuries nonexistent expect them and any vacancies that do
occur that will be decorated by exactly 2 carbon atoms and so the dominant
defect is far vacancies concern and I don't know if you find the striking of everybody knew this already but I was surprised that you might even state quite Sarah strong and family that apart from the overwhelmingly dominant defect which
is the common of the side all vacancies in just about problems still decorated with 2 covenants want it is Of course
that must have consequences for the the diffusion and so on so what I wanted to do in the next few slices of trying to study this complex and using the time finding methods but before I do that I wanted to show you some some results from
the tight binding modeling to restrain conceivable what sort of them what sort of things that I think can do so and if for
example a calculations of the above modulus and the 2 share constant speed and internal energy difference of P BCT in Ireland this is the formation and hear the vacancy this is still quite controversial said that this is just a technical term generalized gradient approximation of the systems function cheery here and and and the 2 sets of experiments on I'm using the the experimental data from Zadar
and and under the he's very very firmly of the opinion that
the the formation energy of the vacancy and I cannot be greater than 1 . 8 5 but the other experiments that that have been reported that about 2 inches closer to the density functional results and then there's something happening here on the tight
binding models of the produce and here
we have the migration energy for the vacancy and again on can compare experiment with the density functional theory and a significant discrepancy should
still is and you know there's still a factor of the density functional theory and doesn't always get things absolutely right but it's the best we can In the source of more concentrated limit this was very gratifying we
calculated these days the
data taken from a paper from from gift the inquiry also very little of this paper industry calculated the the structural parameters of the same tightened also the Exelon high-income white face and just to show that these are in extremely good agreement with experimental so that our our tight binding
models to predict the structure seems I which is extremely important that I think this is what I mean by having you know a fairly recent breakthrough in there in the morning and feel that we have now models which are quantum-mechanical and and and reliable Harrison Taichung electron volts this
is the migration energy of the :colon in
in the alpha phase in other words is the energy difference between up to here in the Chechen fighters in the dollar limits these the time finding compared to the to the density functional theory these are the binding energies over all in electron volts of 1 and 2 carbon atoms to a single vacancy and these are the migration energies of of carbon in the in the gamma the Austin and you might imagine that like hydrogen the
Coburn took a double fault through the neighboring Chechen people
fight but it doesn't it forces it way through forces its way through nearest neighbor bond through the day saddle point on a single fault that has a lower level migration barriers that's quite surprising I'll show you a
picture of that nature on now what we do quite often as we we show energy volume to compare them
without either experimental with with the best series is the density functional theory is a number of different phases of the composition of the 3 c and this summer I'm
high-energy phases that we invented these are quite significant this here we have was showing these curves here and these codes system substitution will face faces in the significance of the time
finding theory is not good at I at representing the substitution of faces and compared to a more accurate quantum-mechanical was very gratifying and I was very pleased
to find is that we do very
faithfully reproduced the the formation energies and energy building codes of the important and combined the Absalon and the same time term let me
just after you a diagram of the Of this object which I talked
about earlier wrongly the combination of 2 2 carbon atoms of vacancies of making cited in the middle of this to here and
the carbon atom or indeed a heightened madam would never
occupied vacant site itself as he saw moments ago there's a very high tendency for producing substitution faces and so they occupied their respective opted evil
sites here and but there's more to it than that the on these 2 carbon atoms form molecule the distance the bond lengths here is about the same as the bond length in diamond as well at exactly the same as the bombing diamond you might ask
yourself what's going on here better mentioned a while ago that some people think that even harder problems with former Giants steal from an interesting told the last talking yesterday that what happens when you dissolve fullerenes put its of carbonyl called molecules into interest in what happens to turn into because this bond is short but is not
as strong as that of the problem bond and diamond you might ask what happens when you when you take a
hydrogen molecule you dump it into into a metal the bands of the war the U.S. states of the of the hydrogen molecule the below the day bands of the transition metal and so reoccupied 2 electrons and both on the antibody levels of filled in the molecule breaks apart is my motivation to call on anymore that's that's why associates on the surface of metal and something similar might expect to happen and when you do
the same thing to company but that the company the company
s so you can't pay levels in the transition at the levels all mixed up together is less obvious but you're going to quench up this century to belong to some extent it happens whenever listed form of bond and interestingly
this is the configuration finally arrived at both in the density functional theory and in that
time finding fishery and see why that is because the common in this
orientation conform 3 further bombs modified in Matanzas if it was trying to form
them the thing that we wouldn't it but was there with with its neighboring Byron atoms in these bonds are all exactly the same length as well so this is
ultimately the structure that you'd expect to see in that the defect complex that I mentioned a moment ago very quickly after the show you know movies on the show you the snapshots this
is this is a cop and feeling in Austin lights of the little carbon peeking out here is
pushing its way through it's almost as if at the saddle point you have a stacking which is always
rebounded as a heresy in metallurgy at the point of the saddle point and that the government
has its way through the doesn't hold 1st detected legal fight and then on to the next of people like just forces its way straight
through the nearest neighbor bond between 2 iron atoms but ended up front you would find me and this this polarized living with
his physicist way of thinking about a carbon atom
variety in which you get this large distortion because the opted agent is not a regular in
the ACC and these 2 ,comma iron atoms of pushed aside here and the other 1 direction but once the Coburn migrated this distortion is now in the 1 directions in London by orienting .period Poland so this is a unit to a physicist the carbon as it diffuses in line is carrying this whole room with this is something that we were able to
to to calculate and to and the simulation in the tight binding theory this is this sequence of snapshots This
is what we call the minimum energy path the the path of the of the particle takes along the minimum energy as it rises to the saddle point and then falls down into the next minimum a
move now to hydrogen in either these tight binding calculations and everything I'm going to show from now on is based on on these 2 diagrams so
take it or leave it will be done this here we have this is the position here we have taken a lattice of iron atoms in the BCC structure in place to hide anatomy detective people site and then we relaxed the iron atoms around it and then we've kept the INS frozen and we've moved to hydrogen around calculated the
potential energy the total energy and we plotted it in a diagram like this and then we run the 2nd calculation in which we move the origin he
announced it is the is the center of the of of the Chechen people sign up for the Tetris evil evil side here and here and placed behind enactment saddle
point we've relaxed the iron atoms around it and then moved on the same thing again before we've we've mapped out the potential energy surface so that some that's the answer us from which everything else follows what which wanted us to calculate the if 70 of hydrogen in mind thank you 5 minutes so we do that using refinements path
intervals theory as some of you will redefine the speech will become quantum electrodynamics
heroes popular with an annual through direct difficult book on statistical mechanics but
ultimately the partition function of a quantum mechanical system according to find can be mapped onto a classical train beads of single
particle moving some potentially as a partition function which is mapped onto
a classical partition function of a string of beads which are joined by spring constants of this strength and have a kinetic energy and this becomes exact and the limits of the large number of beads was interested then an integration of all possible
path reminds you of the QED notion that will the
principle of factional Fermat's principle that when a photon takes a call from here to here that she knows somehow in its mind all
the different possible possibly contagion accompanies the action on each part and then it takes the pulse of the minimum actions that marvelous and there is the quantum-mechanical action
here the basic areas is 1 of the painting temperature to know
partition function you everything because then you can calculate the free energy and you can also calculate the
park position probability density from that and now we can see a very strong and Stockton honoring his behavior in the free energy of the migration of a hydrogen atom from montage of
together is not constant said high temperature the classical behavior of low-temperature the
barrier itself is reduced through quantum-mechanical tumbling and there is a reasonable comparison here with experimental data so far as to calculate the deficiency of hydrogen and assume acting as a classical
particle you would you fall into a significant error now the 2nd strand is the theory of Gregory
lost he also follows
find in defining a constrained on constraint
partition function through this constraint density and then they we have something called the continent from distant states theory rate constant is a mistake shouldn't be a C here so it's a ratio of a constraint partition function and the total partition function at the reactants states and then
no 1 can use a velocity here from Nextel distribution and so on can predict the the transition rate for the for the
quantum-mechanical tunneling and these are the possible probability density
distributions for the particle at high temperature about thousand helping down to low temperature about 20 Calvin's you can see that even at high temperature the possible
at the equilibrium to turn to tracking site is quite widely distributed the becomes focused to a narrow distribution at low temperature which is counterintuitive and then even more striking is high temperature
and the particle when constraint isn't there when we constrain the partition
function in this part of probability density is is distributed around the saddle point high temperature but is still quite widely distributed is
not the point particle cabinet low-temperature you proton splits into 2 and 1 has a tumbling
stated practically located at half the federal sites themselves as no probability density actually our very little she up and so from that we can
calculate if we know the transition probabilities
transition rate we can calculate the Einstein equations justification one-sixth of that and divide by the hoping Justin square and we have the diffusion of the reported that the
facility is a function of temperature and these are outdated here the path integral Compton transition state theory which is not a straight line is non-Armenians experimental data always posted straight lines because that's how the experiments were to try to extract the prefect and and and and and an energy barrier and then and then use and plot those on ordinary
the ugliness tie-dyed but it said striking that we get consistent agreement with experiment certainly at high
temperature anything about these these of theoretical
calculations by other people called Central molecular-dynamics I'm go into that but somewhere very gratified that we can predict this is admonition that
efficiency of hydrogen as a function of temperature something
is justified the conclude he
supernatural their mission and a lack of all registered candidates
engineer .period character that he had heard that something like Gateshead thank you very active hearing anything was new the land that had last questions and dead back if it breaks you've got this son Philip vacancy defects shared can this be extended to instruct you find in a grain boundary to predict you diffusion along the grain boundary all the stability of the state borrowing to remain at
grain boundary structure the
boundary to do that the other is a possible we started to do calculations like that of the facility of -dash alone this the case using the
same approach is here with something similar in the sense in the central and molecular as a continent chemical companies equally treating the hydrogen that the company has to love and reconnaissance interstitial enough of what it would mean is that the the grain boundary at the will of the that is the case and doesn't provide a full of new partly for countries that didn't get trapped in the financing at a time in real sense the dissertation obstacle to confusion in the case of said that that all the answers the 1st part of the question in terms of hydrogen borrowings another massive borrowing wouldn't think of it being quantum particles in sufficiently amounts would have worked on borrowing and investment in earlier days so when you say these methods you mean density functional is here we did we have government that will make for about 10 years ago looking at the embodiment of copper exactly using company chemical methods and try to find your cellular phone won't tational power sold up to the level
where you could do a Jedi defects like at the grain boundary roster osseointegrated reveals a great battle as it is known here
guests this commenter yet is part of a breakthrough really offensive Functional Theory finally becoming unit coming home to roost because people now have access to hide our computers which they didn't even 20 years ago with
Denny a yet to qualified that by saying these are special bond said a mother of 4 yet so effective can and going back to your carbon vacancies in the
concentrations are incredibly low so so is itself any consequence what it means is that there are neither
vacancies there's nothing except in company ,comma not neutral and default and steel but ending up in every detail the high court this is this is this is
Aston absent says 1
one-percent governs the use this garden is the standard minus a 10 year minus 6 cents the minuses 6 of 10 to the
minus 5 it's a significant it's very very
small theaters nothing must be produced but it is assumed that every carbon atom room where that every vacancies said carbon at you know how that would influence the diffusion of iron we haven't
done a calculation that I take I mentioned that has the right breaks away from it and the cultural center would have to carry the damn thing and so on
Bloomberg is calculations that we haven't yet made a symposium
a sense enough to argue that if there is diffusion in irony and this is the object of the meaning of these concentrations of very small this is quite low temperature people's
confidence in the future and we haven't seen parts like this ,comma temperature everything changes in making these things become less prevalent compared to the vague or the 2nd question is about the
diamond like Bond get him and so again that relies on having their due out Benetton's quite close to each other at noon and we know that actually there approach much closer than there is a strong reflection as
well yeah so the chances of this happening of various projects while I I don't know
Harry I mean if you would place if you're Maxwell's Demon and you cannot break the will to govern continue pocketed placed 1 of them here and 1 of their many went
the way they would need to go in doesn't the nearest neighboring sites actually the state yeah because of 1 here and 1 wrecked exactly
as what we have here you know you have replaced 1 of them here and 1 of them that and they would again moved together ministers the ground state here so I mean I think what you're
saying is yes of course in all of the theory of chemical bonding you have to feel like you have the floor of this House and attractive part of some repulsive ,comma stadium at the nearest never vessel including in the field the the continent and of not living in the house this is the ground state along with and saying is that there is experimental evidence is enough from its nuclear accident that the carbon atoms do not buy the nearest neighbor he said is that not enough that very thing most of was going well I I assume that somebody in there has to be some
internal friction between the 2 so what would you think life I get appointed to determine whether carbon atoms of 1 of the things that you catered half being named I knew that the covenants never occupied the minister in
situations like this right but that's not exactly what this phase diagram is telling you the phase diagram is telling you differently and if you believe
that there is the functional theory than telling you that this is a problem this is the most prevalent anything coming of competitors says this was a binding energy for this thing so there
also considered to have these traps and 1 of the reasons and this is the binding energies this is a problem of the Minnesota not
nearest neighbors and of course you could
have 2 of these and 1 of those which are separated by a long way away but that actually have a higher energy this function that and this is what I showed in this table here
is that you have to buy energy of 2 carbon atoms to a vacancy is positive 1 electron volts so if you've got 2 carbon atoms in the matrix and you've got a vacancy than in Game 1 and a half electoral votes if you put 2 of the 3 objects together it said that that was small enough that you might not think so it might be good because we know we get bigger computers we can system but this is what we call
convergence tests in the business and with careful that we make big running on these things yourself in give and so in this town with bigger and bigger sales and all things considered the difficult calculations and specially for the density functional theory you have to work quite hard that's why time finding my contention pipeline is just because that's the function of the this that's just like we can throw away we can cut the apron strings the density functional theory the following is lot of time finding are there any
questions from the audience and In many online whatever of moisture but employee also on the year when your are on your wall prediction the to cognizant was going to go with wait-and-see that any
measurements Our anywhere the
actual measurements of wait and see the use of it he must which include the effect of this fall that would reduce the impossible to exclude called for on the article was so rude
crude in Kruger variability he is vacancies used measurements of the accounting for all oil variation to the golden color and composition little 1st say
this is not my predictions with predictions the MIT group that 1st flight after not 1 word that I haven't in the literature
so I was astonished to find this heated debate
among all of this is the formation and the vacancies that something different but here we have the migration energy my understanding is that that's pretty well agreed on not from Xavier think I think there are yes the
people who believe that is the people believe that information is about to electoral votes I think that's the Scandinavians they believe that the migration it is much better for much much smaller something closer to this value and then Sega takes the view that we have this the formation
energy in this for migration energy in both those states put together consistently will give you
roughly same sitting whether Collins involved my understanding is that they are very very careful to it appears on principles of the and is the game they planned to go with a mail not fully show that controls 8 of this the campaign but this still hotly debated I was amazed the experimental people do not agree with that this difficult calculation because the beating he faces and stable at low temperatures very hard actually to measure the vacancy concentration because it's so small Bolivian wanted to see and I think I don't know the answer to question expressed question for the experiment of England France we can do this so the compilation of the Harry proposal we can start moving the vacancy with its combination of finding the minimum energy costs and trying to come late because the prefect will be hard because some collective vibrational modes which is pushing the thing up to all of the saddle point of view make the calculations with Australia's Conn it is the
answer does not question the decision I don't know where we're going and yeah while they're on the front end of the year and baking bread that without the


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