00:01

but without but they will make a Staten Island to continue today on the growth of their right but this time they're going to have more than 1 solid so a with problems there and you have substitution of studies for example manganese acidic enough for whatever and just a reminder you me however no alone which has a composition see and to identify the composition that interface to draw a timeline of the the phase diagram and that gives us the equilibrium composition of the type which is in contact with Arsenal and where we have the composition of Austinite with an equilibrium that fat and this is part of a binary system but the fact that these compositions are connected by a a line of faith it means that we have local equilibrium at the interface that at position of the face and he obtained an election would be that Pioline by drawing a convention to the free energy because of the and Austinite because that gives us the composition of last nite and the creation in equilibrium at each other sir if you want to extend this now among the component system then obviously believes girls will become surfaces in 3 dimensions I and assure you this diagram in 1 of the lectures where we not surfaces in 3 dimensions of letters yet and instead of a convention we have a tangent plane which touches those surfaces and it touches them simultaneously gives us the composition of the new phrases which are in equilibrium just like a common tension construction but now we have a plane touching USA since the projection of these points on 2 who's going uses the tag but we have the additional freedom that I can actually get a whole set of points which will remain in contact with the two-engine planes if I lock that engine that so I can generate an infinite said of Thailand's only science ex-convent plot which defines might have felt scanner phase at a constant feature I can have many combinations of fat and Austin which are in equilibrium with each other because of now got next degree of freedom by adding manganese system the severed head .period that so that is going to be very important when I'm going to look at an antiques because you see that substitution of solutes diffuse something like ECU orders of magnitude slower than carbon atoms the fact that we have a choice of Thailand's that we can take to define equilibrium at the interface helps us to maintain both solutes diffusing at the same time and still having equilibrium and think and explained that in a bit more detail as we go to the lecture so this is an isotope of section all of the iron manganese carbon phase diagram of plotting manganese here on the vertical axis on the horizontal axis and it's at a constant temperature thank and yet we have all these guidelines which defined far-right which is in equilibrium with us tonight so far the premises of his lecture and as you think that we can calculate the phase yeah and we can use of idea of software that's available to do that and calculation office diagrams actually is completely based on experiments if so you do thermodynamic measurements create thermodynamic databases and that allows you to calculate the Thailand compositions such as weapons and all this information is available to us 7 happy with that you realize that when we say calculation of a diagram we must 1st have the thermodynamic data so someone has done a huge amount of work to collect all the dynamic data experimentally and to put them into software which lets us do extrapolations of those data and estimates phase diagrams so 1 that they said I can get it without any different no that when 2 of

04:52

the composition program at the Fed just 19 faces so here we are the distance that and the contemplation and let's assume that there is a depleted and ultimately is enriched and this is my compositions here we see gamma and see again when this interface moves I will have to displace some obvious 7 as the interface advances and I'll come up with an equation that the velocity of the interface my declared that the amendment also added that the In order to maintain the contemplation of the fact which is different from that of the US nite I see the amount of money the speed of the game so this is the rate at which started his petition grade at which delegates gains by ocean must be equal the influx of stallion taken by the fusion From the peak at the interface must June at the interface this is the flux australia fusing From named face and that we know is a diffusion coefficient times the gradient of concentration which you see them I have of the money received by divided by the diffusion distance said the so there is nothing really new so far this is a very familiar equation you not that the magnitude solid his pollution must be equal to the rate at which is being carried away by diffusion if the amendment maintain look at equilibrium at the interface now the problem with this is what we actually need have to sell you for which we have to write such an equation so if any the

07:56

same equation for 2 different assignments then I have the velocity of the interface yeah see gamut out of 1 of the for example ,comma minus C have the again warned must be equal the 2 feasibility of 1 times ingredients In the concentration of 1 at the interface and a 2nd equation it now in terms of net said manganese can have when the seat of government 2 In the diffusion coefficient of 2 times the gradient interior so he could you could assume that 1 is carbon June is manganese and experimentally that substitution of solutes diffuse much slower that interstitial targets so we know that the diffusion coefficient of 2 is much much smaller then the diffusion coefficient of 1 now we have to satisfy these equations the simultaneously In order to maintain local equilibrium at the interface so must these equations must be satisfied simultaneously it must be satisfied to maintain local equilibrium and then you have a basic problem the velocity in both of those equations is exactly the same there is only 1 interface which is moving back the diffusion coefficients at different by some 8 orders of magnitude and lose concentration differences in the 2 equations are not that different so how can we satisfy these 2 equations simultaneously when we have such a large discrepancy In the diffusion coefficients if you simply take at line which passes through see so that's that's a question is difficult to do this because the diffusion coefficients are so different the philosophy industry equations the it is identical In his equations since there is only 1 interface moving there is only 1 interface moving so if you exceed them out out and see out them simply by picking entire line which passes through Sunni by we want in general be able to satisfy these equations the Republic see cannot conceit of gamma and therefore these quantities because we have 1 into so From the trial passing To see Bob then hidden will in general be possible to satisfy these equations simultaneously it will not be possible general set his these conditions because the concentration terms are similar the city not different by 8 orders of magnitude as a few coefficients now not fair goal on you explained how to solve this I want to show you 1 slide which comes from the

14:14

irreversible thermodynamics that I was talking about earlier previously rarely had just 1 diffusion coefficient and 1 ingredient in a binary system now that you have to gradients and the gradient of manganese can influence the flux of government and similarly there gradient of carbon can influence the flux of manganese so strictly speaking we now need for diffusion coefficients the first one is the diffusion coefficient of the 2nd 1 the diffusion coefficient of manganese and then the crossed diffusion coefficient how the gradient of manganese influences carbon diffusion and how the gradient all uh ,comma influences the manganese division so it is possible to do this said many of the the diffusion data that we have will allow you to have a matrix of diffusion coefficients including the 1 1 B 2 1 1 2 and but for the purposes of today's I'm going to neglect the cost diffusion coefficient just to simplify the problems but when you are using things like mobility databases and so on they might have crossed diffusion coefficients as well and in some cases it's possible get thermodynamic representations of the the Cross diffusion coefficient in other words we derive the and somewhat In other cases it might be possible to neglect cost diffusion coefficients because the movement of manganese is unlikely to be strongly affected by the gradient of problems the manganese moves much much slower than :colon however the gradient of card at the moment the problem will be strongly influenced by gradients of so navigate a focus just diffusion coefficients for that particular animal rather than the crossed diffusion coefficients the purpose of going

16:29

back to these equations at the top the problem is that they is much smaller than the 1 now these terms on the left-hand side in these 2 equations are not that different than not different by 8 orders of magnitude at the velocity is the same and concentration differences are not that different for manganese and problems but we had this minister said gradients on the right-hand side this is gradient of province and this is the gradient of manganese so here the 1st possible solutions supposing you choose at the airline which reduces the concentration gradient of carbon so instead of having a bread and it makes it extremely flat then the product off the last diffusion coefficient and the gradient might become compatible to the product of the smaller diffusion coefficient of manganese and it's great so 1 possibility is to choose a timeline of the very large number that we have available on our planet phase such that the gradient of problem is reduced and then the flux of manganese can keep up with the flux of carbon yeah I have a summons that again later but you understand we now have a choice of guidelines not a single guidelines which passes through seemed given the test of time and if you take the timeline which minimizes the gradient of carbon then the product of the last diffusion coefficient and small gradient of become compatible to that for mankind Is there any other way so far as we should have minimized the gradient of carbon and pick the Thai-language does that to Sylvester maintaining local equilibrium at the interface because compositions are still fixed by guidelines is just not that language is passing through see box so that's the 1st solution was the 2nd solution absolutely right so the division coverage and of manganese displacement so that they could Thailand which maximizes the gradient of manganese then the product of a small diffusion coefficient and the last gradient might be compatible to that for problems get so just write that down and then I will come back in a bit more detail so there are 2 solutions new solutions given that we can think about given the Thailand does not have to pass to see them Is that we take a timeline which maximizes the gradient of province also minimizes the gradient of take which minimizes created of carbon to compensate for its largest diffusion coefficient large diffusion so what I want it is a flat gradient Of course it's a hideous plucking the concentration of carbon this is C Bob and this is silly can offer and see gunmen so if I want a very gentle gradient of carbon then the equilibrium composition of Austinite must be similar to the average composition of the estate spectacle I've but the Thailand which make Saddam out of almost equal to 2nd solution used to break the line which maximizes the gradient of manganese maximizes gradient also manganese I want this team gradient of manganese how I'm just going to instead In other words very little manganese must partitioned into the US tonight and that can only happen if the composition of the fact that retrospective manganese is similar to see bar so that they can tie which allows the composition of the With respect to my needs to be the same as the average is that the Fed will grow at almost the same manganese concentration as you lot so I'm not going to ask you whether you are happy with this stuff up because I haven't shown you this on diagram but beautifully understand what we're doing we have compensating for the very last discrepancies between the diffusion coefficient of manganese and copper but a let's look

25:05

at the 1st case they're being granted USA gradient of carbon it's this is again manganese being planted on the vertical axis carbon on the horizontal axis and the granddaughter specifies our family composition so if I go horizontal line he said that give me the manganese concentration and a vertical line gives me because concentration of our allies that sir but I want to do In order to minimize the gradient of province is debate at Thailand's ritual giving the same composition in the US tonight as India along with suspected the federal budget airline to that led up and then hits this phase boundaries defines the guidelines so that's my vertical construction line through the Alec composition when it hits the phrase boundary automatically defines the Thai-language controls the interface compositions so here for example is in equilibrium composition of Austinite and this is the equilibrium composition of the I can do and the concentration profile at the interface simply by looking at those composition so here for example is the concentration profile for all carbon and you can see that the gradient of Holland India last nite is that agenda and here it is the concentration profile for manganese which event takes this plan which is included composition of the last nite this which is included the composition of and this is the average manganese concentration so we have almost flat gradient on carbon India last nite to compensate for its large diffusion coefficient and manganese is being partitioned quite a lot between the fact that Austinite so muted that long-range diffusion of manganese so this is going to be a slow growth process if an accord is a partitioning local equilibrium model local equilibrium because the coalition that interface are connected by time of the phase diagram and partitioning because the manganese has to defuse last distance since there a big difference in become manganese concentration of the family and a few allies as a whole this soccer's when the island it is close to the Gamma Gamma phase boundaries another was a driving force for transformation is small and what happened to OK let's look at the this half a 2nd alone but so now we are going to transform under conditions where the allies close to the fact that fondly In other words large starting points and what we want is a steep gradient of manganese in the fair In other words the maintenance contemplation of the allied with the very similar do the manganese equilibrium concentration of them so there has underlined this point department guidelines so it was invested construction line again where it intersects the phrase boundary defines the pilot which governs interface compositions and that the average manganese concentration is not the same as the equilibrium concentration in and now about the composition profiles he conceded that the gradient of manganese indeed also to compensate for it's very slow diffusion rate and similarly plot the current constitution profile there is a long-range diffusion of this None transformation tends to be faster because we are petitioning very little manganese so it's quite negligible partitioning local equilibrium and me and there's very little partitioning of manganese but we are still maintaining local equilibrium because the interface compositions are defined by deadline there no U.S. didn't know which 1 debate yeah the transforming still had it known that they should go for petitioning the local equilibrium or negligible partitioning political if not the was long-range diffusion of manganese ore where steep gradient of many so we wanted to do it is I'm going to draw this diagram again and they cannot for example about transforming it Anheuser-Busch saturation and try and see whether can get petitioning local equilibrium so so this is mine opponent phase

30:50

diagram carbon manganese can have fun and In between me and the others cannot face there and let's assume that the broken has which is transforming at a large super situations located over here that happens if I try to transforming in such a way that the gradient of Providence flat fundamental political lines To this end and that gives me a Parliament connecting the the announcement composition and somebody down but as possible but it's possible to have these compositions at the interface for an ally but that so much average composition is this circle this is what we are claiming to be the compositions at the interface is that possible initially that the manganese concentration of note the fact announced 19 greater than yeah that's not possible so if you try to transform the allies in that region by the partitioning of predicted mechanism it will not work and I'd like to demonstrate and likely to show for yourself that it might take now an ally at the levels of the saturation and I tried to transform it by NP and the mechanisms that are not possible With the that and handed it to me I was market as a part of your assessment because so what you have to do is take an ally which is close to the gamma phased bonding and try and transform it by the end of the early mechanism and proved that that's not possible so it is like a down so this is your homework so for now Close To the scandal ,comma 1st half hour the experiment with me the it is impossible the transformers by the end of the year only mechanism the investment you completed the assessment group to next time the Canadian on it not in Korean current Aberdeen in English the name then I will market not if I take my

35:04

face that this is the usual manganese governed phase diagram and the red lines of the timelines lines and if I construct right angles triangles here give because remember we were using radical construction lines and horizontal construction and they join up the medicine is of those triangles then this will be the region about that dashed for the division that you will only be able to transform analyzed by the PPE mechanisms and the best line you will only be able to transform the allies by the end and Americans that it can't be that Ashland we have demonstrated over so there is no chance you know you cannot actually get it case so the system doesn't actually have to make a choice if you transform at the house of a saturation there'll be negligible partitioning of manganese if you transform Italo super saturation is long-range diffusion of manganese and the transformation of the very again just identifying the

36:24

remains now if you in programs like the Giants you will find that as you know the transformation temperature the diffusion by the concentration gradient of manganese becomes extremely narrow and steep and it gets to atomic dimensions and that's not politically correct navigate the cannot tolerate concentration gradients which are that large because of the effects come into play and you get to the point where many simply will not move the problem is able to move but manganese is not able moves as that the decimation temperature we will get to a point where you can no longer have equilibrium the manganese is effectively frozen and is trapped as the fire crews so as a

37:33

transformation temperatures reviews In his manganese this season is to be averted a few seasons In give the but can't can still this year's so we cannot any longer have equilibrium between the frighten Austinite careful equilibrium breaks down and the debt instead the state of Parana where the interstitial solutes can move but not the substitution of sorts instead we get a particular group instead manganese does not issue but subject to to the constraint because equilibrium between announced its companies locally in equilibrium but not the magazine progress subject to the constraint as local equilibrium that interface now we can probably use the equilibrium phase because the manganese trying show remains constant fear not moving we have to define a new phase diagram which we call that political and if you look quite different this is not of clear phase diagram and that is that the two-phase boundaries between and announced so here we have right since Austinite and this is itself of the scanner we do face bond is needed the points on the vertical axis and somebody probably Our likened the guidelines on this diagram so remember manganese is not petitioning so what will the Thailand's on this diagram look like that is unknown yet the horizontal now they're not strictly horizontal because you know if you have different carbon concentration in the Austinite and that is undermining the there's not move you will get a different concentration of manganese and fair cannot is the manganese to two-iron ratio that remained constant but because the current constitution assessment it's almost horizontal the that's all apparently faith that and you know the software like the candidate and so on you can also calculate apparently from phase diagram as well as an equipment and they often rendered calculations this month Museum it is year that the growth of what happens In fact the Libyan because then introduces the problem that no window manganese and because in the steel industry the process still extremely rapidly there are millions and millions of tons usually the couldn't make so High Court ruled that the Fed will almost always win by equilibrium again so this is very convenient because then you can just use all the theory binary transformation but many others only the problem is petitioning so

44:48

phase diagram so here we have a lot of them are drawn by the headlines on the outside represent the equilibrium phase diagram with guidelines which are defined by thermodynamics and inside the right to life represented by political phase diagram can somebody tell me why the equilibrium and that equilibrium they've these meat on the horizontal axis why do they coincide on the horizontal axis there no manganese so there is no difference between equilibrium and baklava and why does the bad equilibrium phase by at that point on the vertical axis there's no carbon right and manganese is not moving so far announced that have you have exactly the same manganese concentration the Thailand has shrunk to to a point if there is no government so the bag faced Adam lies with you the equilibrium phase diagram and it will need to take liberal phase diagram when there is no manganese at all in this field the so this was quite complicated enough to learn about just after having at lunch but I think you answered some of the questions very well where TO BE notes that have also annually very easily able to explain the role of the 3rd element the substitution of on the kinetics of the group of so that's all there is .period today and in the next election will be talking about the the electorate is the other major phase in the vast majority of that manufacturer