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chief and but out make a start so we have actually finished or of the displays of transformations which lead to a shape change with the loud cheer component modern side they 9 and and we're going to raise the temperature again and talk about Of that formation by the diffusional mechanisms which involves a lot of confusion and the vast majority of the 1 . 2 billion tons of steel that make every year contained as the majority face what we are going to talk about today not nite not much inside not weakness and that the vast majority of I would say 90 per cent of all years that you the dominant phase is the fact that we haven't talked about it it's a very important to phase in steals and the 2nd most important phase is probably quite like and I will deal with that 1 after another to lectures but in the days don't use about them and I'm going to use some specific terminology a lot you won't

01:20

be felt right here Longwood but it's important to understand what it means a lot movement his father reach forms at the OS 9 grain boundaries and because of Austinite grain boundaries easy diffusion parts it tends to grow more rapidly along the boundaries than into the grain so the shape often optimal replied does not reflect its Chris symmetry you don't get nice beautiful shades of its straight facets because it's dominated by the grain boundary and again looking at a partially transformed some on the other hand in market for creates probably on dirt particles inside the grains of Boston tonight and the cortege it has shape which is a reflection of the symmetry of the far-right and of the Austinite enriching growth so received some nice faceted states fascinating means you develop some plain faces with particular crystallography the mechanism of transformation is otherwise the same the shape is different because these grains of grow inside the Austinite interact regularly new created and these are new created at the Austin going about the Arsenal grain boundaries are the easiest nutrition sites In steel conclusions of the next easiest nutrition this summer said the letter moving

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fast as a shape which does not reflect its grasslands cemetery Chris basically dominated by easing Grover along the Austinite going exterminated easier growth along the Austin on and it didn't part in contrast firms Intel granular half after his nuclear In trucker annually and then it is shady reflects the symmetry of the fried and of the Austinite images grows it's superimposed symmetry of government shape reflects the superimposed of and gamma if it was going in a liquid then obviously its shape would be determined just by the symmetry of the far-right but it's not it's growing in another solid and therefore it's a superimposed images of the 2 phases and both of these transformations can only happen at temperatures will find itself can be used although the landscape of your transmission problem so both transformations can only temperatures so typically about 600 degrees centigrade where the iron atoms are mobile so the grass doesn't just in awe of the diffusion of power but you must also be able to move the iron otherwise you get a shape deformation and strain energy and all the rest so there is no shape deformation here ricocheted component there only 1 volume change the Polish Press low-cost nite completely flat and transform it to 1 of these parents it will not lead to a shape change other than what has changed the that no shape deformations other than volume change so this

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is an illustration of the geomorphic verite they concede there are some nice flat interfaces Chris admits particular personal graphic indices this is what of good you can only see the shapes venue partially transformed the material if you've got 100 percent transmission and the fire grains of touched each other then the shape is not determined by symmetry but by and this is an

08:17

election lawful which is growing along an Austinite grain boundaries and the thing that I wanted to notice is that it's like a thin layer which forms at the bonding and grows rapidly along on but the growth rate normally to the boundary is slow because this is the diffusion of transmission and you're building up carbon in front of the interface so unlike what we did in the last match of a and then played growing and the partition carbon is being left behind with the tape advancing into fresh Austin he said you have a plane which is moving so the problem piles up in front of the far-right and therefore this growth rate will not be constant In yesterday's lectured the lengthening rate of the blade of life was the constant trade in the equation for velocity we did not have a time dependence of the lost in the last the only defendant depended on the concentration terms fusion of vision and the Cape radius the diffusion distance was constant equal the radius yet the situation is completely different because we are of moving effectively a plane and there is no known leaving behind of carbon so you accumulate carbon in front of the face more and this is another example

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of a little maybe you can see that the thickening great knowledge of the boundary is much lower than the lengthening ingrate and notice also that this layer is not a single crystal of union created many grains of right along the Bundy but they not limited by thickening somebody jeeps this problem as one-dimensional growth of that because it's effectively a plane moving normal and diffusion is only happening in 1 direction that's so the difference between the calculations we did yesterday and what we are

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going to do today is that the the velocity of growth will not be constant agreed change as the thickness of the fare increases do you think that the velocity should decrease as the particle becomes thick for increase yeah but it will decrease and why is that and you know you are absolutely right the velocity will decrease as the product of becomes thicker any ideas well so it's because you are accumulating more and more carbon in front of the interface so you have to diffuse over longer and longer distances that so imagine that you're looking at the pond that bond is a point of water and this winter and you form a layer of ice on the surface the ice then becomes thicker so it takes longer for heat from the worker be fused to the surface and Nelson litigation to happen so the freezing rate of the pond slows down as the ice becomes thicker that's very lucky because otherwise the whole of the the water would freeze and any patience I would suffer if you so there's something 94 many Democratic Kompong between the soda and divide that into metallic components slow down as it becomes thicker because we need to diffuse material between the wire and solid if you look at oxidation and form oxide layer on the surface the party has to diffuse through the oxide to the metal as the oxide becomes thicker oxidation rate will slow down so we need to discover that relationship in any the theory that the 1st and we are going to resume again as we did yesterday that local equilibrium exists at the interface in other words interface compositions are given by a timeline off the phase diagram so we will consider diffusion controlled growth consider diffusion control group local equilibrium at the interface and by local

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equilibrium mean that the

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composition of the far-right at the interface of a given by the state boundaries and the composition of the Austinite which is in contact with the family will be given by this concentration here all from the phase diagram exodus this is these points are determined by the Commandant and touching to 2 free energy services as we did in the last lecture so when these 2 phases are in contact the composition of the US cannot exceed Seaga mouth and that of the movie see up again and this is our see bodies is the average carbon concentrations in the steel but this so let's proceed

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as we did in the last lecture

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and defined the Fed concentration profile at the interface the federal of distance I said and concentration plodded along here and as a result of the partitioning the province of that provide which looks like this this is seen bar here we have variety and here we are and this point here is that star as we did in the last lecture the concentration here scene Denmark and here it's see Alpha Gamma and this distance here here is the diffusion distance so far there is nothing here which is different from what we had for the lengthening rate of weakness and Anakin immediately right down immigration for the rate at which problem is being partitioned into the Austinite being equal to the rate at which is being taken away by diffusion from the interface so as these as this interface no we will have to to would that much carbon into the Austinite but maintain see GAM have a constant it has to be carried away by diffusion a letter from the interface so the velocity so this this is against the gamut of and this is the Alpha Gamma and since EPA so the rate at which the interface moves which is the however the said style by the teacher multiplied by the amount of carbon that the are petitioning that its eagerness of minus see again nasty the rate at which is being carried away from the interface by fusion beaches the diffusion coefficient times c gamma our minus the but divided by the diffusion distance but these 2 terms must be this is how much carbon is being dumped into the frightening a unit of time and this is how much carbon is being carried away from the interface in that time period if the students are not equally I'm out of on the constant and that's not fusion program and that is that this gradient the Gambia is aiming to be constant but in practice it will be like an functions so this gradient is really evaluated at the position of the interface everyone that now the problem is that was the time the division distance is not constant because we've got a plane moving and there's nowhere for the problem to go except in front of the sober accumulating problems as the interface moves so we've got to have another condition so for all the diffusion so that other conditions comes from mass balance it's a fire drill this concentration propaganda this is the distance as his concentration you 1st this is the amount of carbon but the amount of carbon that has been rejected as far grows and this is the amount of carbon that has accumulated inside the Austinite the fire labels says this has been then the area has a and B must be equal to conserve Mass yeah the variance and being must be equal conserved 2nd I don't another equations the seabed -minus see offered them into the thickness of the Farrar said stock must equal the area the which is see them out minus In said the upon dude because it's a triangle so it's hard so do yeah simply given by sea by minus the Alpha Gamma the volunteer program at times that establishes the thickness all of and the area is trying CDM out permanency but times this diffusion here provide like you because it's a crime yeah so now have an equation for the diffusion since I can write to be perfusion distance as sequel Steve our minds city from In his style provided by the gamma alpha minus Steve are and multiplied by 2 just rearrangement of this equation here Is it OK now just summarize how far we've got

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so this is the local equilibrium conditions here we have the diffusion distance the concentration in the arsenic cannot exceed the game out and this is the concentration in the fire it this is the relationship of the concentration terms retrospective the phase diagram and this is the

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rate at which solid despite the because this concentration minuses concentration times the velocity of the interface the rate at which started its pushed into the US and that has to be carried away by these blocks which is because we are assuming of constant diffusion coefficient that's given by fixes personal as diffusion coefficient times the gradient I've lost his mind sign because this gradient is actually negative yeah the 1st 2 terms must be equal

23:05

must equal this and therefore we get the equation which has an unknown which is the diffusion distance and to get the diffusion distance we have mass balance that this area must be there to this area you and this is the mass balance equation which allow substitute would the Z it also said the EU had been using In due course equations I want hear about that OK so all we have to do is

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is to substitute this equation which will call equation too Inter equation 1 here right Zebedee here is underneath let me see if I can put up to majors at the time but it doesn't doesn't

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help because you just don't let many say right equation 1 out again yet so equation brand was that the velocity which is the set star by the team In the gamma out of my Missey Alpha Gamma With the quarrel the diffusion coefficient standards gradient which is seen gamut of see divided by said the this is a great loss and now I'm going to substitute for a Z B into this equation so I wanted to check in place and make a mistake again From now on it's your duty because you identify the mistake the last so we have is that stop by the teams I want to isolate the velocity on 1 side of the equation so I'm going to take the CDM our reminds Scialfa ,comma onto the other side so that's just taking this term here 1 to the other side diffusion coefficient comes on top and we have a currency can help minus and since said leaders at the bottom Ivanov another to here which gamma minor see to identify divided by -minus see and as that start the bottom and 2 at the top so this is to that correct 2 at bottom yes you're right what about you right so I can simplify this by taking that step the sides have sent staff the gains set the city workers and BT over here and then but the which I'm not going to redirect this is basically this past him and into the that studies estimate on 1 side and the team on the other side of the plane that I get Z star square being equal to something times the right so far integrated therefore said the external squared it is proportional to the crime for another words Z style is proportional to the new part Hong so the thickening the thickness of the far-right with very little time to the power of heart but this is called parabolic thickening sewing oxidation the oxide he's known as parabolic thickening in some cases like that the materials to diffused through the off side to reach the medal of the Matadors too diffuse to the oxide reach the surface exactly the same that the up metallic layering is sold or something a parabolic littered with time so this is called parabolic thickening the fact that the thickness versus time to follow something like this that clearly the slope of that line is decreasing as time ingredients that music growth rate is slowing down therefore "quotation mark rate slows down there's the Ferrari and so so this is an important result if you have a very large Austinite grain size then it would be very difficult to complete the transformation because he would have been is growing from suffered take a very long time for them to reach the center of the great so large graveside specimens In the same amount of time as a small grains I specimens you will get less fair right so this is the

31:00

same calculation there we now have that 2 equations 1 that the date that is but Asian market quoted blocks from the interface and this is our must balance equation

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and you go to the max and you find that the velocity vary with the thickness of the sample and the velocity of growth decreases as the sample thickness increase and that the thickness is proportional to the square root of dying once again this is a very properly equation because we we have the diffusion coefficients we have terms from the phase diagram and the average composition of the steel and can predates the thickness as a function of time happy with that we are only considering a binary alloy at the moment which is I'm covered so this is for a binary alive is only 1 salient which is controlling the thickening rate of VAT and this is

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actually how the thickness with very tight and the slope of SCO is the velocity of the growth and clearly the slope is decreasing as it thickens and victims yeah not I said is a very important collision because it takes account of all or the the following elements you know the phase diagram and this is quite an

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interesting calculation and it's actually reflected in practice as well that look back plant the fact thickness he oversees the time I'm bloody actually behalf that newspapers diffusion transformations like-for-like are not limited by the Austinite grain boundary the significance the boundary can go this way and that it might incite plates and accolades and weakness and that will not cross an Austinite grain boundaries because their displays and in all the systematic movement effective which cannot be sustained across a changing crystallography but fusion transmission and indirect across and grain boundaries so here is the half thickness being flooded with his time and what I want you to know it Is that I'm taking the carbon concentration by equal amounts so he said the differences . 0 2 . 0 2 . 0 2 and 1 0 2 but there is a very rapid change in Dianetics he compared with you but low-carbon concentrations the growth rate is far more sensitive to the concentration of carbon that type of concentration this is exactly what is found in practice and the reason for this going back to our request yeah but

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when your average carbon concentration approaches the solubility of problems in Paris there is no need to to politicians the the I'm getting very close to the solubility of Parliament on Friday and by little problem is partitioned into the Arsenal so the gradually becomes very large it's see bodies equaled Yossi Alpher gamma than the growth rate is infinite now it's not possible to get a good trade-off which is infinitely so what happens what becomes a limiting factor instead of the diffusion of carbon in the Austinite ahead of the face but you know you still have to change the crystal structure as the iron atoms crossed the boundary so there is a certain rate at which that can happen and that becomes the limiting factor and that's "quotation mark interface control growth instead of diffusion controlled growth with some other process other than diffusion of Providence become the rate-limiting factor for Leicester striker so the drug

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trade is very sensitive to the carbon concentration at low-carbon concentrations "quotation mark it's very sensitive the problem concentration as see bar approaches the solubility of problems in the facts because then there is very little problem partitioned into the US 9 then very little problems petition In Uganda consumer becomes close to see off again on some other process will become rate-limiting instead of the diffusion of power eventually about comes the quality of the game commentary tends to infinity if it is diffusion controlled but in practice some other factor will become rate-limiting In practice other factors become regular meetings for example the transfer of iron atoms across the face so obviously if you have completely pure the fact that is not going to grow at an infinite range from us it will be a transfer of iron atoms across the boundary which is a thermally activated process limit the growth rate of the mother he's a diffusion controlled growth model which is used that the growth process is controlled by the if you do not covered in the Austinite and had been some say my handwriting isn't very good at it but I'm trying the cost of everything but this many

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of the Steelers that reproduced today for structural applications have low carbon concentrations in and not very far from . 0 5 4 1 0 3 great sense of this extremely important to control that concentration accurately even tho you're producing hundreds of millions of tons of this kind of material every year we don't control it you get different properties and variations in properties during the steel production process now the reason why it's parabolic is illustrated here that as my father becomes sticking to this area here must be equal to the area under the triangle that as the Fed becomes thicker the area under this triangle must also increase and therefore the diffusion distance is becoming longer and longer as far Pickens and therefore the growth rate slows down as the firm become thicker now today's lecture we have dealt with the binary system and it's very easy do the concentrations at the interface but just by drawing a line under phase diagram for the transmission temperature here and the average government them ready familiar with the term timeline so it's basically saying Look I've got phase diagram here if I have a steal this composition than the equilibrium composition of the guidance given by this point and equilibrium composition of Boston and by this point and this line is what connects compositions of the 2 phases which are in contact and in equilibrium it but that's called guys and together they depend on each other so it's very easy for a boundary the take case I'm just going to introduce you to what happens when we had other allowing elements but before we can treat that problem I need to teach you something called irreversible thermodynamics which are covered in the next election but I just want to introduce you to the problem but said that or the phrase boundaries are obtained by drawing attention which is common duty free energy services of up and down and that gives us the equilibrium compositions and straightforward what happens when I had another telling element along here so hear the are plotting carbon and let's say I had manganese along this axis then what should be get the free energy cos who become surfaces in 3 dimensions so something like this in both In the 3rd dimension and the tangent becomes contact plane which is touching those who free energy services but when you have a contact Lane there's not going to be a unique concept for this and this because I can I can rock that plane yeah and still objected to touch the services that a variety of .period so we don't have a unique concept you actually at a constant temperature will have an infinite number of pilots that so this is what look like 4 0 at the system that we have the iron and manganese and public these are actually surfaces but and this is my my friend and plain by attaching to the surface is yes I can get the Thai language at last on this horizontal plane yeah but I can actually walk that playing this you new method that and if you touch other places so there's a whole set of guidelines which defines and out of the gamma feel at a constant temperature In the binary system there was a unique temperature and a unique set of equilibrium compositions but here we have a lot more choice it is how we define the interface compositions when it comes to to more than 1 salient diffusing In another entity that problem I need to introduce you to my component diffusion and in order to do that I need to treat irreversible thermodynamics which is a very easy subject In the next lecture the today