 So let's get into material phase. Dr. Brush had showed these slides similar. This is typical when in high school or like physics or chemistry class, you think phase diagram, you think this, the pressure, temperature, ice, water, vapor. But material scientists, we're not too concerned with liquid phases and we're not too concerned with vapor phases most of the time. What we're really interested in is the phases that make up the solid phase. Now that might sound confusing because I just said phases that make up solid phase. This is a simplified version of water phase diagram. The actual phase diagram of water is much more complex because the phase of solid can change depending on the temperature and pressure. So all these different numbers indicate the different phases of ice, of solid ice, right? If you guys are familiar with Kurt Vonnegut's novel, I believe it's Cat's Cradle, I haven't read it myself, but I've heard. In the novel, there's this substance called ice nine and it's a science fiction, I guess. And I guess the ice nine substance is supposed to be super deadly or something and all the countries want it as uses a weapon or something because it turns everything ice, I don't know. Anyways, well, in fact, there really does exist a phase of ice called ice nine. And then the word phase is nearly synonymous with crystal structures. So if something has a different phase, it has a different crystal structure, okay? But I say nearly, there's some cases where like, well, that's maybe a little different or not necessarily true. So binary phase diagrams like Dr. Brush had talked about, this is an example of salt, sodium chloride, dissolving in water. So this is like more typical phase diagram. We're not too concerned about pressure. Sometimes we are, but not usually. We just have temperature on the y-axis, on the x-axis is the percentage, usually weight percent, could be atomic percent or mole percent of the component added to the left component, which on the left-hand side, we have 100% water, right? So this is like the normal phase diagram at zero degrees, it freezes and so on. On the right-hand side, 100% sodium chloride, just solid salt, okay? And so you can imagine if you have liquid water and you add spoonfuls of salt, the salt will dissolve. And so in this region, we have what we call complete solubility, right? You keep on adding salt, it keeps on dissolving and you make a solution. The sodium and chlorine ions are dissolving, they're separating into their ions, right? Complete solubility in this case. But then you reach a given temperature, you reach a boundary and this is called the solubility limit, where you can no longer add any more salt to the liquid. It doesn't dissolve anymore, it's a solubility limit. And this is also called a phase boundary. So then the next phase is, if you keep on adding salt, you're just increasing the weight percentage of solid salt. So this is a mixture of liquid brine and solid salt. All right, so we're gonna look at more things like this. Oh, and so you have phase boundaries like this, we're just flat lines, vertical lines and this composition would represent this 100% hydrated sodium chloride. So the hydrated sodium chloride is a different crystal structure than sodium chloride that's not hydrated. All right, so here's another binary phase, right? Here you have the mixture of two phases. So I wanna give some examples of other phase diagrams. I know Brush did this as well, but so this is phases of chocolate, okay? Chocolate exists in different phases, the cocoa butter and the sugar, I'm not too familiar, but something's going on where the phase of chocolate can change. And this is another example of a phase diagram, this is called a time temperature transformation diagram for tempering chocolate. Because when you make chocolate, you want to temper it, which means you set it at a certain temperature to change the phase because there's a certain phase, I don't know which one that we like to eat because it has the right melting temperature, something like that and it tastes better, I don't know. But one thing I do know is that if you take chocolate and you put in the freezer and you leave it there for a long time, what happens is you'll have phase separation where some of the sugar and I think the sugar and the cocoa butter will separate from each other and that's what makes this dusty appearance if you ever have chocolate that you leave in the freezer too long and that's called chocolate bloom. And that apparently does not taste as good. And but you can fix it by just reheating the chocolate and tempering it again and that should fix it. Anyways, so that's time temperature transformation diagram. Here's another diagram called the continuous cooling transformation diagram. So there's a test that we do and also that we do with the juniors and sophomores in lab called the Jomney test where you take the steel cylinder and you heat it up to 800 degrees and then while it's red hot, you take it out and you put it on this water jet and the water jet cools the end, but only the end here. And so what happens is that the cooling rate here is faster than the cooling rate here at the top. And so what you'll do is you'll dissect this specimen after it's cooled down and you'll look at the properties at different spots and that represents the different cooling rates. And so like hardness or strength or you can do a micrograph of the image and see what the grains look like. Anyways, and so the different cooling rates will change the mechanical properties. Deep cut, yeah. Okay, another phase diagram is the Ellingham diagram. This can tell you what species will reduce or oxidize other species at different temperatures and different partial pressures of oxygen. So here's an example of smelting. We take an iron oxide ore and we want to reduce it into iron metal. The way we reduce it, we use carbon. That's why carbon is very important. We turn carbon into carbon monoxide and carbon monoxide is able to reduce iron oxide into iron metal. Poor Bay diagram, you see this more in chemistry, I guess, but I use it myself for some of the synthesis I do. It's more for aqueous chemistry though because it involves water and ions dissolving solution but it's a type of phase diagram. Okay, so let's get into what we'll be talking about and the questions we'll cover. So binary isomorphous alloys like Dr. Brush would cover, these are completely soluble solutions, a solid solution. So it's just like adding salt to water that dissolves but we're adding a solid to another solid and it will diffuse and create a homogeneous crystal structure, a homogeneous phase. So no matter what percentage of nickel we add to copper, the crystal structure is gonna be the same. Okay, we're just substituting atoms. And that's because, again, Dr. Brush had mentioned in the lecture, and I always get this wrong, Hume, I think the Hume-Hothory rules, something like that, right? Hume-Hothory rules, the atomic sizes are similar so it creates a completely substitutional alloy. And the lever rule, so let's go through this problem. Actually, I'll let you do it yourself and this is directly from the book. So I mean, it's not anything new but your homework should cover problems like this. So just to go over, how do you do this? Go ahead and calculate what the weight percentage of the alpha phase. So this is the same copper-nickel diagram and we're going through this mixture of a, the mixture of a solid and liquid and we're at point C, 1250 degrees Celsius. You should calculate the weight percentage of alpha, the solid particles, okay, for this composition at 35% nickel. If we're at this temperature, we've precipitated alpha, we've reached equilibrium at this temperature, what's the weight percentage of solid compared to the liquid? And you're going to use the lever rule and then I'll go through the lever rule once I get an answer in case people don't, we weren't following with the last lecture. So we have an answer, 70, okay, we got two different answers, 73%, 27%. So just by looking at this, we can figure out which one's right or which one's wrong. I think we just mixed up. So if we start from the liquid phase, and let's say we hit point B, right? So it's 100% liquid and then we hit point B, then we just start precipitating, so it's like 1% solid and then we start to increase solid. So at this point, we should have less solid than liquid. Yeah, so 20, oh wait, now we're saying, yeah, less solid than liquid, so it's 27%. So the way we do this using the lever rule, all we look at is just the fraction length of one side to the total length. So for alpha, the solid, here's alpha, the phase boundary of alpha right here at 43% nickel, okay. When you're looking at the solid, the phase on the right-hand side, you always look at the lever on the left-hand side. And like I said, just look at the extreme. Once you hit the liquidist phase boundary, you should have almost 100% liquid, so it's gonna be the longer lever there. So we take this length, that'd be 35 minus 32, divide it by the total length, which would be 43 minus 32, okay. So it's R divided by R plus S. That's four, and I even color coordinated it for you, this alpha phase, all right, is represented by the length of this lever, I guess you could say, line. And then for the liquid is the opposite, right? It's the opposite one. So that's the lever rule, yeah, 27%. Okay, so that makes sense to everyone. So far, pretty simple. Oh yeah, what is the weight percent composition of alpha at 1250, okay. So in other words, alpha, the solid, I mean the answer is given right here, sorry. What percentage is nickel and what percentage is copper that makes up alpha? All you need to do is look at the solubility limit, all right? You don't need to do any math really, just look at the solubility limit at that given temperature. So at this given temperature, the solubility limit of nickel is 43%, right? You can't get higher than 43% at that temperature. And then the opposite for copper. And the liquid, on the other hand, the liquid has a weight percentage of 32% nickel in the liquid, okay? So that makes sense. Finding the weight percent composition, all you need to do is look at the solubility limit. So I mean, as we decrease the temperature and we wait for equilibrium, that solubility limit is changing. So as we look, as we decrease the temperature, the amount of nickel in alpha decreases, which means if we had sat here for a while and we built up our alpha and we come down here, what happens is the existing alpha needs to get rid of nickel, right? Nickel becomes removed at that point. And then eventually you'll have 35%. So it went from 43% nickel. Oh, I guess I should have let you, 43% nickel down to 35% once you, if you decrease the temperature all the way down to room temperature, okay? Of course, there's some kinetic limitations as well. I mean, if you were to cool this quickly, what would happen is you have an alpha precipitate that has a higher percentage. Say you have alpha precipitate at 46% and you quickly cool it and the next layer is gonna have even less and less and less. Because it takes time for atoms to diffuse, right? And lower temperature, at high temperatures, kinetics are faster, but the thermodynamic driving forces are lower. And we'll look at that a little bit later in steel. So here's another binary phase diagram. This is called a eutectic alloy because it has what's called a eutectic point, okay? Where the, what's interesting is that the melting temperature is lower than the individual melting temperatures of the individual solids. This is a copper and silver metal. And so this is not a solid solution. I mean, it's not completely solid solution. You have on the boundaries, the alpha phase is a solid solution, the beta phase is a solid solution, but at room temperature in the middle, you're gonna have a mixture of phases, alpha and beta, okay? And at a given temperature, the composition of alpha and beta are gonna be different. And at the eutectic temperature, if you took material at this eutectic point, 71.9% was silver as a liquid and then you froze it, you reach, you solidify it. The microstructure is unique. It makes this lamella structure, okay? And we're seeing this micrograph, the dark, this is aluminum copper, so it's a little bit different, but it should look the same for silver and copper. The dark region could be the aluminum-rich region, I'm not sure which one's which, and the light region would be the copper-rich phase, I mean. Okay, so the question is, you know, eutectic composition, eutectic alloy prepared by solidifying to just below this eutectic temperature, 77.9 degrees Celsius, and held to reach equilibrium. So we completely solidify this material. Question, we have four parts. What is the weight percent of the beta phase of this material? And now, even though it looks a little different than the first completely solid solution, isomorphous phase diagram, but that we can still use the lever rule to figure that out. So we're gonna have two segments, right? So go ahead and calculate, and this time we're looking at, well, the same, the phase on the right-hand side, beta. So go ahead and calculate that out. I actually, I haven't done this myself, or I don't think I prepared the answer, so I'm gonna do that real quick. You shout out the answer when you get it. You guys have an answer for number one. What is the weight percent beta phase at this eutectic composition and temperature? Call out on someone. Okay, so Salinas is 23.2. I believe we made the mistake again of reversing it, because I got, unless I could have got the answer wrong, I had 76.8. So let's take a look. So we're looking for the beta phase, okay? Again, you can always just go to the extremes. If we go further right, are we increasing the percentage of beta or increasing the percentage of alpha? So as we go further right, we're gonna reach 100% silver is gonna be increasing the percentage of beta. So we should be fairly high percentage of beta, above 50%, right? Yeah, so that's just one way of looking at it. So you take this lever on the left-hand side to represent beta divided by the total length, and you should get 76.8% beta phase. Next question is, what is the weight percent silver in beta? This one should be really straightforward. All you have to do is just look at the diagram. Yeah, so we get 91.2%, right? All you need to do is look at the solubility limit. All right, so at this temperature, you know, I guess it might be easier to look at the opposite of the way. Let's look at alpha real quick. What's the percentage of silver in alpha, all right? So at 0% silver, we have no silver in alpha. This is, remember, this is a region of solid solubility. Okay, so you can add silver, you can keep on adding silver until this point, 8%. And then it's no longer soluble. And that's why you start creating the beta phase at larger percentages, all right? So the same thing here, the percentage of copper in beta would be 100 minus 91.2 is that solubility limit, or the percentage of silver in beta is 91.2. So beta is the silver-rich phase, alpha is the copper-rich phase. Okay, what is the crystal structure of alpha and beta? All right, so this one, you need some previous knowledge. Does anyone know the crystal structure? Or how you can find out the crystal structure? I mean, like I said, you need to know, you need to know what the crystal structure of copper is and what the crystal structure of silver is. So the answer is FCC. Both of them are FCC crystal structures, right? Just look at 100% copper. 100% copper is FCC. 100% silver is FCC, which is kind of strange because they're both FCC, but they don't make a completely soluble phase diagram. So if we go back, look at the copper-nickel example. Copper and nickel are both FCC. They are completely soluble. You can substitute as many copper or nickels in for copper and it'll have the same phase, right? And remember, it's because their atomic radii are fairly similar. They're pretty close, but we look at silver. Silver is much larger than copper, right? So at 779 degrees Celsius, you can only add eight, you can only substitute 8% by weight. I like to think of atomic percentage, but the numbers are different. You can only substitute 8% by weight silver into copper, right? And then beyond that, then you start growing the beta-rich phase, okay? So kind of interesting thing about that. They're both FCC crystal structures, but they're different phases because there's incomplete solubility. The next question was, what is the weight percent silver in alpha phase at room temperature at equilibrium? So this graph doesn't even show room temperature, but just assume it's at the bottom or even it's gonna be the same at the bottom. And this is sort of, well, it's not a trick question, but I mean, so what's the answer for this? What's the weight percent silver in alpha phase at room temperature? It's interesting to think about. Yeah, zero percent, that's correct. At room temperature, silver and copper do not mix, which is, I didn't know that until before today when I was looking this up, but I was like, oh, they don't make sense because the atomic sizes are so different. It's only at higher temperatures that you can get a solubility of one component to another component. Now, however, I said before, kinetics are also a factor, and we'll see that more with the steel structures. But if you were to synthesize an alloy at like whatever, 600 degrees, you're gonna have some solubility and then you quench it to room temperature. If you quench it, which means you cool it down really rapidly, you're not gonna give enough time for the atoms to diffuse. So you might be stuck with some silver inside the alpha phase, even if that's not an equilibrium. So we call that, that's a metastable phase. It's not an equilibrium. They're non-equilibrium phase. And in steel, that happens all the time. Okay. This is just showing a type of hardening. In class, we talked about salt solution hardening. So that's if you had like copper and nickel, for example, if you replace some nickel into copper because of the size difference, you're creating these stress concentrations because of the lattice mismatch, right? And that is gonna increase the strength of the material. It impedes dislocation movement. There's another type of strengthening mechanism called precipitation hardening. And that's happens in these alloys that have these secondary phases. So if aluminum copper alloy, for example, is not completely soluble, you'll have a secondary phase, copper alloy material. So in order to make these alloys and precipitation hardening, what you'll do is you'll solutionize the material. So you'll have a percentage of copper around this percentage that gets you into this completely soluble region. So you'll set it at 500 degrees, let it sit. So it becomes a solid solution. And then you quench the material, bring it down to room temperature. When you quench the material, like I said, kinetics, it's too slow for the atoms to diffuse and create these secondary phases. So you get this solid solution, which is a meta stable phase. And then what you'll do is increase the temperature again, slightly higher to allow the kinetics to phase separate. And when it creates these secondary particles that increases the strength. And so this is the aging time. And so you start to see a strength increase with the more secondary particles you create. But eventually what happens is that, here you have a coherent phase boundary where the lattice is more or less aligned. And because it's coherent, there's this buildup of stress. But if you over age it, what happens is you get this incoherent phase boundary and that alleviates the stress. And so strength ends up decreasing. Anyways, so this is the equilibrium phase where the aluminum rich phase at room temperature, aluminum is a hundred percent. And then you have the secondary particle, the copper aluminum particle. So that's the equilibrium phase. Let's talk about iron carbon phase diagram. So this is steel, basically. And notice here that the percent weight carbon is very low. Not much carbon can go into steel, into iron, okay? So carbon is an interstitial alloy component, okay? Because it's such a small size compared to iron. This is, it has a eutectic point where we go from a liquid to two phases of solid. It also has another point where we have a solid austenite gamma phase that will transition into two different phases. And this is called the eutectoid point. And so this point is very important for making different steels. Most structural steels will have very low percentages of carbon, like less than 1%. If you have higher percentages of carbon, you get really brittle material, like cast iron pans. Cast iron has a really high percentage of carbon because you get a lower melting temperature. But as you know, cast iron is really brittle, right? Not very ductile. So the different phases of iron, we have the alpha phase. So that's like 100% iron, or with slight solubility of carbon, okay? Lower temperature. So it has a BCC crystal structure, and then carbon will be in the interstitial sites. I'm not exactly sure which interstitial site it goes in. There's tetrahedrals and octahedral. And when I was doing my background research on this, there was a bit of conflicting information in the short amount of time that I was looking for the answer. So I'm not too certain where it goes. And then at higher temperatures, you have a phase transition from BCC to FCC structure called austenite. And the carbon, again, is in interstitials. Again, I don't know if it's a tetrahedral or octahedral. And then at higher carbon concentrations, you have this solid, I guess it would be a covalently bonded solid, cementite. It's a molecular structure, all right? It doesn't have any different solubility of carbon. This is a set molecule. You can't change the amount of carbon in this. So cementite has its own crystal structure. And just briefly, you wanna talk about stainless steel. So in stainless steel, you add nickel or chromium, and that helps prevent the corrosion of the steel because you'll make this chromium oxide or nickel oxide surface layer that is more corrosion resistant than iron oxide is. It's more stable. Iron oxide will flake, where chromium oxide should make a stable oxide layer. And there's a certain calculation you can do to see what kind of oxides will make stable or unstable oxide layers. And so what's interesting about stainless steel is because of the high concentration of nickel and chromium, it only has an austenitic phase. It's always FCC. It doesn't have a BCC phase. One more thing I wanna add. What's interesting is that the density between BCC and FCC is different. I believe on homework one or two, you had a problem where you calculated the density between the two. I do this interesting demo for K through 12 students where I take this steel wire and it's at the eutectoid composition. So we're going from alpha to, even low carbon should be fine, alpha to austenite. And what I do is I have this wire and I suspend it across two ring stands and I send an electric AC current through the wire. So it heats up when you send AC current. And I also have a weight hanging in the middle of the wire so it's weighted down. And so you guys know what happens as you heat up a material, it expands, right? So what happens when I turn on the AC power, the material glows hot and expands and the weight dips down because it's expanded. And also it transforms to austenite. So what's interesting is when I flip the switch off and it begins to cool, it cools much slower. When it begins to cool, and as you probably know, when things cool, generally they contract, their density increases. So as it cools, the weight starts to go up, all right? But you reach the transition between FCC high temperature austenite to BCC, which has a lower density. So what happens is as it's cooling, it reaches that transition and all of a sudden it drops because you have a sudden change in density and all of a sudden the wire elongates. So it's a really cool demo to do when you see it heat up, it goes down, it cools, it goes back up and then it drops because of the phase transition. Anyways, so okay, let's do this question. It's 210, so those of that are still here. We can do this together. I didn't do this, I didn't write it out so I'm gonna do it with you. So we have a eutectoid steel prepared at 1200 degrees and we quench it just below 727 eutectoid temperature and we reach equilibrium. What is the weight percent cement type? Cement type, remember, is this molecule here? So we're gonna use the lever rule again. Do we have an answer? Yeah, 11%, that's what I calculated as well. So 11% of the phase is, excuse me, 11% of the microstructure is cementite phase. And how about the weight percentage of carbon in alpha? Alpha phase at this point, 0.022. Again, to find the percentage of a component in the phase, you just need to look at the solubility limit at that given temperature, so it's 0.022. Carbon is the solubility limit in alpha phase iron. And how about the microstructure? So we didn't really go over this, but the microstructure, right? Again, depends on your composition and what phase you're transitioning from into. So again, in the last example, we had a eutectic microstructure. We went from a liquid to the eutectic point into two solids and we got that lamella structure. For the eutectoid, you're gonna get the same type of structure. So it's gonna give this lamella pattern where you have a carbon rich phase, which is the cementite and a alpha iron rich phase, which is the alpha, right? But the only difference is that we went from a solid to another solid or two different solids. Austenite to pearlite. Here's something I wanna emphasize. So the name of the microstructure is pearlite. Pearlite is not a phase. And sometimes I'll see it incorrectly used as a phase. Pearlite is the name of the microstructure. The phase is alpha and cementite. Pearlite is a microstructure. Austenite is a phase. Yeah, so the different microstructures are affected by how we cool the material because kinetics plays an important role in the microstructure as well. And so we look at a time temperature transformation diagram. So typically, like in the example, we start at a temperature above the eutectoid temperature. So it's 100% austenite. Then we cool it or quench it. And depending for the TTT diagram, it's isothermal, but you can have different transitions. So in this example, let's say we start at this temperature and within the first couple of seconds, we quench it to 600 degrees. So what happens is over time that austenite, even though we're below that temperature, it takes time for the austenite to transform into a different phase, which is micro structures pearlite. It takes time to transform into ferrite and cementite to make the pearlite microstructure. And if you quench it to a lower temperature, you can get this different microstructure called bainite. And if you really quench it really quickly, here you get a metastable phase. And this one you can call a phase, martensite. Martensite is when the carbon does not have time to diffuse out of the austenite and you get a different crystal structure. So this is an unstable crystal structure. It's a metastable, it's not an equilibrium basically. And that's why you don't see it on the phase diagram, because phase diagrams are only for equilibrium. This is not an equilibrium. So if you quench it quickly from austenite down to low temperatures, the carbon is not able to diffuse out of the crystal quick enough, so it gets stuck. And that gives you this body centered tetragonal phase. And that greatly increases the hardness and strength of the material, but it decreases the ductility, all right? So what you can do is you can temper the material. So you'll take this martensite phase and you'll reheat it, anneal it, and allow it to recrystallize some pearlite. And that will soften the material, but you can still retain a pretty good strength. This is the last slide. I forgot the animations here. Just talking about, you know, hypo and hyper eutectoid microstructures. So the last example is a eutectoid microstructure and you got this nice lamella structure, but what if the composition is slightly lower than the eutectoid composition, which is hypo eutectoid or slightly higher, which is hyper eutectoid? The microstructure looks a bit different because you're going from a salt, a completely homogeneous austenite phase, and then you're going through this mixed region of alpha and austenite so that alpha will start precipitating out. And this is called heterogeneous precipitation if it's happening at the grain boundary. And why it happens at the grain boundaries is because the grain boundaries are higher energy and it precipitates there in order to lower the energy of the system. You could also have homogeneous precipitation where it happens within the austenite grain, but that's a higher energy requirement. So it's less likely to happen. So you grow this alpha phase and this is called pro eutectoid, which means we're above the eutectoid temperature. So now we got all these different words, hypo, hyper and pro, which means above the temperature. And then you go below the temperature and then the remaining austenite will start to give you the pearlite microstructure. And this is just from your book. There's different calculations you can do to calculate the fraction of pro eutectoid alpha or pro eutectoid cementite and then also the weight percentage of the pearlite. So there's just, we don't have any examples to give but those is just how you do that. So any questions? Okay, if no questions, you guys have a good weekend. I have my office hours on Monday next week after class. And you remember you have a midterm on Wednesday. I will get you a homework six today or tomorrow. Does Martensite slowly turn into austenite over a long period of time? Yeah, theoretically, yes, because there's this thermodynamic driving force, right? It's metastable. It wants to be, the more stable phase is not austenite, sorry, it would be ferrite, ferrite and cementite. However, like I said, kinetics is a limiting factor, right? At room temperature, the diffusion is going to be slow and I guess over a long, long period of time it might happen, it's the same issue with diamond, right? Diamond is not the equilibrium phase of carbon but I mean, it lasts for a good amount of time that I know of because that's the same issue. Yeah, if we want to talk about kinetics for the people that are still here, this diagram, the TTT diagram is very interesting. It gives you the kind of C-shaped curve and this indicates how kinetics plays a role. So if we're below the eutectoid temperature that is a thermodynamic driving force for a phase transformation, all right? Temperature difference is the thermodynamic driving force. However, look at this log scale of time. If you're just slightly below the temperature, it's gonna take forever, not forever, a long, long time for you to have a phase transformation from austenite to perlite, okay? But as you decrease the temperature more and more the amount of time that it takes decreases, all right? And that's because you have an increase in the thermodynamic driving force, right? You have a higher thermodynamic driving force for phase transformation, it's gonna happen faster. However, you reach the certain point where it starts to increase in time again and that's because kinetics are starting to slow down. At lower temperatures, you have slower kinetics. Even though you have a very high driving force thermodynamically, the kinetics are slower so it's gonna take longer. So that kind of answers your question, I guess. Yeah, I guess martensite is pretty stable at room temperature.