 So again, it's kind of a true question because it depends on you know, which way are we applying a force to the material, right on which axis and Let's see Selena says plywood because the wood fibers go in different ways Yeah, so that's correct The pine plywood if we were just to try to karate chop it the pine plywood would be superior Okay, and that's because we have The different directions of the grains going cross laminate and we're making a composite That's going to be stronger in all different directions rather than the solid pine board where it's uni directional All right, and this is why you know If if you're familiar with baseball with baseball bats, right baseball bats professional baseball bats are made out of wood All right solid piece of wood and the the wood has a certain direction of the grain and Usually on these bats there's like maybe a little dot that indicates which way you're supposed to be swinging the bat because if you swing it The wrong way and the ball hits along a certain Direction of the grain it can it's more prone to breaking all right So that's what we call an isotropic material or the pine plywood is taking care of this problem It's making more isotropic. We're changing the direction of the grain making layers. So it's like a composite Yeah, so like I said, it's it's a bit of a trick question, but okay, and so let's move on And then I have a lot of slides so I'm going to kind of quickly go through this right So we take elemental properties the properties of elements their atomic arrangement. We can change that then through processing We can change their microstructure different microstructures can also give us different unique properties Here's an image of titanium oxide nanotubes And then so these will give us the material properties that we can use through our designing and manufacturing For certain applications devices So we have an example of a Computer chip here and inside the computer computer chip. There are billions of semiconductor Transistors silicon dope silicon transistors billions of them inside and that's what makes our computers do or their calculations We have lithium-ion batteries orthopedics for implants like Titanium metal implants and so there's certain properties you have to consider like the the biocompatibility of the material You don't want to put a material in that's going to make a sick That's going to leech into our body or maybe corrode due to our body and leech into us And you also want a material that has a compatible Young's modulus if you have a strong gradient of young's modulus between your bone and the the implant that's going to lead to a Problems as well. And then also like for example steel structural engineering Dr. Brush on Monday's class mentioned the historical ages, right stone age iron or bronze age iron age And I think another one that's very important is the steel age, right? So when we take iron and we add carbon to make it stronger It allows us to do things that we haven't done before like build skyscrapers There's a there's a great example also during I believe maybe the 1700s or so There was a I think it was Beethoven, but it might be Bach I forget the details of the story but one of these composers makes the song for piano or harpsichord or some instrument some stringed instrument and The song is so intense that it can never be completely played through because the the piano wires keep breaking Okay, and it's not until a certain Advancement in the technology of making these steel wires that allows you to that finally this song could be played completely without the steel piano wires breaking So it's kind of a interesting and antidote What is the bottom? Tetrahedron probably yeah, let's see performance properties processing and structure So microstructure is here what I say, right structure can play an important role, right? Like in this example here. I have titanium oxide and they're they're made as nanotubes All right, you could also have titanium oxide made as spherical particles and they're going to for this application was for I believe a Electrolysis of water so using light UV energy to to break water down And so the advantage of having nanotubes they have a high surface area allowing the more water to break down. Oh I skipped ahead. So here's another example of Taking a single element. All right in this case. It's carbon and there's two different types of carbon and you guys can help me I kind of gave it away. What are the two different types of carbon this single element can can exist as Okay, thank you Gregory. So graphite and diamond and that's given by their crystal structures And dr. Brush had mentioned this and we'll we'll go over it more in detail next week in these lectures the crystal structure a crystal is the repeating Symmetry of how the atoms are arranged. All right So carbon can be arranged in two different crystal structures one is in these planar units where you have these sheets of carbon and Then they're hexagonally coordinated in a plane and then you also have it Coordinated in tetrahedrons like this and so these make two distinct different Materials and yes, Sophia and Gregory's mentioned it graphite and diamond So one is graphite and one is diamond and just by changing the arrangement just by changing the atomic arrangement of the same atom You drastically change the properties of the material right graphite Obviously, we have optical properties graphite is opaque. It's black. It's shiny Maybe slightly reflective diamond on the other hand is transparent. Okay, and so what are Next question what are Some different applications of these different materials of carbon of these different forms of carbon, so let's start with graphite Who can tell me one or two? different applications of Graphite good pencils is one Can we get another one cooling and cooling because maybe it has high thermal connectivity? Lubricant perfect. Okay, you guys are you spot on. Yeah, so my examples are pencil lead and lithium-ion battery anode. All right, let's start with the pencil lead and Someone mentioned lubricant and that's exactly why we use it as a pencil lead All right, so I believe the lead itself is a composite of graphite and some other clay like material That can change the hardness of the pencil But graphite because it's made out of these layers of carbon these sheets called graphene The sheets are not very well bonded together. I believe it's the Vanderwalls bonds that keep them together So the bonding is very weak between the sheets that allows the sheets to be to be peeled off very easily And that's why it's used as a lubricant In fact in many mechanical processes graphite is added as a lubricant to reduce wear between You know rubbing services and for the same reason in pencil lead when you put it across a piece of paper The graphene sheets are flaking off and they're they remain on the paper for lithium-ion batteries for the anode first off, it's a it's a common misconception that lithium-ion batteries like your phone battery or yourself your Your computer battery your laptop battery that it's a misconception that they contain lithium metal None of these batteries none of the commercial batteries for your like your car or whatever Electronic devices contain lithium metal. That is a misconception. It'd be way too dangerous to have a rechargeable battery There's too much liability to have Lithium metal now primary batteries those that do not recharge you can buy those at the like the store Primary batteries do contain lithium metal, but those are not for recharging But in place of lithium metal the anode is graphite and they use graphite because graphite has this nice Interplanar spacing that lithium can get into or ions different ions can get into in between Yeah, lithium ions are the ones that occasionally explode and and that can be because of Quick cycling or charging there could be different defects but over time the batteries will wear down sometimes lithium metal does form deposits on the surface of the graphite and if the Over many many cycles that lithium metal can grow and these are called dendrites And if they reach the other side of the battery then it's short circuits and that creates a lot of heat but Commercial lithium-ion batteries for electronic applications do not contain lithium metal. So how about diamond? What are a couple? What are a couple? Applications of diamond a different form of carbon Good saw edges tools. Why would we use? Why would we use it for tools like saws a hardness because diamond is the hardest material We know of so we use it for things that need to cut things, right? So here we have someone also mentioned jewelry All right, so but diamond coated saw blades right or different cutting tools. It's very hard. So it's going to cut other materials, right? If diamond is the hardest material How do we polish diamond into these different shapes? Okay, Justin says with diamond. It looks like Liam said lasers. I'm not too sure perhaps with lasers as well But yeah, so Diamonds are polished with other diamonds the very very small like diamond grit, you know We can still crush diamond diamond is a ceramic material. It doesn't have a very high toughness Right if you apply a lot of force to it You can still break it but it's still very hard hardness and toughness not necessarily the same thing Okay And also we use diamond as jewelry because it's it has nice optical properties It has a very high index of refraction so the light can bend a lot whenever it reflects inside also large You know diamond itself is not Too scarce of material, but you know large diamonds are are more rare But mostly the cost is controlled by the industry anyways, how do they Lab grown so I'm not sure about jewelry for lab grown diamonds But I do know that you there are lab grown diamonds, and I'm not sure how what impact it has on the economy but to make a lab grown diamond they have these these machines and basically their big metal components and They you need to apply a large amount of pressure right diamond only forms at a high pressure and temperature And so to to create such a high pressure. I believe what they do is they they take these metal You know blocks and they heat them up and when a material gets heat heated up when it increases its temperature It expands so if you have two metal blocks and then inside is your carbon and you heat them both up They're going to expand against each other and that creates an enormous amount of pressure enough to you know Make diamond which diamond remember you probably know this diamond at room temperature and atmospheric pressure is not stable right the most stable phase of Carbon is graphite. So the to make diamond you have to reach that that equilibrium environment, which is high pressure and high temperature All right, you guys are there's too much chat. I can't keep up So if you have something important to say you're gonna have to say it out loud. Let's move on So today we talked about electron configuration and we have a couple problems dealing with that right and so Dr. Brush probably showed this He showed this slide I know but So if we look at the the periodic table of elements right it and I know dr. Brush and mentioned this that the The orbitals of these materials will fill based on the you know the order of the periodic table Right, so we start with the s orbitals and we work our way to the second principle number 2s And then that has sub orbitals P and so on Okay, so the way these orbitals fill up is Goes by what's called the poly exclusion principle and that's for each sub orbital You can only only two electrons are allowed to occupy that shell the sub orbital Okay, so for s we have only one sub orbital orbital for P. We have three for D We have five for F. We have seven and so on and the way we We add the electrons to these orbitals goes by what's called the off-bowl rule Wait, okay We start at we always fill it in at the lowest energy, right? The electrons always want to take the lowest energy available, right? If we're talking about for example, like potential energy, we want the lowest negative potential energy Okay, so that's the order that they fill these shells They always go to the lowest energy now what's important about the off-bowl rule is that it doesn't necessarily go Spd once you get to 3p you want to go fill start filling the 4s rather than the 3d even though 3d has a lower principle number than the 4s And that's because the 4s when you occupy the 4s it has a lower energy in the 3d That's partially occupied, but we'll see this sort of breaks down a little bit later when we talk about ionization And then also we Dr. Brush mentioned the Bohr model, right? And so this is a kind of a way we can illustrate how to fill these different shells however You really have to forget about the Bohr model because that's not a good representation of what these these orbitals these electron orbitals look like, right? So these electron orbitals or electron clouds look more like these shapes, okay? And so this is an example of the probability of finding an electron in these electron orbitals for like 1s 2s and 3s So s is very easy because it's it's Spherical and it's very easy to calculate because it's symmetric but when you get to p and d and f then they they get more complex and The way to calculate these probabilities of finding the electron in these different shells is like Dr. Brush had mentioned through the hydrogen that through the wave function And the easiest to calculate is hydrogen wave function because it only has one electron You do not need to know Any of this but you should know that the electron orbitals do take up different shapes at least to the you know The the p shapes those are you should should know and then I think further on if you get into more advanced Classes you should you should know about the d's as well I deal a lot of electrochemistry deals with the d orbitals and the d orbitals for Transition metals can help determine the shape of these crystals and the shape of these molecules that we use in our materials Okay, and then the quantum numbers It's kind of like a barcode or a serial number for each electron that exists in an atom It has a specific quantum number associated with it and this is something you should know If and we'll have an example problem that you should be able to identify the quantum number for a given electron Okay, so and it starts off very easily easy with principal number, right? That's just the different the principal level, right one two and three and so on Okay, and this is an example for sodium So the sodium was an example before right and this is the electron configuration of sodium if we look on the periodic table Okay, well this one doesn't give it but sodium would be so we have hydrogen lithium sodium is this one right here So if we were to fill it up, we would say hydrogen has 1s then healing has 2s and then so on Excuse me 1s 2 and then 2s 2 2p 6 and then sodium is right here the valence electron of sodium would be 3s 1 right so this is how you would write that out and so the question is if we want to take this one electron here the valence electron What is the quantum number? That is used to identify that one valence electron Okay, so this is the example I have so it's 3s 1 or remember so the principal number is 3 Orbital angular momentum that relates with you know the whether it's s or p So in this case, it's zero s is always zero Okay, p would be one for example, so it's zero magnetic The quantum number, okay, that also refers to the symmetry of these sub orbitals for s The it doesn't have any unique symmetry like p does it's always going to be zero and then spin is arbitrary up or down or Positive one half or negative one half so you can assign it positive one half for exist this example But there will be another problem after this So here's our first a problem, and I want you guys to take a Good 30 seconds. It shouldn't take too long, but we'll go over it together But I won't give you some time to do it yourself, and then we can come together as a class To solve it. So this is just looking at the electron Configuration for oxygen and iron and I want you to find oxygen and ion o2 minus and also iron 2 plus so the ferrous ion But my recommendation is if you're not too familiar with this and we'll do this together start with the neutral atom Okay, don't worry about the ion yet Just find the electron configuration of the neutral atom, and then we can worry about that ionization later So I'll give you a good minute or so try to write this down and we can we can talk about it together Okay, how does the quiz work is it just lecture or actual canvas quiz? So right now I have we haven't done this before so in my mind It's going to be a canvas quiz that we will Locate time during lecture for or during quiz section for and it will only be available during that time Maybe some so there might be some grace period before and after but Well, I think that's going to be how it is. We'll try it out see how it works Okay, so let's go over this problem. Let's start with oxygen and let's start with Oxygen the neutral atom of oxygen so not the ion And if we'll go through this but if if something does not make sense to you Please shout out and we can we can go over it again a little bit more slowly but Who who can give me the electron configuration of oxygen the neutral atom of oxygen 1s to 2s to 2p 4 yes, that's correct So I'll put it up here. So here's the neutral Adam of oxygen 1s to 2s to 2p4 Here it is written out So, you know if this was on a test or homework I think this was this is going to be the expected answer I just to write this this long list of letters and numbers But I also drew out the you know The filling of these orbitals and the filling of these orbitals, you know We use these up half arrows and down half arrows to represent each electron that gets filled And remember because of the poly exclusion principle each suborbital can only Occupied have two electrons occupied at once and when you get to a spot such as the top orbitals here where we start occupying on Do the off-bowl principle We're going to try to minimize the energy of these electrons so the best way to fill it up is to first fill up one in each and Then we'll pair them up because it takes additional energy to pair up Two electrons together that the analogy I like to use is you know if you're getting on a bus You know you always when people get on the bus that you always try to go for an empty seat And then when the bus gets filled then you start doubling up, right? That's the analogy So how about oh in the up arrow represents up spin and down arrows down spin or positive one half and negative one half For the quantum number. How about now? Let's look at the anion All right anion means we're giving the molecule or the we're giving the atom more electrons, all right Oxygen if we look at the periodic table Oxygen would like to receive two electrons. They always want to fill up this what we call the noble gases, right? If that makes it a complete Octet or completely filled orbitals if it receives those two electrons So what would the the configuration be for oxygen two minus? That's right two p six. So we're adding two electrons They're just gonna fill in those those vacant half spots of the p groups, right? So that's oxygen anion How about iron? Let's start with just the neutral atom for iron who can who can give me a a a electron configuration All right, so we have 1s to 2s to 2p 6 3s to 3p 6 4s to 3d 6. Yeah, that's correct now According remember according to the off-bow rule, right? We would fill the 4s first and then fill the 3d Just like you wrote out you have the 3d 6 after 4s 2. However In the in the in Callister your textbook and also I think this is the correct way to do it I would put the four the higher principal numbers After even though they're the ones that you don't necessarily fill up First and the reason is and you'll see the reason is because you want to ask yourself which which electrons have the highest energy Is it the 3d electrons or is it the 4s electrons? Okay now Even we'll see that when we when we ionize this ion so let's go to the iron 2 plus What is the configuration for iron 2 plus and I I guess I gave away a really big hint So it's gonna be obvious But who can and you can just give me give me the 3d's and 4s is what was that look like? If you don't want to write up the whole thing 3d 4 4s 2. Okay. I'm glad you brought that up. So that is not Going to be the correct answer the correct answer would be to remove the 4s electrons Before touching the 3d electrons and I actually now now you've made me a little bit nervous because I want to make sure I'm pretty sure that's correct, but if you guys find otherwise you shout out. I'm pretty sure this is correct Because it's the the lowest energy state if we were to you know Say we did did it your way and say we left two electrons in here and then We take two away from the D instead of the 4s Then we don't have a it's lower energy to have this partial half filled and partially filled d orbitals than to have You know the 4s with Unfilled on half filled 3d. That's just the way it is for energy-wise It's always trying to have the lowest energy state and in this case it'd be to take away the 4s first So this is this is where it gets a little bit complicated So, you know, if we look at let's not go to the transition metals yet Let's just look at potassium and calcium for example All right, so if we get to argon argon has a full Was a 3p 3p6 and now we get to potassium. What are we going to fill first? again, it is it You're going to be a lower energy to partially fill The 4s or is it lower energy to partially fill the 3d and in this case for potassium It'd be lower energy to first fill half fill the 4s and then let you see that it's more evident in calcium If you have a Completely filled orbital that's usually more stable less fill less energy than if you have a unfilled Like d orbital. Yeah, half filled would be more stable Oh, okay. Yeah, so you you do bring up a good point So if it would be 3d 4s one would be to have filled So in this case, I think you should double-check me on that, but I'm pretty sure I'm correct But I could be wrong pretty sure I'm corrected to remove the 4s, but you know, anyways, so that's the ferrous ion ferrous iron, which is iron 2 plus And also you can replace a lot of this with the noble metal or excuse me not the noble the noble gas Configuration because the noble gas configuration is going to represent if you just put this in brackets It's going to represent all the way up to 3p6 and then you can continue after that Okay, let's move on. Okay. How about the quantum number? For iron, so let's say given the quantum number give the quantum number for iron Of the electron removed from iron 2 plus during its oxidation. So first off when you know what oxidation means Oxidation means we're taking electrons away from the ion or element Okay, so if we take an electron away from iron 2 plus it becomes what? Iron 3 plus. Yeah, so if we take a negative charge away from the iron 2 plus it oxidizes It becomes more positively charged. It becomes iron 3 plus Okay, and now the question is which electron are we from this diagram? Are we taking away because we want we want to find the quantum number of that specific electron So which electron are we talking about in this energy diagram? In other words, which electron has the higher energy Yeah, the negative spin in the 3d Okay So I've highlighted here. This is the electron. We're talking about it's part of the d orbitals Okay, in this case, we're calling it a negative spin And it's part of the principal number is three because it's part of this three energy level energy state All right, so oil rig oxidation is loss and reduction is gain. That's yeah I always use that as well. Let's say oxidation or reduction is gain and it sticks Okay, now how about L the the orbital? angular Momentum quantum number remember L Corresponds to like spd and f So we say three we say two Okay, so two is correct because remember L is always going to be it can be any number from zero to one minus n Okay, so it can't be three and if we look at principal number three The orbitals that are allowed to be in principal number three are s orbitals p orbitals and d orbitals So that would correspond to zero one and two. So in this case L would be two because we're talking about the d orbitals if we're just talking about this one electron to now what about the this is the magnetic quantum number and Okay, so this one's a bit arbitrary because we don't know which orbital this corresponds to The magnetic number will correspond to these different symmetries these different sub orbitals, right of the d Orbitals, okay, and remember the number is available for the magnetic quantum number are Negative negative L So it could be negative two all the way integer values all the way to positive L a positive two So just arbitrarily we're going to say it's this first one this first symmetry which would be negative two All right, so that represents this symmetry You don't need for you know, whatever exam you don't need to know these symmetries But you do need to know, you know, you can assign these numbers And then how about the magnetic spin? Quantum number Yeah, so again, this is a bit arbitrary but since since our arrow is pointing down. I like to give it a negative one half Okay, so you should that's what you should know what to do is find the The electron configuration of different atoms I think you know, like I said, it gets a little bit more complicated and as we saw for the transition Metals, but before the transition metals you should know It should be pretty clear how to come up with these numbers and then also the finding the quantum number of an electron Okay, so you that's what you should know Um, so we're going to talk a little bit more about bonding. I think I'm going to skip over this a little bit You don't need to necessarily know This part, but I think later in this course you will be talking about band theory Or like these electron energy bands and these what's what's important about these energy bands and how different elements Uh And this is we're talking about a bulk material now We went from a single atom and now we're talking about a bulk material and the electron energies of a bulk material and they fill up what we call bands and the bands are important because it will tell you What type of material? You're dealing with electronically that speaking. So whether it's uh, I have some examples here. Well, we have magnesium silicon Here's an example of sp hybridization. So here we in silicon and other like, uh, covalent materials like carbon They'll the s orbitals and p orbitals will combine to make an sp hybrid So for example graphene remember carbon is bonded to three different other carbons that'd be sp2 hybridization carbon and diamond or silicon is uh, the diamond Crystal structure has sp3 hybridization and then they can also so on this is called molecular orbital theory But you don't need to know that for this class But eventually I think when we start talking about electronic properties You will need to know a bit about the the band structure And so like I said, the different band structures can tell you information on its electronic properties Whether it's an unfilled band or it has a band overlap. Those are different Conductors like metals will have that type of band structure insulators and semiconductors have what's called a band gap and then this is very important for different semiconductor devices like uh Solar cells for example solar cells the the voltage That generated by a solar cell is related to the band gap or for example the led If you have an light emitting diode the color of the wavelength of the light or the color of the light Corresponds to the band gap of that material. Okay. Anyways, so but we'll we will talk a bit about bonding Today so there's different type of bonding covalent bonding as you you probably know, this is pretty standard stuff You should already know a covalent bonding is the sharing of electrons between atoms Ionic bonding is the stealing or giving of electrons Between different atoms. So we get what we call ions So a lot of ceramic materials are made out of these Ionic bonded materials covalently and ionic bonded materials are typically insulators or semi conducting materials and then metallic bonding uh, so you'll have electrons that are that are Part of bonding that and then you have electrons that are part of conduction and we call that the valence electrons sea of valence electrons um Okay, and of course a lot of the conduction and like thermal conductivity and electrical conductivity Are our functions of temperature right as we increase the temperature that can change the conductivities It can change the number of electrons in the sea of electrons or it can change the number of electrons that Maybe are not part of bonding and covalent materials like silicon And so temperature has a big effect on those properties as well so You know, it's easy to to make this diagram and in kind of categorize materials as being either covalent or ionic But in reality There's very few materials that are purely covalent or purely ionic and in reality there there's a bit of mixed character Uh, if you if you combine different elements in the molecules There's a bit of mixed character and we call that the percent ionic character um, so for example like some some I guess you could consider silicon Like uh and carbon diamond as purely covalent. All right, but um other you know In general if you mix a a metal or transition metal with a non-metal and you get a a Ionic compound so some examples are like lithium oxide titanium oxide iron oxide aluminum oxide or alumina Sodium chloride, which is very common uh salt table salt um, and then covalent compounds are typically uh more similar compounds So like the oxygen molecule or nitrogen molecule or a diamond So um, uh, let's think Well, here's some examples examples hydrogen so hydrogen is one that gets stuck over here as well hydrogen fluoride gallium arsenide CO2 gas or silicon semi-metal are considered mostly covalent so but We can calculate the percent ionic character using this equation So the next problem is to calculate the percent ionic character of si-02 Where x a is going to be the larger And excuse me. I forgot to mention that this is the Electronegativities. All right. Electronegativity is it's you know, it's ability Or it's willingness to accept electrons, right? So we talked about oxygen oxygen forms the anion o2 minus to complete its orbital And so it's it's more willing to To receive electrons than give away where the transition metals and other metals are or more willing to give away Their electrons so they have lower Electronegativities so x a is always going to be the element with the higher Electronegativity xb will be the element with the lower electron activity So from this chart of electronegativities find silicon and oxygen and calculate the percent ionic character. So I'll give you A few seconds for that All right, uh, who who has an answer? Who would like to share an answer for ionic character of silicon oxide? So silicon is a semi-metal Oxygen is a non-metal. So if you think it's uh, probably kind of covalent Yeah, so we have 51 percent since we square the value doesn't matter, which is uh, there's Yeah, I guess it doesn't matter does it Because if you take the difference, it'll be negative if it's negative you square it becomes positive. Yeah, I guess it doesn't matter Um, yeah, 51 percent is is what I also got Yeah, so x a 3.5 for silicon for or excuse me for oxygen 3.5 for silicon 1.8 and then uh, 51.4 percent so you know silicon Isn't necessarily silicon oxide. That is not necessarily entirely covalently bonded. It also has a bit of ionicity as well now let's talk about interatomic distance or essentially the distance between Ions or atoms in a solid now for ionic materials if we consider the material To be a point charge, right? So this one's a positive plus one charge. This is negative minus one charge There will be a coulombic interaction between those ions, right? So you'll have a an attractive force between them because one's positive when it's negative and the positive and negative attract to each other But also remember that there's still an electron cloud of negative charge surrounding the the ion This still has that cloud. So if they get too close together those electron clouds would interact and then That will create a coulombic repulsion force. So you have two competing forces You have an attractive coulombic force and a repulsive coulombic force So we have this diagram here. We're in the blue We have the attractive force in the I believe it's green is repulsive force And then the sum of them the two is this red line here All right. And so the question is, you know, what's the equilibrium distance that these ions will want to be at You know, that's the bonding distance. All right, so that's when the force the attractive force in the repulsive force is net zero Okay, so there's no no attraction and no net repulsion And we can look at it more On an energy scale for potential energy where energy is just the integral of the force versus distance And so now we have a repulsive energy And an attractive energy. Okay. And so again at the equilibrium distance are not Between the two ions The potential energy will be a minimum Okay, the lowest potential energy is where it's more the most comfortable at right So the net energy is the sum of the attractive energy Which is the negative of a constant a and these constants depend on, you know, the system and Perhaps the coordination as well and then r is the distance That these ions are apart from each other So it's the attractive energy and the repulsive potential energy another constant and then r to a power of n And typically n is around eight and I have a problem later on where we can do some calculations But first here's a problem Just conceptually if we take a look at these these different energy wells for energy potential energy versus atomic spacing of the two different material atoms We have some questions we can consider So we have two different materials material a material b material a as a oops Excuse me is a bit more steep of a well and material b is more shallow and spread out First question is which material has a higher melting temperature Okay, so when you think about what what is melting temperature mean? And which one of these would be considering having the higher melting temperature And you can say yes for material a and no for material b if we if we don't get some answers here Okay, yeah, so many of you are seeing a you might have seen the answer that already had And now let's consider why does material a yeah the answer is a Why does material a have a higher Would be have a higher melting temperature than material b does anyone want to Speak up or write and chat impossible Is it because a can absorb the energy wells deeper so a can take in more energy before it breaks apart Right. Yeah, so it's taking more energy before the atomic spacing and like you said breaks apart that breaks its crystal Structure so so the melted the definition of melting temperature is basically, you know Well, of course, it's going from a solid to a liquid But also, you know, you think of this we have this crystalline structure where the atoms are arranged in a certain way And then they gain enough energy where that it goes from crystalline to amorphous Like in a liquid, right and they lose that they lose that Coordination with their neighbors so having a steeper well would Have a higher melting temperature now. How about thermal expansion coefficient? So if you're not familiar with this term, it's basically how much does the material expand when we heat the material up in general materials In general materials will expand when they get hotter So which one of these materials will have the higher thermal expansion coefficient? Okay, so he Looks like a lot of you are seeing B. Maybe not too sure if someone has an idea Go ahead and speak up or write in the chat. Why was would material be in the answer? I have his material be why would material be Have a higher thermal expansion coefficient or in other words, but I'll let you guys go go ahead So we're not let's say we're not reaching the melting temperature. We're below the melting temperature We're still a solid and we just increase the temperature and as we increase the temperature the solid will we'll get a little bit bigger Why why might that be? It takes less energy to influence the bonds between the molecules Yeah, perfect. And we can tell that by the diagram because it's more it's more spread out So so essentially, you know, if we think of the atoms in a solid We it's easy to think of them as frozen in space But that's not necessarily true atoms and solid are have a lot of energy at room temperature and they're vibrating around All right, so we see this and it's only at this this lowest point At zero kelvin at zero kelvin. There's no thermal energy, right? It's the coldest temperature you can be at At zero kelvin, you're just going to be at this stuck at this one position But at room temperature you're going to have a bit of energy a bit of thermal energy, right? So you might be higher up on this graph where the you know, the atoms can be the The atom can be a little bit closer at times to its neighbor or a little bit further away at times its neighbor And if you look at this this dashed line the dashed line should represent the average between You know the one side and the other side Okay. Yeah, just a quick question about that. Yeah, the graph we're shown is like a probability distribution of the spacing, right? The graph we're showing is like the range of the spacing possible at an actual the graph we're showing is the energy Um, it will be the attractive minus the repulsive energy um Yeah, I guess you could think of it as distribution Yeah, just trying to understand so let's say like on material B on a single horizontal line Is that the range of the intertonic spacing at a given energy level? Yes. Yes. Yes. Okay. You can do that Yeah, so as we're increasing the temperature, it's going to be more You know some more of the atoms are going to be you know closer or further apart But you see that the average is shifting to the right the average is shifting to higher Intertonic spacing and that's why these material looks expand In general they expand as we heat them up because on average they're going to be further away from each other All right, we're on this more shadow this steeper curve The average is not is not as significant as this one at a given given temperature Okay Yeah, so it just is important to realize that atoms are they're always constantly moving around You know only at absolute zero Kelvin do they they stay still, right? So at room temperature, they're they have a bit of energy Okay, and how about the higher elastic modulus? so If you don't know yet elastic modulus is essentially the stiffness of a material or Basically, how much force you need to apply on a material to give it a little bit of strain And we're in the elastic region, which means That there's not going to be any permanent deformation All right, so again check mark for a and x mark for b so some Yeah, so i'll explain the elastic modulus again Elastic modulus is essentially the stiffness of material. Okay, and that's that's basically, you know, how much force is required to To pull the material apart But while we're still in the elastic region, right? For example, like a rubber band you can you can stretch the rubber band apart and then if you let go it returns to its original shape There's no permanent deformation the same thing if you take a metal Like a aluminum bar and you put a force on it You're going to be changing the dimension of the material Depending on how much force you put on it now for metals that have very high elastic modulus It's going to take more force to change the the dimension Uh, and this is before permanent deformation. Yeah, if you put too much force Then you'll you'll you know permanently change the shape and this is not that does not include the elastic region elastic modulus Yeah, higher modulus means it will stretch Nope, not quite not quite a higher the modulus does not That's yeah, the modulus and when it will break not related um Higher modulus means that it takes more force to elastically deform So elastically means it's not going to break or permanent. It does not permanently deform Uh, it just takes more force to to strain it a little bit. All right, so it looks like overwhelmingly more people are saying Yes for a does anyone want to have a x shout out explanation of why a would be The material with higher elastic modulus I think it would be a Because on the underneath the slope This is a bit ahead I guess but the area underneath the slope is the Energy absorbed so if you have a deeper well, it would take more energy absorbed before you get into plastic deformations Yeah, that's that's a great explanation. I believe that's also uh in the textbook It should should say that as well. Yeah, so we're taking it takes more energy, right is the area uh under the slope to Change the atomic spacing a little bit, right? So that's where we want to change the atomic spacing by applying force Which is force times distance is energy, right? So the steeper the curve. It takes more energy to change the atomic distance It will take more force Yeah, I guess you can also say though the average slope here is less steep Or more steep Should be more steep. Yeah, all right. Let's move on So here's a problem still dealing with the energy in atomic spacing And this problem wants you to calculate the equilibrium bonding energy. You know, it's uh I think we'll go through this together because it's it's it's just more of a proof than a calculation Um, so as we said if we're looking at potential energy versus in atomic spacing We have a repulsive energy and an attractive energy And the sum of the two is the net energy. Okay, and of course the equilibrium distance are not Is going to be at the point of minimum potential energy. So the question is, you know, how can we uh Here's the question determine e not the equilibrium energy bonding essentially bonding energy Determine the bonding energy In terms of a b and n. So we we want to remove r from the equation basically So the question is how how can we go about doing that? And I think the big hint here is that remember The equilibrium Distance and energy is going to be at the minimum point. So that should be a big hint And another hint is that we're going to have to use some some a little bit of calculus, but not too much So those two things together that should that should light off a light in your head when we're talking about minimum and calculus What do we want to do? We're going to start we're starting with this equation here. Yeah, so we're going to take the derivative of this equation And uh, why remember? Yeah set the derivative equal to zero, right? So we're taking the derivative of this curve here the red curve And when the the the curve The derivative of the curve is zero that will be the minimum point And then we're going to try to solve for r not at that minimum So we're going to take this equation Differentiate the equation respect the r. Okay, so we have a constant negative constant over r and a positive constant over r to a a power of n All right, does anyone uh want to give uh an answer for the derivative of each of these? So we can start with this this first term here. What's the derivative of this term? With respect to r. So basically this is one over r, right? That's right. So I gave away the next one, but oh well Yeah, so the first term is uh, it will become a over r squared The second one is uh, you take the exponent out becomes a negative as well So negative uh n b and R n comes r n plus one And then as we said before we're going to set the derivative We're going to set this derivative equal to zero and that will be the minimum of the energy curve Okay, and then we can then we can solve for r and that will be r or not Okay, so we set equal to zero we solve for r or not Okay, and we can separate these terms to get r not on one side Okay, and so now we have a value of r not which is the equilibrium atomic spacing And it's a given in terms of the constants a b and n which are constants that are usually given um in a problem okay, so Then what you would do is go back to the original equation substitute the r for the r not that we just found And then that gives you your final equation where you can Find the energy the the bonding energy Given these constant values, which again like I said would in a problem would be given to you as values Um, I don't I there might be a homework problem Similar to this but I'm not I'm not sure I haven't seen the homework yet Um, but the next one will be oh you guys it's 210. Is it not 210? Is that the end of class? I believe it's 210 Yes, okay. So in that case, uh, this that's and that's the end of class, right? um I will Yeah, I will post these slides online, but there's only a few more. There's only one more problem basically uh, calculating the The r not value For lithium chloride given some constants. Uh, so pretty straightforward I'll post it on canvas also later this week. I think I'll post Maybe a survey or something to see what time will work for office hours Also, Sid the other ta will also have office hours. So we'll find the time that works for everyone And of course you guys are welcome to email me At any time if you have a question. So go ahead Quizzes occur on canvas not this week this week will not have a quiz The first quiz will be wednesday next wednesday And like I said, I I will send out enough information Maybe a day in advance. So Yeah, next quiz and homework will be due wednesday Um, and like dr. Brush said that should be figured out by tomorrow. All right. Have a good weekend guys