1 00:00:17,266 --> 00:00:23,416 Happy Monday everyone! How you all doing? You  know it's good because it's a goodie bag day   2 00:00:24,933 --> 00:00:34,700 and so I'll get to what you have in your hands in  this lecture. Today-- So we've been talking about   3 00:00:34,700 --> 00:00:40,300 these things for a while now, right? We've built  up an understanding of the stamp and the basis,   4 00:00:41,016 --> 00:00:46,066 and then we understood how to talk about it  like in terms of the planes and the symmetries,   5 00:00:46,616 --> 00:00:53,733 and then we shined x-rays on it, and now we're  going to start taking them all apart. And so don't   6 00:00:53,733 --> 00:01:00,533 be sad, don't be sad, because actually that's more  real-- that's more real. And that's what we'll   7 00:01:00,533 --> 00:01:06,466 talk about today. So what our plan is-- you know--  So today we're going to start creating defects   8 00:01:07,100 --> 00:01:14,783 in the perfect order that we've had so far. And  in your goody bag you have a defect generation   9 00:01:14,783 --> 00:01:20,933 machine, which we'll talk about. And then on--  And so today we're gonna talk about one kind   10 00:01:20,933 --> 00:01:24,783 of defect, that's a point defect, and then  on Wednesday we'll talk about line defects,   11 00:01:25,333 --> 00:01:29,983 and then we'll just mess the whole thing up,  and we're going to make it amorphous. So that's   12 00:01:30,700 --> 00:01:34,533 where we're going. And beyond that if you  want to know more about where we're going,   13 00:01:35,265 --> 00:01:41,583 there's the concept map up there for exam 3.  Which again, you know we don't pick these dates,   14 00:01:41,583 --> 00:01:46,933 so this date came later in the semester that  we wanted but it's that's what it is. I think   15 00:01:46,933 --> 00:01:53,733 it's all the way up in early December. But--  Because of the fact that there's a Thanksgiving   16 00:01:55,100 --> 00:02:01,183 holiday in between and there's one topic here  we have to start before the exam. It's not here   17 00:02:01,183 --> 00:02:05,500 because it won't be on the exam but we're going to  start polymers but won't be on the exam. I'm going   18 00:02:05,500 --> 00:02:11,583 to spend the whole lecture before exam three just  reviewing for exam three, because we're gonna have   19 00:02:11,583 --> 00:02:15,583 that Thanksgiving break and all that. So that's  what's not listed here these are just the topics   20 00:02:15,583 --> 00:02:20,933 that are covered on exam three. Okay. Good. If  anyone has any questions please do let me know.   21 00:02:21,983 --> 00:02:28,616 The concept map. Now the thesis of 3.091  you have seen in multiple different ways.   22 00:02:28,616 --> 00:02:33,333 I have tried to convey to you that  the electronic structure of atoms   23 00:02:33,333 --> 00:02:38,933 is the key to life. It's the key to chemistry.  It's the key to understanding and within that   24 00:02:38,933 --> 00:02:42,300 you get things like this which is what we've  been talking about recently like composition   25 00:02:42,866 --> 00:02:49,733 and arrangement. Right? That's these crystals  that's these different-- BCC FCC. Okay.   26 00:02:50,700 --> 00:02:54,066 And then the chemistry you put inside. But  you see the other thing about it is defects.   27 00:02:54,866 --> 00:03:01,900 Because the thing is that defects, which is the  topic of today and Wednesday, they are absolutely   28 00:03:01,900 --> 00:03:07,500 crucial for understanding the properties.  If they're there and I just told you they're   29 00:03:07,500 --> 00:03:15,500 always there. The question is how much are they  there? And so if you don't know about defects--   30 00:03:15,500 --> 00:03:22,300 if you don't know about defects then you  really cannot fully understand properties. 31 00:03:25,266 --> 00:03:30,783 There is a very strong correlation between the  two and that's why we have to talk about them.   32 00:03:31,333 --> 00:03:37,266 We have to understand them. Now I love  this quote from Colin Humphreys he said,   33 00:03:37,266 --> 00:03:42,383 "Crystals are like people, it is the defects  in them which tend to make them interesting."   34 00:03:43,100 --> 00:03:48,216 Yeah. And that's actually really true because  defects, right, defects sound you know... 'I   35 00:03:48,216 --> 00:03:55,016 don't want to defect.' No, actually oftentimes  you do want defects. Sometimes you don't. So   36 00:03:55,016 --> 00:03:58,533 there are some kinds that are kind of like  maybe not things you want in your crystal   37 00:03:58,533 --> 00:04:03,900 and then there are other kinds that actually you  are engineering purposefully to be there. Either   38 00:04:03,900 --> 00:04:08,700 way you got to understand them. Right? And that's  what we're doing today because --Gesundheit-- so   39 00:04:08,700 --> 00:04:14,133 you know if you take this three layer-- We talk  about graphene. It's a one atom thick material.   40 00:04:14,133 --> 00:04:19,983 Pretty cool-- every atom's on the surface. Here's  another example of what's called a 2D material.   41 00:04:19,983 --> 00:04:24,300 Why? It's not 2D but it's called a 2D material  because it gets you like... you know more   42 00:04:24,300 --> 00:04:28,700 publicity on your work. This is molybdenum--  this is molybdenum disulfide it's really cool   43 00:04:28,700 --> 00:04:34,466 material. It's three atoms thick. So it's kind of  like 2D-ish, right? Yeah but see that's the model.   44 00:04:34,466 --> 00:04:40,783 That's the model. This is reality. This is real--  How do you see-- How do we see atoms like this?   45 00:04:41,500 --> 00:04:49,183 That's a real picture. Do we use x-rays?  No? What do we use to see atoms that well?   46 00:04:50,700 --> 00:04:57,500 Electrons. Electrons are our light, right? That's  what we're using. This is an electron picture,   47 00:04:57,500 --> 00:05:01,500 electron. And if you do that you can  see individual atoms and look at that   48 00:05:01,500 --> 00:05:09,100 there's there's places where atoms are missing all  over the place. That's reality. That's reality.   49 00:05:09,100 --> 00:05:16,616 And those where you have one atom missing or  where you have one thing that is localized and   50 00:05:16,616 --> 00:05:22,066 disruptive to the regularity of the lattice...  that's called a point defect. So let's write that   51 00:05:22,066 --> 00:05:30,533 down. That's the one that we're talking about  today. So the point defect, 'point defect', is   52 00:05:31,983 --> 00:05:38,700 where you have a localized...  localized disruption...   53 00:05:43,816 --> 00:05:47,816 in the regularity, 'regularity'. 54 00:05:49,016 --> 00:05:52,700 The periodicity the repeating of the lattice. 55 00:05:56,066 --> 00:06:00,783 And it could be on or between,  we'll see this, on or between   56 00:06:02,300 --> 00:06:09,583 sites. Right? It could be a defect that is, like  you see here, there's an actual atom missing. What   57 00:06:09,583 --> 00:06:15,816 could be something that maybe you've got in there  in between sites? But either way it's a disruption   58 00:06:16,383 --> 00:06:23,183 that's localized to a point or almost a point.  And so it is --Gesundheit-- that you can see that   59 00:06:23,183 --> 00:06:28,066 if we just make these disruptions in something.  Alumina. We talk about alumina, right? Remember   60 00:06:28,066 --> 00:06:34,066 alumina's really strong lattice energies? So  it's like sandpaper. Oh, it's also toothpaste.   61 00:06:35,266 --> 00:06:39,816 It's in a lot of stuff. Alumina is a great--  But look at this. That's alumina with almost   62 00:06:39,816 --> 00:06:47,016 no defects. It's still got some. You can never get  rid of them all! But here it is when I purposely   63 00:06:47,016 --> 00:06:51,582 engineer the defects in alumina and I put a  little titanium or iron. Or here's it when   64 00:06:51,582 --> 00:06:58,533 I put chromium. So you can-- There's one property  where the localized disruption, and it's not a lot   65 00:06:58,533 --> 00:07:05,816 as we'll see, the localized disruption changes  the properties. That is key. That's just color.   66 00:07:06,383 --> 00:07:13,666 Right? This applies to most properties of  materials. And so this first one, the point   67 00:07:13,666 --> 00:07:19,016 defects that we're talking about today, you can  kind of think of those as zero dimensional because   68 00:07:19,016 --> 00:07:22,533 they're they're localized. You know. They  don't really go off in a line. They don't   69 00:07:22,533 --> 00:07:28,216 go off in a plane or a volume. And you can  have defects that are that cover all of those   70 00:07:28,216 --> 00:07:35,332 possibilities. But these are points. Alright?  This is what the word localized means here, okay?   71 00:07:36,216 --> 00:07:42,066 Okay. Now in this class, we're not going to cover  all of them, but we will cover these two. Today:   72 00:07:42,066 --> 00:07:47,500 this one. On Wednesday: that one. And that'll  give you enough of a sense of the role of defects   73 00:07:47,500 --> 00:07:53,816 and how to think about defects and crystals.  Right? So this is how we think and classify   74 00:07:53,816 --> 00:07:59,183 defects. Okay. Now the four-- so now we're  going to point defects-- now the four,   75 00:07:59,183 --> 00:08:05,666 there are different types of point defects that  can happen. The one that you saw here is a certain   76 00:08:05,666 --> 00:08:11,333 one. That's called a vacancy. It's because there's  an atom that's vacant. So you literally just lost   77 00:08:11,333 --> 00:08:19,183 an atom somewhere in there. Okay? Now that's a  vacancy and that always exists. But you could also   78 00:08:19,183 --> 00:08:23,733 have taken something like one of the atoms that's  already in there, maybe an aluminum or an oxygen   79 00:08:23,733 --> 00:08:28,533 that's in the lattice, and you could substitute  something in place of that. That's another-- Why   80 00:08:28,533 --> 00:08:33,816 is that a point defect? Because I didn't like  tear something out. But no, but you changed the   81 00:08:33,816 --> 00:08:39,900 regularity. Localized disruption and regularity.  So if I put something else in for aluminum   82 00:08:39,900 --> 00:08:45,333 that's a point defect. Right? And again, now go  back to here. You can see it here. So we classify   83 00:08:45,333 --> 00:08:51,183 these, right? There's a vacancy, which is an atom  missing. There's what's called an interstitial,   84 00:08:51,183 --> 00:08:56,216 which is an atom that goes in between the other  atoms. Here it's a self interstitial so it's the   85 00:08:56,216 --> 00:09:01,816 same type of atom. And these are-- This is where  you have a different type of atom in between and   86 00:09:01,816 --> 00:09:06,216 this is where you have a different type of atom  as well. Those are both called impurities and I   87 00:09:06,216 --> 00:09:12,466 will talk about those all today. We're gonna start  and focus a lot of our attention on the vacancy.   88 00:09:13,500 --> 00:09:18,700 And that's what I want you to use this goodie bag  to understand, is the vacancies. Okay. Vacancies.   89 00:09:18,700 --> 00:09:26,783 Why do vacancies happen? What are vacancies? To  understand vacancies in crystals we have to talk   90 00:09:26,783 --> 00:09:36,300 about this guy. And oh... this guy was brilliant.  This-- I'm sure you know his name is Svante. Yeah,   91 00:09:36,300 --> 00:09:43,100 it's written right there. Svante Arrhenius.  Arrhenius studied in the late 1800s so many   92 00:09:43,100 --> 00:09:49,016 different things and made so many contributions  that it's almost hard to catalog. He was   93 00:09:49,016 --> 00:09:53,983 brilliant. And you know he won the nobel prize  in chemistry for his work on electrolytes.   94 00:09:55,333 --> 00:10:01,666 But he also worked on immunology. He was the very  first person in the late 1800s to come up with a   95 00:10:01,666 --> 00:10:07,666 model for global warming and the role of CO2 in  the temperature change of the planet. And his   96 00:10:07,666 --> 00:10:14,533 predictions were actually pretty darn good. He  was brilliant. And one of the things that he did   97 00:10:14,533 --> 00:10:21,816 is, he observed what it were called activated  processes, and how they depended on temperature.   98 00:10:22,933 --> 00:10:27,733 And so we have this equation that I need to  talk about today and it's going to come back.   99 00:10:28,533 --> 00:10:33,665 So we're going to talk about this equation,  which is the Arrhenius equation, that relates   100 00:10:33,665 --> 00:10:42,300 the rate of some process to the temperature. And  the activation energy for that process. So we got   101 00:10:42,300 --> 00:10:49,333 to talk about what all that means, alright? Now  we will be using this. Today we're going to use   102 00:10:49,333 --> 00:10:55,816 it to think about concentrations of vacancies in  a crystal which follow Arrhenius-like behavior.   103 00:10:57,333 --> 00:11:02,783 Right? But then we're going to come back to it  when we go into reaction kinetics in a couple   104 00:11:02,783 --> 00:11:07,983 of weeks. Where we talk about reaction rates. So  we'll be using Arrhenius multiple times throughout   105 00:11:07,983 --> 00:11:16,383 the rest of the semester. So what is it? So the  Arrhenius-- So the general Arrhenius equation can   106 00:11:16,383 --> 00:11:23,666 be written like this. Arrhenius, he was not in  the army but this is just the general equation.   107 00:11:24,383 --> 00:11:31,816 Okay. So let's put equation there. And so we have  k, which is some rate, equals A. I'll talk about   108 00:11:31,816 --> 00:11:42,216 each of these. Times e the exponential of e to  the minus Ea over RT. What are these things?   109 00:11:42,216 --> 00:11:48,216 So this is the general equation for the rate of  some process. As we're going to see this applies   110 00:11:48,216 --> 00:11:55,016 to many, many processes including vacancies.  Okay. But this is sort of the rate. So you can   111 00:11:55,016 --> 00:12:02,616 think of this as-- Okay. Let's just-- That's the  rate of a process rate. The rate of some process.   112 00:12:02,616 --> 00:12:08,066 Okay. I mean you could think about it as the  number of times something happens per second.   113 00:12:08,066 --> 00:12:13,333 That's a rate. Right? It doesn't have to be those  units, but that's like a rate. Right? How often   114 00:12:13,333 --> 00:12:22,300 does this happen. The rate-- But now so that's  dependent on something called the pre-exponential,   115 00:12:22,300 --> 00:12:31,183 that I will talk about. 'Pre-exponential--  exponential'. That is a factor that is a constant. 116 00:12:34,700 --> 00:12:40,133 And here we have this exponent-- and this  is such a beautiful expression. So this is   117 00:12:42,133 --> 00:12:51,266 the average thermal energy. 'average kinetic  energy, average thermal energy' Right? It's   118 00:12:51,266 --> 00:12:55,733 taking temperature and it's making an energy out  of it. Now remember we've already talked about   119 00:12:55,733 --> 00:13:03,900 this before. That you know you don't get what you  get are distributions. So you know this would be T   120 00:13:04,700 --> 00:13:10,383 high-- remember I've drawn this exact thing and  this might be T low and this might be-- You know,   121 00:13:12,383 --> 00:13:20,066 this might be the you know the probability of  something happening. Probability of occurring.   122 00:13:20,616 --> 00:13:24,933 And then in this case we talked about this  as the kinetic energy of the molecules.   123 00:13:24,933 --> 00:13:31,333 That's a graph we showed already. But so the--  But this RT is an average. But so I just want   124 00:13:31,333 --> 00:13:37,665 to make sure you don't forget. This is a number.  This is a number. You've got at 300 degrees, at a   125 00:13:37,665 --> 00:13:41,665 thousand degrees, you calculate a number here.  But whenever you're talking about temperature,   126 00:13:41,665 --> 00:13:46,866 you're talking about distributions. There's some  average of the distribution but you're always   127 00:13:46,866 --> 00:13:54,866 talking about distributions. That's important for  understanding Arrhenius. Okay. Now this thing here   128 00:13:55,983 --> 00:14:10,066 is called the activation energy. Activation  energy. And that is the energy that you have   129 00:14:10,066 --> 00:14:15,100 to get over for something to happen. For  the thing to happen. Let's take-- I love   130 00:14:15,100 --> 00:14:21,183 this analogy of the bookcase. I'm going to draw  that now. So let's suppose that you have energy,   131 00:14:22,133 --> 00:14:27,016 like that. Okay. So maybe this is like potential  energy. Yeah, let's go ahead and say potential   132 00:14:27,666 --> 00:14:36,216 energy. Then if I've got a bookcase and it's very  very heavy. And I try-- and I want to push it over   133 00:14:36,216 --> 00:14:42,216 on this hinge. So I want to rotate it and push  over. Then you could imagine that at some point   134 00:14:42,933 --> 00:14:47,733 it's going to look like this. And then  at another point, it's going to look   135 00:14:47,733 --> 00:14:52,700 like this. Right? So this is like step one,  and that's step two, and that's step three.   136 00:14:53,983 --> 00:15:03,266 And now I'm pushing this thing over. Well this is  the activated state. Why? Because it's where I've   137 00:15:03,266 --> 00:15:08,216 gotten to the highest energy, and that's where  this energy graph is important. This energy axis,   138 00:15:08,216 --> 00:15:14,700 this is the activated state of the bookcase.  Right? So if I plot the the energies. 139 00:15:16,783 --> 00:15:22,783 Right? You can say one, two, three. You  can think about it like that. Right?   140 00:15:23,666 --> 00:15:27,100 I've literally-- So because it's a potential  energy, right? So it's like here's the   141 00:15:27,100 --> 00:15:31,666 gravitational pull, here it went up a little bit.  Right? So you can think about it just like that.   142 00:15:32,300 --> 00:15:37,900 And here it came back down. That's why I like  this analogy because it really gives you intuitive   143 00:15:37,900 --> 00:15:43,665 feeling for what's happening here. There's a  process. The process is pushing the bookcase over.   144 00:15:44,616 --> 00:15:51,183 That bookcase has some energy associated  with it. Here and here. Potential energy.   145 00:15:51,183 --> 00:15:56,383 And it's got some energy I gotta put into  it to activate it to go from here to here.   146 00:15:57,500 --> 00:16:03,816 Right? That's why that's called the activation  energy. That's what this Ea means for the general   147 00:16:03,816 --> 00:16:09,583 Arrhenius equation. You're pushing the bookcase  over. Yeah but how are you going to push it over?   148 00:16:10,133 --> 00:16:13,266 Well clearly you're going to run  around the room and accidentally   149 00:16:13,266 --> 00:16:18,066 knock into it because that's temperature.  Maybe that's not a good-- But if you had a   150 00:16:18,066 --> 00:16:22,783 lot of people running around a bookcase maybe  once in a while they'd kind of bang into it.   151 00:16:23,416 --> 00:16:29,900 Thermal energy. Right? And then maybe another  time, you increase how fast everyone's running,   152 00:16:31,333 --> 00:16:37,816 and you give them more energy. So now not only  are they hitting it more frequently but they're   153 00:16:37,816 --> 00:16:42,866 they're actually hitting it with more energy.  They're able to give it more energy. Now you make   154 00:16:42,866 --> 00:16:48,300 everyone run really fast. And the chances that  this thing goes through that process are higher.   155 00:16:50,066 --> 00:16:55,983 That's what that is. That's a probability,  right? This is what this exponential is. That   156 00:16:55,983 --> 00:17:02,783 was the brilliance of what he did right.  So this thermal energy is like, you know,   157 00:17:02,783 --> 00:17:08,616 it's how much-- It's like a probability but that's  why it goes into an exponential. Because when you   158 00:17:08,616 --> 00:17:14,066 increase temperature, again it's not just that  you're increasing how much energy over here,   159 00:17:15,183 --> 00:17:19,099 Right? How this is get like kinetic energy of  some molecules. Maybe how much energy those   160 00:17:19,099 --> 00:17:26,616 molecules have but you're increasing how many of  them are above some threshold. So your chances   161 00:17:28,133 --> 00:17:32,933 go exponentially higher. Well you think if  it was harder and harder to push. But this   162 00:17:32,933 --> 00:17:38,533 is going to go the other way too. You could have  sometimes somebody might knock it the other way.   163 00:17:38,533 --> 00:17:43,333 It looks kind of hard from this picture.  But there's a chance. It's just that   164 00:17:43,333 --> 00:17:48,933 the activation energy going this way, right?  Going this way, the activation energy is here.   165 00:17:49,816 --> 00:17:57,100 'Ea' and going this way the activation  energy would be here. So this would be 'Ea'   166 00:17:58,133 --> 00:18:10,616 for, let's see, three to one. And this  would be 'Ea' for one to three. Now again,   167 00:18:11,583 --> 00:18:17,266 I am giving you the general Arrhenius. We will  be coming back to this when we do reaction rates.   168 00:18:18,300 --> 00:18:22,383 We will be coming back to this picture, and we  will be talking about reactions, and then we'll   169 00:18:22,383 --> 00:18:27,416 be using that, and going to equilibrium. Today,  I want to give you a sense for what Arrhenius is   170 00:18:27,416 --> 00:18:35,900 because this is where the equation comes from. And  because if you think about now defect formation.   171 00:18:37,416 --> 00:18:44,866 Defect formation is an activated-- it's a  thermally activated process. But that's exactly   172 00:18:44,866 --> 00:18:52,300 the point. So that's why if we write this down--  I've said this now multiple times the vacancy... 173 00:18:54,700 --> 00:19:03,100 'vacany'. No. Vacancy is  always present. Always present! 174 00:19:05,900 --> 00:19:14,383 Why? Because it's thermally activated. So unless  I can get to T equals zero-- thermally activated. 175 00:19:16,866 --> 00:19:21,100 There's always a chance that I  push a vacancy into the material.   176 00:19:21,816 --> 00:19:24,533 There's also always a chance  that the vacancy gets pushed out.   177 00:19:25,666 --> 00:19:31,100 So those are happening because of temperature.  You can think about that. It kind of makes sense,   178 00:19:31,100 --> 00:19:35,500 right? Atoms are moving. Those are the people--  right-- there's the people in the room.   179 00:19:36,783 --> 00:19:43,816 And now all of a sudden, something happens  somewhere that allows an atom to come out.   180 00:19:44,383 --> 00:19:50,300 We'll talk about that in a second. And create  a vacancy. Now there's a chance that it can go   181 00:19:50,300 --> 00:19:56,133 back too, right? And so there's at some point  there's an equilibrium concentration. Both of   182 00:19:56,133 --> 00:20:02,933 those are thermally activated processes that have  an Arrhenius like behavior. And so you get to... 183 00:20:05,583 --> 00:20:17,100 the very nice expression for concentration.  So you can get-- can get? Yeah,   184 00:20:17,100 --> 00:20:24,783 why not-- get concentration. So  the concentration at equilibrium. 185 00:20:27,183 --> 00:20:32,700 Since vacancy formation is thermally activated  and it's thermally deactivated. There's some--   186 00:20:32,700 --> 00:20:37,016 you know, you can say well when it's activated  and deactivated in the same rates you're in   187 00:20:37,016 --> 00:20:42,066 equilibrium. That's how you get a concentration.  And I don't need you to know the math   188 00:20:42,066 --> 00:20:48,216 but I need-- This is where it comes from. The  number of vacancies divided by the total number   189 00:20:48,216 --> 00:20:57,333 of sites is equal to e to the minus E vacancy--  I will talk about this-- vacancy divided by,   190 00:20:59,583 --> 00:21:05,333 let's use RT still. RT. Now here's the thing  about RT. Let's write this down because this   191 00:21:05,333 --> 00:21:13,183 is really important, right? If-- we talked about  this before-- if I'm using RT then it's per mole. 192 00:21:15,816 --> 00:21:21,666 Per mole use RT. This is the ideal  gas constant, right? That's not just   193 00:21:21,666 --> 00:21:25,500 used for ideal gases. This is used for a  lot of things. That's the gas constant. 194 00:21:27,816 --> 00:21:36,700 Gas constant. That's equal to-- let's see if i  have down here-- 8.314 joules per mole Kelvin.   195 00:21:38,133 --> 00:21:45,500 So you see if I'm working in per mole, then I use  R. This is-- the energy unit the-- those energy   196 00:21:45,500 --> 00:21:53,733 units have to be the same. They got to cancel. So  if my activation energy is in per mole, fine, use   197 00:21:53,733 --> 00:22:01,416 the gas constant. If the activation energy is in  per atom then we just use the Boltzmann constant:   198 00:22:02,933 --> 00:22:09,666 kBT. Where the Boltzmann constant  is something we have seen,   199 00:22:09,666 --> 00:22:18,066 it is equal to the ideal gas constant divided by  Avogadro's number. Remember that Avogadro's number   200 00:22:18,066 --> 00:22:29,733 goes in and out atomic macroscopic worlds  so R and kB same thing. Okay. One thing--   201 00:22:29,733 --> 00:22:36,700 notice that's per Kelvin. Whenever you have  equations like this that come from thermodynamics,   202 00:22:36,700 --> 00:22:42,133 which is where these things come from.  There is only one temperature unit. There   203 00:22:42,133 --> 00:22:48,133 is no other. And it is Kelvin. You have to be  aware of that. If you see something in Celsius,   204 00:22:48,133 --> 00:22:54,700 it's not going to work. It's got to be Kelvin.  All of these equations have to use Kelvin. Okay.   205 00:22:56,066 --> 00:23:00,466 So that now-- you can see at any  time, you know, any time you see 206 00:23:04,066 --> 00:23:08,066 an equation with an exponential.  What's the first thing you want to do?   207 00:23:09,666 --> 00:23:14,933 I mean it's like an-- it's almost like an  instinctual reaction. You see an exponential. Take   208 00:23:14,933 --> 00:23:20,866 a log. Don't say anything until you take a log.  Right? So that's an-- so that-- so we're talking   209 00:23:20,866 --> 00:23:26,383 about energy of the vacancy in a minute. But if  you take a log of this. Then you get that the log   210 00:23:27,733 --> 00:23:36,066 of what '|n(Nv)'. Well I'll talk  about that. Equals log of N.   211 00:23:37,733 --> 00:23:44,133 Let's do it this way. Minus  log of n equals E vacancy. 212 00:23:47,016 --> 00:23:55,100 Okay. Divided by RT. That's just taking an  exponential, a logarithm of this equation. And   213 00:23:55,100 --> 00:24:01,416 now I can talk about these Nv and N. So Nv is--  this is literally a concentration. This is the   214 00:24:01,416 --> 00:24:07,333 concentration of vacancies that are forming in my  crystal. Why did i get this expression and notice   215 00:24:07,333 --> 00:24:12,383 the constant cancelled. This pre-exponential  factor cancelled. It canceled because   216 00:24:12,383 --> 00:24:16,300 I'm taking a concentration. I'm looking at the  rate going one way and the rate going the other.   217 00:24:17,183 --> 00:24:23,583 And I get to take a ratio of those. That leads  me to this expression. That's how you get from   218 00:24:23,583 --> 00:24:32,300 Arrhenius rates to some concentration. Okay. But  you still-- but notice it's still-- we call this   219 00:24:32,300 --> 00:24:38,133 Arrhenius-like because it's still an exponential  dependence. It's not a rate, it's a concentration.   220 00:24:38,133 --> 00:24:43,016 It's okay. It's a concentration in equilibrium.  So this would be like the number of vacancies,   221 00:24:44,383 --> 00:24:51,500 number of vacancies. And this one here  'n' would be like the number of sites,   222 00:24:51,500 --> 00:24:56,533 number of lattice sites. So it's like you  know concentration. Lattice sites. Right? 223 00:24:58,933 --> 00:25:07,733 And what is this? This is exactly here, here we  go. I have my crystal. Okay. Here's my crystal and   224 00:25:08,616 --> 00:25:11,900 here it is... I think I'll  stop here. And now I did this.   225 00:25:12,933 --> 00:25:17,183 We're going to go graphical and this and this. 226 00:25:20,066 --> 00:25:28,300 That energy is literally the energy difference.  It's literally the energy difference between   227 00:25:28,300 --> 00:25:31,983 having a vacancy and not having  a vacancy. How much energy--   228 00:25:32,700 --> 00:25:36,200 Question? [STUDENT:] Isn't there supposed to  be a negative sign in front of the E vacancy? 229 00:25:36,200 --> 00:25:40,383 [PROFESSOR:] Yes there is. Oh yes there  is. Yes there is. Thank you very much.   230 00:25:41,016 --> 00:25:49,183 Yes. So that's-- Okay. So now the energy  difference between having a vacancy and not,   231 00:25:49,183 --> 00:25:58,066 is the vacancy formation energy. E vacancy. Now  sometimes, and this is unfortunate, but sometimes   232 00:25:58,700 --> 00:26:05,900 you will see the vacancy formation energy written  as the activation energy. That's fine. I mean it   233 00:26:05,900 --> 00:26:11,333 just it's written that way to get across the  point that it's an Arrhenius-like behavior.   234 00:26:12,616 --> 00:26:15,183 But actually the act-- but  if you're clear about it.   235 00:26:16,133 --> 00:26:22,933 And that's why I want to go through the bookcase  example, right? The formation energy which is this   236 00:26:22,933 --> 00:26:28,933 energy of the vacancy forming is the difference  between here and here. The activation energy   237 00:26:29,500 --> 00:26:36,383 is this hill that you got to get over to go back  and forth. Okay? So the formation energy between   238 00:26:36,383 --> 00:26:42,933 having a vacancy and not is what goes into our our  equation. Alright. Now we're going to use this.   239 00:26:42,933 --> 00:26:49,333 So we will see how this works in just a few  minutes. But again there are so many processes   240 00:26:49,980 --> 00:26:56,616 that are thermally activated. There are so many  processes that have Arrhenius-like behavior.   241 00:26:57,183 --> 00:27:02,300 That are Arrhenius-like. And if you go to  Dartmouth then they'll give you goodie bags   242 00:27:02,300 --> 00:27:07,266 with live crickets. And actually I really  hope not. But this is one of the labs that   243 00:27:07,266 --> 00:27:12,383 they have where they take crickets and they  measure the number of times a cricket chirps.   244 00:27:13,183 --> 00:27:18,866 And they're like, well okay. Let's measure the  cricket chirp over 13 seconds. We're gonna cool   245 00:27:18,866 --> 00:27:23,733 them down, hopefully not too cold, and then we're  going to heat them up, hopefully not too hot.   246 00:27:25,100 --> 00:27:30,133 Because crickets are nice, right? And so  then-- and they ca-- but look at that. And   247 00:27:30,133 --> 00:27:35,500 they count it. And then what do they do? Well they  didn't know about Arrhenius yet until somebody   248 00:27:35,500 --> 00:27:41,333 from MIT went and visited. So the first thing  they did is they plotted the data. Look at that.   249 00:27:41,333 --> 00:27:46,866 Chirps per 13 seconds plotted. And they're all  sitting there trying to fit a straight line to   250 00:27:46,866 --> 00:27:51,733 it. And then someone from this class is up  there visiting. They're like, you know what   251 00:27:51,733 --> 00:27:56,383 i think, this looks like a thermally activated  process. So i think it's probably exponential.   252 00:27:57,183 --> 00:28:02,783 And then they fit this nice exponential and  it fits the the cricket tripping beautifully.   253 00:28:03,816 --> 00:28:12,466 And you can go even further because you see  if you got this far. Well now you see this   254 00:28:12,466 --> 00:28:17,416 is a line. This is a line and we're going to do  that a lot when we go into reaction kinetics.   255 00:28:18,383 --> 00:28:25,266 If you have a exponential and you take a log,  that's a line versus 1 over T. Right? That's a   256 00:28:25,266 --> 00:28:30,066 line versus 1 over T. And so that's another way  you could look at data. They didn't do it there.   257 00:28:30,700 --> 00:28:41,500 But, you know, you could plot for example--  you could plot 1 over T versus the log of   258 00:28:42,216 --> 00:28:50,300 the number of vacancies. But the lattice-- the  number of vacancies is what we want. That ratio   259 00:28:50,300 --> 00:28:54,466 is the concentration. That concentration  is in equilibrium at some temperature.   260 00:28:55,183 --> 00:29:00,866 Okay. The lattice-- the number of lattice sites  is simply how many lattice sites you have,   261 00:29:00,866 --> 00:29:05,666 in whatever volume you have, for whatever crystal  structure you have, for whatever element you have.   262 00:29:06,216 --> 00:29:10,700 We'll see that in a few examples. So that's just  a concert-- it's the number of sites you have in   263 00:29:10,700 --> 00:29:15,333 the chunk of material. And then instead of-- The  question this equation tells you the answer to,   264 00:29:15,333 --> 00:29:20,216 is how many of those have a vacancy?  Because it's a thermally activated process.   265 00:29:21,183 --> 00:29:28,383 And if you plot that log in Nv versus  temperature you get this really nice   266 00:29:28,383 --> 00:29:36,866 linear line. And the slope of that  line is equal to minus E vacancy 267 00:29:39,183 --> 00:29:47,016 divided by R or it could be kB. R.  Let's write this again per mole. 268 00:29:50,533 --> 00:29:56,216 Or it could be kB if it's  per atom. You will see both.   269 00:29:56,933 --> 00:30:02,066 You will see both. And this  intercept-- intercept-- 270 00:30:05,183 --> 00:30:11,583 is equal to the-- let's see-- the intercept  is equal-- what do i have here? The   271 00:30:12,533 --> 00:30:15,900 log of n. Did i write it right? Log of n. 272 00:30:20,066 --> 00:30:22,066 Okay. Alright. 273 00:30:24,783 --> 00:30:30,133 Now, okay. Oh yeah. What else can you  do? Well before we go on to the defects,   274 00:30:30,133 --> 00:30:35,900 this explains the doping. I kept calling  the doping in semiconductors a thermally   275 00:30:35,900 --> 00:30:43,500 activated process. But look at what happens.  This is the carrier concentration in that   276 00:30:43,500 --> 00:30:46,300 conduction band. The thing you've  been you've been learning about,   277 00:30:46,300 --> 00:30:51,100 right? And thinking about. But look at it  now versus temperature. It's a straight line.   278 00:30:52,300 --> 00:30:55,983 It's a straight line. This is-- this  is experimentally what you observe.   279 00:30:56,933 --> 00:31:01,016 And the reason is because it's a thermally  activated process. And in fact, in this case,   280 00:31:02,066 --> 00:31:08,133 what is the activation energy? Right? The  activation energy for getting an electron into   281 00:31:08,133 --> 00:31:15,983 the conduction band is the gap. Right? And so now  you say germanium has a smaller gap than silicon,   282 00:31:15,983 --> 00:31:22,300 which has a smaller gap than gallium arsenide.  The slopes are different. The slopes are different   283 00:31:23,266 --> 00:31:29,666 because the energy that it takes in that activated  process is the gap. That's why the slopes are   284 00:31:29,666 --> 00:31:36,216 different. Right? Okay. Alright. Now on to--  oh no i didn't-- I did want to mention this   285 00:31:36,216 --> 00:31:43,900 because it's so cool. Where are these vacancies  going? Did you actually just take an atom from   286 00:31:43,900 --> 00:31:49,016 the middle of a crystal and remove it? No.  Because that would cost way too much energy,   287 00:31:49,583 --> 00:31:53,900 right? And so instead they have  to-- you call out to the surface.   288 00:31:54,700 --> 00:31:58,933 It's a call out to the surface. Or,  you know, maybe the surface calls in.   289 00:31:58,933 --> 00:32:03,816 It all has to happen on the surface. So what  ends up happening is a surface atom may go away   290 00:32:05,266 --> 00:32:10,616 and then another one may take its place, right?  And then the next one, and then the next one,   291 00:32:10,616 --> 00:32:14,066 and that's literally how you can rip  an atom out from somewhere inside.   292 00:32:15,416 --> 00:32:21,583 But by the same-- that's literally pushing the  bookcase over. Right? And now you can push it   293 00:32:21,583 --> 00:32:29,333 the other way and the surface atom could go  in to the crystal so that some atom inside is   294 00:32:29,333 --> 00:32:33,583 able to fill a vacancy. It all comes to  the surface. This is a beautiful paper,   295 00:32:34,383 --> 00:32:40,300 where they're showing how you get these rings.  This was published almost 20 years ago now. But   296 00:32:40,300 --> 00:32:46,866 how-- they're studying how do vacancies actually  pull atoms from the surface specifically.   297 00:32:46,866 --> 00:32:51,983 And what they did is they change the temperature  and they see islands growing and shrinking. Where   298 00:32:51,983 --> 00:32:57,983 are those islands going and where are they coming  from? Vacancies. It's all about the vacancies,   299 00:32:57,983 --> 00:33:01,900 right? And one of the things I loved about  this, is this is the abstract of this paper.   300 00:33:01,900 --> 00:33:08,616 Look at this. Here we show the vacancy generation  and annihilation, right? Both ways on the 1-1-0   301 00:33:08,616 --> 00:33:14,466 surface of an ordered nickel aluminum  inter-metallic alloy. Oh, I love reading   302 00:33:14,466 --> 00:33:19,333 that because you guys all are experts in this  now. You know what that means. You know what that   303 00:33:19,333 --> 00:33:25,583 means. Where do vacancies come from? Okay. And  now we got to make vacancies. Right? And so this   304 00:33:25,583 --> 00:33:30,066 is the kind of problem you might get. How many  vacancies are in a centimeter cubed of copper?   305 00:33:31,100 --> 00:33:35,733 How many vacancies are in a centimeter cubed  of copper? Well, now you know how to do it.   306 00:33:35,733 --> 00:33:43,583 You're just going to apply this Arrhenius-like  behavior. You're going to apply this equation to   307 00:33:45,016 --> 00:33:48,616 figure that out. And i won't go through  all the math but i do want to just   308 00:33:48,616 --> 00:33:52,466 give you a sense of the types of questions  that you can now answer; that you know 309 00:33:55,016 --> 00:34:00,866 how to think about vacancy formation.  So for example, in this one you've got   310 00:34:01,983 --> 00:34:06,533 step one. Step one: you would find N. 311 00:34:09,333 --> 00:34:15,333 Step one: you'd find N. How many sites do I  have? Because remember this equation is about   312 00:34:15,333 --> 00:34:20,300 a concentration between the number of vacancies  and the number of available sites for vacancies.   313 00:34:20,300 --> 00:34:31,900 And so step one-- well-- so step one you'd say N  equals Avogadro's number times 8.4 grams per mole.   314 00:34:32,783 --> 00:34:38,616 Right? Divided by all this-- is such old-school  stuff right now, right? Grams per mole. Then you   315 00:34:38,616 --> 00:34:50,466 look that up in the periodic table and it's 8  times 10 to the 22nd sites per centimeter cubed. 316 00:34:53,815 --> 00:34:57,733 Why am I using centimeter cubed? Well because  that's what i was given the density in. So I'm   317 00:34:57,733 --> 00:35:05,016 just leaving it in those units for now.  Right? And then step two you can find Nv.   318 00:35:06,216 --> 00:35:16,933 So now we can apply our our equation.  Nv equals N, I won't repeat it, times   319 00:35:16,933 --> 00:35:30,066 e. Now I've got my kB instead of R. So it's 9.9  electron volts divided by and then this is kBT.   320 00:35:30,783 --> 00:35:37,100 Now I get-- so I'm given that it's a thousand--  wait a second. What's the term, oh a thousand   321 00:35:37,100 --> 00:35:46,933 degrees. So do I put T equals a thousand. No!  No! You never use-- you only use Kelvin. 1273,   322 00:35:47,733 --> 00:35:50,933 right? T is always in Kelvin  for any of these thermodynamic   323 00:35:51,983 --> 00:35:59,900 equations. And I won't go through the math but  it goes something like 2.2 times 10 to the 19th 324 00:36:02,216 --> 00:36:08,466 vacancies. I'll write the units here just for  completeness. Vacancies per centimeter cubed.   325 00:36:10,383 --> 00:36:14,066 Now that seems like a lot but it's actually  not. You say it's like one in a thousand or   326 00:36:14,066 --> 00:36:19,733 one in ten thousand atoms are missing and I'm at  a really high temperature. If I were at-- then   327 00:36:19,733 --> 00:36:25,816 this is the power of what Arrhenius gave us.  If-- Because it's exponential. It's all about   328 00:36:25,816 --> 00:36:31,666 probabilities and sampling and how many times  did i bump into that bookcase. If I'm down at   329 00:36:31,666 --> 00:36:38,066 room temperature I've got so much less energy,  and so many more chances-- so many fewer chances   330 00:36:38,066 --> 00:36:43,983 to deliver that energy. Right? Where the surface  is taking atoms in and out to create vacancies.   331 00:36:43,983 --> 00:36:50,866 That at room temperature the number of vacancies  is 10 to the seventh instead of 10 to the 19th.   332 00:36:51,733 --> 00:36:56,466 Right? So that's the power of that exponential.  That's the power of the exponential. You might   333 00:36:56,466 --> 00:37:01,416 also be asked questions like this one. Right? So  --oh no like-- let me do this one. Then I'll talk   334 00:37:01,416 --> 00:37:06,383 about your goodie bag. Where instead of now--  Okay. What-- Example two. What is the vacancy   335 00:37:06,383 --> 00:37:12,383 formation energy in aluminum? And now notice,  instead of giving you the vacancy formation energy   336 00:37:12,933 --> 00:37:18,616 per atom, I'm giving you other stuff. I'm  actually giving you how many vacancies you got,   337 00:37:19,983 --> 00:37:26,133 at some temperature. Well that's-- This just going  in a different direction but it's using the same   338 00:37:26,133 --> 00:37:33,500 math. So you can go in different ways, arrive at  the same kinds of equations, and get all of these   339 00:37:33,500 --> 00:37:42,783 things, and I won't go through the details.  But in this case you get that Ea equals minus   340 00:37:43,416 --> 00:37:50,533 kBT. I'm using kB because look at that...  the formation energy I'm asking is what is   341 00:37:50,533 --> 00:37:55,500 the vacancy formation energy-- Okay, well actually  look at that. No, I just want to do it per atom.   342 00:37:56,383 --> 00:38:05,183 It didn't say per atom but if I wanted to do a per  atom, I'd use kBT times log Nv over N. And so you   343 00:38:05,183 --> 00:38:19,016 see 0.75 eV per atom. Now what's interesting,  copper was-- copper was 0.9, aluminum .75.   344 00:38:20,866 --> 00:38:27,700 You're going to have a lot more vacancies  because it's exponential. This seems like-- 0.9,   345 00:38:27,700 --> 00:38:34,216 .75 is kind of the same. No. It's going into an  exponential, so it has a really big difference   346 00:38:34,216 --> 00:38:38,466 on how many vacancies you have at any given  temperature. Aluminum is going to have a lot   347 00:38:38,466 --> 00:38:46,783 more because it's easier to get them in there.  Right? Notice I did the thing that I said other   348 00:38:46,783 --> 00:38:52,616 people do and I don't really like. That's the  energy of the vacancy. The vacancy formation. 349 00:38:56,866 --> 00:39:00,066 People call it activation  energy all over the place.   350 00:39:00,783 --> 00:39:03,900 Okay. Now this is your goodie bag.  Now why am I giving to you? Because   351 00:39:05,183 --> 00:39:11,416 first of all, this is the most sophisticated  vacancy generation machine you'll ever find.   352 00:39:11,983 --> 00:39:18,466 There are exactly 500 beads in this. Exactly.  There are not 501. There are not 499. And you know   353 00:39:18,466 --> 00:39:25,816 why? Because Laura has spent 7,000 hours counting  beads in every single one of these. So you have   354 00:39:25,816 --> 00:39:32,783 exactly the right number. Then there's precision  tape and polycarbonate films maybe. And what you   355 00:39:32,783 --> 00:39:38,216 guys can do is build your own crystal. It's a 2d  crystal. Here's what's so cool about this. Try to   356 00:39:38,216 --> 00:39:45,300 get those vacancies out. Look at this! Dude-- None  of you can see what I'm talking about. [LAUGHTER] 357 00:39:45,816 --> 00:39:51,266 There's a big vacancy there, I've literally  made this right in front of me. This is here.   358 00:39:53,333 --> 00:39:56,066 And now I'm gonna say--  okay, I'll use temperature. 359 00:40:00,216 --> 00:40:07,583 There's so many more. There's so many more because  I use temperature. This is temperature. You are   360 00:40:07,583 --> 00:40:13,666 temperature. And you can run around, and you can  shake it, and all you bring it to the dance floor,   361 00:40:13,666 --> 00:40:19,816 and on. Then you're like how can I get-- Whoa,  wait a second. I'll just quietly go down in   362 00:40:19,816 --> 00:40:25,266 temperature and I'll get rid of them. Yeah,  tell that to your friends down the street. See   363 00:40:25,266 --> 00:40:30,133 how long they go until they stop trying because  you guys know not to try because you'll never get   364 00:40:30,133 --> 00:40:36,300 rid of them. You'll never get rid of them. You'll  always have vacancies and this is proof that you   365 00:40:36,300 --> 00:40:42,300 will always have vacancies. You can try to tap it  like that. See if you can get rid of the defects.   366 00:40:42,300 --> 00:40:46,866 You can't. Luckily that's a good thing because  defects are what make everything interesting.   367 00:40:47,733 --> 00:40:54,066 Everything. This is your goodie bag. So you  can touch and feel-- Oh, but we got to cover   368 00:40:54,066 --> 00:41:01,583 the other case. Because-- See I could have had  not just a metal, where every atom is the same,   369 00:41:02,466 --> 00:41:06,933 but i could have had an ionic solid. You can  make point defects in ionic solids as well.   370 00:41:07,816 --> 00:41:15,500 Right? So yeah. So if I had a defect in an ionic  solid-- well now you got to consider the charge.   371 00:41:15,500 --> 00:41:18,933 I can't just keep pulling-- If this is sodium  chloride, I can't just keep pulling out   372 00:41:19,583 --> 00:41:25,583 like one type of atom. If I take a sodium  atom out. Like imagine that's a plus,   373 00:41:25,583 --> 00:41:32,133 minus, plus, minus. Right? The size-- if I take a  sodium atom out then it becomes charged. Because   374 00:41:32,133 --> 00:41:37,500 remember the ionic bond is one of them, grabbed  it and it has it. And so if I take one out,   375 00:41:37,500 --> 00:41:43,416 I've charged the crystal. You can't do that. It  won't let you. So if I take a sodium atom out,   376 00:41:43,416 --> 00:41:48,066 a chlorine is going to come too. It's got to  come too. You got to keep it charged neutral,   377 00:41:48,783 --> 00:41:53,900 if it starts charging neutral. So these  have special names because of that.   378 00:41:55,016 --> 00:42:02,216 And there are two types of defects in ionic  point defects. We're still with point defects.   379 00:42:02,216 --> 00:42:10,300 Local disruption in the regularity. One is called  the shocky defect, right? So in the shocky defect 380 00:42:12,383 --> 00:42:25,900 you got both an anion and a cation are removed.  Cation. Now here's the thing- I should have put   381 00:42:25,900 --> 00:42:32,866 's' because you may need to take  more than one out. Alright? Removed--   382 00:42:34,466 --> 00:42:35,983 and because you got to ensure-- 383 00:42:38,616 --> 00:42:49,733 ensure charge neutrality. Charge neutrality. So  like you know-- If I had so inquiry that's fine.   384 00:42:49,733 --> 00:42:54,616 But what if I had you know something else.  What if I had instead of sodium chloride.   385 00:42:54,616 --> 00:43:00,700 What if I had like calcium chloride. So now what  if I had calcium chloride. Well that looks like   386 00:43:00,700 --> 00:43:07,666 that. Because calcium goes to two plus. We  know this. Right? But chlorine is only minus   387 00:43:07,666 --> 00:43:15,733 one so that ionic crystal is different. And  what it means is that if I remove-- if I remove 388 00:43:18,466 --> 00:43:22,783 a calcium it's going to come out  as Ca2 plus but that means i need 389 00:43:25,416 --> 00:43:30,466 to remove two Cl minus atoms. 390 00:43:32,783 --> 00:43:36,700 That's the thing about shocking defects. You  got to keep the charge balanced. So now you--   391 00:43:36,700 --> 00:43:43,016 It's not just a one for one. This could actually  be a way to take atoms out. Or if I want to take   392 00:43:43,816 --> 00:43:46,300 chlorine out of this, we'll take some calcium out.   393 00:43:46,933 --> 00:43:50,300 Chlorine will come out too. Right?  Could be a way to engineer it. 394 00:43:52,383 --> 00:43:55,583 So that's a that's a shocking defect. But  the simpler thing that could have happened   395 00:43:56,300 --> 00:44:01,900 is just that one of these atoms kind of moved  over. So now I didn't remove it from the crystal   396 00:44:03,333 --> 00:44:11,100 but it just kind of wandered over into some site.  So like you know... here's BCC. I can have like   397 00:44:11,100 --> 00:44:17,983 an atom-- so this doesn't look like an ionic solid  but suppose-- it doesn't matter. I could have an   398 00:44:17,983 --> 00:44:24,066 atom leave a site and go-- Notice that there  are these voids, right? They're these spaces in   399 00:44:24,066 --> 00:44:32,066 between other atoms. Well those spaces are places  where atoms can go. They're not-- It's not part   400 00:44:32,066 --> 00:44:38,133 of the regular lattice but it's just-- it's like  a hole, right? Remember the packing fractions.   401 00:44:38,783 --> 00:44:43,983 We never got above about three quarters. We  never got about three-- that means there's   402 00:44:43,983 --> 00:44:49,583 still a bunch of volume in there that's free  volume. Right? Where is it? Well this kind of   403 00:44:49,583 --> 00:44:57,183 defect will find it. Right? So you could have  the smaller ion migrate over, create a vacancy,   404 00:44:58,216 --> 00:45:06,616 and it's going to find a place where it likes  to go. Ah. Okay. Yeah, we'll do this. And so-- 405 00:45:09,500 --> 00:45:11,583 so that's called a Frenkel defect. 406 00:45:15,333 --> 00:45:23,266 So Frenkel defect is the other kind of special  name we give to a vacancy in an ionic solid, and   407 00:45:24,133 --> 00:45:34,133 it's where one ion-- right-- anion  or cation. Anion or cation. Moves 408 00:45:37,733 --> 00:45:49,183 to some open space. Open space in the lattice.  And you can already kind of feel where this   409 00:45:49,183 --> 00:45:56,133 might be kind of common. It might be common in  situations where you've got a big size difference,   410 00:45:56,700 --> 00:46:03,266 right? So like the silver halides are a  good example. Like silver chloride, silver   411 00:46:04,466 --> 00:46:10,383 bromide, silver iodide. Those  are all good examples because   412 00:46:11,266 --> 00:46:16,700 what happens there is this ionic structure has  a very big mismatch between the atom sizes.   413 00:46:17,816 --> 00:46:23,333 And so you can see. Let's blow up a picture of  this is silver iodide, a cartoon. Look at that.   414 00:46:23,333 --> 00:46:27,583 So those are the silver atoms and what you see  is because there's such a big difference in size,   415 00:46:27,583 --> 00:46:31,900 you're going to have these pretty big voids.  And one of the atoms is small enough that it   416 00:46:31,900 --> 00:46:38,616 actually doesn't mind-- it's actually pretty  easy to move it. Ah now, if you think about it.   417 00:46:39,983 --> 00:46:46,300 Well if you have enough vacancies in there, then  maybe those ions can actually move really freely.   418 00:46:46,933 --> 00:46:51,733 Because they're so small and the voids  are all kind of nearby. And you actually   419 00:46:51,733 --> 00:46:57,733 can get a conductor, a good conductor, this  way. You're creating vacancies on purpose   420 00:46:58,383 --> 00:47:03,666 so that one of the ions can move around. The  smaller one, right? That's what we do. We make   421 00:47:03,666 --> 00:47:10,466 these solid-state ionic conductors. You need  the vacancies. You need the vacancies. Okay.   422 00:47:10,466 --> 00:47:20,133 Now, I told you that we got this map here. We've  talked about literally just one. Luckily I don't   423 00:47:20,133 --> 00:47:25,983 have nearly the same amount of material to talk  about these others. The vacancy is clearly the one   424 00:47:25,983 --> 00:47:32,133 that I'm very interested in. The substi-- the  self-interstitial is actually pretty easy to   425 00:47:32,133 --> 00:47:36,383 understand. The self-interstitial is actually  pretty easy to understand because it simply   426 00:47:36,383 --> 00:47:43,816 doesn't really happen much. And the reason is, if  you look at this. Here's a picture of is basically   427 00:47:43,816 --> 00:47:49,100 what i drew on the board, right? But now I've  put-- so these are-- this is not a vacancy,   428 00:47:50,300 --> 00:47:55,733 right? This is a kind of point defect but it's  not a vacancy. I've actually added an atom into   429 00:47:55,733 --> 00:48:01,416 the lattice and I've squeezed it in between all  the others. You can just feel how much energy,   430 00:48:01,416 --> 00:48:05,583 how much strain, those other atoms are gonna  have to make and how much energy that's going   431 00:48:05,583 --> 00:48:12,216 to cost. Those are high energy defect. So  a self-interstitial-- a self-interstitial--   432 00:48:12,216 --> 00:48:19,416 self just means it's the same atom as the rest of  them, is very infrequent. Is very infrequent. The   433 00:48:19,416 --> 00:48:28,216 self-interstitial-- let's see-- I'll just use this  one again. The self-interstitial has an energy of   434 00:48:28,216 --> 00:48:36,066 formation of something like you know five electron  volts. And you think but-- five electron volts. 435 00:48:38,300 --> 00:48:43,100 Self-interstitial. Self-interstitial. 436 00:48:45,500 --> 00:48:48,783 It went in between, so it's not substitutional   437 00:48:48,783 --> 00:48:55,900 it's interstitial and itself because it's the  same atom type. The energy energy of formation 438 00:48:59,583 --> 00:49:06,533 is 5ev. I think 5ev doesn't even sound that much  higher than like the one ev you had for copper,   439 00:49:06,533 --> 00:49:15,016 right? 0.9 ev. But it goes into the exponential,  right? So it's like one per centimeter cubed.   440 00:49:15,016 --> 00:49:20,933 Literally. You get like one of these happening  per centimeter cubed instead of 10 to the 20th,   441 00:49:20,933 --> 00:49:26,383 or 10 to the 10th, or you know many many orders  of magnitude higher. So the self-interstitial is   442 00:49:26,383 --> 00:49:32,383 actually not very interesting. It's actually  not very interesting. Now because we have   443 00:49:32,383 --> 00:49:36,783 like half a minute left, I'm not gonna  talk about these. We'll have a very brief   444 00:49:36,783 --> 00:49:40,216 discussion about these last two types of  point defects and then we're gonna make   445 00:49:40,216 --> 00:49:47,066 line defects on Wednesday. And my why this  matters, I'll give you on Wednesday for this.