WEBVTT 00:00:00.000 --> 00:00:03.056 The following content is provided under a Creative 00:00:03.056 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:07.229 Your support will help MIT OpenCourseWare continue to 00:00:07.229 --> 00:00:10.684 offer high-quality educational resources for free. 00:00:10.684 --> 00:00:13.550 To make a donation or view additional materials from 00:00:13.550 --> 00:00:17.480 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:17.480 --> 00:00:18.730 ocw.mit.edu. 00:00:21.625 --> 00:00:24.290 PROFESSOR: I know I'm not Dr. Sadoway. 00:00:24.290 --> 00:00:27.920 I'm one of Dr. Sadoway's younger colleagues so-- 00:00:27.920 --> 00:00:31.270 but class is beginning, so let's get started. 00:00:31.270 --> 00:00:35.010 Dr. Sadoway, of course, would like you to know that he would 00:00:35.010 --> 00:00:38.850 very much love to be with you here today and he would 00:00:38.850 --> 00:00:41.490 probably like that very much more than what he's doing now, 00:00:41.490 --> 00:00:43.920 which is sitting in a secured area secured by the Secret 00:00:43.920 --> 00:00:46.670 Service about to meet the President. 00:00:46.670 --> 00:00:51.630 So you can ask him all about it when he comes back. 00:00:51.630 --> 00:00:55.410 Associated with that, I have one request for you. 00:00:55.410 --> 00:00:58.990 Today, when you're leaving, some of you may be used to 00:00:58.990 --> 00:01:00.480 leaving that way. 00:01:00.480 --> 00:01:01.950 Don't leave that way. 00:01:01.950 --> 00:01:03.250 Leave any other way. 00:01:03.250 --> 00:01:04.330 This way's fine. 00:01:04.330 --> 00:01:05.710 In the back is fine. 00:01:05.710 --> 00:01:07.320 Just don't leave that way. 00:01:07.320 --> 00:01:09.090 OK. 00:01:09.090 --> 00:01:14.800 So last time, we talked about x-rays 00:01:14.800 --> 00:01:17.370 defraction and Bragg's Law. 00:01:17.370 --> 00:01:20.700 And x-ray defraction and Bragg's Law has a lot to do 00:01:20.700 --> 00:01:22.360 with perfect crystals. 00:01:22.360 --> 00:01:24.120 So perfection, right? 00:01:24.120 --> 00:01:27.300 We've been dealing with perfect crystal so far and 00:01:27.300 --> 00:01:29.840 today, we're going to be dealing with imperfections. 00:01:29.840 --> 00:01:31.430 So defects. 00:01:31.430 --> 00:01:34.130 And in the field of material science, the field that I work 00:01:34.130 --> 00:01:36.130 in along with Dr. Sadoway. 00:01:36.130 --> 00:01:39.970 there's a saying due to one of the most famous material 00:01:39.970 --> 00:01:44.130 scientists that says that crystals are like people. 00:01:44.130 --> 00:01:46.500 It's the defects that make them interesting. 00:01:46.500 --> 00:01:49.450 So now you've heard that saying and you can roll your 00:01:49.450 --> 00:01:52.450 eyes from now on every time you hear it because it's 00:01:52.450 --> 00:01:54.660 repeated it very often. 00:01:54.660 --> 00:01:56.080 So let's see. 00:01:56.080 --> 00:01:58.040 What do we mean by defects? 00:01:58.040 --> 00:02:00.900 Well, there's two types of defects, broadly speaking, 00:02:00.900 --> 00:02:04.840 that we're going to be talking about, and we can classify 00:02:04.840 --> 00:02:07.010 those into two categories. 00:02:07.010 --> 00:02:08.260 One of them is chemical. 00:02:11.140 --> 00:02:12.750 So far, we've been dealing with 00:02:12.750 --> 00:02:14.200 chemically perfect materials. 00:02:14.200 --> 00:02:17.720 So ones that are made up of one element or ones that are 00:02:17.720 --> 00:02:22.220 made up in stoichiometric quantities of two elements, 00:02:22.220 --> 00:02:24.110 but you can also have chemical imperfections. 00:02:24.110 --> 00:02:25.640 You can have impurities. 00:02:25.640 --> 00:02:28.690 You can have alloying elements and we're also going to be 00:02:28.690 --> 00:02:30.395 talking about atomic arrangement. 00:02:40.900 --> 00:02:43.420 And in the case of atomic arrangement, we're dealing 00:02:43.420 --> 00:02:45.000 with structure, right? 00:02:45.000 --> 00:02:46.500 Here we're dealing with chemistry. 00:02:46.500 --> 00:02:48.250 Here we're dealing with structure. 00:02:48.250 --> 00:02:50.230 You know about crystal structure so you know what 00:02:50.230 --> 00:02:53.290 perfect crystals look like, but real materials are not 00:02:53.290 --> 00:02:57.410 perfect, neither in the chemical sense nor in the 00:02:57.410 --> 00:02:58.330 structural sense. 00:02:58.330 --> 00:03:02.360 So perfect crystals don't really exist. You have always 00:03:02.360 --> 00:03:05.540 some forms of imperfections and we'll go over those today. 00:03:05.540 --> 00:03:10.040 So in the case of chemical imperfections, we have, 00:03:10.040 --> 00:03:11.730 broadly speaking, two types. 00:03:11.730 --> 00:03:12.980 Good ones-- 00:03:14.560 --> 00:03:16.910 Dr. Sadoway labels them with a smiley face so I 00:03:16.910 --> 00:03:18.090 will do that, too. 00:03:18.090 --> 00:03:20.120 And bad ones are a sad face. 00:03:20.120 --> 00:03:23.890 So both are defects and whether they're good or bad 00:03:23.890 --> 00:03:26.080 depends on their utility. 00:03:26.080 --> 00:03:28.790 Are they useful or are they detrimental? 00:03:28.790 --> 00:03:30.620 If they are detrimental, we call them impurities. 00:03:37.810 --> 00:03:40.720 And if they are good, we call them other things. 00:03:40.720 --> 00:03:41.970 For example, dopants. 00:03:45.310 --> 00:03:46.540 We studied dopants, right? 00:03:46.540 --> 00:03:48.620 Dopants are a type of impurity, they're a kind of 00:03:48.620 --> 00:03:50.270 imperfection, but they're good. 00:03:50.270 --> 00:03:50.770 We use dopants. 00:03:50.770 --> 00:03:52.860 We use them in semiconductors. 00:03:52.860 --> 00:03:59.320 Also, alloying elements, you can put in 00:03:59.320 --> 00:04:01.520 the elements yourself. 00:04:01.520 --> 00:04:05.490 Those are examples of good chemical imperfections. 00:04:05.490 --> 00:04:08.670 When it comes to atomic arrangements, we're going to 00:04:08.670 --> 00:04:10.690 spend a little bit of time talking about that in more 00:04:10.690 --> 00:04:12.960 detail in just a minute. 00:04:12.960 --> 00:04:16.480 But broadly speaking, they are situations where you don't 00:04:16.480 --> 00:04:17.810 have perfect crystal in order. 00:04:17.810 --> 00:04:20.250 You have disruptions and that perfect crystal in order-- 00:04:20.250 --> 00:04:23.260 either in the form of missing atoms or extra atoms or 00:04:23.260 --> 00:04:25.420 differently oriented unit cells of the 00:04:25.420 --> 00:04:26.300 crystal and so forth. 00:04:26.300 --> 00:04:27.530 So we'll talk about that a little bit 00:04:27.530 --> 00:04:30.350 more in just a minute. 00:04:30.350 --> 00:04:35.615 So one thing that I forgot to mention maybe is that we have 00:04:35.615 --> 00:04:37.870 a test coming up-- 00:04:37.870 --> 00:04:38.220 That is, I'm sorry. 00:04:38.220 --> 00:04:39.580 Celebration of learning, second 00:04:39.580 --> 00:04:41.030 celebration of learning. 00:04:41.030 --> 00:04:42.930 And those are your room assignments. 00:04:42.930 --> 00:04:45.730 You don't have to necessarily write them down now, but 00:04:45.730 --> 00:04:46.580 you'll see them again. 00:04:46.580 --> 00:04:48.670 So I just wanted you to see them. 00:04:48.670 --> 00:04:56.230 A through Ha in 10-250, He through Sm, 26-100, 00:04:56.230 --> 00:04:59.510 So through Z, 4-270. 00:04:59.510 --> 00:05:04.360 OK, so let's go into the taxonomy of defects. 00:05:04.360 --> 00:05:06.430 So I mentioned that there are a number of different kinds of 00:05:06.430 --> 00:05:13.120 defects, and we can do better than to say simply, defects 00:05:13.120 --> 00:05:15.660 exist. We can actually start to classify them. 00:05:15.660 --> 00:05:17.380 So there are, broadly speaking, four types of 00:05:17.380 --> 00:05:21.050 defects, which we classify based on dimensionality. 00:05:21.050 --> 00:05:24.190 So there's 0-dimensional defects and 0-dimensional 00:05:24.190 --> 00:05:28.850 defects are point defects or point defect clusters. 00:05:28.850 --> 00:05:29.800 It's just like in math. 00:05:29.800 --> 00:05:32.110 A point has 0 dimension, right? 00:05:32.110 --> 00:05:36.150 1-dimensional defects or line defects, things that thread 00:05:36.150 --> 00:05:39.870 through a material like a shoestring or something, and 00:05:39.870 --> 00:05:43.600 we'll have an example of that in the form of dislocations. 00:05:43.600 --> 00:05:45.990 Then we have 2-dimensional defects. 00:05:45.990 --> 00:05:47.700 Those are interfacial defects. 00:05:47.700 --> 00:05:50.270 So if you have interfaces between two different kinds of 00:05:50.270 --> 00:05:53.700 materials or if you have two crystals that are misoriented 00:05:53.700 --> 00:05:55.980 with respect to each other, those are examples of 00:05:55.980 --> 00:05:57.660 interfacial defects. 00:05:57.660 --> 00:05:59.830 And we also have bulk defects-- 00:05:59.830 --> 00:06:02.250 3-dimensional defects like inclusions. 00:06:02.250 --> 00:06:05.110 We'll go over some of those. 00:06:05.110 --> 00:06:07.490 So let's start out with point defects. 00:06:07.490 --> 00:06:09.830 Point defects are those 0-dimensional defects. 00:06:09.830 --> 00:06:11.820 They're points, just like in math. 00:06:11.820 --> 00:06:14.190 And there are a number of different point defects that 00:06:14.190 --> 00:06:15.340 we can look at. 00:06:15.340 --> 00:06:17.780 We have our substitutional impurities, interstitial 00:06:17.780 --> 00:06:18.750 impurities. 00:06:18.750 --> 00:06:26.380 The general overall recurring theme in these point defects, 00:06:26.380 --> 00:06:29.860 regardless what type they are, is that they are localized 00:06:29.860 --> 00:06:30.730 disruptions. 00:06:30.730 --> 00:06:33.260 So a lattice, a crystalline lattice, is a regular 00:06:33.260 --> 00:06:36.150 arrangement of atoms, and a point defect is a very local 00:06:36.150 --> 00:06:39.240 disruption in that regular crystalline arrangement. 00:06:39.240 --> 00:06:43.310 And those disruptions can occur on lattice sites. 00:06:43.310 --> 00:06:46.130 So basically, on the positions where you would see atoms 00:06:46.130 --> 00:06:48.690 normally, they can also occur between lattice sites. 00:06:48.690 --> 00:06:53.690 So they're localized rifts, you can say, in the 00:06:53.690 --> 00:06:57.710 periodicity of a crystalline material. 00:06:57.710 --> 00:06:59.760 And here's just an illustration of the way that 00:06:59.760 --> 00:07:01.370 these different point defects play out. 00:07:01.370 --> 00:07:04.200 So let's start out by looking at this one. 00:07:04.200 --> 00:07:06.740 This is a substitutional impurity atom. 00:07:06.740 --> 00:07:08.550 So it's an impurity. 00:07:08.550 --> 00:07:11.190 So it's a type of chemical imperfection. 00:07:11.190 --> 00:07:16.710 You can imagine that this is, for example, some kind of FCC 00:07:16.710 --> 00:07:19.010 material like copper, for instance, and suppose that you 00:07:19.010 --> 00:07:23.950 have an impurity of some sort like iron, and it sits there 00:07:23.950 --> 00:07:27.030 and it replace one of the copper atoms. So this is 00:07:27.030 --> 00:07:28.580 called a substitutional impurity. 00:07:28.580 --> 00:07:31.570 It substitutes for the regular atom that would have sat at 00:07:31.570 --> 00:07:33.050 that location. 00:07:33.050 --> 00:07:36.160 Substitutional impurities. 00:07:36.160 --> 00:07:37.980 There's another picture. 00:07:37.980 --> 00:07:40.340 There's your substitutional impurity up there. 00:07:40.340 --> 00:07:42.000 We'll get to the other ones in just a moment. 00:07:46.170 --> 00:07:48.560 We already talked about some substitutional impurities. 00:07:48.560 --> 00:07:50.740 So dopants. 00:07:50.740 --> 00:07:54.010 If you have boron or phosphorus or silicon, that 00:07:54.010 --> 00:07:57.140 boron or that phosphorus replaces the silicon that 00:07:57.140 --> 00:08:00.020 would have sat at a certain lattice site. 00:08:00.020 --> 00:08:03.730 So the dopants we've studied so far are types of 00:08:03.730 --> 00:08:07.830 substitutional impurities and we call them good impurities 00:08:07.830 --> 00:08:10.640 because they give us desirable properties. 00:08:10.640 --> 00:08:11.670 They are dopants. 00:08:11.670 --> 00:08:13.270 They're good impurities. 00:08:13.270 --> 00:08:15.540 Then we have alloying elements. 00:08:15.540 --> 00:08:21.320 I am not a very big fan of sodas, but if you were 00:08:21.320 --> 00:08:25.000 somebody else who is a big fan of sodas, then you might, for 00:08:25.000 --> 00:08:27.810 example, drink a lot of sodas out of aluminum cans. 00:08:27.810 --> 00:08:30.660 Those aluminum cans are really not pure aluminum. 00:08:30.660 --> 00:08:31.950 They're alloys. 00:08:31.950 --> 00:08:35.750 They're alloys with other metals to give them the good 00:08:35.750 --> 00:08:37.910 properties that they need in order for the 00:08:37.910 --> 00:08:39.240 forming process to occur. 00:08:39.240 --> 00:08:42.090 So if you ask yourself, how do you actually 00:08:42.090 --> 00:08:43.780 make aluminum cans? 00:08:43.780 --> 00:08:46.230 They're stamped out from sheets of aluminum, but it's 00:08:46.230 --> 00:08:47.520 not just aluminum by itself. 00:08:47.520 --> 00:08:50.010 Aluminum by itself would just tear if you do that. 00:08:50.010 --> 00:08:51.910 So if you alloy it, you give it better 00:08:51.910 --> 00:08:54.010 properties so it's ductile. 00:08:54.010 --> 00:08:59.250 You can deform it to very large strains and that's a 00:08:59.250 --> 00:09:01.950 good thing in the case of alloying elements. 00:09:01.950 --> 00:09:05.140 Another one that he showed you was nickel and gold. 00:09:05.140 --> 00:09:07.370 That's if you want to change the color of gold, if you want 00:09:07.370 --> 00:09:09.610 to be very creative when you're proposing. 00:09:09.610 --> 00:09:15.230 So that's a good kind of substitutional impurity. 00:09:15.230 --> 00:09:17.360 There are also contaminants. 00:09:17.360 --> 00:09:21.520 Contaminants are bad kinds of impurities, but before we get 00:09:21.520 --> 00:09:23.710 to the contaminants, let me just show you what good 00:09:23.710 --> 00:09:24.760 impurities can do. 00:09:24.760 --> 00:09:26.860 So this is the Hope Diamond. 00:09:26.860 --> 00:09:31.080 It's in the American gem collection. 00:09:31.080 --> 00:09:34.230 You can actually find out more about it. 00:09:34.230 --> 00:09:38.670 I'm not a big gem expert, but anybody who looks at this Hope 00:09:38.670 --> 00:09:41.450 Diamond can immediately see that it's a 00:09:41.450 --> 00:09:42.890 really pretty diamond. 00:09:42.890 --> 00:09:45.670 But you guys are ahead of everybody, because in addition 00:09:45.670 --> 00:09:49.020 to knowing that it's a pretty diamond, the fact that it has 00:09:49.020 --> 00:09:53.320 boron impurities in it already tells you what the majority 00:09:53.320 --> 00:09:55.100 charge carrier is. 00:09:55.100 --> 00:09:58.220 So when you go to this gem collection, you can educate 00:09:58.220 --> 00:10:01.160 everybody else. 00:10:01.160 --> 00:10:05.020 So those are all good impurities. 00:10:05.020 --> 00:10:06.460 There are also bad impurities-- 00:10:06.460 --> 00:10:08.180 contaminants. 00:10:08.180 --> 00:10:11.310 Lithium in sodium chloride is an example. 00:10:11.310 --> 00:10:16.630 So if you were using saline solution, for instance, in an 00:10:16.630 --> 00:10:19.070 IV and you had lithium in there, that is very 00:10:19.070 --> 00:10:21.070 detrimental to the person who's receiving that. 00:10:21.070 --> 00:10:22.350 That's definitely a contaminant. 00:10:22.350 --> 00:10:24.200 You don't want those. 00:10:24.200 --> 00:10:26.160 That could make you die. 00:10:26.160 --> 00:10:33.280 So let's move on to some other types of point defects. 00:10:33.280 --> 00:10:34.900 Here's another type of point defect. 00:10:34.900 --> 00:10:36.410 So just now we talked about the 00:10:36.410 --> 00:10:38.390 substitutional impurity atom. 00:10:38.390 --> 00:10:40.490 Now we're going to talk about the interstitial. 00:10:40.490 --> 00:10:42.610 The interstitial's very different from the 00:10:42.610 --> 00:10:43.970 substitutional. 00:10:43.970 --> 00:10:47.130 In the case of the substitutional, we have a 00:10:47.130 --> 00:10:51.730 lattice site, which instead of being occupied by the regular 00:10:51.730 --> 00:10:54.800 atom that would have occupied it in a perfect crystal, is 00:10:54.800 --> 00:10:58.340 occupied by a chemically distinct atom. 00:10:58.340 --> 00:11:02.010 In the case of an interstitial impurity, that impurity can 00:11:02.010 --> 00:11:06.900 sit in the space in between lattice sites, so-called 00:11:06.900 --> 00:11:08.150 interstitial sites. 00:11:08.150 --> 00:11:10.590 That's why we call them interstitial impurities. 00:11:10.590 --> 00:11:14.830 And interstitial impurities or interstitial atoms can be both 00:11:14.830 --> 00:11:18.430 chemical impurities, and obviously, they are rifts in 00:11:18.430 --> 00:11:20.230 the atomic arrangement so they are structural 00:11:20.230 --> 00:11:22.520 impurities as well. 00:11:22.520 --> 00:11:23.530 Why do I say chemical? 00:11:23.530 --> 00:11:26.700 The reason is because if this is, for example, iron, if this 00:11:26.700 --> 00:11:30.870 is an iron matrix and you have a carbon atom sitting in the 00:11:30.870 --> 00:11:35.780 interstitial site which makes steel, then that's an example 00:11:35.780 --> 00:11:39.460 of a structural defect, but it's also a chemical defect. 00:11:39.460 --> 00:11:43.190 If, for example, you have, on the other hand, iron sitting 00:11:43.190 --> 00:11:45.670 in a nuclear reactor and it's getting bombarded all the time 00:11:45.670 --> 00:11:48.160 by energetic neutrons, then interstitials are being 00:11:48.160 --> 00:11:50.140 created by atoms getting knocked out of their lattice 00:11:50.140 --> 00:11:53.350 sites and they're getting put into interstitial sites. 00:11:53.350 --> 00:11:56.820 So that's creating defects that are chemically the same 00:11:56.820 --> 00:11:59.960 as the surrounding matrix material, but which are 00:11:59.960 --> 00:12:01.050 structurally distinct. 00:12:01.050 --> 00:12:04.090 So those are interstitial atoms. 00:12:04.090 --> 00:12:06.860 So here's another picture of interstitial 00:12:06.860 --> 00:12:09.720 atoms. There it is. 00:12:09.720 --> 00:12:12.060 It's not sitting on a regular lattice site. 00:12:12.060 --> 00:12:14.630 It's sitting in between lattice sites. 00:12:14.630 --> 00:12:19.120 It's sitting in the space, in the interstitial space between 00:12:19.120 --> 00:12:24.400 atoms. And I already mentioned to you the fact that if you 00:12:24.400 --> 00:12:29.760 put carbon into iron, those atoms go into interstitial 00:12:29.760 --> 00:12:33.970 sites and there would give iron some of its beneficial 00:12:33.970 --> 00:12:36.340 properties, which we look for in steel. 00:12:36.340 --> 00:12:38.780 So some of the good mechanical properties. 00:12:38.780 --> 00:12:42.340 Here's another example of a situation where an atom goes 00:12:42.340 --> 00:12:46.020 into a lattice and create an interstitial impurity. 00:12:46.020 --> 00:12:48.970 So lanthanum-nickel 5 is a prototype 00:12:48.970 --> 00:12:51.560 hydrogen storage material. 00:12:51.560 --> 00:12:53.180 It takes up a huge amount of hydrogen. 00:12:53.180 --> 00:12:56.090 It takes up a greater density of hydrogen than liquid 00:12:56.090 --> 00:12:59.040 hydrogen, actually, so if you expose this to hydrogen, the 00:12:59.040 --> 00:13:02.340 hydrogen just goes right in, and it sits in the 00:13:02.340 --> 00:13:07.950 lanthanum-nickel 5 lattice as an interstitial atom. 00:13:07.950 --> 00:13:11.240 So this is considered to be as a prototype 00:13:11.240 --> 00:13:12.390 hydrogen storage material. 00:13:12.390 --> 00:13:15.420 Unfortunately, it's extremely expensive so it's not being 00:13:15.420 --> 00:13:18.510 used very much these days, but on the other hand, it goes 00:13:18.510 --> 00:13:21.400 well with our gem theme in this particular lecture in 00:13:21.400 --> 00:13:24.150 terms of expensive things. 00:13:24.150 --> 00:13:27.530 Here's another example of an interstitial impurity. 00:13:27.530 --> 00:13:29.890 This one is not an alloying element. 00:13:29.890 --> 00:13:31.880 It's a contaminant. 00:13:31.880 --> 00:13:35.780 So hydrogen, but this time in iron. 00:13:35.780 --> 00:13:38.710 So hydrogen in lanthanum-nickel 5 is good. 00:13:38.710 --> 00:13:40.130 We want to store it. 00:13:40.130 --> 00:13:44.530 Hydrogen in iron is bad because it actually degrades 00:13:44.530 --> 00:13:47.520 the mechanical properties of the iron, unlike carbon, which 00:13:47.520 --> 00:13:49.160 gives us steel, which is good. 00:13:49.160 --> 00:13:50.910 You put hydrogen in, it embrittles it. 00:13:50.910 --> 00:13:54.300 So hydrogen embrittlement in steels is a big problem. 00:13:54.300 --> 00:13:57.340 And it's actually one of the challenges 00:13:57.340 --> 00:13:58.680 to a hydrogen economy. 00:13:58.680 --> 00:14:04.160 If you have steel pipelines or valves or various pieces of 00:14:04.160 --> 00:14:06.570 machinery, structural components that are made out 00:14:06.570 --> 00:14:09.290 of iron that are constantly exposed to hydrogen, over 00:14:09.290 --> 00:14:10.150 time, they're going to brittle. 00:14:10.150 --> 00:14:12.630 They're going to become very difficult to use. 00:14:12.630 --> 00:14:19.260 It's one of the challenges in that whole undertaking. 00:14:19.260 --> 00:14:20.050 OK. 00:14:20.050 --> 00:14:23.490 So we're going fairly at a clip here through these 00:14:23.490 --> 00:14:25.870 taxonomy of point defects. 00:14:25.870 --> 00:14:30.010 So in the taxonomy of point defects, perhaps the easiest 00:14:30.010 --> 00:14:32.760 defect to understand is the vacancy. 00:14:32.760 --> 00:14:35.160 So when you think of the vacancy, think of the hole 00:14:35.160 --> 00:14:38.700 that we talked about in the case of semiconductors. 00:14:38.700 --> 00:14:40.480 Vacancy is nothing. 00:14:40.480 --> 00:14:42.410 It's a missing atom. 00:14:42.410 --> 00:14:46.470 So if you have a crystalline lattice and it's FCC or it's 00:14:46.470 --> 00:14:48.930 BCC or it's simple cubic, whatever you like, and you 00:14:48.930 --> 00:14:50.930 know that there's supposed to be an atom at a certain 00:14:50.930 --> 00:14:55.930 lattice site and it's not there, that's a vacancy. 00:14:55.930 --> 00:14:58.870 That's a situation where you have an unoccupied lattice 00:14:58.870 --> 00:15:02.800 site and there are different ways to form these vacancies. 00:15:02.800 --> 00:15:04.780 They can be formed during crystallization. 00:15:04.780 --> 00:15:07.650 If you heat up a material, the number of vacancies decreases. 00:15:07.650 --> 00:15:10.740 So if you quench it really quickly, you can actually trap 00:15:10.740 --> 00:15:14.180 the vacancies before they can leave in service under extreme 00:15:14.180 --> 00:15:14.760 conditions. 00:15:14.760 --> 00:15:17.140 I mentioned just a moment ago that interstitials can be 00:15:17.140 --> 00:15:20.520 created if you irradiate a material, if you bombard it 00:15:20.520 --> 00:15:23.390 with energetic particles, like neutrons for instance, you'll 00:15:23.390 --> 00:15:27.000 create interstitials, sure, by knocking atoms out of their 00:15:27.000 --> 00:15:29.880 atomic sites, but what's left behind after you 00:15:29.880 --> 00:15:31.720 knock that atom out? 00:15:31.720 --> 00:15:33.340 Vacancies. 00:15:33.340 --> 00:15:35.910 So actually, you create two defects at the same time: 00:15:35.910 --> 00:15:37.160 vacancies and interstitials. 00:15:40.170 --> 00:15:44.250 So I think we probably have a picture here of a vacancy. 00:15:44.250 --> 00:15:45.210 A vacancy is nothing. 00:15:45.210 --> 00:15:47.450 It's just empty space. 00:15:47.450 --> 00:15:48.700 That's a vacancy. 00:15:51.100 --> 00:15:53.140 There you go again. 00:15:53.140 --> 00:15:54.390 Nothing. 00:15:56.660 --> 00:16:00.290 So we've gone through a bunch of taxonomy, right? 00:16:00.290 --> 00:16:03.090 So we know now that there are a number of different kinds of 00:16:03.090 --> 00:16:04.960 point defects in crystals. 00:16:04.960 --> 00:16:06.390 We've talked about interstitials. 00:16:06.390 --> 00:16:09.040 We talked about vacancies. 00:16:09.040 --> 00:16:11.130 We've talked about substitutionals. 00:16:11.130 --> 00:16:13.750 What can we say about these defects quantitatively? 00:16:13.750 --> 00:16:20.430 So let's take the vacancy and derive or write down what is 00:16:20.430 --> 00:16:23.200 the number of vacancies that you can expect to find in a 00:16:23.200 --> 00:16:25.720 given material at a certain temperatures? 00:16:25.720 --> 00:16:27.930 So to do that, let's be a little bit more quantitative. 00:16:27.930 --> 00:16:30.443 Suppose that you have a crystal. 00:16:33.620 --> 00:16:37.800 I'm showing you a plane, for example, a 1 1 1 plane in an 00:16:37.800 --> 00:16:42.990 FCC material and how do you create a vacancy? 00:16:42.990 --> 00:16:46.070 You simply remove an atom. 00:16:46.070 --> 00:16:47.150 So you had an atom. 00:16:47.150 --> 00:16:48.920 Now you have no atom. 00:16:48.920 --> 00:16:50.320 You've created a vacancy. 00:16:50.320 --> 00:16:53.020 When you created that vacancy, you broke all the bonds 00:16:53.020 --> 00:16:55.610 between the atom that used to be there and the neighboring 00:16:55.610 --> 00:16:59.040 atoms. Breaking bonds costs energy. 00:16:59.040 --> 00:17:01.580 So it costs energy to create a vacancy. 00:17:01.580 --> 00:17:04.600 It costs energy to remove an atom from the place where it 00:17:04.600 --> 00:17:06.730 would have been because you're breaking bonds. 00:17:06.730 --> 00:17:10.470 So in this case, I have six bonds that I broke. 00:17:10.470 --> 00:17:14.930 If I were looking at some material, for example, placing 00:17:14.930 --> 00:17:17.510 our cubic material in 3D, I would find that I would be 00:17:17.510 --> 00:17:21.260 breaking 12 bonds to the 12 nearest neighbors, and so on 00:17:21.260 --> 00:17:24.170 for all the different crystal structures. 00:17:24.170 --> 00:17:27.260 So we actually then take that information, the fact that 00:17:27.260 --> 00:17:31.290 we're breaking bonds, and encapsulate it in a single 00:17:31.290 --> 00:17:33.330 descriptions of how much energy it 00:17:33.330 --> 00:17:35.310 costs to create a vacancy. 00:17:35.310 --> 00:17:40.870 And we call that the vacancy formation energy. 00:17:40.870 --> 00:17:47.340 So this is an energy and so it's expressed in eV. 00:17:47.340 --> 00:17:50.620 Its units are electron volts. 00:17:50.620 --> 00:17:55.500 You can convert them to joules, anything you like. 00:17:55.500 --> 00:18:01.820 And if you wanted to then compute how many vacancies 00:18:01.820 --> 00:18:06.320 there are in a given crystal, well, first of all, it costs 00:18:06.320 --> 00:18:08.720 energy to make them, so why would you ever even have a 00:18:08.720 --> 00:18:10.470 vacancy in the material? 00:18:10.470 --> 00:18:13.270 Well, no material is perfect. 00:18:13.270 --> 00:18:17.120 We know that from studying materials, but what causes it 00:18:17.120 --> 00:18:20.030 is the fact that at finite temperature because of the 00:18:20.030 --> 00:18:22.430 Boltzmann distribution that Dr. Sadoway told you about a 00:18:22.430 --> 00:18:26.540 few lectures ago, just like in the case of intrinsic charge 00:18:26.540 --> 00:18:30.790 carrier promotion in semiconductors, you can get 00:18:30.790 --> 00:18:32.640 thermal formation of vacancies. 00:18:32.640 --> 00:18:36.320 So that Maxwell Boltzmann distribution can actually 00:18:36.320 --> 00:18:38.310 cause there to be vacancies despite the 00:18:38.310 --> 00:18:40.290 fact that there are-- 00:18:40.290 --> 00:18:42.220 that it costs energy to do that. 00:18:42.220 --> 00:18:45.410 So how can we actually use that to express how many 00:18:45.410 --> 00:18:48.370 vacancies we have in a given material? 00:18:48.370 --> 00:18:52.150 So I'm going to write down an expression for how many 00:18:52.150 --> 00:18:56.590 vacancies you can expect to find at a given temperature on 00:18:56.590 --> 00:19:00.030 the basis of their formation energy, OK? 00:19:00.030 --> 00:19:01.530 So let's do that. 00:19:01.530 --> 00:19:04.510 This is going to be the fraction of vacant sites. 00:19:04.510 --> 00:19:06.260 So if you have a given material-- 00:19:06.260 --> 00:19:08.930 FCC, BCC, whatever you like-- you know that there's a 00:19:08.930 --> 00:19:11.870 certain number of lattice sites per unit volume, and you 00:19:11.870 --> 00:19:14.010 learn how to calculate those things. 00:19:14.010 --> 00:19:16.650 And to quantify the number of vacancies, you have to 00:19:16.650 --> 00:19:20.590 basically say, what fraction of those sites does not 00:19:20.590 --> 00:19:21.390 contain an atom? 00:19:21.390 --> 00:19:24.860 Is that 1/100 of a percent or is it 1% or how many? 00:19:24.860 --> 00:19:32.200 So this is actually going to be expressed as a ratio, which 00:19:32.200 --> 00:19:33.480 I'm going to call this. 00:19:33.480 --> 00:19:48.670 This is the number of vacancies per unit volume and 00:19:48.670 --> 00:19:58.195 this is the number of atomic sites, also per 00:19:58.195 --> 00:20:05.200 unit volume, OK. 00:20:08.180 --> 00:20:12.200 So this is the definition of the fraction of vacant sites. 00:20:12.200 --> 00:20:13.420 And how do we express it? 00:20:13.420 --> 00:20:17.860 Well, we express it using a very simple formula. 00:20:17.860 --> 00:20:21.590 This formula contains a factor here which is experimentally 00:20:21.590 --> 00:20:22.110 determined. 00:20:22.110 --> 00:20:26.190 This is an empirical factor and then an exponential. 00:20:26.190 --> 00:20:32.710 So the exponent we take here, the vacancy formation energy, 00:20:32.710 --> 00:20:38.120 and we divide it by the thermal energy at the given 00:20:38.120 --> 00:20:40.510 temperature of interest. 00:20:40.510 --> 00:20:44.200 So this is actually telling you that to form vacancies, 00:20:44.200 --> 00:20:47.910 you actually have two competing factors. 00:20:47.910 --> 00:20:52.130 On the one hand, you have the bonding energy that makes the 00:20:52.130 --> 00:20:54.540 difficult-to-form vacancies because you're breaking bonds, 00:20:54.540 --> 00:20:55.810 you're taking it an atom out. 00:20:55.810 --> 00:20:58.720 On the other hand, you have this thermal energy, Boltzmann 00:20:58.720 --> 00:21:01.300 constant times the temperature, and the thermal 00:21:01.300 --> 00:21:04.210 energy is competing with that bonding energy. 00:21:04.210 --> 00:21:06.640 And when that thermal energy is high enough, you can 00:21:06.640 --> 00:21:10.740 actually start knocking atoms out despite the fact that it 00:21:10.740 --> 00:21:13.930 costs you some energy, and obviously when this ratio is 00:21:13.930 --> 00:21:16.760 very large, that means that the bonding predominates, and 00:21:16.760 --> 00:21:19.250 when it gets smaller, that means the thermal energy is 00:21:19.250 --> 00:21:21.560 more and more sufficient to actually knock atoms out of 00:21:21.560 --> 00:21:24.520 their positions and cause there to be vacancies. 00:21:24.520 --> 00:21:29.500 So when you do these calculations, make sure to use 00:21:29.500 --> 00:21:33.770 the absolute temperature in Kelvin, and dimensional 00:21:33.770 --> 00:21:36.180 analysis will tell you the units of the Boltzmann 00:21:36.180 --> 00:21:40.110 constant have to be energy units per degrees. 00:21:40.110 --> 00:21:42.830 So eV's per Kelvin, for instance. 00:21:42.830 --> 00:21:44.480 So this is the absolute temperature. 00:21:55.980 --> 00:21:58.740 This is the vacancy formation energy and this is the 00:21:58.740 --> 00:21:59.990 Boltzmann constant. 00:22:11.580 --> 00:22:15.910 So what that means is that at any given temperature, you'll 00:22:15.910 --> 00:22:18.790 actually expect to see some fraction of vacancies. 00:22:18.790 --> 00:22:21.970 So let's actually try to do a calculation with an actual 00:22:21.970 --> 00:22:25.360 vacancy formation energy and see how many vacancies we get 00:22:25.360 --> 00:22:27.870 at a given temperature. 00:22:27.870 --> 00:22:34.830 So to do that, we've been provided with what is the 00:22:34.830 --> 00:22:38.100 common currency in science, which is published 00:22:38.100 --> 00:22:43.790 experimental data, which we find from published journals 00:22:43.790 --> 00:22:47.820 which we find online through, for example, Web of Science. 00:22:47.820 --> 00:22:54.950 And from this journal, we find that for copper, the vacancy 00:22:54.950 --> 00:23:04.800 formation energy is 1.03 electron volts. 00:23:04.800 --> 00:23:11.410 Furthermore, in the same journal in the abstract there, 00:23:11.410 --> 00:23:17.450 you'll find the magnitude of this constant A, which as I 00:23:17.450 --> 00:23:20.610 told you is experimentally determined. 00:23:20.610 --> 00:23:24.265 This quantity A we call the entropy factor. 00:23:32.560 --> 00:23:37.120 And even though there's no way to very easily derive it-- 00:23:37.120 --> 00:23:39.800 I can't tell you what's the entropy factor for iron and 00:23:39.800 --> 00:23:42.930 you can't really tell me just by thinking about it-- 00:23:42.930 --> 00:23:47.070 nevertheless, it turns out that this factor usually fall 00:23:47.070 --> 00:23:48.720 within a certain range. 00:23:48.720 --> 00:23:51.590 It's usually between 0.1 and 10. 00:23:51.590 --> 00:23:53.810 That's usually the range and what you find As. 00:23:53.810 --> 00:23:56.750 And in the case of copper, it's very much in that range. 00:23:56.750 --> 00:23:58.520 It's just 1.1. 00:23:58.520 --> 00:24:01.700 So let's use this information to actually figure out how 00:24:01.700 --> 00:24:05.840 many vacancies we expect to see in copper at the given 00:24:05.840 --> 00:24:07.090 temperature. 00:24:18.680 --> 00:24:19.040 OK. 00:24:19.040 --> 00:24:23.970 So here's my fraction of vacancies and we know that it 00:24:23.970 --> 00:24:30.910 is going to be expressed as 1.1 times exponent minus the 00:24:30.910 --> 00:24:36.280 formation energy, which is 1.03 eV, and then we'll put in 00:24:36.280 --> 00:24:39.600 Boltzmann's constant, and then let's pick a temperature. 00:24:39.600 --> 00:24:41.540 For the moment, let's just take room temperature. 00:24:41.540 --> 00:24:44.480 So T, room temperature, and room 00:24:44.480 --> 00:24:47.760 temperature's about 300 K. 00:24:47.760 --> 00:24:50.010 So when we put in all these numbers, it's just a matter of 00:24:50.010 --> 00:24:50.840 calculating. 00:24:50.840 --> 00:24:52.960 This is on your sheet of constants. 00:24:52.960 --> 00:24:55.960 This is the temperature which we choose at room temperature. 00:24:55.960 --> 00:25:02.940 Let's actually write down T, room temperature, is about 300 00:25:02.940 --> 00:25:08.890 K, and we find a certain number of vacancies. 00:25:08.890 --> 00:25:17.880 And the number of vacancies that we find is 2.19 times 10 00:25:17.880 --> 00:25:24.950 to the minus 18 vacancies. 00:25:24.950 --> 00:25:27.500 So this is the fraction of vacant sites. 00:25:27.500 --> 00:25:28.840 Well, is that a lot? 00:25:28.840 --> 00:25:31.640 Is that a little? 00:25:31.640 --> 00:25:33.950 How can we determine whether this is a lot or a little? 00:25:33.950 --> 00:25:37.780 We compare it to the number of atoms that there actually are, 00:25:37.780 --> 00:25:42.190 and in the case of solid materials, we expect there to 00:25:42.190 --> 00:25:45.010 be something on the order-- this has to be compared to 00:25:45.010 --> 00:25:47.460 something on the order of Avogadro's number, but we can 00:25:47.460 --> 00:25:52.680 actually calculate more explicitly that this turns out 00:25:52.680 --> 00:25:56.750 to be something like 10 to the 5th vacancies 00:25:56.750 --> 00:26:00.840 per centimeter cubed. 00:26:00.840 --> 00:26:04.350 And if in a real material, a solid material like silicon, 00:26:04.350 --> 00:26:10.140 for instance, or boron or whatever you're interested in, 00:26:10.140 --> 00:26:14.250 your number of atoms is something like 10 to the 23rd, 00:26:14.250 --> 00:26:17.440 Avogadro's number, right, then this is 00:26:17.440 --> 00:26:20.640 actually a very tiny number. 00:26:20.640 --> 00:26:23.180 Compare 10 to the 5th to 10 to the 23rd. 00:26:23.180 --> 00:26:26.610 The number of atoms that are missing at room temperature is 00:26:26.610 --> 00:26:28.130 very low in copper. 00:26:28.130 --> 00:26:32.250 We can compute that using this expression. 00:26:32.250 --> 00:26:35.100 However, even though it's low, it's not zero. 00:26:35.100 --> 00:26:37.440 And if we continue going down in temperature, we'll find 00:26:37.440 --> 00:26:40.110 that the number is lower and lower and lower, but it never 00:26:40.110 --> 00:26:43.680 really goes to zero because we have this expression which 00:26:43.680 --> 00:26:45.580 gives us the total number. 00:26:45.580 --> 00:26:48.240 So let's do another one and this time, let's take a 00:26:48.240 --> 00:26:49.070 different temperature. 00:26:49.070 --> 00:26:52.350 Let's take the melting temperature of copper. 00:26:52.350 --> 00:26:56.000 The melting temperature of copper is considerably higher. 00:26:56.000 --> 00:27:00.430 It's about 1085 degrees Celsius and we can go through 00:27:00.430 --> 00:27:02.300 exactly the same calculation. 00:27:02.300 --> 00:27:11.900 1.1 times all these quantities here times melting 00:27:11.900 --> 00:27:14.510 temperature, OK? 00:27:14.510 --> 00:27:25.100 And when we do this, we get a vacant site fraction which is 00:27:25.100 --> 00:27:35.050 1.67 times 10 to the minus 4 and that corresponds to 1.41 00:27:35.050 --> 00:27:38.880 times 10 to the 19th vacancies per centimeter cubed. 00:27:42.630 --> 00:27:44.160 So what do we know by-- 00:27:44.160 --> 00:27:46.510 what can we see now by comparing these two 00:27:46.510 --> 00:27:47.130 quantities? 00:27:47.130 --> 00:27:49.630 Number of vacancies, add room temperature, number of 00:27:49.630 --> 00:27:51.440 vacancies at melting temperature. 00:27:51.440 --> 00:27:54.540 How many orders of magnitude do they differ by? 00:27:54.540 --> 00:28:02.130 Huge difference in the number of vacancies that we find at 00:28:02.130 --> 00:28:03.200 two different temperatures. 00:28:03.200 --> 00:28:06.430 And why do we see such a huge difference? 00:28:06.430 --> 00:28:10.040 Let's actually write down what that difference is. 00:28:10.040 --> 00:28:12.292 Let's write down the ratio. 00:28:12.292 --> 00:28:18.630 The fraction of vacant sites at melting temperature divided 00:28:18.630 --> 00:28:24.170 by fraction of vacant sites at room temperature is something 00:28:24.170 --> 00:28:31.170 like 7.6 times 10 to the 13th. 00:28:31.170 --> 00:28:33.640 That's the difference in number of vacancies you get 00:28:33.640 --> 00:28:35.400 just by increasing the temperature from room 00:28:35.400 --> 00:28:37.020 temperature to melting temperature. 00:28:37.020 --> 00:28:37.970 Why is that? 00:28:37.970 --> 00:28:41.830 Well, one way to look at that is just from the expression 00:28:41.830 --> 00:28:45.590 that we have to calculate the number. 00:28:45.590 --> 00:28:47.380 Here's where the temperatures go. 00:28:47.380 --> 00:28:50.180 So any difference in temperature if it's a factor 00:28:50.180 --> 00:28:52.912 of two or if it's a factor of three or if it's a factor of 00:28:52.912 --> 00:28:55.740 four, it's going to go into the exponential. 00:28:55.740 --> 00:28:58.340 So that exponential is actually making a huge 00:28:58.340 --> 00:29:00.600 difference as a function of temperature in terms of number 00:29:00.600 --> 00:29:02.280 of defects that you get. 00:29:02.280 --> 00:29:03.570 The higher you go up in temperature, 00:29:03.570 --> 00:29:04.680 you don't get just-- 00:29:04.680 --> 00:29:07.420 you go up a factor of four in temperature, you don't just 00:29:07.420 --> 00:29:10.560 get a factor of four increase in the number of defects. 00:29:10.560 --> 00:29:12.560 You get that in the exponential. 00:29:12.560 --> 00:29:15.520 So the factor of four is hugely magnified by the 00:29:15.520 --> 00:29:17.830 exponential. 00:29:17.830 --> 00:29:21.490 So that means that at any given temperature, even the 00:29:21.490 --> 00:29:23.720 lowest temperatures, you expect to see some defects, 00:29:23.720 --> 00:29:27.310 but if you increase the temperature, you see a hugely 00:29:27.310 --> 00:29:28.940 larger number of defects. 00:29:28.940 --> 00:29:30.580 And you can use this sort of expression 00:29:30.580 --> 00:29:31.740 for any kind of defect. 00:29:31.740 --> 00:29:35.260 So I talked about vacancies right now and vacancies have a 00:29:35.260 --> 00:29:38.130 specific formation energy, but interstitials also have 00:29:38.130 --> 00:29:40.380 formation energies, substitutionals also have 00:29:40.380 --> 00:29:41.160 formation energies. 00:29:41.160 --> 00:29:43.940 So you can use this expression to determine the fraction of 00:29:43.940 --> 00:29:48.230 defects per lattice site for any kind of defect so long as 00:29:48.230 --> 00:29:50.700 you have the formation energy of that defect. 00:29:50.700 --> 00:29:54.410 So just to show you how difficult it is actually to 00:29:54.410 --> 00:30:01.420 remove defects, if you have a crystalline material, defects 00:30:01.420 --> 00:30:03.645 want to stay even at the lowest temperatures. 00:30:03.645 --> 00:30:09.600 I have this interesting little piece of art to show you. 00:30:09.600 --> 00:30:14.990 This particular piece of art was actually discovered, I 00:30:14.990 --> 00:30:20.040 guess, by some scientist at the University of Toronto 00:30:20.040 --> 00:30:23.855 where Dr. Sadoway went to school, and this particular-- 00:30:27.180 --> 00:30:27.790 what do they call it? 00:30:27.790 --> 00:30:29.040 They call it The Atomix. 00:30:31.890 --> 00:30:34.570 Let me write down the name of it in case you want to look it 00:30:34.570 --> 00:30:38.000 up because I think they sold a lot more of these to material 00:30:38.000 --> 00:30:39.940 scientists than they sold to anybody else. 00:30:46.720 --> 00:30:52.460 And all this is two plastic plates, two PMMA plates, 00:30:52.460 --> 00:30:56.320 polymethyl methacrylates, or plexiglass. 00:30:56.320 --> 00:31:00.290 And in between them, there's a little hole that's cut, a gap, 00:31:00.290 --> 00:31:03.330 and in that gap are a number of ball bearings. 00:31:03.330 --> 00:31:05.730 And the ball bearings are kind of like atom, right, so they 00:31:05.730 --> 00:31:06.940 move around. 00:31:06.940 --> 00:31:10.020 And here we're going to the document camera right now. 00:31:10.020 --> 00:31:12.970 So if you shake these things around and the ball bearings 00:31:12.970 --> 00:31:16.270 are moving around, that's like introducing temperature. 00:31:16.270 --> 00:31:19.630 That's like taking a crystal, melting it, all the atoms are 00:31:19.630 --> 00:31:21.110 bouncing around. 00:31:21.110 --> 00:31:24.390 You will even see some vapor atoms when these sort of leave 00:31:24.390 --> 00:31:28.150 the surface and fly through the air, but then if you stop, 00:31:28.150 --> 00:31:29.850 that's like quenching. 00:31:29.850 --> 00:31:33.570 That's like suddenly I've taken this crystal, which was 00:31:33.570 --> 00:31:35.990 originally molten, and I've dropped the temperature. 00:31:35.990 --> 00:31:39.040 Here's what I see. 00:31:39.040 --> 00:31:40.290 So can you see that? 00:31:42.660 --> 00:31:43.910 How to use this thing-- 00:31:49.360 --> 00:31:51.600 there we go. 00:31:51.600 --> 00:31:54.100 So you can actually see a lot of the defects that we were 00:31:54.100 --> 00:31:56.680 talking about just a moment ago. 00:31:56.680 --> 00:32:03.100 Here you can see areas of perfect crystalline order. 00:32:03.100 --> 00:32:05.570 Here's another area of perfect crystalline order. 00:32:05.570 --> 00:32:08.840 So you have many, many crystals that are adjacent to 00:32:08.840 --> 00:32:09.760 each other. 00:32:09.760 --> 00:32:11.880 They're oriented differently. 00:32:11.880 --> 00:32:15.780 So they're forming misorientation defects between 00:32:15.780 --> 00:32:16.330 themselves. 00:32:16.330 --> 00:32:18.960 So for example, here's a grain boundary. 00:32:18.960 --> 00:32:20.830 This is a crystalline grain. 00:32:20.830 --> 00:32:23.180 And inside this crystal, you see a vacancy. 00:32:23.180 --> 00:32:25.340 It's right there, So here's another 00:32:25.340 --> 00:32:27.090 instance of the vacancy. 00:32:27.090 --> 00:32:29.140 There's another vacancy. 00:32:29.140 --> 00:32:33.540 And what happens if I try to remove some of the disorder? 00:32:33.540 --> 00:32:36.640 By the way, interesting thing is that some of the vapor is 00:32:36.640 --> 00:32:37.720 also left here. 00:32:37.720 --> 00:32:40.050 So there's the vapor. 00:32:40.050 --> 00:32:43.210 If I then try to remove some of these defects, I can just 00:32:43.210 --> 00:32:45.270 tap on this. 00:32:45.270 --> 00:32:48.610 If I just continue to tap on it, I'm removing defects. 00:32:48.610 --> 00:32:50.480 The whole thing is crystallizing more and more 00:32:50.480 --> 00:32:54.180 and more so now I put it down again. 00:32:57.460 --> 00:32:59.730 OK. 00:32:59.730 --> 00:33:01.650 You still see the vapor phase. 00:33:01.650 --> 00:33:04.820 Now you see a big huge crystal right here with some grain 00:33:04.820 --> 00:33:06.680 boundaries around it. 00:33:06.680 --> 00:33:09.820 Here's another big huge crystal. 00:33:09.820 --> 00:33:11.440 Here's another crystal. 00:33:11.440 --> 00:33:13.470 There's a smaller crystal. 00:33:13.470 --> 00:33:16.420 Each one of them is bounded by grain boundaries, but what do 00:33:16.420 --> 00:33:18.450 you see in each of these crystals? 00:33:18.450 --> 00:33:19.570 There's a vacancy. 00:33:19.570 --> 00:33:20.510 There's a vacancy. 00:33:20.510 --> 00:33:21.820 There's a vacancy. 00:33:21.820 --> 00:33:24.360 And you can actually sit here-- 00:33:24.360 --> 00:33:25.240 well, not here. 00:33:25.240 --> 00:33:29.100 Maybe later, but if you want to take a look at one of these 00:33:29.100 --> 00:33:32.170 things, you can probably go to Dr. Sadoway's office and pick 00:33:32.170 --> 00:33:35.110 it up and he'll let you play with it for a little while. 00:33:35.110 --> 00:33:36.990 You can try to get all these vacancies out. 00:33:36.990 --> 00:33:38.860 You can try to get all the defects out. 00:33:38.860 --> 00:33:42.490 No matter how hard you try, if you spent hours, you'll get 00:33:42.490 --> 00:33:46.000 things to be more and more and more perfect by tapping on it, 00:33:46.000 --> 00:33:48.610 but there's always going to be a vacancy. 00:33:48.610 --> 00:33:49.090 Always. 00:33:49.090 --> 00:33:53.560 And even if you are extremely patient, you get things down 00:33:53.560 --> 00:33:55.850 to just one vacancy and you think that all you have to do 00:33:55.850 --> 00:33:58.410 now is just give it a little bit more of a tap to remove 00:33:58.410 --> 00:34:03.760 that one vacancy, well, more often than not, you'll find 00:34:03.760 --> 00:34:05.740 that with that tap you'll remove the vacancy, but create 00:34:05.740 --> 00:34:07.380 another vacancy somewhere else. 00:34:07.380 --> 00:34:09.500 So you'll always find these vacancies in 00:34:09.500 --> 00:34:11.750 these crystalline materials. 00:34:15.100 --> 00:34:18.230 It's just a consequence of the fact that when you're 00:34:18.230 --> 00:34:20.630 agitating a material like you're doing here-- you're 00:34:20.630 --> 00:34:21.620 shaking it-- 00:34:21.620 --> 00:34:23.590 that's the same thing that happens if you have some 00:34:23.590 --> 00:34:25.670 finite temperatures, some non-zero temperature in the 00:34:25.670 --> 00:34:28.060 material, you're always going to be creating some defect. 00:34:28.060 --> 00:34:30.659 So that's exactly what this expression is giving you. 00:34:30.659 --> 00:34:32.770 It's telling you that there's going to be defects at any 00:34:32.770 --> 00:34:36.120 temperature, but their number goes up dramatically as you 00:34:36.120 --> 00:34:38.160 increase the temperature. 00:34:38.160 --> 00:34:42.710 So let's go back to the slides real quick now. 00:34:42.710 --> 00:34:43.550 OK. 00:34:43.550 --> 00:34:47.620 So everything I've told you so far is concerned with defects 00:34:47.620 --> 00:34:52.880 in crystals that are of one type, so that are made up of a 00:34:52.880 --> 00:34:55.010 single element. 00:34:55.010 --> 00:35:01.670 But in the case of, for example, things like ionic 00:35:01.670 --> 00:35:05.410 crystals, and ionic crystals are made up of multiple 00:35:05.410 --> 00:35:09.730 elements with multiple charge states, you can get new kinds 00:35:09.730 --> 00:35:12.010 of point defects that you can't see in a 00:35:12.010 --> 00:35:14.110 single element material. 00:35:14.110 --> 00:35:17.250 So we'll talk a little bit about those and when it comes 00:35:17.250 --> 00:35:21.860 to those defects in ionic materials, we have to expand 00:35:21.860 --> 00:35:23.380 the taxonomy a little bit. 00:35:23.380 --> 00:35:26.090 The taxonomy is now going to include defects called 00:35:26.090 --> 00:35:28.390 Schottky imperfections, Frenkel 00:35:28.390 --> 00:35:30.900 imperfections, and F-centers. 00:35:30.900 --> 00:35:35.880 So let's go to a visualization of what these are. 00:35:35.880 --> 00:35:39.690 Here you see an ionic crystal. 00:35:39.690 --> 00:35:43.460 So you have alternating types of atoms. You have these big 00:35:43.460 --> 00:35:47.900 ones, which are presumably the negatively charge ones, and 00:35:47.900 --> 00:35:50.390 then you have the small positively charged ones, and 00:35:50.390 --> 00:35:53.970 here you have an example of a Schottky imperfection. 00:35:53.970 --> 00:35:57.450 So a Schottky imperfection, it's kind of like a vacancy. 00:35:57.450 --> 00:36:01.220 It's missing atoms. The main difference between a Schottky 00:36:01.220 --> 00:36:08.600 imperfection and a vacancy by itself is the fact that in a 00:36:08.600 --> 00:36:11.620 material that involves charged atoms-- 00:36:11.620 --> 00:36:12.420 ions, right-- 00:36:12.420 --> 00:36:16.180 in an ionic crystal, when you take atoms out, you have to 00:36:16.180 --> 00:36:18.980 make sure to maintain charge neutrality. 00:36:18.980 --> 00:36:20.780 So these materials are charge neutral. 00:36:20.780 --> 00:36:23.640 They have equal numbers of positive and negative ions, 00:36:23.640 --> 00:36:25.290 but you want to make sure that you take these 00:36:25.290 --> 00:36:26.360 out in equal numbers. 00:36:26.360 --> 00:36:29.140 So in the Schottky defect, you take out one negative and one 00:36:29.140 --> 00:36:33.490 positive ion, or basically one unit, one stoichiometric unit. 00:36:33.490 --> 00:36:37.120 If you add zirconium oxide, which is ZrO2, you would have 00:36:37.120 --> 00:36:41.590 to take out three atoms to maintain charge neutrality. 00:36:41.590 --> 00:36:44.230 That would be the Schottky defect. 00:36:44.230 --> 00:36:46.780 So here is another example, another visualization of a 00:36:46.780 --> 00:36:47.600 Schottky defect. 00:36:47.600 --> 00:36:51.120 So when you take these two atoms out, nothing says that 00:36:51.120 --> 00:36:53.750 they have to be taken out from right next to each other. 00:36:53.750 --> 00:36:55.270 You can take out one here. 00:36:55.270 --> 00:36:56.870 You can take out one there. 00:36:56.870 --> 00:36:59.590 It's good both ways because in the end, it's just about 00:36:59.590 --> 00:37:00.380 charge neutrality. 00:37:00.380 --> 00:37:05.200 It's about maintaining a charge neutral material. 00:37:05.200 --> 00:37:09.350 So we can actually write down reactions to describe the 00:37:09.350 --> 00:37:12.650 formation of these Schottky defects. 00:37:12.650 --> 00:37:15.320 So let's do that. 00:37:15.320 --> 00:37:19.260 When we write down reactions to describe the formation of 00:37:19.260 --> 00:37:23.360 Schottky defects, we first recognize the fact that we're 00:37:23.360 --> 00:37:24.780 dealing with empty sites. 00:37:24.780 --> 00:37:26.770 We're dealing with void. 00:37:26.770 --> 00:37:30.560 We want to see how this void, or in scientific parlance, 00:37:30.560 --> 00:37:38.750 null, is decomposed into two vacant sites in the particular 00:37:38.750 --> 00:37:40.640 ionic crystal that we're dealing with. 00:37:40.640 --> 00:37:42.870 So let's-- to make things specific, 00:37:42.870 --> 00:37:44.650 deal with sodium chloride. 00:37:44.650 --> 00:37:46.770 So sodium chloride, we have two type of 00:37:46.770 --> 00:37:49.510 atoms. Sodium and chloride. 00:37:49.510 --> 00:37:51.880 And to maintain charge neutrality, we have to remove 00:37:51.880 --> 00:37:52.970 one of each. 00:37:52.970 --> 00:37:56.350 So this is actually-- this null space is actually going 00:37:56.350 --> 00:38:00.950 to be composed of two vacancies: a vacant site on a 00:38:00.950 --> 00:38:04.350 sodium lattice where a sodium atom would have been sitting 00:38:04.350 --> 00:38:06.180 and a vacant site where a chlorine 00:38:06.180 --> 00:38:07.430 would have been sitting. 00:38:07.430 --> 00:38:11.570 And because this entire process takes place in the 00:38:11.570 --> 00:38:17.580 presence of materials that are composed of ions-- 00:38:17.580 --> 00:38:19.120 so ionic solids-- 00:38:19.120 --> 00:38:24.220 these two vacancies, in fact, have some charge them. 00:38:24.220 --> 00:38:27.900 So when we think about the charge of these vacancies, 00:38:27.900 --> 00:38:30.200 what we actually have to think of, it's a little bit 00:38:30.200 --> 00:38:32.070 counterintuitive. 00:38:32.070 --> 00:38:35.430 The sodium in a sodium chloride crystal is charge 00:38:35.430 --> 00:38:38.950 positive, but what does that make the vacancy? 00:38:38.950 --> 00:38:43.180 So if you have a lattice of atoms that are charge positive 00:38:43.180 --> 00:38:47.110 like the sodium atoms and you remove one of them, what is 00:38:47.110 --> 00:38:49.560 the effective charge of that vacancy? 00:38:49.560 --> 00:38:52.180 You have nothing, as Dr. Sadoway would say, 00:38:52.180 --> 00:38:54.150 in the land of plus. 00:38:54.150 --> 00:38:56.780 So the charge of this vacancy, the effective charge of this 00:38:56.780 --> 00:38:58.960 vacancy, is going to be negative. 00:38:58.960 --> 00:39:04.490 And we mark that with this little thing right there. 00:39:04.490 --> 00:39:15.695 So void or nothing in land of plus is negative. 00:39:18.320 --> 00:39:22.160 We mark that with one of these apostrophes. 00:39:22.160 --> 00:39:25.010 So what about this vacancy? 00:39:25.010 --> 00:39:28.270 That vacancy is created on a lattice of sites which are 00:39:28.270 --> 00:39:30.030 usually charge negative. 00:39:30.030 --> 00:39:33.500 So if you have these chlorine atoms that are charged 00:39:33.500 --> 00:39:36.510 negative and you remove one of them, now you have void in a 00:39:36.510 --> 00:39:37.820 land of plus. 00:39:37.820 --> 00:39:40.720 So this is going to be effectively charge positive 00:39:40.720 --> 00:39:47.160 and so we have this void in land of minus. 00:39:47.160 --> 00:39:48.835 It is positive. 00:39:51.790 --> 00:39:53.290 And we do it-- 00:39:53.290 --> 00:40:00.800 we annotate it with one of these dots. 00:40:00.800 --> 00:40:03.960 We can do the same thing for other kinds of crystals. 00:40:03.960 --> 00:40:07.120 So I mentioned that in this case, a Schottky defect would 00:40:07.120 --> 00:40:09.970 just be composed of these two atoms, because these two atoms 00:40:09.970 --> 00:40:12.300 constitute the structural unit for this crystal. 00:40:12.300 --> 00:40:15.590 But if we had some other, more complicated crystal, like, for 00:40:15.590 --> 00:40:19.110 examples, zirconium oxide, then we would still write down 00:40:19.110 --> 00:40:21.680 a similar reaction. 00:40:21.680 --> 00:40:25.745 So we could put a Schottky defect into zirconium oxide. 00:40:30.670 --> 00:40:31.970 OK. 00:40:31.970 --> 00:40:34.010 And so now we have to figure out how this 00:40:34.010 --> 00:40:35.000 reaction plays out. 00:40:35.000 --> 00:40:36.970 We have to create vacancies. 00:40:36.970 --> 00:40:40.680 Here's our vacancy on the zirconium. 00:40:40.680 --> 00:40:45.120 And because the structural unit contains two oxygens, we 00:40:45.120 --> 00:40:46.700 have to create two oxygen vacancies. 00:40:49.680 --> 00:40:52.460 And now we have to think about how do we maintain charge 00:40:52.460 --> 00:40:53.570 neutralities? 00:40:53.570 --> 00:40:56.960 What is the effective charge on all of these atoms? 00:40:56.960 --> 00:41:02.600 So the zirconium sites are usually the positively charged 00:41:02.600 --> 00:41:05.940 atoms, so when we remove one of them, that's removing 00:41:05.940 --> 00:41:08.820 something, that's putting void basically 00:41:08.820 --> 00:41:09.990 into the land of plus. 00:41:09.990 --> 00:41:14.540 So we have now a negatively charged vacancy, and this 00:41:14.540 --> 00:41:18.025 negatively charged vacancy has four negative charges, an 00:41:18.025 --> 00:41:20.250 effective minus 4 negative charge. 00:41:20.250 --> 00:41:22.980 And the oxygens are the negatively charged ions, and 00:41:22.980 --> 00:41:25.745 so when we create voids there, these two vacancies have an 00:41:25.745 --> 00:41:28.260 effective positive charge, and because the charges have to 00:41:28.260 --> 00:41:32.700 balance, we know that this has to be effectively two negative 00:41:32.700 --> 00:41:34.030 charges and there are two vacancies. 00:41:34.030 --> 00:41:35.700 So we have charge neutrality. 00:41:35.700 --> 00:41:41.230 So that's how the Schottky defects work. 00:41:41.230 --> 00:41:42.480 OK. 00:41:45.920 --> 00:41:47.920 So let's move on to Frenkel defects. 00:41:47.920 --> 00:41:50.010 In the case of Frenkel defects, it's really not so 00:41:50.010 --> 00:41:54.400 different from Schottky defects in some sense, except 00:41:54.400 --> 00:42:09.660 now instead of dealing with a situation where we maintain 00:42:09.660 --> 00:42:14.230 charge neutrality by removing two atoms, we actually 00:42:14.230 --> 00:42:19.670 displace one atom from its initial location to a 00:42:19.670 --> 00:42:21.480 different part of the crystal. 00:42:21.480 --> 00:42:24.850 So we're creating actually a vacancy right there, and this 00:42:24.850 --> 00:42:27.800 atom, which was originally sitting on a lattice site, is 00:42:27.800 --> 00:42:29.730 now displaced to an interstitial location. 00:42:29.730 --> 00:42:31.310 So that's an interstitial. 00:42:31.310 --> 00:42:34.620 So a Frenkel defect is a vacancy and an interstitial. 00:42:34.620 --> 00:42:37.940 And here's another view of a Frenkel defect. 00:42:37.940 --> 00:42:42.790 Here, I've removed an atom from one of the lattice sites 00:42:42.790 --> 00:42:44.810 and moved it over to here. 00:42:44.810 --> 00:42:48.230 So that's my Frenkel defect. 00:42:48.230 --> 00:42:57.020 And in the case of Frenkel defects I can also write down 00:42:57.020 --> 00:42:58.780 reactions for Frenkel defects. 00:43:01.920 --> 00:43:03.170 Let's do that. 00:43:13.560 --> 00:43:15.120 OK. 00:43:15.120 --> 00:43:18.840 So Frenkel defects usually occur in crystals with widely 00:43:18.840 --> 00:43:25.630 differing atomic radii, and in ionic crystals, the radius of 00:43:25.630 --> 00:43:32.060 whatever is positively charged would have to be much, much 00:43:32.060 --> 00:43:34.800 less than whatever the radius of whatever's negatively 00:43:34.800 --> 00:43:39.840 charged occasionally, or very rarely, but I suppose it's 00:43:39.840 --> 00:43:44.230 still possible, you would have to have basically a very big 00:43:44.230 --> 00:43:46.110 difference in radius between these two cases. 00:43:46.110 --> 00:43:49.380 An example of one of these situations is, for example, 00:43:49.380 --> 00:43:54.990 silver bromide, where here the silver's positively charged 00:43:54.990 --> 00:43:59.470 and the bromide ion is negatively charged. 00:43:59.470 --> 00:44:04.710 And we can write down a reaction to describe the 00:44:04.710 --> 00:44:08.390 Frenkel defect formation just like we did in the case of the 00:44:08.390 --> 00:44:09.980 Schottky defect formation. 00:44:09.980 --> 00:44:13.020 So in the case of a Frenkel defect formation, how do we 00:44:13.020 --> 00:44:14.490 actually go about this? 00:44:14.490 --> 00:44:19.830 We have, for example, can start out with a silver atom 00:44:19.830 --> 00:44:23.760 site and we're going to displace that silver atom away 00:44:23.760 --> 00:44:26.470 from its original site so it now sits in an interstitial 00:44:26.470 --> 00:44:30.450 position and we're going to leave behind a vacancy. 00:44:30.450 --> 00:44:31.700 So let's do that. 00:44:35.380 --> 00:44:35.760 OK. 00:44:35.760 --> 00:44:47.400 So we're going to have silver interstitial site and let's 00:44:47.400 --> 00:44:49.070 just be clear-- 00:44:49.070 --> 00:44:52.450 say that this is on a regular silver site. 00:44:52.450 --> 00:44:59.740 And then we have a vacancy left over on the silver site 00:44:59.740 --> 00:45:01.400 and this is the reaction for the formation 00:45:01.400 --> 00:45:02.850 of our Frenkel defect. 00:45:02.850 --> 00:45:06.300 Frenkel defects, just like Schottky defects, preserve 00:45:06.300 --> 00:45:07.600 charge neutrality. 00:45:07.600 --> 00:45:09.630 So how do we actually mark down charge 00:45:09.630 --> 00:45:10.600 neutrality in this case? 00:45:10.600 --> 00:45:15.405 Well, there's no change in charges in the original state 00:45:15.405 --> 00:45:17.550 so we'll just mark that with an X. 00:45:17.550 --> 00:45:22.390 And the vacancy is sitting in a place that used to be 00:45:22.390 --> 00:45:25.940 positive so it's a hole in the land of positive so we know 00:45:25.940 --> 00:45:27.960 that this one's going to be negative. 00:45:27.960 --> 00:45:31.930 And this silver ion, which was displaced from its original 00:45:31.930 --> 00:45:35.360 lattice site, is now going to be sitting in an interstitial 00:45:35.360 --> 00:45:38.680 site which was originally a land of zero. 00:45:38.680 --> 00:45:41.380 So this one's going to be charged positive. 00:45:41.380 --> 00:45:43.530 And now we've balanced, once again, this reaction. 00:45:43.530 --> 00:45:44.580 We have charge neutrality. 00:45:44.580 --> 00:45:48.500 We've created a defect and this is defect, just like in 00:45:48.500 --> 00:45:52.490 the case of vacancies, costs us energy to make. 00:45:52.490 --> 00:45:55.000 So we can actually write down a formation 00:45:55.000 --> 00:45:57.200 energy for Frenkel defects. 00:46:03.720 --> 00:46:06.270 And this formation energy is usually a little bit higher 00:46:06.270 --> 00:46:12.030 than the formation energy of vacancies so it's going to be 00:46:12.030 --> 00:46:14.450 something more perhaps on the order of 2 eV. 00:46:18.550 --> 00:46:19.800 OK. 00:46:23.180 --> 00:46:24.430 So we have gone through-- 00:46:27.070 --> 00:46:29.580 before I go to this one, let me just mention one last 00:46:29.580 --> 00:46:34.080 defect that you might run into if you're working in ionically 00:46:34.080 --> 00:46:34.990 bonded materials. 00:46:34.990 --> 00:46:38.900 An F-center is a situation where you have a vacancy with 00:46:38.900 --> 00:46:40.620 a bound electron inside of it. 00:46:40.620 --> 00:46:44.850 And F-centers have the property that they give 00:46:44.850 --> 00:46:47.340 ceramics a tint, a hue. 00:46:47.340 --> 00:46:50.970 They actually scatter light in the visible range 00:46:50.970 --> 00:46:53.320 so you can see them. 00:46:53.320 --> 00:46:56.330 So with a very short amount of time left, I wanted to tell 00:46:56.330 --> 00:46:59.125 you about a couple of the other defects that you will 00:46:59.125 --> 00:47:01.380 encounter in crystals and one of the most interesting ones 00:47:01.380 --> 00:47:06.590 to me is the dislocation and dislocations are line defects. 00:47:06.590 --> 00:47:08.640 They're 1D defects. 00:47:08.640 --> 00:47:13.280 So if you look in, for example, a corn ear right 00:47:13.280 --> 00:47:17.470 here, you can see dislocations as the termination of a single 00:47:17.470 --> 00:47:18.280 atomic plane. 00:47:18.280 --> 00:47:21.050 So here's a picture of what a dislocation 00:47:21.050 --> 00:47:22.520 looks like in a crystal. 00:47:22.520 --> 00:47:24.620 You have these atomic planes and here you have 00:47:24.620 --> 00:47:25.990 one that just ends. 00:47:25.990 --> 00:47:27.320 That's a dislocation. 00:47:27.320 --> 00:47:29.280 Some of you probably have dislocations in your 00:47:29.280 --> 00:47:30.460 fingerprints. 00:47:30.460 --> 00:47:33.210 So after the class is over, you can look for dislocations 00:47:33.210 --> 00:47:35.520 in your fingerprints. 00:47:35.520 --> 00:47:36.580 They're line defects. 00:47:36.580 --> 00:47:38.280 So here's another example of that. 00:47:38.280 --> 00:47:45.350 You see that there's an extraatomic plane which ends. 00:47:45.350 --> 00:47:47.370 That's a dislocation. 00:47:47.370 --> 00:47:49.930 We mark it with one of these Ts. 00:47:49.930 --> 00:47:52.520 Here's a picture of a dislocation. 00:47:52.520 --> 00:47:56.420 Dislocations actually help materials to deform easily 00:47:56.420 --> 00:48:01.670 without having to shear off. 00:48:01.670 --> 00:48:04.600 Here's a little picture of mine which I really like. 00:48:04.600 --> 00:48:07.880 This is the only way that people really had to study 00:48:07.880 --> 00:48:11.030 dislocations before computers existed. 00:48:11.030 --> 00:48:13.630 So now we can study, for example, dislocation by 00:48:13.630 --> 00:48:15.760 simulating them in real crystals. 00:48:15.760 --> 00:48:20.100 And this is a mid-20th century computer. 00:48:20.100 --> 00:48:22.080 It's a raft of bubbles. 00:48:22.080 --> 00:48:25.350 It's just a bunch of bubbles that somebody blew on the 00:48:25.350 --> 00:48:28.590 surface, soap bubbles, and you can deform them. 00:48:28.590 --> 00:48:31.770 You can deform this raft of bubbles by shearing it and 00:48:31.770 --> 00:48:33.020 here you see-- 00:48:39.520 --> 00:48:40.090 what's wrong? 00:48:40.090 --> 00:48:41.340 Why isn't it going? 00:48:45.560 --> 00:48:48.370 There it is. 00:48:48.370 --> 00:48:56.320 There's your dislocation running through and you see 00:48:56.320 --> 00:48:59.070 lots of dislocations running through this crystal. 00:48:59.070 --> 00:49:03.840 This was, by the way, done by Lawrence Bragg, who you heard 00:49:03.840 --> 00:49:06.430 about in connection with x-ray scattering. 00:49:06.430 --> 00:49:09.990 You'll hear about Bragg again when we get to DNA. 00:49:09.990 --> 00:49:11.900 So keep him in mind.