1 00:00:00,000 --> 00:00:03,056 The following content is provided under a Creative 2 00:00:03,056 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:07,229 Your support will help MIT OpenCourseWare continue to 4 00:00:07,229 --> 00:00:10,684 offer high-quality educational resources for free. 5 00:00:10,684 --> 00:00:13,550 To make a donation or view additional materials from 6 00:00:13,550 --> 00:00:17,480 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,480 --> 00:00:18,730 ocw.mit.edu. 8 00:00:21,625 --> 00:00:24,290 PROFESSOR: I know I'm not Dr. Sadoway. 9 00:00:24,290 --> 00:00:27,920 I'm one of Dr. Sadoway's younger colleagues so-- 10 00:00:27,920 --> 00:00:31,270 but class is beginning, so let's get started. 11 00:00:31,270 --> 00:00:35,010 Dr. Sadoway, of course, would like you to know that he would 12 00:00:35,010 --> 00:00:38,850 very much love to be with you here today and he would 13 00:00:38,850 --> 00:00:41,490 probably like that very much more than what he's doing now, 14 00:00:41,490 --> 00:00:43,920 which is sitting in a secured area secured by the Secret 15 00:00:43,920 --> 00:00:46,670 Service about to meet the President. 16 00:00:46,670 --> 00:00:51,630 So you can ask him all about it when he comes back. 17 00:00:51,630 --> 00:00:55,410 Associated with that, I have one request for you. 18 00:00:55,410 --> 00:00:58,990 Today, when you're leaving, some of you may be used to 19 00:00:58,990 --> 00:01:00,480 leaving that way. 20 00:01:00,480 --> 00:01:01,950 Don't leave that way. 21 00:01:01,950 --> 00:01:03,250 Leave any other way. 22 00:01:03,250 --> 00:01:04,330 This way's fine. 23 00:01:04,330 --> 00:01:05,710 In the back is fine. 24 00:01:05,710 --> 00:01:07,320 Just don't leave that way. 25 00:01:07,320 --> 00:01:09,090 OK. 26 00:01:09,090 --> 00:01:14,800 So last time, we talked about x-rays 27 00:01:14,800 --> 00:01:17,370 defraction and Bragg's Law. 28 00:01:17,370 --> 00:01:20,700 And x-ray defraction and Bragg's Law has a lot to do 29 00:01:20,700 --> 00:01:22,360 with perfect crystals. 30 00:01:22,360 --> 00:01:24,120 So perfection, right? 31 00:01:24,120 --> 00:01:27,300 We've been dealing with perfect crystal so far and 32 00:01:27,300 --> 00:01:29,840 today, we're going to be dealing with imperfections. 33 00:01:29,840 --> 00:01:31,430 So defects. 34 00:01:31,430 --> 00:01:34,130 And in the field of material science, the field that I work 35 00:01:34,130 --> 00:01:36,130 in along with Dr. Sadoway. 36 00:01:36,130 --> 00:01:39,970 there's a saying due to one of the most famous material 37 00:01:39,970 --> 00:01:44,130 scientists that says that crystals are like people. 38 00:01:44,130 --> 00:01:46,500 It's the defects that make them interesting. 39 00:01:46,500 --> 00:01:49,450 So now you've heard that saying and you can roll your 40 00:01:49,450 --> 00:01:52,450 eyes from now on every time you hear it because it's 41 00:01:52,450 --> 00:01:54,660 repeated it very often. 42 00:01:54,660 --> 00:01:56,080 So let's see. 43 00:01:56,080 --> 00:01:58,040 What do we mean by defects? 44 00:01:58,040 --> 00:02:00,900 Well, there's two types of defects, broadly speaking, 45 00:02:00,900 --> 00:02:04,840 that we're going to be talking about, and we can classify 46 00:02:04,840 --> 00:02:07,010 those into two categories. 47 00:02:07,010 --> 00:02:08,260 One of them is chemical. 48 00:02:11,140 --> 00:02:12,750 So far, we've been dealing with 49 00:02:12,750 --> 00:02:14,200 chemically perfect materials. 50 00:02:14,200 --> 00:02:17,720 So ones that are made up of one element or ones that are 51 00:02:17,720 --> 00:02:22,220 made up in stoichiometric quantities of two elements, 52 00:02:22,220 --> 00:02:24,110 but you can also have chemical imperfections. 53 00:02:24,110 --> 00:02:25,640 You can have impurities. 54 00:02:25,640 --> 00:02:28,690 You can have alloying elements and we're also going to be 55 00:02:28,690 --> 00:02:30,395 talking about atomic arrangement. 56 00:02:40,900 --> 00:02:43,420 And in the case of atomic arrangement, we're dealing 57 00:02:43,420 --> 00:02:45,000 with structure, right? 58 00:02:45,000 --> 00:02:46,500 Here we're dealing with chemistry. 59 00:02:46,500 --> 00:02:48,250 Here we're dealing with structure. 60 00:02:48,250 --> 00:02:50,230 You know about crystal structure so you know what 61 00:02:50,230 --> 00:02:53,290 perfect crystals look like, but real materials are not 62 00:02:53,290 --> 00:02:57,410 perfect, neither in the chemical sense nor in the 63 00:02:57,410 --> 00:02:58,330 structural sense. 64 00:02:58,330 --> 00:03:02,360 So perfect crystals don't really exist. You have always 65 00:03:02,360 --> 00:03:05,540 some forms of imperfections and we'll go over those today. 66 00:03:05,540 --> 00:03:10,040 So in the case of chemical imperfections, we have, 67 00:03:10,040 --> 00:03:11,730 broadly speaking, two types. 68 00:03:11,730 --> 00:03:12,980 Good ones-- 69 00:03:14,560 --> 00:03:16,910 Dr. Sadoway labels them with a smiley face so I 70 00:03:16,910 --> 00:03:18,090 will do that, too. 71 00:03:18,090 --> 00:03:20,120 And bad ones are a sad face. 72 00:03:20,120 --> 00:03:23,890 So both are defects and whether they're good or bad 73 00:03:23,890 --> 00:03:26,080 depends on their utility. 74 00:03:26,080 --> 00:03:28,790 Are they useful or are they detrimental? 75 00:03:28,790 --> 00:03:30,620 If they are detrimental, we call them impurities. 76 00:03:37,810 --> 00:03:40,720 And if they are good, we call them other things. 77 00:03:40,720 --> 00:03:41,970 For example, dopants. 78 00:03:45,310 --> 00:03:46,540 We studied dopants, right? 79 00:03:46,540 --> 00:03:48,620 Dopants are a type of impurity, they're a kind of 80 00:03:48,620 --> 00:03:50,270 imperfection, but they're good. 81 00:03:50,270 --> 00:03:50,770 We use dopants. 82 00:03:50,770 --> 00:03:52,860 We use them in semiconductors. 83 00:03:52,860 --> 00:03:59,320 Also, alloying elements, you can put in 84 00:03:59,320 --> 00:04:01,520 the elements yourself. 85 00:04:01,520 --> 00:04:05,490 Those are examples of good chemical imperfections. 86 00:04:05,490 --> 00:04:08,670 When it comes to atomic arrangements, we're going to 87 00:04:08,670 --> 00:04:10,690 spend a little bit of time talking about that in more 88 00:04:10,690 --> 00:04:12,960 detail in just a minute. 89 00:04:12,960 --> 00:04:16,480 But broadly speaking, they are situations where you don't 90 00:04:16,480 --> 00:04:17,810 have perfect crystal in order. 91 00:04:17,810 --> 00:04:20,250 You have disruptions and that perfect crystal in order-- 92 00:04:20,250 --> 00:04:23,260 either in the form of missing atoms or extra atoms or 93 00:04:23,260 --> 00:04:25,420 differently oriented unit cells of the 94 00:04:25,420 --> 00:04:26,300 crystal and so forth. 95 00:04:26,300 --> 00:04:27,530 So we'll talk about that a little bit 96 00:04:27,530 --> 00:04:30,350 more in just a minute. 97 00:04:30,350 --> 00:04:35,615 So one thing that I forgot to mention maybe is that we have 98 00:04:35,615 --> 00:04:37,870 a test coming up-- 99 00:04:37,870 --> 00:04:38,220 That is, I'm sorry. 100 00:04:38,220 --> 00:04:39,580 Celebration of learning, second 101 00:04:39,580 --> 00:04:41,030 celebration of learning. 102 00:04:41,030 --> 00:04:42,930 And those are your room assignments. 103 00:04:42,930 --> 00:04:45,730 You don't have to necessarily write them down now, but 104 00:04:45,730 --> 00:04:46,580 you'll see them again. 105 00:04:46,580 --> 00:04:48,670 So I just wanted you to see them. 106 00:04:48,670 --> 00:04:56,230 A through Ha in 10-250, He through Sm, 26-100, 107 00:04:56,230 --> 00:04:59,510 So through Z, 4-270. 108 00:04:59,510 --> 00:05:04,360 OK, so let's go into the taxonomy of defects. 109 00:05:04,360 --> 00:05:06,430 So I mentioned that there are a number of different kinds of 110 00:05:06,430 --> 00:05:13,120 defects, and we can do better than to say simply, defects 111 00:05:13,120 --> 00:05:15,660 exist. We can actually start to classify them. 112 00:05:15,660 --> 00:05:17,380 So there are, broadly speaking, four types of 113 00:05:17,380 --> 00:05:21,050 defects, which we classify based on dimensionality. 114 00:05:21,050 --> 00:05:24,190 So there's 0-dimensional defects and 0-dimensional 115 00:05:24,190 --> 00:05:28,850 defects are point defects or point defect clusters. 116 00:05:28,850 --> 00:05:29,800 It's just like in math. 117 00:05:29,800 --> 00:05:32,110 A point has 0 dimension, right? 118 00:05:32,110 --> 00:05:36,150 1-dimensional defects or line defects, things that thread 119 00:05:36,150 --> 00:05:39,870 through a material like a shoestring or something, and 120 00:05:39,870 --> 00:05:43,600 we'll have an example of that in the form of dislocations. 121 00:05:43,600 --> 00:05:45,990 Then we have 2-dimensional defects. 122 00:05:45,990 --> 00:05:47,700 Those are interfacial defects. 123 00:05:47,700 --> 00:05:50,270 So if you have interfaces between two different kinds of 124 00:05:50,270 --> 00:05:53,700 materials or if you have two crystals that are misoriented 125 00:05:53,700 --> 00:05:55,980 with respect to each other, those are examples of 126 00:05:55,980 --> 00:05:57,660 interfacial defects. 127 00:05:57,660 --> 00:05:59,830 And we also have bulk defects-- 128 00:05:59,830 --> 00:06:02,250 3-dimensional defects like inclusions. 129 00:06:02,250 --> 00:06:05,110 We'll go over some of those. 130 00:06:05,110 --> 00:06:07,490 So let's start out with point defects. 131 00:06:07,490 --> 00:06:09,830 Point defects are those 0-dimensional defects. 132 00:06:09,830 --> 00:06:11,820 They're points, just like in math. 133 00:06:11,820 --> 00:06:14,190 And there are a number of different point defects that 134 00:06:14,190 --> 00:06:15,340 we can look at. 135 00:06:15,340 --> 00:06:17,780 We have our substitutional impurities, interstitial 136 00:06:17,780 --> 00:06:18,750 impurities. 137 00:06:18,750 --> 00:06:26,380 The general overall recurring theme in these point defects, 138 00:06:26,380 --> 00:06:29,860 regardless what type they are, is that they are localized 139 00:06:29,860 --> 00:06:30,730 disruptions. 140 00:06:30,730 --> 00:06:33,260 So a lattice, a crystalline lattice, is a regular 141 00:06:33,260 --> 00:06:36,150 arrangement of atoms, and a point defect is a very local 142 00:06:36,150 --> 00:06:39,240 disruption in that regular crystalline arrangement. 143 00:06:39,240 --> 00:06:43,310 And those disruptions can occur on lattice sites. 144 00:06:43,310 --> 00:06:46,130 So basically, on the positions where you would see atoms 145 00:06:46,130 --> 00:06:48,690 normally, they can also occur between lattice sites. 146 00:06:48,690 --> 00:06:53,690 So they're localized rifts, you can say, in the 147 00:06:53,690 --> 00:06:57,710 periodicity of a crystalline material. 148 00:06:57,710 --> 00:06:59,760 And here's just an illustration of the way that 149 00:06:59,760 --> 00:07:01,370 these different point defects play out. 150 00:07:01,370 --> 00:07:04,200 So let's start out by looking at this one. 151 00:07:04,200 --> 00:07:06,740 This is a substitutional impurity atom. 152 00:07:06,740 --> 00:07:08,550 So it's an impurity. 153 00:07:08,550 --> 00:07:11,190 So it's a type of chemical imperfection. 154 00:07:11,190 --> 00:07:16,710 You can imagine that this is, for example, some kind of FCC 155 00:07:16,710 --> 00:07:19,010 material like copper, for instance, and suppose that you 156 00:07:19,010 --> 00:07:23,950 have an impurity of some sort like iron, and it sits there 157 00:07:23,950 --> 00:07:27,030 and it replace one of the copper atoms. So this is 158 00:07:27,030 --> 00:07:28,580 called a substitutional impurity. 159 00:07:28,580 --> 00:07:31,570 It substitutes for the regular atom that would have sat at 160 00:07:31,570 --> 00:07:33,050 that location. 161 00:07:33,050 --> 00:07:36,160 Substitutional impurities. 162 00:07:36,160 --> 00:07:37,980 There's another picture. 163 00:07:37,980 --> 00:07:40,340 There's your substitutional impurity up there. 164 00:07:40,340 --> 00:07:42,000 We'll get to the other ones in just a moment. 165 00:07:46,170 --> 00:07:48,560 We already talked about some substitutional impurities. 166 00:07:48,560 --> 00:07:50,740 So dopants. 167 00:07:50,740 --> 00:07:54,010 If you have boron or phosphorus or silicon, that 168 00:07:54,010 --> 00:07:57,140 boron or that phosphorus replaces the silicon that 169 00:07:57,140 --> 00:08:00,020 would have sat at a certain lattice site. 170 00:08:00,020 --> 00:08:03,730 So the dopants we've studied so far are types of 171 00:08:03,730 --> 00:08:07,830 substitutional impurities and we call them good impurities 172 00:08:07,830 --> 00:08:10,640 because they give us desirable properties. 173 00:08:10,640 --> 00:08:11,670 They are dopants. 174 00:08:11,670 --> 00:08:13,270 They're good impurities. 175 00:08:13,270 --> 00:08:15,540 Then we have alloying elements. 176 00:08:15,540 --> 00:08:21,320 I am not a very big fan of sodas, but if you were 177 00:08:21,320 --> 00:08:25,000 somebody else who is a big fan of sodas, then you might, for 178 00:08:25,000 --> 00:08:27,810 example, drink a lot of sodas out of aluminum cans. 179 00:08:27,810 --> 00:08:30,660 Those aluminum cans are really not pure aluminum. 180 00:08:30,660 --> 00:08:31,950 They're alloys. 181 00:08:31,950 --> 00:08:35,750 They're alloys with other metals to give them the good 182 00:08:35,750 --> 00:08:37,910 properties that they need in order for the 183 00:08:37,910 --> 00:08:39,240 forming process to occur. 184 00:08:39,240 --> 00:08:42,090 So if you ask yourself, how do you actually 185 00:08:42,090 --> 00:08:43,780 make aluminum cans? 186 00:08:43,780 --> 00:08:46,230 They're stamped out from sheets of aluminum, but it's 187 00:08:46,230 --> 00:08:47,520 not just aluminum by itself. 188 00:08:47,520 --> 00:08:50,010 Aluminum by itself would just tear if you do that. 189 00:08:50,010 --> 00:08:51,910 So if you alloy it, you give it better 190 00:08:51,910 --> 00:08:54,010 properties so it's ductile. 191 00:08:54,010 --> 00:08:59,250 You can deform it to very large strains and that's a 192 00:08:59,250 --> 00:09:01,950 good thing in the case of alloying elements. 193 00:09:01,950 --> 00:09:05,140 Another one that he showed you was nickel and gold. 194 00:09:05,140 --> 00:09:07,370 That's if you want to change the color of gold, if you want 195 00:09:07,370 --> 00:09:09,610 to be very creative when you're proposing. 196 00:09:09,610 --> 00:09:15,230 So that's a good kind of substitutional impurity. 197 00:09:15,230 --> 00:09:17,360 There are also contaminants. 198 00:09:17,360 --> 00:09:21,520 Contaminants are bad kinds of impurities, but before we get 199 00:09:21,520 --> 00:09:23,710 to the contaminants, let me just show you what good 200 00:09:23,710 --> 00:09:24,760 impurities can do. 201 00:09:24,760 --> 00:09:26,860 So this is the Hope Diamond. 202 00:09:26,860 --> 00:09:31,080 It's in the American gem collection. 203 00:09:31,080 --> 00:09:34,230 You can actually find out more about it. 204 00:09:34,230 --> 00:09:38,670 I'm not a big gem expert, but anybody who looks at this Hope 205 00:09:38,670 --> 00:09:41,450 Diamond can immediately see that it's a 206 00:09:41,450 --> 00:09:42,890 really pretty diamond. 207 00:09:42,890 --> 00:09:45,670 But you guys are ahead of everybody, because in addition 208 00:09:45,670 --> 00:09:49,020 to knowing that it's a pretty diamond, the fact that it has 209 00:09:49,020 --> 00:09:53,320 boron impurities in it already tells you what the majority 210 00:09:53,320 --> 00:09:55,100 charge carrier is. 211 00:09:55,100 --> 00:09:58,220 So when you go to this gem collection, you can educate 212 00:09:58,220 --> 00:10:01,160 everybody else. 213 00:10:01,160 --> 00:10:05,020 So those are all good impurities. 214 00:10:05,020 --> 00:10:06,460 There are also bad impurities-- 215 00:10:06,460 --> 00:10:08,180 contaminants. 216 00:10:08,180 --> 00:10:11,310 Lithium in sodium chloride is an example. 217 00:10:11,310 --> 00:10:16,630 So if you were using saline solution, for instance, in an 218 00:10:16,630 --> 00:10:19,070 IV and you had lithium in there, that is very 219 00:10:19,070 --> 00:10:21,070 detrimental to the person who's receiving that. 220 00:10:21,070 --> 00:10:22,350 That's definitely a contaminant. 221 00:10:22,350 --> 00:10:24,200 You don't want those. 222 00:10:24,200 --> 00:10:26,160 That could make you die. 223 00:10:26,160 --> 00:10:33,280 So let's move on to some other types of point defects. 224 00:10:33,280 --> 00:10:34,900 Here's another type of point defect. 225 00:10:34,900 --> 00:10:36,410 So just now we talked about the 226 00:10:36,410 --> 00:10:38,390 substitutional impurity atom. 227 00:10:38,390 --> 00:10:40,490 Now we're going to talk about the interstitial. 228 00:10:40,490 --> 00:10:42,610 The interstitial's very different from the 229 00:10:42,610 --> 00:10:43,970 substitutional. 230 00:10:43,970 --> 00:10:47,130 In the case of the substitutional, we have a 231 00:10:47,130 --> 00:10:51,730 lattice site, which instead of being occupied by the regular 232 00:10:51,730 --> 00:10:54,800 atom that would have occupied it in a perfect crystal, is 233 00:10:54,800 --> 00:10:58,340 occupied by a chemically distinct atom. 234 00:10:58,340 --> 00:11:02,010 In the case of an interstitial impurity, that impurity can 235 00:11:02,010 --> 00:11:06,900 sit in the space in between lattice sites, so-called 236 00:11:06,900 --> 00:11:08,150 interstitial sites. 237 00:11:08,150 --> 00:11:10,590 That's why we call them interstitial impurities. 238 00:11:10,590 --> 00:11:14,830 And interstitial impurities or interstitial atoms can be both 239 00:11:14,830 --> 00:11:18,430 chemical impurities, and obviously, they are rifts in 240 00:11:18,430 --> 00:11:20,230 the atomic arrangement so they are structural 241 00:11:20,230 --> 00:11:22,520 impurities as well. 242 00:11:22,520 --> 00:11:23,530 Why do I say chemical? 243 00:11:23,530 --> 00:11:26,700 The reason is because if this is, for example, iron, if this 244 00:11:26,700 --> 00:11:30,870 is an iron matrix and you have a carbon atom sitting in the 245 00:11:30,870 --> 00:11:35,780 interstitial site which makes steel, then that's an example 246 00:11:35,780 --> 00:11:39,460 of a structural defect, but it's also a chemical defect. 247 00:11:39,460 --> 00:11:43,190 If, for example, you have, on the other hand, iron sitting 248 00:11:43,190 --> 00:11:45,670 in a nuclear reactor and it's getting bombarded all the time 249 00:11:45,670 --> 00:11:48,160 by energetic neutrons, then interstitials are being 250 00:11:48,160 --> 00:11:50,140 created by atoms getting knocked out of their lattice 251 00:11:50,140 --> 00:11:53,350 sites and they're getting put into interstitial sites. 252 00:11:53,350 --> 00:11:56,820 So that's creating defects that are chemically the same 253 00:11:56,820 --> 00:11:59,960 as the surrounding matrix material, but which are 254 00:11:59,960 --> 00:12:01,050 structurally distinct. 255 00:12:01,050 --> 00:12:04,090 So those are interstitial atoms. 256 00:12:04,090 --> 00:12:06,860 So here's another picture of interstitial 257 00:12:06,860 --> 00:12:09,720 atoms. There it is. 258 00:12:09,720 --> 00:12:12,060 It's not sitting on a regular lattice site. 259 00:12:12,060 --> 00:12:14,630 It's sitting in between lattice sites. 260 00:12:14,630 --> 00:12:19,120 It's sitting in the space, in the interstitial space between 261 00:12:19,120 --> 00:12:24,400 atoms. And I already mentioned to you the fact that if you 262 00:12:24,400 --> 00:12:29,760 put carbon into iron, those atoms go into interstitial 263 00:12:29,760 --> 00:12:33,970 sites and there would give iron some of its beneficial 264 00:12:33,970 --> 00:12:36,340 properties, which we look for in steel. 265 00:12:36,340 --> 00:12:38,780 So some of the good mechanical properties. 266 00:12:38,780 --> 00:12:42,340 Here's another example of a situation where an atom goes 267 00:12:42,340 --> 00:12:46,020 into a lattice and create an interstitial impurity. 268 00:12:46,020 --> 00:12:48,970 So lanthanum-nickel 5 is a prototype 269 00:12:48,970 --> 00:12:51,560 hydrogen storage material. 270 00:12:51,560 --> 00:12:53,180 It takes up a huge amount of hydrogen. 271 00:12:53,180 --> 00:12:56,090 It takes up a greater density of hydrogen than liquid 272 00:12:56,090 --> 00:12:59,040 hydrogen, actually, so if you expose this to hydrogen, the 273 00:12:59,040 --> 00:13:02,340 hydrogen just goes right in, and it sits in the 274 00:13:02,340 --> 00:13:07,950 lanthanum-nickel 5 lattice as an interstitial atom. 275 00:13:07,950 --> 00:13:11,240 So this is considered to be as a prototype 276 00:13:11,240 --> 00:13:12,390 hydrogen storage material. 277 00:13:12,390 --> 00:13:15,420 Unfortunately, it's extremely expensive so it's not being 278 00:13:15,420 --> 00:13:18,510 used very much these days, but on the other hand, it goes 279 00:13:18,510 --> 00:13:21,400 well with our gem theme in this particular lecture in 280 00:13:21,400 --> 00:13:24,150 terms of expensive things. 281 00:13:24,150 --> 00:13:27,530 Here's another example of an interstitial impurity. 282 00:13:27,530 --> 00:13:29,890 This one is not an alloying element. 283 00:13:29,890 --> 00:13:31,880 It's a contaminant. 284 00:13:31,880 --> 00:13:35,780 So hydrogen, but this time in iron. 285 00:13:35,780 --> 00:13:38,710 So hydrogen in lanthanum-nickel 5 is good. 286 00:13:38,710 --> 00:13:40,130 We want to store it. 287 00:13:40,130 --> 00:13:44,530 Hydrogen in iron is bad because it actually degrades 288 00:13:44,530 --> 00:13:47,520 the mechanical properties of the iron, unlike carbon, which 289 00:13:47,520 --> 00:13:49,160 gives us steel, which is good. 290 00:13:49,160 --> 00:13:50,910 You put hydrogen in, it embrittles it. 291 00:13:50,910 --> 00:13:54,300 So hydrogen embrittlement in steels is a big problem. 292 00:13:54,300 --> 00:13:57,340 And it's actually one of the challenges 293 00:13:57,340 --> 00:13:58,680 to a hydrogen economy. 294 00:13:58,680 --> 00:14:04,160 If you have steel pipelines or valves or various pieces of 295 00:14:04,160 --> 00:14:06,570 machinery, structural components that are made out 296 00:14:06,570 --> 00:14:09,290 of iron that are constantly exposed to hydrogen, over 297 00:14:09,290 --> 00:14:10,150 time, they're going to brittle. 298 00:14:10,150 --> 00:14:12,630 They're going to become very difficult to use. 299 00:14:12,630 --> 00:14:19,260 It's one of the challenges in that whole undertaking. 300 00:14:19,260 --> 00:14:20,050 OK. 301 00:14:20,050 --> 00:14:23,490 So we're going fairly at a clip here through these 302 00:14:23,490 --> 00:14:25,870 taxonomy of point defects. 303 00:14:25,870 --> 00:14:30,010 So in the taxonomy of point defects, perhaps the easiest 304 00:14:30,010 --> 00:14:32,760 defect to understand is the vacancy. 305 00:14:32,760 --> 00:14:35,160 So when you think of the vacancy, think of the hole 306 00:14:35,160 --> 00:14:38,700 that we talked about in the case of semiconductors. 307 00:14:38,700 --> 00:14:40,480 Vacancy is nothing. 308 00:14:40,480 --> 00:14:42,410 It's a missing atom. 309 00:14:42,410 --> 00:14:46,470 So if you have a crystalline lattice and it's FCC or it's 310 00:14:46,470 --> 00:14:48,930 BCC or it's simple cubic, whatever you like, and you 311 00:14:48,930 --> 00:14:50,930 know that there's supposed to be an atom at a certain 312 00:14:50,930 --> 00:14:55,930 lattice site and it's not there, that's a vacancy. 313 00:14:55,930 --> 00:14:58,870 That's a situation where you have an unoccupied lattice 314 00:14:58,870 --> 00:15:02,800 site and there are different ways to form these vacancies. 315 00:15:02,800 --> 00:15:04,780 They can be formed during crystallization. 316 00:15:04,780 --> 00:15:07,650 If you heat up a material, the number of vacancies decreases. 317 00:15:07,650 --> 00:15:10,740 So if you quench it really quickly, you can actually trap 318 00:15:10,740 --> 00:15:14,180 the vacancies before they can leave in service under extreme 319 00:15:14,180 --> 00:15:14,760 conditions. 320 00:15:14,760 --> 00:15:17,140 I mentioned just a moment ago that interstitials can be 321 00:15:17,140 --> 00:15:20,520 created if you irradiate a material, if you bombard it 322 00:15:20,520 --> 00:15:23,390 with energetic particles, like neutrons for instance, you'll 323 00:15:23,390 --> 00:15:27,000 create interstitials, sure, by knocking atoms out of their 324 00:15:27,000 --> 00:15:29,880 atomic sites, but what's left behind after you 325 00:15:29,880 --> 00:15:31,720 knock that atom out? 326 00:15:31,720 --> 00:15:33,340 Vacancies. 327 00:15:33,340 --> 00:15:35,910 So actually, you create two defects at the same time: 328 00:15:35,910 --> 00:15:37,160 vacancies and interstitials. 329 00:15:40,170 --> 00:15:44,250 So I think we probably have a picture here of a vacancy. 330 00:15:44,250 --> 00:15:45,210 A vacancy is nothing. 331 00:15:45,210 --> 00:15:47,450 It's just empty space. 332 00:15:47,450 --> 00:15:48,700 That's a vacancy. 333 00:15:51,100 --> 00:15:53,140 There you go again. 334 00:15:53,140 --> 00:15:54,390 Nothing. 335 00:15:56,660 --> 00:16:00,290 So we've gone through a bunch of taxonomy, right? 336 00:16:00,290 --> 00:16:03,090 So we know now that there are a number of different kinds of 337 00:16:03,090 --> 00:16:04,960 point defects in crystals. 338 00:16:04,960 --> 00:16:06,390 We've talked about interstitials. 339 00:16:06,390 --> 00:16:09,040 We talked about vacancies. 340 00:16:09,040 --> 00:16:11,130 We've talked about substitutionals. 341 00:16:11,130 --> 00:16:13,750 What can we say about these defects quantitatively? 342 00:16:13,750 --> 00:16:20,430 So let's take the vacancy and derive or write down what is 343 00:16:20,430 --> 00:16:23,200 the number of vacancies that you can expect to find in a 344 00:16:23,200 --> 00:16:25,720 given material at a certain temperatures? 345 00:16:25,720 --> 00:16:27,930 So to do that, let's be a little bit more quantitative. 346 00:16:27,930 --> 00:16:30,443 Suppose that you have a crystal. 347 00:16:33,620 --> 00:16:37,800 I'm showing you a plane, for example, a 1 1 1 plane in an 348 00:16:37,800 --> 00:16:42,990 FCC material and how do you create a vacancy? 349 00:16:42,990 --> 00:16:46,070 You simply remove an atom. 350 00:16:46,070 --> 00:16:47,150 So you had an atom. 351 00:16:47,150 --> 00:16:48,920 Now you have no atom. 352 00:16:48,920 --> 00:16:50,320 You've created a vacancy. 353 00:16:50,320 --> 00:16:53,020 When you created that vacancy, you broke all the bonds 354 00:16:53,020 --> 00:16:55,610 between the atom that used to be there and the neighboring 355 00:16:55,610 --> 00:16:59,040 atoms. Breaking bonds costs energy. 356 00:16:59,040 --> 00:17:01,580 So it costs energy to create a vacancy. 357 00:17:01,580 --> 00:17:04,600 It costs energy to remove an atom from the place where it 358 00:17:04,600 --> 00:17:06,730 would have been because you're breaking bonds. 359 00:17:06,730 --> 00:17:10,470 So in this case, I have six bonds that I broke. 360 00:17:10,470 --> 00:17:14,930 If I were looking at some material, for example, placing 361 00:17:14,930 --> 00:17:17,510 our cubic material in 3D, I would find that I would be 362 00:17:17,510 --> 00:17:21,260 breaking 12 bonds to the 12 nearest neighbors, and so on 363 00:17:21,260 --> 00:17:24,170 for all the different crystal structures. 364 00:17:24,170 --> 00:17:27,260 So we actually then take that information, the fact that 365 00:17:27,260 --> 00:17:31,290 we're breaking bonds, and encapsulate it in a single 366 00:17:31,290 --> 00:17:33,330 descriptions of how much energy it 367 00:17:33,330 --> 00:17:35,310 costs to create a vacancy. 368 00:17:35,310 --> 00:17:40,870 And we call that the vacancy formation energy. 369 00:17:40,870 --> 00:17:47,340 So this is an energy and so it's expressed in eV. 370 00:17:47,340 --> 00:17:50,620 Its units are electron volts. 371 00:17:50,620 --> 00:17:55,500 You can convert them to joules, anything you like. 372 00:17:55,500 --> 00:18:01,820 And if you wanted to then compute how many vacancies 373 00:18:01,820 --> 00:18:06,320 there are in a given crystal, well, first of all, it costs 374 00:18:06,320 --> 00:18:08,720 energy to make them, so why would you ever even have a 375 00:18:08,720 --> 00:18:10,470 vacancy in the material? 376 00:18:10,470 --> 00:18:13,270 Well, no material is perfect. 377 00:18:13,270 --> 00:18:17,120 We know that from studying materials, but what causes it 378 00:18:17,120 --> 00:18:20,030 is the fact that at finite temperature because of the 379 00:18:20,030 --> 00:18:22,430 Boltzmann distribution that Dr. Sadoway told you about a 380 00:18:22,430 --> 00:18:26,540 few lectures ago, just like in the case of intrinsic charge 381 00:18:26,540 --> 00:18:30,790 carrier promotion in semiconductors, you can get 382 00:18:30,790 --> 00:18:32,640 thermal formation of vacancies. 383 00:18:32,640 --> 00:18:36,320 So that Maxwell Boltzmann distribution can actually 384 00:18:36,320 --> 00:18:38,310 cause there to be vacancies despite the 385 00:18:38,310 --> 00:18:40,290 fact that there are-- 386 00:18:40,290 --> 00:18:42,220 that it costs energy to do that. 387 00:18:42,220 --> 00:18:45,410 So how can we actually use that to express how many 388 00:18:45,410 --> 00:18:48,370 vacancies we have in a given material? 389 00:18:48,370 --> 00:18:52,150 So I'm going to write down an expression for how many 390 00:18:52,150 --> 00:18:56,590 vacancies you can expect to find at a given temperature on 391 00:18:56,590 --> 00:19:00,030 the basis of their formation energy, OK? 392 00:19:00,030 --> 00:19:01,530 So let's do that. 393 00:19:01,530 --> 00:19:04,510 This is going to be the fraction of vacant sites. 394 00:19:04,510 --> 00:19:06,260 So if you have a given material-- 395 00:19:06,260 --> 00:19:08,930 FCC, BCC, whatever you like-- you know that there's a 396 00:19:08,930 --> 00:19:11,870 certain number of lattice sites per unit volume, and you 397 00:19:11,870 --> 00:19:14,010 learn how to calculate those things. 398 00:19:14,010 --> 00:19:16,650 And to quantify the number of vacancies, you have to 399 00:19:16,650 --> 00:19:20,590 basically say, what fraction of those sites does not 400 00:19:20,590 --> 00:19:21,390 contain an atom? 401 00:19:21,390 --> 00:19:24,860 Is that 1/100 of a percent or is it 1% or how many? 402 00:19:24,860 --> 00:19:32,200 So this is actually going to be expressed as a ratio, which 403 00:19:32,200 --> 00:19:33,480 I'm going to call this. 404 00:19:33,480 --> 00:19:48,670 This is the number of vacancies per unit volume and 405 00:19:48,670 --> 00:19:58,195 this is the number of atomic sites, also per 406 00:19:58,195 --> 00:20:05,200 unit volume, OK. 407 00:20:08,180 --> 00:20:12,200 So this is the definition of the fraction of vacant sites. 408 00:20:12,200 --> 00:20:13,420 And how do we express it? 409 00:20:13,420 --> 00:20:17,860 Well, we express it using a very simple formula. 410 00:20:17,860 --> 00:20:21,590 This formula contains a factor here which is experimentally 411 00:20:21,590 --> 00:20:22,110 determined. 412 00:20:22,110 --> 00:20:26,190 This is an empirical factor and then an exponential. 413 00:20:26,190 --> 00:20:32,710 So the exponent we take here, the vacancy formation energy, 414 00:20:32,710 --> 00:20:38,120 and we divide it by the thermal energy at the given 415 00:20:38,120 --> 00:20:40,510 temperature of interest. 416 00:20:40,510 --> 00:20:44,200 So this is actually telling you that to form vacancies, 417 00:20:44,200 --> 00:20:47,910 you actually have two competing factors. 418 00:20:47,910 --> 00:20:52,130 On the one hand, you have the bonding energy that makes the 419 00:20:52,130 --> 00:20:54,540 difficult-to-form vacancies because you're breaking bonds, 420 00:20:54,540 --> 00:20:55,810 you're taking it an atom out. 421 00:20:55,810 --> 00:20:58,720 On the other hand, you have this thermal energy, Boltzmann 422 00:20:58,720 --> 00:21:01,300 constant times the temperature, and the thermal 423 00:21:01,300 --> 00:21:04,210 energy is competing with that bonding energy. 424 00:21:04,210 --> 00:21:06,640 And when that thermal energy is high enough, you can 425 00:21:06,640 --> 00:21:10,740 actually start knocking atoms out despite the fact that it 426 00:21:10,740 --> 00:21:13,930 costs you some energy, and obviously when this ratio is 427 00:21:13,930 --> 00:21:16,760 very large, that means that the bonding predominates, and 428 00:21:16,760 --> 00:21:19,250 when it gets smaller, that means the thermal energy is 429 00:21:19,250 --> 00:21:21,560 more and more sufficient to actually knock atoms out of 430 00:21:21,560 --> 00:21:24,520 their positions and cause there to be vacancies. 431 00:21:24,520 --> 00:21:29,500 So when you do these calculations, make sure to use 432 00:21:29,500 --> 00:21:33,770 the absolute temperature in Kelvin, and dimensional 433 00:21:33,770 --> 00:21:36,180 analysis will tell you the units of the Boltzmann 434 00:21:36,180 --> 00:21:40,110 constant have to be energy units per degrees. 435 00:21:40,110 --> 00:21:42,830 So eV's per Kelvin, for instance. 436 00:21:42,830 --> 00:21:44,480 So this is the absolute temperature. 437 00:21:55,980 --> 00:21:58,740 This is the vacancy formation energy and this is the 438 00:21:58,740 --> 00:21:59,990 Boltzmann constant. 439 00:22:11,580 --> 00:22:15,910 So what that means is that at any given temperature, you'll 440 00:22:15,910 --> 00:22:18,790 actually expect to see some fraction of vacancies. 441 00:22:18,790 --> 00:22:21,970 So let's actually try to do a calculation with an actual 442 00:22:21,970 --> 00:22:25,360 vacancy formation energy and see how many vacancies we get 443 00:22:25,360 --> 00:22:27,870 at a given temperature. 444 00:22:27,870 --> 00:22:34,830 So to do that, we've been provided with what is the 445 00:22:34,830 --> 00:22:38,100 common currency in science, which is published 446 00:22:38,100 --> 00:22:43,790 experimental data, which we find from published journals 447 00:22:43,790 --> 00:22:47,820 which we find online through, for example, Web of Science. 448 00:22:47,820 --> 00:22:54,950 And from this journal, we find that for copper, the vacancy 449 00:22:54,950 --> 00:23:04,800 formation energy is 1.03 electron volts. 450 00:23:04,800 --> 00:23:11,410 Furthermore, in the same journal in the abstract there, 451 00:23:11,410 --> 00:23:17,450 you'll find the magnitude of this constant A, which as I 452 00:23:17,450 --> 00:23:20,610 told you is experimentally determined. 453 00:23:20,610 --> 00:23:24,265 This quantity A we call the entropy factor. 454 00:23:32,560 --> 00:23:37,120 And even though there's no way to very easily derive it-- 455 00:23:37,120 --> 00:23:39,800 I can't tell you what's the entropy factor for iron and 456 00:23:39,800 --> 00:23:42,930 you can't really tell me just by thinking about it-- 457 00:23:42,930 --> 00:23:47,070 nevertheless, it turns out that this factor usually fall 458 00:23:47,070 --> 00:23:48,720 within a certain range. 459 00:23:48,720 --> 00:23:51,590 It's usually between 0.1 and 10. 460 00:23:51,590 --> 00:23:53,810 That's usually the range and what you find As. 461 00:23:53,810 --> 00:23:56,750 And in the case of copper, it's very much in that range. 462 00:23:56,750 --> 00:23:58,520 It's just 1.1. 463 00:23:58,520 --> 00:24:01,700 So let's use this information to actually figure out how 464 00:24:01,700 --> 00:24:05,840 many vacancies we expect to see in copper at the given 465 00:24:05,840 --> 00:24:07,090 temperature. 466 00:24:18,680 --> 00:24:19,040 OK. 467 00:24:19,040 --> 00:24:23,970 So here's my fraction of vacancies and we know that it 468 00:24:23,970 --> 00:24:30,910 is going to be expressed as 1.1 times exponent minus the 469 00:24:30,910 --> 00:24:36,280 formation energy, which is 1.03 eV, and then we'll put in 470 00:24:36,280 --> 00:24:39,600 Boltzmann's constant, and then let's pick a temperature. 471 00:24:39,600 --> 00:24:41,540 For the moment, let's just take room temperature. 472 00:24:41,540 --> 00:24:44,480 So T, room temperature, and room 473 00:24:44,480 --> 00:24:47,760 temperature's about 300 K. 474 00:24:47,760 --> 00:24:50,010 So when we put in all these numbers, it's just a matter of 475 00:24:50,010 --> 00:24:50,840 calculating. 476 00:24:50,840 --> 00:24:52,960 This is on your sheet of constants. 477 00:24:52,960 --> 00:24:55,960 This is the temperature which we choose at room temperature. 478 00:24:55,960 --> 00:25:02,940 Let's actually write down T, room temperature, is about 300 479 00:25:02,940 --> 00:25:08,890 K, and we find a certain number of vacancies. 480 00:25:08,890 --> 00:25:17,880 And the number of vacancies that we find is 2.19 times 10 481 00:25:17,880 --> 00:25:24,950 to the minus 18 vacancies. 482 00:25:24,950 --> 00:25:27,500 So this is the fraction of vacant sites. 483 00:25:27,500 --> 00:25:28,840 Well, is that a lot? 484 00:25:28,840 --> 00:25:31,640 Is that a little? 485 00:25:31,640 --> 00:25:33,950 How can we determine whether this is a lot or a little? 486 00:25:33,950 --> 00:25:37,780 We compare it to the number of atoms that there actually are, 487 00:25:37,780 --> 00:25:42,190 and in the case of solid materials, we expect there to 488 00:25:42,190 --> 00:25:45,010 be something on the order-- this has to be compared to 489 00:25:45,010 --> 00:25:47,460 something on the order of Avogadro's number, but we can 490 00:25:47,460 --> 00:25:52,680 actually calculate more explicitly that this turns out 491 00:25:52,680 --> 00:25:56,750 to be something like 10 to the 5th vacancies 492 00:25:56,750 --> 00:26:00,840 per centimeter cubed. 493 00:26:00,840 --> 00:26:04,350 And if in a real material, a solid material like silicon, 494 00:26:04,350 --> 00:26:10,140 for instance, or boron or whatever you're interested in, 495 00:26:10,140 --> 00:26:14,250 your number of atoms is something like 10 to the 23rd, 496 00:26:14,250 --> 00:26:17,440 Avogadro's number, right, then this is 497 00:26:17,440 --> 00:26:20,640 actually a very tiny number. 498 00:26:20,640 --> 00:26:23,180 Compare 10 to the 5th to 10 to the 23rd. 499 00:26:23,180 --> 00:26:26,610 The number of atoms that are missing at room temperature is 500 00:26:26,610 --> 00:26:28,130 very low in copper. 501 00:26:28,130 --> 00:26:32,250 We can compute that using this expression. 502 00:26:32,250 --> 00:26:35,100 However, even though it's low, it's not zero. 503 00:26:35,100 --> 00:26:37,440 And if we continue going down in temperature, we'll find 504 00:26:37,440 --> 00:26:40,110 that the number is lower and lower and lower, but it never 505 00:26:40,110 --> 00:26:43,680 really goes to zero because we have this expression which 506 00:26:43,680 --> 00:26:45,580 gives us the total number. 507 00:26:45,580 --> 00:26:48,240 So let's do another one and this time, let's take a 508 00:26:48,240 --> 00:26:49,070 different temperature. 509 00:26:49,070 --> 00:26:52,350 Let's take the melting temperature of copper. 510 00:26:52,350 --> 00:26:56,000 The melting temperature of copper is considerably higher. 511 00:26:56,000 --> 00:27:00,430 It's about 1085 degrees Celsius and we can go through 512 00:27:00,430 --> 00:27:02,300 exactly the same calculation. 513 00:27:02,300 --> 00:27:11,900 1.1 times all these quantities here times melting 514 00:27:11,900 --> 00:27:14,510 temperature, OK? 515 00:27:14,510 --> 00:27:25,100 And when we do this, we get a vacant site fraction which is 516 00:27:25,100 --> 00:27:35,050 1.67 times 10 to the minus 4 and that corresponds to 1.41 517 00:27:35,050 --> 00:27:38,880 times 10 to the 19th vacancies per centimeter cubed. 518 00:27:42,630 --> 00:27:44,160 So what do we know by-- 519 00:27:44,160 --> 00:27:46,510 what can we see now by comparing these two 520 00:27:46,510 --> 00:27:47,130 quantities? 521 00:27:47,130 --> 00:27:49,630 Number of vacancies, add room temperature, number of 522 00:27:49,630 --> 00:27:51,440 vacancies at melting temperature. 523 00:27:51,440 --> 00:27:54,540 How many orders of magnitude do they differ by? 524 00:27:54,540 --> 00:28:02,130 Huge difference in the number of vacancies that we find at 525 00:28:02,130 --> 00:28:03,200 two different temperatures. 526 00:28:03,200 --> 00:28:06,430 And why do we see such a huge difference? 527 00:28:06,430 --> 00:28:10,040 Let's actually write down what that difference is. 528 00:28:10,040 --> 00:28:12,292 Let's write down the ratio. 529 00:28:12,292 --> 00:28:18,630 The fraction of vacant sites at melting temperature divided 530 00:28:18,630 --> 00:28:24,170 by fraction of vacant sites at room temperature is something 531 00:28:24,170 --> 00:28:31,170 like 7.6 times 10 to the 13th. 532 00:28:31,170 --> 00:28:33,640 That's the difference in number of vacancies you get 533 00:28:33,640 --> 00:28:35,400 just by increasing the temperature from room 534 00:28:35,400 --> 00:28:37,020 temperature to melting temperature. 535 00:28:37,020 --> 00:28:37,970 Why is that? 536 00:28:37,970 --> 00:28:41,830 Well, one way to look at that is just from the expression 537 00:28:41,830 --> 00:28:45,590 that we have to calculate the number. 538 00:28:45,590 --> 00:28:47,380 Here's where the temperatures go. 539 00:28:47,380 --> 00:28:50,180 So any difference in temperature if it's a factor 540 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 541 00:28:52,912 --> 00:28:55,740 four, it's going to go into the exponential. 542 00:28:55,740 --> 00:28:58,340 So that exponential is actually making a huge 543 00:28:58,340 --> 00:29:00,600 difference as a function of temperature in terms of number 544 00:29:00,600 --> 00:29:02,280 of defects that you get. 545 00:29:02,280 --> 00:29:03,570 The higher you go up in temperature, 546 00:29:03,570 --> 00:29:04,680 you don't get just-- 547 00:29:04,680 --> 00:29:07,420 you go up a factor of four in temperature, you don't just 548 00:29:07,420 --> 00:29:10,560 get a factor of four increase in the number of defects. 549 00:29:10,560 --> 00:29:12,560 You get that in the exponential. 550 00:29:12,560 --> 00:29:15,520 So the factor of four is hugely magnified by the 551 00:29:15,520 --> 00:29:17,830 exponential. 552 00:29:17,830 --> 00:29:21,490 So that means that at any given temperature, even the 553 00:29:21,490 --> 00:29:23,720 lowest temperatures, you expect to see some defects, 554 00:29:23,720 --> 00:29:27,310 but if you increase the temperature, you see a hugely 555 00:29:27,310 --> 00:29:28,940 larger number of defects. 556 00:29:28,940 --> 00:29:30,580 And you can use this sort of expression 557 00:29:30,580 --> 00:29:31,740 for any kind of defect. 558 00:29:31,740 --> 00:29:35,260 So I talked about vacancies right now and vacancies have a 559 00:29:35,260 --> 00:29:38,130 specific formation energy, but interstitials also have 560 00:29:38,130 --> 00:29:40,380 formation energies, substitutionals also have 561 00:29:40,380 --> 00:29:41,160 formation energies. 562 00:29:41,160 --> 00:29:43,940 So you can use this expression to determine the fraction of 563 00:29:43,940 --> 00:29:48,230 defects per lattice site for any kind of defect so long as 564 00:29:48,230 --> 00:29:50,700 you have the formation energy of that defect. 565 00:29:50,700 --> 00:29:54,410 So just to show you how difficult it is actually to 566 00:29:54,410 --> 00:30:01,420 remove defects, if you have a crystalline material, defects 567 00:30:01,420 --> 00:30:03,645 want to stay even at the lowest temperatures. 568 00:30:03,645 --> 00:30:09,600 I have this interesting little piece of art to show you. 569 00:30:09,600 --> 00:30:14,990 This particular piece of art was actually discovered, I 570 00:30:14,990 --> 00:30:20,040 guess, by some scientist at the University of Toronto 571 00:30:20,040 --> 00:30:23,855 where Dr. Sadoway went to school, and this particular-- 572 00:30:27,180 --> 00:30:27,790 what do they call it? 573 00:30:27,790 --> 00:30:29,040 They call it The Atomix. 574 00:30:31,890 --> 00:30:34,570 Let me write down the name of it in case you want to look it 575 00:30:34,570 --> 00:30:38,000 up because I think they sold a lot more of these to material 576 00:30:38,000 --> 00:30:39,940 scientists than they sold to anybody else. 577 00:30:46,720 --> 00:30:52,460 And all this is two plastic plates, two PMMA plates, 578 00:30:52,460 --> 00:30:56,320 polymethyl methacrylates, or plexiglass. 579 00:30:56,320 --> 00:31:00,290 And in between them, there's a little hole that's cut, a gap, 580 00:31:00,290 --> 00:31:03,330 and in that gap are a number of ball bearings. 581 00:31:03,330 --> 00:31:05,730 And the ball bearings are kind of like atom, right, so they 582 00:31:05,730 --> 00:31:06,940 move around. 583 00:31:06,940 --> 00:31:10,020 And here we're going to the document camera right now. 584 00:31:10,020 --> 00:31:12,970 So if you shake these things around and the ball bearings 585 00:31:12,970 --> 00:31:16,270 are moving around, that's like introducing temperature. 586 00:31:16,270 --> 00:31:19,630 That's like taking a crystal, melting it, all the atoms are 587 00:31:19,630 --> 00:31:21,110 bouncing around. 588 00:31:21,110 --> 00:31:24,390 You will even see some vapor atoms when these sort of leave 589 00:31:24,390 --> 00:31:28,150 the surface and fly through the air, but then if you stop, 590 00:31:28,150 --> 00:31:29,850 that's like quenching. 591 00:31:29,850 --> 00:31:33,570 That's like suddenly I've taken this crystal, which was 592 00:31:33,570 --> 00:31:35,990 originally molten, and I've dropped the temperature. 593 00:31:35,990 --> 00:31:39,040 Here's what I see. 594 00:31:39,040 --> 00:31:40,290 So can you see that? 595 00:31:42,660 --> 00:31:43,910 How to use this thing-- 596 00:31:49,360 --> 00:31:51,600 there we go. 597 00:31:51,600 --> 00:31:54,100 So you can actually see a lot of the defects that we were 598 00:31:54,100 --> 00:31:56,680 talking about just a moment ago. 599 00:31:56,680 --> 00:32:03,100 Here you can see areas of perfect crystalline order. 600 00:32:03,100 --> 00:32:05,570 Here's another area of perfect crystalline order. 601 00:32:05,570 --> 00:32:08,840 So you have many, many crystals that are adjacent to 602 00:32:08,840 --> 00:32:09,760 each other. 603 00:32:09,760 --> 00:32:11,880 They're oriented differently. 604 00:32:11,880 --> 00:32:15,780 So they're forming misorientation defects between 605 00:32:15,780 --> 00:32:16,330 themselves. 606 00:32:16,330 --> 00:32:18,960 So for example, here's a grain boundary. 607 00:32:18,960 --> 00:32:20,830 This is a crystalline grain. 608 00:32:20,830 --> 00:32:23,180 And inside this crystal, you see a vacancy. 609 00:32:23,180 --> 00:32:25,340 It's right there, So here's another 610 00:32:25,340 --> 00:32:27,090 instance of the vacancy. 611 00:32:27,090 --> 00:32:29,140 There's another vacancy. 612 00:32:29,140 --> 00:32:33,540 And what happens if I try to remove some of the disorder? 613 00:32:33,540 --> 00:32:36,640 By the way, interesting thing is that some of the vapor is 614 00:32:36,640 --> 00:32:37,720 also left here. 615 00:32:37,720 --> 00:32:40,050 So there's the vapor. 616 00:32:40,050 --> 00:32:43,210 If I then try to remove some of these defects, I can just 617 00:32:43,210 --> 00:32:45,270 tap on this. 618 00:32:45,270 --> 00:32:48,610 If I just continue to tap on it, I'm removing defects. 619 00:32:48,610 --> 00:32:50,480 The whole thing is crystallizing more and more 620 00:32:50,480 --> 00:32:54,180 and more so now I put it down again. 621 00:32:57,460 --> 00:32:59,730 OK. 622 00:32:59,730 --> 00:33:01,650 You still see the vapor phase. 623 00:33:01,650 --> 00:33:04,820 Now you see a big huge crystal right here with some grain 624 00:33:04,820 --> 00:33:06,680 boundaries around it. 625 00:33:06,680 --> 00:33:09,820 Here's another big huge crystal. 626 00:33:09,820 --> 00:33:11,440 Here's another crystal. 627 00:33:11,440 --> 00:33:13,470 There's a smaller crystal. 628 00:33:13,470 --> 00:33:16,420 Each one of them is bounded by grain boundaries, but what do 629 00:33:16,420 --> 00:33:18,450 you see in each of these crystals? 630 00:33:18,450 --> 00:33:19,570 There's a vacancy. 631 00:33:19,570 --> 00:33:20,510 There's a vacancy. 632 00:33:20,510 --> 00:33:21,820 There's a vacancy. 633 00:33:21,820 --> 00:33:24,360 And you can actually sit here-- 634 00:33:24,360 --> 00:33:25,240 well, not here. 635 00:33:25,240 --> 00:33:29,100 Maybe later, but if you want to take a look at one of these 636 00:33:29,100 --> 00:33:32,170 things, you can probably go to Dr. Sadoway's office and pick 637 00:33:32,170 --> 00:33:35,110 it up and he'll let you play with it for a little while. 638 00:33:35,110 --> 00:33:36,990 You can try to get all these vacancies out. 639 00:33:36,990 --> 00:33:38,860 You can try to get all the defects out. 640 00:33:38,860 --> 00:33:42,490 No matter how hard you try, if you spent hours, you'll get 641 00:33:42,490 --> 00:33:46,000 things to be more and more and more perfect by tapping on it, 642 00:33:46,000 --> 00:33:48,610 but there's always going to be a vacancy. 643 00:33:48,610 --> 00:33:49,090 Always. 644 00:33:49,090 --> 00:33:53,560 And even if you are extremely patient, you get things down 645 00:33:53,560 --> 00:33:55,850 to just one vacancy and you think that all you have to do 646 00:33:55,850 --> 00:33:58,410 now is just give it a little bit more of a tap to remove 647 00:33:58,410 --> 00:34:03,760 that one vacancy, well, more often than not, you'll find 648 00:34:03,760 --> 00:34:05,740 that with that tap you'll remove the vacancy, but create 649 00:34:05,740 --> 00:34:07,380 another vacancy somewhere else. 650 00:34:07,380 --> 00:34:09,500 So you'll always find these vacancies in 651 00:34:09,500 --> 00:34:11,750 these crystalline materials. 652 00:34:15,100 --> 00:34:18,230 It's just a consequence of the fact that when you're 653 00:34:18,230 --> 00:34:20,630 agitating a material like you're doing here-- you're 654 00:34:20,630 --> 00:34:21,620 shaking it-- 655 00:34:21,620 --> 00:34:23,590 that's the same thing that happens if you have some 656 00:34:23,590 --> 00:34:25,670 finite temperatures, some non-zero temperature in the 657 00:34:25,670 --> 00:34:28,060 material, you're always going to be creating some defect. 658 00:34:28,060 --> 00:34:30,659 So that's exactly what this expression is giving you. 659 00:34:30,659 --> 00:34:32,770 It's telling you that there's going to be defects at any 660 00:34:32,770 --> 00:34:36,120 temperature, but their number goes up dramatically as you 661 00:34:36,120 --> 00:34:38,160 increase the temperature. 662 00:34:38,160 --> 00:34:42,710 So let's go back to the slides real quick now. 663 00:34:42,710 --> 00:34:43,550 OK. 664 00:34:43,550 --> 00:34:47,620 So everything I've told you so far is concerned with defects 665 00:34:47,620 --> 00:34:52,880 in crystals that are of one type, so that are made up of a 666 00:34:52,880 --> 00:34:55,010 single element. 667 00:34:55,010 --> 00:35:01,670 But in the case of, for example, things like ionic 668 00:35:01,670 --> 00:35:05,410 crystals, and ionic crystals are made up of multiple 669 00:35:05,410 --> 00:35:09,730 elements with multiple charge states, you can get new kinds 670 00:35:09,730 --> 00:35:12,010 of point defects that you can't see in a 671 00:35:12,010 --> 00:35:14,110 single element material. 672 00:35:14,110 --> 00:35:17,250 So we'll talk a little bit about those and when it comes 673 00:35:17,250 --> 00:35:21,860 to those defects in ionic materials, we have to expand 674 00:35:21,860 --> 00:35:23,380 the taxonomy a little bit. 675 00:35:23,380 --> 00:35:26,090 The taxonomy is now going to include defects called 676 00:35:26,090 --> 00:35:28,390 Schottky imperfections, Frenkel 677 00:35:28,390 --> 00:35:30,900 imperfections, and F-centers. 678 00:35:30,900 --> 00:35:35,880 So let's go to a visualization of what these are. 679 00:35:35,880 --> 00:35:39,690 Here you see an ionic crystal. 680 00:35:39,690 --> 00:35:43,460 So you have alternating types of atoms. You have these big 681 00:35:43,460 --> 00:35:47,900 ones, which are presumably the negatively charge ones, and 682 00:35:47,900 --> 00:35:50,390 then you have the small positively charged ones, and 683 00:35:50,390 --> 00:35:53,970 here you have an example of a Schottky imperfection. 684 00:35:53,970 --> 00:35:57,450 So a Schottky imperfection, it's kind of like a vacancy. 685 00:35:57,450 --> 00:36:01,220 It's missing atoms. The main difference between a Schottky 686 00:36:01,220 --> 00:36:08,600 imperfection and a vacancy by itself is the fact that in a 687 00:36:08,600 --> 00:36:11,620 material that involves charged atoms-- 688 00:36:11,620 --> 00:36:12,420 ions, right-- 689 00:36:12,420 --> 00:36:16,180 in an ionic crystal, when you take atoms out, you have to 690 00:36:16,180 --> 00:36:18,980 make sure to maintain charge neutrality. 691 00:36:18,980 --> 00:36:20,780 So these materials are charge neutral. 692 00:36:20,780 --> 00:36:23,640 They have equal numbers of positive and negative ions, 693 00:36:23,640 --> 00:36:25,290 but you want to make sure that you take these 694 00:36:25,290 --> 00:36:26,360 out in equal numbers. 695 00:36:26,360 --> 00:36:29,140 So in the Schottky defect, you take out one negative and one 696 00:36:29,140 --> 00:36:33,490 positive ion, or basically one unit, one stoichiometric unit. 697 00:36:33,490 --> 00:36:37,120 If you add zirconium oxide, which is ZrO2, you would have 698 00:36:37,120 --> 00:36:41,590 to take out three atoms to maintain charge neutrality. 699 00:36:41,590 --> 00:36:44,230 That would be the Schottky defect. 700 00:36:44,230 --> 00:36:46,780 So here is another example, another visualization of a 701 00:36:46,780 --> 00:36:47,600 Schottky defect. 702 00:36:47,600 --> 00:36:51,120 So when you take these two atoms out, nothing says that 703 00:36:51,120 --> 00:36:53,750 they have to be taken out from right next to each other. 704 00:36:53,750 --> 00:36:55,270 You can take out one here. 705 00:36:55,270 --> 00:36:56,870 You can take out one there. 706 00:36:56,870 --> 00:36:59,590 It's good both ways because in the end, it's just about 707 00:36:59,590 --> 00:37:00,380 charge neutrality. 708 00:37:00,380 --> 00:37:05,200 It's about maintaining a charge neutral material. 709 00:37:05,200 --> 00:37:09,350 So we can actually write down reactions to describe the 710 00:37:09,350 --> 00:37:12,650 formation of these Schottky defects. 711 00:37:12,650 --> 00:37:15,320 So let's do that. 712 00:37:15,320 --> 00:37:19,260 When we write down reactions to describe the formation of 713 00:37:19,260 --> 00:37:23,360 Schottky defects, we first recognize the fact that we're 714 00:37:23,360 --> 00:37:24,780 dealing with empty sites. 715 00:37:24,780 --> 00:37:26,770 We're dealing with void. 716 00:37:26,770 --> 00:37:30,560 We want to see how this void, or in scientific parlance, 717 00:37:30,560 --> 00:37:38,750 null, is decomposed into two vacant sites in the particular 718 00:37:38,750 --> 00:37:40,640 ionic crystal that we're dealing with. 719 00:37:40,640 --> 00:37:42,870 So let's-- to make things specific, 720 00:37:42,870 --> 00:37:44,650 deal with sodium chloride. 721 00:37:44,650 --> 00:37:46,770 So sodium chloride, we have two type of 722 00:37:46,770 --> 00:37:49,510 atoms. Sodium and chloride. 723 00:37:49,510 --> 00:37:51,880 And to maintain charge neutrality, we have to remove 724 00:37:51,880 --> 00:37:52,970 one of each. 725 00:37:52,970 --> 00:37:56,350 So this is actually-- this null space is actually going 726 00:37:56,350 --> 00:38:00,950 to be composed of two vacancies: a vacant site on a 727 00:38:00,950 --> 00:38:04,350 sodium lattice where a sodium atom would have been sitting 728 00:38:04,350 --> 00:38:06,180 and a vacant site where a chlorine 729 00:38:06,180 --> 00:38:07,430 would have been sitting. 730 00:38:07,430 --> 00:38:11,570 And because this entire process takes place in the 731 00:38:11,570 --> 00:38:17,580 presence of materials that are composed of ions-- 732 00:38:17,580 --> 00:38:19,120 so ionic solids-- 733 00:38:19,120 --> 00:38:24,220 these two vacancies, in fact, have some charge them. 734 00:38:24,220 --> 00:38:27,900 So when we think about the charge of these vacancies, 735 00:38:27,900 --> 00:38:30,200 what we actually have to think of, it's a little bit 736 00:38:30,200 --> 00:38:32,070 counterintuitive. 737 00:38:32,070 --> 00:38:35,430 The sodium in a sodium chloride crystal is charge 738 00:38:35,430 --> 00:38:38,950 positive, but what does that make the vacancy? 739 00:38:38,950 --> 00:38:43,180 So if you have a lattice of atoms that are charge positive 740 00:38:43,180 --> 00:38:47,110 like the sodium atoms and you remove one of them, what is 741 00:38:47,110 --> 00:38:49,560 the effective charge of that vacancy? 742 00:38:49,560 --> 00:38:52,180 You have nothing, as Dr. Sadoway would say, 743 00:38:52,180 --> 00:38:54,150 in the land of plus. 744 00:38:54,150 --> 00:38:56,780 So the charge of this vacancy, the effective charge of this 745 00:38:56,780 --> 00:38:58,960 vacancy, is going to be negative. 746 00:38:58,960 --> 00:39:04,490 And we mark that with this little thing right there. 747 00:39:04,490 --> 00:39:15,695 So void or nothing in land of plus is negative. 748 00:39:18,320 --> 00:39:22,160 We mark that with one of these apostrophes. 749 00:39:22,160 --> 00:39:25,010 So what about this vacancy? 750 00:39:25,010 --> 00:39:28,270 That vacancy is created on a lattice of sites which are 751 00:39:28,270 --> 00:39:30,030 usually charge negative. 752 00:39:30,030 --> 00:39:33,500 So if you have these chlorine atoms that are charged 753 00:39:33,500 --> 00:39:36,510 negative and you remove one of them, now you have void in a 754 00:39:36,510 --> 00:39:37,820 land of plus. 755 00:39:37,820 --> 00:39:40,720 So this is going to be effectively charge positive 756 00:39:40,720 --> 00:39:47,160 and so we have this void in land of minus. 757 00:39:47,160 --> 00:39:48,835 It is positive. 758 00:39:51,790 --> 00:39:53,290 And we do it-- 759 00:39:53,290 --> 00:40:00,800 we annotate it with one of these dots. 760 00:40:00,800 --> 00:40:03,960 We can do the same thing for other kinds of crystals. 761 00:40:03,960 --> 00:40:07,120 So I mentioned that in this case, a Schottky defect would 762 00:40:07,120 --> 00:40:09,970 just be composed of these two atoms, because these two atoms 763 00:40:09,970 --> 00:40:12,300 constitute the structural unit for this crystal. 764 00:40:12,300 --> 00:40:15,590 But if we had some other, more complicated crystal, like, for 765 00:40:15,590 --> 00:40:19,110 examples, zirconium oxide, then we would still write down 766 00:40:19,110 --> 00:40:21,680 a similar reaction. 767 00:40:21,680 --> 00:40:25,745 So we could put a Schottky defect into zirconium oxide. 768 00:40:30,670 --> 00:40:31,970 OK. 769 00:40:31,970 --> 00:40:34,010 And so now we have to figure out how this 770 00:40:34,010 --> 00:40:35,000 reaction plays out. 771 00:40:35,000 --> 00:40:36,970 We have to create vacancies. 772 00:40:36,970 --> 00:40:40,680 Here's our vacancy on the zirconium. 773 00:40:40,680 --> 00:40:45,120 And because the structural unit contains two oxygens, we 774 00:40:45,120 --> 00:40:46,700 have to create two oxygen vacancies. 775 00:40:49,680 --> 00:40:52,460 And now we have to think about how do we maintain charge 776 00:40:52,460 --> 00:40:53,570 neutralities? 777 00:40:53,570 --> 00:40:56,960 What is the effective charge on all of these atoms? 778 00:40:56,960 --> 00:41:02,600 So the zirconium sites are usually the positively charged 779 00:41:02,600 --> 00:41:05,940 atoms, so when we remove one of them, that's removing 780 00:41:05,940 --> 00:41:08,820 something, that's putting void basically 781 00:41:08,820 --> 00:41:09,990 into the land of plus. 782 00:41:09,990 --> 00:41:14,540 So we have now a negatively charged vacancy, and this 783 00:41:14,540 --> 00:41:18,025 negatively charged vacancy has four negative charges, an 784 00:41:18,025 --> 00:41:20,250 effective minus 4 negative charge. 785 00:41:20,250 --> 00:41:22,980 And the oxygens are the negatively charged ions, and 786 00:41:22,980 --> 00:41:25,745 so when we create voids there, these two vacancies have an 787 00:41:25,745 --> 00:41:28,260 effective positive charge, and because the charges have to 788 00:41:28,260 --> 00:41:32,700 balance, we know that this has to be effectively two negative 789 00:41:32,700 --> 00:41:34,030 charges and there are two vacancies. 790 00:41:34,030 --> 00:41:35,700 So we have charge neutrality. 791 00:41:35,700 --> 00:41:41,230 So that's how the Schottky defects work. 792 00:41:41,230 --> 00:41:42,480 OK. 793 00:41:45,920 --> 00:41:47,920 So let's move on to Frenkel defects. 794 00:41:47,920 --> 00:41:50,010 In the case of Frenkel defects, it's really not so 795 00:41:50,010 --> 00:41:54,400 different from Schottky defects in some sense, except 796 00:41:54,400 --> 00:42:09,660 now instead of dealing with a situation where we maintain 797 00:42:09,660 --> 00:42:14,230 charge neutrality by removing two atoms, we actually 798 00:42:14,230 --> 00:42:19,670 displace one atom from its initial location to a 799 00:42:19,670 --> 00:42:21,480 different part of the crystal. 800 00:42:21,480 --> 00:42:24,850 So we're creating actually a vacancy right there, and this 801 00:42:24,850 --> 00:42:27,800 atom, which was originally sitting on a lattice site, is 802 00:42:27,800 --> 00:42:29,730 now displaced to an interstitial location. 803 00:42:29,730 --> 00:42:31,310 So that's an interstitial. 804 00:42:31,310 --> 00:42:34,620 So a Frenkel defect is a vacancy and an interstitial. 805 00:42:34,620 --> 00:42:37,940 And here's another view of a Frenkel defect. 806 00:42:37,940 --> 00:42:42,790 Here, I've removed an atom from one of the lattice sites 807 00:42:42,790 --> 00:42:44,810 and moved it over to here. 808 00:42:44,810 --> 00:42:48,230 So that's my Frenkel defect. 809 00:42:48,230 --> 00:42:57,020 And in the case of Frenkel defects I can also write down 810 00:42:57,020 --> 00:42:58,780 reactions for Frenkel defects. 811 00:43:01,920 --> 00:43:03,170 Let's do that. 812 00:43:13,560 --> 00:43:15,120 OK. 813 00:43:15,120 --> 00:43:18,840 So Frenkel defects usually occur in crystals with widely 814 00:43:18,840 --> 00:43:25,630 differing atomic radii, and in ionic crystals, the radius of 815 00:43:25,630 --> 00:43:32,060 whatever is positively charged would have to be much, much 816 00:43:32,060 --> 00:43:34,800 less than whatever the radius of whatever's negatively 817 00:43:34,800 --> 00:43:39,840 charged occasionally, or very rarely, but I suppose it's 818 00:43:39,840 --> 00:43:44,230 still possible, you would have to have basically a very big 819 00:43:44,230 --> 00:43:46,110 difference in radius between these two cases. 820 00:43:46,110 --> 00:43:49,380 An example of one of these situations is, for example, 821 00:43:49,380 --> 00:43:54,990 silver bromide, where here the silver's positively charged 822 00:43:54,990 --> 00:43:59,470 and the bromide ion is negatively charged. 823 00:43:59,470 --> 00:44:04,710 And we can write down a reaction to describe the 824 00:44:04,710 --> 00:44:08,390 Frenkel defect formation just like we did in the case of the 825 00:44:08,390 --> 00:44:09,980 Schottky defect formation. 826 00:44:09,980 --> 00:44:13,020 So in the case of a Frenkel defect formation, how do we 827 00:44:13,020 --> 00:44:14,490 actually go about this? 828 00:44:14,490 --> 00:44:19,830 We have, for example, can start out with a silver atom 829 00:44:19,830 --> 00:44:23,760 site and we're going to displace that silver atom away 830 00:44:23,760 --> 00:44:26,470 from its original site so it now sits in an interstitial 831 00:44:26,470 --> 00:44:30,450 position and we're going to leave behind a vacancy. 832 00:44:30,450 --> 00:44:31,700 So let's do that. 833 00:44:35,380 --> 00:44:35,760 OK. 834 00:44:35,760 --> 00:44:47,400 So we're going to have silver interstitial site and let's 835 00:44:47,400 --> 00:44:49,070 just be clear-- 836 00:44:49,070 --> 00:44:52,450 say that this is on a regular silver site. 837 00:44:52,450 --> 00:44:59,740 And then we have a vacancy left over on the silver site 838 00:44:59,740 --> 00:45:01,400 and this is the reaction for the formation 839 00:45:01,400 --> 00:45:02,850 of our Frenkel defect. 840 00:45:02,850 --> 00:45:06,300 Frenkel defects, just like Schottky defects, preserve 841 00:45:06,300 --> 00:45:07,600 charge neutrality. 842 00:45:07,600 --> 00:45:09,630 So how do we actually mark down charge 843 00:45:09,630 --> 00:45:10,600 neutrality in this case? 844 00:45:10,600 --> 00:45:15,405 Well, there's no change in charges in the original state 845 00:45:15,405 --> 00:45:17,550 so we'll just mark that with an X. 846 00:45:17,550 --> 00:45:22,390 And the vacancy is sitting in a place that used to be 847 00:45:22,390 --> 00:45:25,940 positive so it's a hole in the land of positive so we know 848 00:45:25,940 --> 00:45:27,960 that this one's going to be negative. 849 00:45:27,960 --> 00:45:31,930 And this silver ion, which was displaced from its original 850 00:45:31,930 --> 00:45:35,360 lattice site, is now going to be sitting in an interstitial 851 00:45:35,360 --> 00:45:38,680 site which was originally a land of zero. 852 00:45:38,680 --> 00:45:41,380 So this one's going to be charged positive. 853 00:45:41,380 --> 00:45:43,530 And now we've balanced, once again, this reaction. 854 00:45:43,530 --> 00:45:44,580 We have charge neutrality. 855 00:45:44,580 --> 00:45:48,500 We've created a defect and this is defect, just like in 856 00:45:48,500 --> 00:45:52,490 the case of vacancies, costs us energy to make. 857 00:45:52,490 --> 00:45:55,000 So we can actually write down a formation 858 00:45:55,000 --> 00:45:57,200 energy for Frenkel defects. 859 00:46:03,720 --> 00:46:06,270 And this formation energy is usually a little bit higher 860 00:46:06,270 --> 00:46:12,030 than the formation energy of vacancies so it's going to be 861 00:46:12,030 --> 00:46:14,450 something more perhaps on the order of 2 eV. 862 00:46:18,550 --> 00:46:19,800 OK. 863 00:46:23,180 --> 00:46:24,430 So we have gone through-- 864 00:46:27,070 --> 00:46:29,580 before I go to this one, let me just mention one last 865 00:46:29,580 --> 00:46:34,080 defect that you might run into if you're working in ionically 866 00:46:34,080 --> 00:46:34,990 bonded materials. 867 00:46:34,990 --> 00:46:38,900 An F-center is a situation where you have a vacancy with 868 00:46:38,900 --> 00:46:40,620 a bound electron inside of it. 869 00:46:40,620 --> 00:46:44,850 And F-centers have the property that they give 870 00:46:44,850 --> 00:46:47,340 ceramics a tint, a hue. 871 00:46:47,340 --> 00:46:50,970 They actually scatter light in the visible range 872 00:46:50,970 --> 00:46:53,320 so you can see them. 873 00:46:53,320 --> 00:46:56,330 So with a very short amount of time left, I wanted to tell 874 00:46:56,330 --> 00:46:59,125 you about a couple of the other defects that you will 875 00:46:59,125 --> 00:47:01,380 encounter in crystals and one of the most interesting ones 876 00:47:01,380 --> 00:47:06,590 to me is the dislocation and dislocations are line defects. 877 00:47:06,590 --> 00:47:08,640 They're 1D defects. 878 00:47:08,640 --> 00:47:13,280 So if you look in, for example, a corn ear right 879 00:47:13,280 --> 00:47:17,470 here, you can see dislocations as the termination of a single 880 00:47:17,470 --> 00:47:18,280 atomic plane. 881 00:47:18,280 --> 00:47:21,050 So here's a picture of what a dislocation 882 00:47:21,050 --> 00:47:22,520 looks like in a crystal. 883 00:47:22,520 --> 00:47:24,620 You have these atomic planes and here you have 884 00:47:24,620 --> 00:47:25,990 one that just ends. 885 00:47:25,990 --> 00:47:27,320 That's a dislocation. 886 00:47:27,320 --> 00:47:29,280 Some of you probably have dislocations in your 887 00:47:29,280 --> 00:47:30,460 fingerprints. 888 00:47:30,460 --> 00:47:33,210 So after the class is over, you can look for dislocations 889 00:47:33,210 --> 00:47:35,520 in your fingerprints. 890 00:47:35,520 --> 00:47:36,580 They're line defects. 891 00:47:36,580 --> 00:47:38,280 So here's another example of that. 892 00:47:38,280 --> 00:47:45,350 You see that there's an extraatomic plane which ends. 893 00:47:45,350 --> 00:47:47,370 That's a dislocation. 894 00:47:47,370 --> 00:47:49,930 We mark it with one of these Ts. 895 00:47:49,930 --> 00:47:52,520 Here's a picture of a dislocation. 896 00:47:52,520 --> 00:47:56,420 Dislocations actually help materials to deform easily 897 00:47:56,420 --> 00:48:01,670 without having to shear off. 898 00:48:01,670 --> 00:48:04,600 Here's a little picture of mine which I really like. 899 00:48:04,600 --> 00:48:07,880 This is the only way that people really had to study 900 00:48:07,880 --> 00:48:11,030 dislocations before computers existed. 901 00:48:11,030 --> 00:48:13,630 So now we can study, for example, dislocation by 902 00:48:13,630 --> 00:48:15,760 simulating them in real crystals. 903 00:48:15,760 --> 00:48:20,100 And this is a mid-20th century computer. 904 00:48:20,100 --> 00:48:22,080 It's a raft of bubbles. 905 00:48:22,080 --> 00:48:25,350 It's just a bunch of bubbles that somebody blew on the 906 00:48:25,350 --> 00:48:28,590 surface, soap bubbles, and you can deform them. 907 00:48:28,590 --> 00:48:31,770 You can deform this raft of bubbles by shearing it and 908 00:48:31,770 --> 00:48:33,020 here you see-- 909 00:48:39,520 --> 00:48:40,090 what's wrong? 910 00:48:40,090 --> 00:48:41,340 Why isn't it going? 911 00:48:45,560 --> 00:48:48,370 There it is. 912 00:48:48,370 --> 00:48:56,320 There's your dislocation running through and you see 913 00:48:56,320 --> 00:48:59,070 lots of dislocations running through this crystal. 914 00:48:59,070 --> 00:49:03,840 This was, by the way, done by Lawrence Bragg, who you heard 915 00:49:03,840 --> 00:49:06,430 about in connection with x-ray scattering. 916 00:49:06,430 --> 00:49:09,990 You'll hear about Bragg again when we get to DNA. 917 00:49:09,990 --> 00:49:11,900 So keep him in mind.