1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,830 Commons license. 3 00:00:03,830 --> 00:00:06,860 Your support will MIT OpenCourseWare continue to 4 00:00:06,860 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:20,856 --> 00:00:23,410 PROFESSOR: Today, big announcement. 9 00:00:23,410 --> 00:00:24,650 Wednesday, no lecture. 10 00:00:24,650 --> 00:00:28,880 Instead, Celebration Part 2. 11 00:00:28,880 --> 00:00:30,370 And I'm going to say a few words about it. 12 00:00:30,370 --> 00:00:31,840 There is the room assignments. 13 00:00:31,840 --> 00:00:33,310 I think they're the same as last time. 14 00:00:35,920 --> 00:00:39,800 If you miss the exam because of illness, there will be a 15 00:00:39,800 --> 00:00:42,090 make-up test on November 4th during class. 16 00:00:42,090 --> 00:00:44,060 There's no weekly quiz tomorrow. 17 00:00:44,060 --> 00:00:47,820 I'll be available for office hours 4:00 to 5:30 this 18 00:00:47,820 --> 00:00:51,350 afternoon over here at 8-205. 19 00:00:51,350 --> 00:00:52,490 So a couple of things. 20 00:00:52,490 --> 00:00:55,820 I'm going to say few words about the 21 00:00:55,820 --> 00:00:58,100 quiz, the test, rather. 22 00:00:58,100 --> 00:00:59,560 The celebration. 23 00:00:59,560 --> 00:01:03,820 So the coverage is going to go starting from the time of the 24 00:01:03,820 --> 00:01:08,170 last celebration up through now, but I think in view of 25 00:01:08,170 --> 00:01:11,720 the fact that we started defects on Friday, and my 26 00:01:11,720 --> 00:01:14,730 thanks go to Professor Demkowicz, who jumped in the 27 00:01:14,730 --> 00:01:18,320 breach and lectured in my place so that I could get 28 00:01:18,320 --> 00:01:21,180 drawn into some of the activities associated with the 29 00:01:21,180 --> 00:01:23,740 visit of the President. 30 00:01:23,740 --> 00:01:29,420 You will not have had the time to go through your recitation 31 00:01:29,420 --> 00:01:31,150 cycle on this new material. 32 00:01:31,150 --> 00:01:33,482 So I'm not going to put anything on defects on the 33 00:01:33,482 --> 00:01:34,300 exam, all right? 34 00:01:34,300 --> 00:01:39,000 So we'll go up through the end of the unit on x-rays right up 35 00:01:39,000 --> 00:01:41,470 through Bragg's Law, indexing crystals. 36 00:01:41,470 --> 00:01:43,930 So that starting Friday, defects. 37 00:01:43,930 --> 00:01:46,550 I'm not going to teach you Friday, teach you Monday, 38 00:01:46,550 --> 00:01:48,140 examine you Wednesday and Tuesday. 39 00:01:48,140 --> 00:01:50,670 Tomorrow I expect you're going to have all sorts of 40 00:01:50,670 --> 00:01:53,830 review-oriented activities in your recitation. 41 00:01:53,830 --> 00:01:57,700 So I don't want you torn between trying to master a lot 42 00:01:57,700 --> 00:01:59,660 of this new material, which is quite different from what you 43 00:01:59,660 --> 00:02:03,230 had in high school, and at the same time trying to have a 44 00:02:03,230 --> 00:02:06,940 catch up on capturing all that material since the second 45 00:02:06,940 --> 00:02:09,180 test. 46 00:02:09,180 --> 00:02:12,470 So that having been said, I'm going to remind you. 47 00:02:12,470 --> 00:02:14,460 I'm going to basically say the same thing I said before the 48 00:02:14,460 --> 00:02:19,380 first celebration, but we need to be reminded. 49 00:02:19,380 --> 00:02:21,310 So what's the purpose of the test? 50 00:02:21,310 --> 00:02:25,040 The purpose of the test is to give you a status report and 51 00:02:25,040 --> 00:02:26,280 send you a message. 52 00:02:26,280 --> 00:02:28,930 And there's really only two answers here that we're 53 00:02:28,930 --> 00:02:29,540 looking for. 54 00:02:29,540 --> 00:02:31,290 You're either going to get a smiley face or you're going to 55 00:02:31,290 --> 00:02:32,170 get a frowny face. 56 00:02:32,170 --> 00:02:34,090 That's all it's about. 57 00:02:34,090 --> 00:02:38,710 I don't care whether it's a 78 or a 75, but 58 00:02:38,710 --> 00:02:40,130 hard 50 is a pass. 59 00:02:40,130 --> 00:02:43,530 And if you're not mastering the material, I intend to tell 60 00:02:43,530 --> 00:02:46,810 you so and then invite you in so that we can figure out how 61 00:02:46,810 --> 00:02:48,900 to get you through. 62 00:02:48,900 --> 00:02:51,500 Because everybody in this room has the intellectual apparatus 63 00:02:51,500 --> 00:02:52,730 to pass this class. 64 00:02:52,730 --> 00:02:56,120 Some of you just are not managing your time well and 65 00:02:56,120 --> 00:02:57,890 you need to be told that. 66 00:02:57,890 --> 00:02:59,320 So we will tell you that. 67 00:02:59,320 --> 00:03:00,900 With one of these. 68 00:03:00,900 --> 00:03:02,640 That's going to be the message. 69 00:03:02,640 --> 00:03:05,220 Go to the right room. 70 00:03:05,220 --> 00:03:08,340 Bring five things with you: Periodic Table, table of 71 00:03:08,340 --> 00:03:13,600 constants, your age sheet, calculator, and a pen, 72 00:03:13,600 --> 00:03:15,190 something to write with. 73 00:03:15,190 --> 00:03:16,930 You'll write on the question paper. 74 00:03:16,930 --> 00:03:19,000 No wireless devices. 75 00:03:19,000 --> 00:03:19,790 Shut them off. 76 00:03:19,790 --> 00:03:20,630 Don't even bring them. 77 00:03:20,630 --> 00:03:22,710 What do you need your cell phone for? 78 00:03:22,710 --> 00:03:24,756 Don't need it during a test. 79 00:03:24,756 --> 00:03:31,190 We're going to start at 11:05 promptly and stop at 11:55. 80 00:03:31,190 --> 00:03:32,650 What's the strategy? 81 00:03:32,650 --> 00:03:35,190 Read the entire paper. 82 00:03:35,190 --> 00:03:36,580 Try every question. 83 00:03:36,580 --> 00:03:37,660 You know this. 84 00:03:37,660 --> 00:03:40,100 You get part marks if you write something. 85 00:03:40,100 --> 00:03:41,280 If you don't write anything for the 86 00:03:41,280 --> 00:03:42,910 question, you get a zero. 87 00:03:42,910 --> 00:03:44,990 So try every question. 88 00:03:44,990 --> 00:03:46,420 And start with the easy one. 89 00:03:46,420 --> 00:03:48,520 The easy one for you may not be the easy one for your 90 00:03:48,520 --> 00:03:50,690 neighbor, but how do you know what the easy one is? 91 00:03:50,690 --> 00:03:53,790 I just put them down as they came out of my mind. 92 00:03:53,790 --> 00:03:56,790 I didn't put them down in ascending order of difficulty, 93 00:03:56,790 --> 00:03:59,570 chronological order, topical order. 94 00:03:59,570 --> 00:04:00,580 They're just-- 95 00:04:00,580 --> 00:04:01,830 they're there. 96 00:04:04,520 --> 00:04:11,155 Leave tracks, tell us how you got to the answer, Work 97 00:04:11,155 --> 00:04:12,250 parametrically. 98 00:04:12,250 --> 00:04:14,500 Don't start plugging in numbers on the first line, 99 00:04:14,500 --> 00:04:16,170 because if you make a computational error on the 100 00:04:16,170 --> 00:04:19,540 first line and drag it through the entire derivation, you'll 101 00:04:19,540 --> 00:04:20,505 make a mess of things. 102 00:04:20,505 --> 00:04:24,880 You'll have wavelengths, size of distance here to Chicago, 103 00:04:24,880 --> 00:04:26,900 light moving at ten times its normal speed 104 00:04:26,900 --> 00:04:27,760 and stuff like that. 105 00:04:27,760 --> 00:04:29,510 It's no good. 106 00:04:29,510 --> 00:04:31,610 Focus on the question. 107 00:04:31,610 --> 00:04:34,570 Don't just say, oh, it's something to do with x-rays, 108 00:04:34,570 --> 00:04:37,110 just give me some stuff that you memorized about x-rays, 109 00:04:37,110 --> 00:04:39,720 some stuff you wrote down in your age sheet about x-rays. 110 00:04:39,720 --> 00:04:41,420 If it's not about the question that we asked, 111 00:04:41,420 --> 00:04:42,120 I'll give you a zero. 112 00:04:42,120 --> 00:04:43,660 I don't care how much you write. 113 00:04:43,660 --> 00:04:46,490 Write on the topic. 114 00:04:46,490 --> 00:04:47,890 And refer to electronic structure. 115 00:04:47,890 --> 00:04:50,960 When you don't know what to say, start talking to me about 116 00:04:50,960 --> 00:04:53,170 electronic structure. 117 00:04:53,170 --> 00:04:54,820 That's the theme of chemistry. 118 00:04:54,820 --> 00:04:58,660 electronic structure dictates behavior. 119 00:04:58,660 --> 00:05:00,510 So talk to me about electronic structure. 120 00:05:00,510 --> 00:05:01,760 Do your own work. 121 00:05:04,720 --> 00:05:08,040 And lastly, it says something here, oh, good luck. 122 00:05:08,040 --> 00:05:08,650 That's what it says. 123 00:05:08,650 --> 00:05:10,240 Good luck. 124 00:05:10,240 --> 00:05:12,380 So last day, Professor Demkowicz 125 00:05:12,380 --> 00:05:14,220 got to the line defects. 126 00:05:14,220 --> 00:05:17,680 He was talking to us about line defects and how they have 127 00:05:17,680 --> 00:05:21,220 an impact on behavior. 128 00:05:21,220 --> 00:05:25,780 So I wanted to pick up the treatment there. 129 00:05:25,780 --> 00:05:28,690 So what's the whole issue behind line defects? 130 00:05:28,690 --> 00:05:33,790 Well, what line defects do is they explain this anomalous 131 00:05:33,790 --> 00:05:37,496 behavior where the measured value of yield strength-- 132 00:05:42,630 --> 00:05:45,900 so I'm going to write sigma y; sigma is 133 00:05:45,900 --> 00:05:49,350 the symbol for strength. 134 00:05:49,350 --> 00:05:58,060 the yield strength as measured is on the order of only about 135 00:05:58,060 --> 00:06:01,120 1/10 of the theoretical value. 136 00:06:01,120 --> 00:06:05,010 It's only about 1/10 of the theoretical value for the 137 00:06:05,010 --> 00:06:06,280 yield strength. 138 00:06:06,280 --> 00:06:07,200 You might, say, wait a minute. 139 00:06:07,200 --> 00:06:09,020 How do you get that theoretical value? 140 00:06:09,020 --> 00:06:10,860 You can calculate this. 141 00:06:10,860 --> 00:06:12,100 Not too badly. 142 00:06:12,100 --> 00:06:16,090 If I take a look at a system of atoms, and this could be a 143 00:06:16,090 --> 00:06:19,130 metallic crystal, you could argue that there are metallic 144 00:06:19,130 --> 00:06:22,360 bonds between all of these atoms. And if what I wanted to 145 00:06:22,360 --> 00:06:25,270 do to shear something-- 146 00:06:25,270 --> 00:06:27,610 so this is the yield strength for shear-- 147 00:06:27,610 --> 00:06:31,620 if I wanted to shear the top plane of atoms versus the 148 00:06:31,620 --> 00:06:34,190 bottom plane of atoms, can you see that to a first 149 00:06:34,190 --> 00:06:37,170 approximation, the energy required would be the energy 150 00:06:37,170 --> 00:06:38,780 to break each one of these bonds? 151 00:06:38,780 --> 00:06:41,930 Because I have to break the bond to release the plane and 152 00:06:41,930 --> 00:06:43,180 then move it. 153 00:06:43,180 --> 00:06:45,340 So if you make an estimation on the 154 00:06:45,340 --> 00:06:46,590 basis of bond strength-- 155 00:06:49,690 --> 00:06:56,990 so you take individual bond strength times bond density or 156 00:06:56,990 --> 00:06:58,730 bond concentration. 157 00:06:58,730 --> 00:07:00,620 When I say density, I don't necessarily mean 158 00:07:00,620 --> 00:07:01,760 mass per unit volume. 159 00:07:01,760 --> 00:07:03,910 I could mean bonds per unit area. 160 00:07:03,910 --> 00:07:05,550 You saw your homework questions. 161 00:07:05,550 --> 00:07:08,410 How many atoms per unit length? 162 00:07:08,410 --> 00:07:10,210 And we said what's the linear density? 163 00:07:10,210 --> 00:07:11,530 And some people were saying, but density is 164 00:07:11,530 --> 00:07:12,460 mass per unit volume. 165 00:07:12,460 --> 00:07:15,370 No, I'm counting atoms per unit length. 166 00:07:15,370 --> 00:07:17,940 Open your mind, OK? 167 00:07:17,940 --> 00:07:20,060 So bond strength, what's bond density? 168 00:07:20,060 --> 00:07:22,460 That's atoms per unit area. 169 00:07:22,460 --> 00:07:25,380 So we can calculate this and we're way off. 170 00:07:25,380 --> 00:07:28,090 We're way off by about a factor of 10. 171 00:07:28,090 --> 00:07:30,820 So it was the dislocation that allowed us to 172 00:07:30,820 --> 00:07:32,650 explain why this happens. 173 00:07:32,650 --> 00:07:37,870 And it was the work of two scientists, one by the name of 174 00:07:37,870 --> 00:07:44,490 Orowan in Hungary and Taylor in the UK. 175 00:07:44,490 --> 00:07:49,290 Orowan, after World War II, went to the UK and then 176 00:07:49,290 --> 00:07:50,755 ultimately came to MIT. 177 00:07:50,755 --> 00:07:54,550 And he spent most of this later part of his career here 178 00:07:54,550 --> 00:07:56,350 in the Mechanical Engineering Department, 179 00:07:56,350 --> 00:07:58,300 from which he retired. 180 00:07:58,300 --> 00:08:00,880 And actually, he's too modest to say it, but Professor 181 00:08:00,880 --> 00:08:06,000 Demkowicz, his PhD was for Professor Argon, and Professor 182 00:08:06,000 --> 00:08:08,630 Argon was one of Orowan's students. 183 00:08:08,630 --> 00:08:10,760 So this is direct lineage. 184 00:08:10,760 --> 00:08:15,180 This is all very clear, so he was the appropriate person to 185 00:08:15,180 --> 00:08:16,770 introduce dislocations. 186 00:08:16,770 --> 00:08:18,210 So what did Orowan do? 187 00:08:18,210 --> 00:08:21,840 Orowan came up with this idea of an interruption. 188 00:08:21,840 --> 00:08:22,790 And how did he get it? 189 00:08:22,790 --> 00:08:26,770 It shows how to look around and, in 190 00:08:26,770 --> 00:08:30,270 the world, see analogies. 191 00:08:30,270 --> 00:08:32,830 Now, we didn't have the powerful electron microscopes 192 00:08:32,830 --> 00:08:33,760 then that we have today. 193 00:08:33,760 --> 00:08:36,900 This was in the 1930s, so people didn't even agree on an 194 00:08:36,900 --> 00:08:38,980 atomic view of things. 195 00:08:38,980 --> 00:08:42,610 So people were thinking, thinking, thinking. 196 00:08:42,610 --> 00:08:43,900 So this is the dislocation. 197 00:08:43,900 --> 00:08:44,540 You can see. 198 00:08:44,540 --> 00:08:46,930 Here, we have three rows of atoms, now there's two rows of 199 00:08:46,930 --> 00:08:49,510 atoms. The middle row stops there. 200 00:08:49,510 --> 00:08:51,750 And I'll show you what the consequence of that is in 201 00:08:51,750 --> 00:08:56,040 terms of being able to shear the crystal of lower values of 202 00:08:56,040 --> 00:08:57,720 applied stress. 203 00:08:57,720 --> 00:08:59,390 So that's the dislocation. 204 00:08:59,390 --> 00:09:00,260 You can see here. 205 00:09:00,260 --> 00:09:03,820 If you break this bond and then propagate that through, 206 00:09:03,820 --> 00:09:05,180 you don't have to shear them all. 207 00:09:05,180 --> 00:09:08,590 You break them one at a time. 208 00:09:08,590 --> 00:09:12,500 So Orowan came home one day in Budapest, and the cleaning 209 00:09:12,500 --> 00:09:17,760 woman was moving the runner on a hallway, the story goes, and 210 00:09:17,760 --> 00:09:20,120 she was about to move the runner. 211 00:09:20,120 --> 00:09:22,700 And Orowan came up the stairs and offered to help her, and 212 00:09:22,700 --> 00:09:25,440 she told him, get out of the way. 213 00:09:25,440 --> 00:09:26,320 Academic. 214 00:09:26,320 --> 00:09:30,140 And what she did, instead of pulling the rug, she did what 215 00:09:30,140 --> 00:09:31,820 we see in the cartoon here. 216 00:09:31,820 --> 00:09:34,810 She put a little kink in the rug, snapped her foot and 217 00:09:34,810 --> 00:09:38,400 propagated the kink and moved the rug a half a foot down the 218 00:09:38,400 --> 00:09:40,710 hallway with minimal energy. 219 00:09:40,710 --> 00:09:43,720 Instead of having to pull the rug with it's coefficient of 220 00:09:43,720 --> 00:09:47,150 fraction over three, four meters, all she had to do was 221 00:09:47,150 --> 00:09:48,970 come up with enough energy to make the kink and 222 00:09:48,970 --> 00:09:50,010 then stamp the foot. 223 00:09:50,010 --> 00:09:52,120 This person's really doing it the hard way. 224 00:09:52,120 --> 00:09:52,750 I don't know. 225 00:09:52,750 --> 00:09:54,070 This guy must have taken classes in 226 00:09:54,070 --> 00:09:55,030 chemistry or something. 227 00:09:55,030 --> 00:09:57,290 But see, all you've got to do-- 228 00:09:57,290 --> 00:09:59,310 once you get that kind you just push 229 00:09:59,310 --> 00:10:01,600 and it'll go by itself. 230 00:10:01,600 --> 00:10:05,660 So Orowan said could this be a metaphor for what's going on 231 00:10:05,660 --> 00:10:07,350 at the atomic level? 232 00:10:07,350 --> 00:10:09,070 And that's where it came up with this idea of the 233 00:10:09,070 --> 00:10:10,320 dislocation. 234 00:10:12,080 --> 00:10:13,860 So there we have it. 235 00:10:17,370 --> 00:10:19,990 So where do we find the dislocations? 236 00:10:19,990 --> 00:10:21,070 Where do we find them? 237 00:10:21,070 --> 00:10:21,790 So what is it? 238 00:10:21,790 --> 00:10:22,810 The dislocation-- 239 00:10:22,810 --> 00:10:24,980 I keep talking about it, what is it? 240 00:10:24,980 --> 00:10:29,920 The dislocation, this is, if you like, it's a line defect. 241 00:10:29,920 --> 00:10:44,050 It's a line defect formed by misregistry of atoms. And with 242 00:10:44,050 --> 00:10:51,005 the misregistry, that leads to a reduction in bond density. 243 00:11:01,950 --> 00:11:05,800 And that broken bond is like the hole, if you like, in the 244 00:11:05,800 --> 00:11:07,610 valence band. 245 00:11:07,610 --> 00:11:09,385 It can propagate very easily. 246 00:11:12,380 --> 00:11:14,840 We're going to learn a little bit later in the lecture where 247 00:11:14,840 --> 00:11:18,650 we find dislocations and how they contribute. 248 00:11:18,650 --> 00:11:22,700 But I want you to hold that in near-term memory. 249 00:11:22,700 --> 00:11:23,070 OK. 250 00:11:23,070 --> 00:11:24,950 So we're going down the list of the 251 00:11:24,950 --> 00:11:28,630 different types of defects. 252 00:11:28,630 --> 00:11:31,950 Oh here, I found this off a coffee table book that's 253 00:11:31,950 --> 00:11:33,640 indicating-- 254 00:11:33,640 --> 00:11:34,865 I think this is a crummy analogy. 255 00:11:34,865 --> 00:11:37,320 It shows this caterpillar moving by. 256 00:11:37,320 --> 00:11:40,200 Instead of moving all of its legs, it causes this thing-- 257 00:11:40,200 --> 00:11:42,980 I think this is a bad analogy. 258 00:11:42,980 --> 00:11:43,790 Just look down here. 259 00:11:43,790 --> 00:11:45,370 You see, you breaking this. 260 00:11:45,370 --> 00:11:48,440 And once you break this, you just keep moving it along. 261 00:11:48,440 --> 00:11:51,030 Propagate the single broken bond instead of breaking them 262 00:11:51,030 --> 00:11:54,200 all at once. 263 00:11:54,200 --> 00:11:58,100 I don't think the caterpillar moves that way, anyway. 264 00:11:58,100 --> 00:12:00,950 It's cute, but it's wrong. 265 00:12:00,950 --> 00:12:03,030 This is a dislocation. 266 00:12:03,030 --> 00:12:04,490 I don't think it has anything to do with mechanical 267 00:12:04,490 --> 00:12:07,100 behavior, but it's a misregistry. 268 00:12:07,100 --> 00:12:07,890 So you can-- 269 00:12:07,890 --> 00:12:11,060 these guys, they write the books and they come up with 270 00:12:11,060 --> 00:12:12,590 this stuff and you study it, and you're 271 00:12:12,590 --> 00:12:13,520 going, I don't get it. 272 00:12:13,520 --> 00:12:13,980 You know what? 273 00:12:13,980 --> 00:12:14,820 You shouldn't get it. 274 00:12:14,820 --> 00:12:15,770 Because this is crummy. 275 00:12:15,770 --> 00:12:17,020 It doesn't make any sense. 276 00:12:20,440 --> 00:12:23,690 How does that impact the yield stress of the corn? 277 00:12:26,330 --> 00:12:27,980 Someday you could write a book. 278 00:12:27,980 --> 00:12:29,560 Better one than this. 279 00:12:29,560 --> 00:12:30,580 All right, so now we're going to go to 280 00:12:30,580 --> 00:12:31,830 two-dimensional defects. 281 00:12:31,830 --> 00:12:34,170 Let's go to two-dimensional defects. 282 00:12:34,170 --> 00:12:38,680 So two-dimensional defects, there's a couple types. 283 00:12:38,680 --> 00:12:40,960 The dislocation is one dimensional. 284 00:12:40,960 --> 00:12:42,210 Two-dimensional defects. 285 00:12:45,220 --> 00:12:46,030 There's two types. 286 00:12:46,030 --> 00:12:48,250 One is the free surface. 287 00:12:48,250 --> 00:12:50,470 We're going to call the free surface a defect, and I'll 288 00:12:50,470 --> 00:12:51,970 explain why in a second. 289 00:12:51,970 --> 00:12:54,630 And then internal surfaces. 290 00:12:54,630 --> 00:12:55,670 Internal-- 291 00:12:55,670 --> 00:12:58,250 I'm going to use surface in quotation marks-- they're 292 00:12:58,250 --> 00:12:59,500 interfaces. 293 00:12:59,500 --> 00:13:02,740 And there's different types of them, OK? 294 00:13:02,740 --> 00:13:05,710 An interface. 295 00:13:05,710 --> 00:13:07,630 There's an interface inside the thing. 296 00:13:07,630 --> 00:13:09,400 So what's the physics here? 297 00:13:09,400 --> 00:13:11,660 Surfaces are high-energy regions. 298 00:13:11,660 --> 00:13:12,410 Why? 299 00:13:12,410 --> 00:13:16,020 Because when you're inside the crystal, you have the 300 00:13:16,020 --> 00:13:18,250 prescribed number of nearest neighbors. 301 00:13:18,250 --> 00:13:19,950 Let's say you're in an FCC crystal. 302 00:13:19,950 --> 00:13:21,350 You're an aluminum atom. 303 00:13:21,350 --> 00:13:23,560 So you're an aluminum atom and you've got 12 nearest 304 00:13:23,560 --> 00:13:26,180 neighbors because you're FCC, except if 305 00:13:26,180 --> 00:13:27,410 you're at the free surface. 306 00:13:27,410 --> 00:13:29,810 If you're an aluminum atom at the free surface you don't 307 00:13:29,810 --> 00:13:30,920 have 12 nearest neighbors. 308 00:13:30,920 --> 00:13:33,770 Because if I look down I've got aluminum atoms all over. 309 00:13:33,770 --> 00:13:36,130 If I look up, I've got nothing. 310 00:13:36,130 --> 00:13:38,740 So axiomatically, I've got a different number of bonds. 311 00:13:38,740 --> 00:13:39,775 Why do we form bonds? 312 00:13:39,775 --> 00:13:42,240 We form bonds in order to lower the 313 00:13:42,240 --> 00:13:43,480 energy of the system. 314 00:13:43,480 --> 00:13:46,850 But axiomatically, the ones at the top can't form the same 315 00:13:46,850 --> 00:13:48,530 number of bonds, so they are not in the 316 00:13:48,530 --> 00:13:50,820 same low energy state. 317 00:13:50,820 --> 00:13:55,520 So once you get the connection between lower number of bonds, 318 00:13:55,520 --> 00:13:59,590 higher energy state, then any place, free surface, internal 319 00:13:59,590 --> 00:14:04,010 surface, is going to be relatively high energy. 320 00:14:04,010 --> 00:14:15,570 Relatively higher energy than atoms in the matrix. 321 00:14:15,570 --> 00:14:16,080 Matrix. 322 00:14:16,080 --> 00:14:17,060 What do I mean by matrix? 323 00:14:17,060 --> 00:14:19,900 In the middle of a crystal. 324 00:14:19,900 --> 00:14:21,820 In the matrix, OK? 325 00:14:21,820 --> 00:14:27,200 So that means that it's not quite as tightly bound, so the 326 00:14:27,200 --> 00:14:31,550 consequence of this is if they're high-energy regions, 327 00:14:31,550 --> 00:14:34,410 so high-energy implies higher reactivity. 328 00:14:37,870 --> 00:14:40,950 And that can be good or it can be bad. 329 00:14:40,950 --> 00:14:46,870 It can be good if you're trying to design a catalyst. 330 00:14:46,870 --> 00:14:49,590 And it can be bad in the case of corrosion. 331 00:14:49,590 --> 00:14:51,170 Where do you think corrosion occurs? 332 00:14:51,170 --> 00:14:52,620 Not deep inside the crystal. 333 00:14:52,620 --> 00:14:56,340 It occurs at the surface along the grain boundary. 334 00:14:56,340 --> 00:14:59,160 So here's a cartoon that shows different 335 00:14:59,160 --> 00:15:01,070 regions within the crystal. 336 00:15:01,070 --> 00:15:03,550 And Professor Demkowicz showed you on Friday-- 337 00:15:03,550 --> 00:15:07,060 and I'll cut to the thing in a second, the Atomix. 338 00:15:07,060 --> 00:15:10,520 but here we see atoms. So this is a simple cubic, this is 339 00:15:10,520 --> 00:15:11,970 simple cubic, this is simple cubic. 340 00:15:11,970 --> 00:15:15,050 But when they meet they don't line up. 341 00:15:15,050 --> 00:15:17,700 They don't line up because this formed from 342 00:15:17,700 --> 00:15:19,340 solidification from the melt. 343 00:15:19,340 --> 00:15:21,300 So there might have been a seed here 344 00:15:21,300 --> 00:15:22,170 and it grows outward. 345 00:15:22,170 --> 00:15:23,480 A seed here and it grows outward. 346 00:15:23,480 --> 00:15:24,680 A seed here and it grows outward. 347 00:15:24,680 --> 00:15:27,290 And when they grow outward they impinge, but they're not 348 00:15:27,290 --> 00:15:29,300 all growing with the same orientation. 349 00:15:29,300 --> 00:15:31,350 You already know what the planes are. 350 00:15:31,350 --> 00:15:32,990 And they could even be the same plane, but they're 351 00:15:32,990 --> 00:15:35,810 starting from a different point. 352 00:15:35,810 --> 00:15:38,240 So there's this misregistry here. 353 00:15:38,240 --> 00:15:40,490 But it's not a misregistry like the dislocation. 354 00:15:40,490 --> 00:15:42,460 It's a two dimensional misregistry. 355 00:15:42,460 --> 00:15:44,810 Actually, let's cut to the document camera. 356 00:15:44,810 --> 00:15:46,060 Dave, could we do that please? 357 00:15:48,500 --> 00:15:50,020 OK, so here's Atomix. 358 00:15:50,020 --> 00:15:55,820 This was, as explained, an object of art made by Francois 359 00:15:55,820 --> 00:15:59,330 Dallegret in Quebec in the '60s. 360 00:15:59,330 --> 00:16:00,270 So it's kinetic. 361 00:16:00,270 --> 00:16:03,390 It's supposed to be after the artist, see? 362 00:16:03,390 --> 00:16:04,040 You know, you, too. 363 00:16:04,040 --> 00:16:05,940 You pick it up on a coffee table, you put it down, now 364 00:16:05,940 --> 00:16:09,930 you have become the artist. You become the artist. 365 00:16:09,930 --> 00:16:11,330 Postmodernism. 366 00:16:11,330 --> 00:16:12,890 After the death of the artist. See? 367 00:16:12,890 --> 00:16:13,950 I'm an artist. Look. 368 00:16:13,950 --> 00:16:17,720 I'm an artist. One of my best works. 369 00:16:17,720 --> 00:16:21,130 So a couple of my professors at the University of Toronto 370 00:16:21,130 --> 00:16:23,680 were at a cocktail party one night and they saw this thing 371 00:16:23,680 --> 00:16:24,490 on a table. 372 00:16:24,490 --> 00:16:26,380 Must've been a wild party because they kept looking at 373 00:16:26,380 --> 00:16:27,110 this thing. 374 00:16:27,110 --> 00:16:29,740 Finally decided to write a paper about it. 375 00:16:29,740 --> 00:16:33,230 And as Professor Demkowicz said, I bet Francois Dallegret 376 00:16:33,230 --> 00:16:36,340 sold more of these to professors of material science 377 00:16:36,340 --> 00:16:38,640 than he sold to art collectors. 378 00:16:38,640 --> 00:16:41,460 So it's 200 ball bearings strategically placed between 379 00:16:41,460 --> 00:16:43,110 two plates of plexiglass. 380 00:16:43,110 --> 00:16:45,940 And as he pointed out on Friday, you can't get 381 00:16:45,940 --> 00:16:49,210 everything to go away in terms of dislocations, but now you 382 00:16:49,210 --> 00:16:51,200 can see misregistry-- 383 00:16:51,200 --> 00:16:53,640 pardon me, vacancies here. 384 00:16:53,640 --> 00:16:55,480 Here's a stacking fault and so on. 385 00:16:55,480 --> 00:16:57,210 And now here you see grain boundaries. 386 00:16:57,210 --> 00:16:58,280 There's the free surface. 387 00:16:58,280 --> 00:16:59,630 Here's the vapor phase. 388 00:16:59,630 --> 00:17:00,100 Everything. 389 00:17:00,100 --> 00:17:00,980 We're having a lot of fun, here. 390 00:17:00,980 --> 00:17:03,020 So we can look at it again. 391 00:17:03,020 --> 00:17:03,690 We can change. 392 00:17:03,690 --> 00:17:04,670 We'll try to anneal it. 393 00:17:04,670 --> 00:17:06,100 So how do we anneal it? 394 00:17:06,100 --> 00:17:07,880 You put it in an oven and you eat it. 395 00:17:07,880 --> 00:17:11,370 This is the mechanical equivalent of annealing. 396 00:17:11,370 --> 00:17:13,930 I'm tapping it, for those of you in the back. 397 00:17:13,930 --> 00:17:18,180 Now, I'm going to put it down and you see I have a much more 398 00:17:18,180 --> 00:17:20,070 refined structure. 399 00:17:20,070 --> 00:17:22,210 So now you can see a large section 400 00:17:22,210 --> 00:17:24,070 here of a single crystal. 401 00:17:24,070 --> 00:17:26,010 Each one of these is called a grain. 402 00:17:26,010 --> 00:17:28,200 A grain is a zone that is a single 403 00:17:28,200 --> 00:17:30,200 crystal with some defects. 404 00:17:30,200 --> 00:17:31,510 You can see the vacancies. 405 00:17:31,510 --> 00:17:33,390 And then look at the grain boundary here. 406 00:17:33,390 --> 00:17:36,370 See this is a nice crystal, this is a nice crystal. 407 00:17:36,370 --> 00:17:39,160 So one grain, two grains, and there's the grain boundary 408 00:17:39,160 --> 00:17:41,340 where these don't line up with those. 409 00:17:41,340 --> 00:17:44,510 Because they started from a different angle so they can't 410 00:17:44,510 --> 00:17:46,290 impinge and blend. 411 00:17:46,290 --> 00:17:48,460 There's grain boundaries here, here, here, and there's 412 00:17:48,460 --> 00:17:49,670 beautiful stuff. 413 00:17:49,670 --> 00:17:51,700 You can see dislocations. 414 00:17:51,700 --> 00:17:52,150 Everything. 415 00:17:52,150 --> 00:17:55,230 And I know he showed you at the end the Bragg bubble wrap. 416 00:17:55,230 --> 00:17:55,660 And you could see-- 417 00:17:55,660 --> 00:17:56,770 [SOUND EFFECT] 418 00:17:56,770 --> 00:17:58,200 PROFESSOR: --dislocations zipping. 419 00:17:58,200 --> 00:18:00,720 When people were trying to compress the bubble wrap, the 420 00:18:00,720 --> 00:18:03,830 way the bubble wrap was compressing the bubbles didn't 421 00:18:03,830 --> 00:18:05,490 all get flat. 422 00:18:05,490 --> 00:18:09,790 The bubbled glided over one another, and the dislocations 423 00:18:09,790 --> 00:18:12,840 relieved the stress. 424 00:18:12,840 --> 00:18:14,090 See what I'm telling you here? 425 00:18:14,090 --> 00:18:16,390 What I'm telling you here is something that you don't get 426 00:18:16,390 --> 00:18:18,380 in a Gen Chem class anywhere else. 427 00:18:18,380 --> 00:18:21,440 If I told you about the chemical origins of 428 00:18:21,440 --> 00:18:23,920 reactivity, you'd go, yeah, that's chemistry. 429 00:18:23,920 --> 00:18:25,470 But what are we talking about here? 430 00:18:25,470 --> 00:18:27,430 We're talking about the chemical origins 431 00:18:27,430 --> 00:18:29,450 of mechanical behavior. 432 00:18:29,450 --> 00:18:31,900 Now that's different. 433 00:18:31,900 --> 00:18:33,610 The chemical origins of mechanical 434 00:18:33,610 --> 00:18:36,420 behavior: only in 3.091. 435 00:18:36,420 --> 00:18:37,320 And why shouldn't we? 436 00:18:37,320 --> 00:18:40,300 Because at the end, everything is chemistry. 437 00:18:40,300 --> 00:18:41,700 Everything is chemistry. 438 00:18:41,700 --> 00:18:45,540 The rest is stamp collecting. 439 00:18:45,540 --> 00:18:47,710 So the grain-- 440 00:18:47,710 --> 00:18:49,060 make sure we know where the grain is. 441 00:18:49,060 --> 00:18:53,130 The grain is like, I want to call single crystal. 442 00:18:53,130 --> 00:18:55,820 The grain is like a single crystal. 443 00:18:55,820 --> 00:18:59,310 And the grains are separated by grain boundaries. 444 00:18:59,310 --> 00:19:03,350 So by managing grain boundaries, control of grain 445 00:19:03,350 --> 00:19:09,040 boundaries, or if you like, management a grain boundaries, 446 00:19:09,040 --> 00:19:14,620 this has an impact on mechanical properties. 447 00:19:14,620 --> 00:19:17,810 This is called grain boundary engineering. 448 00:19:17,810 --> 00:19:21,130 How we control mechanical properties. 449 00:19:21,130 --> 00:19:23,890 Grain boundary engineering. 450 00:19:23,890 --> 00:19:28,065 So for example, if we want high strength-- 451 00:19:33,770 --> 00:19:37,800 and I just told you that the dislocations will allow the 452 00:19:37,800 --> 00:19:38,880 atoms to glide. 453 00:19:38,880 --> 00:19:41,760 Can you see that if the dislocation is present in this 454 00:19:41,760 --> 00:19:45,320 large grain on the bottom here and the dislocation, just as 455 00:19:45,320 --> 00:19:48,470 in the bubble wrap movie, is zipping across, what happens 456 00:19:48,470 --> 00:19:50,730 when it gets to the grain boundary? 457 00:19:50,730 --> 00:19:53,010 The misregistry of atoms stops that 458 00:19:53,010 --> 00:19:55,730 dislocation dead in its tracks. 459 00:19:55,730 --> 00:19:58,720 So if I want high strength, do I want a large number of grain 460 00:19:58,720 --> 00:20:00,180 boundaries per unit area? 461 00:20:00,180 --> 00:20:03,380 Or a small number of grain boundaries per unit area if my 462 00:20:03,380 --> 00:20:06,440 goal is to stop the dislocations? 463 00:20:06,440 --> 00:20:08,200 I want a high number. 464 00:20:08,200 --> 00:20:12,530 High strength means fine grain structure. 465 00:20:12,530 --> 00:20:16,110 Fine grained means small grain size. 466 00:20:16,110 --> 00:20:17,360 Fine grain structure. 467 00:20:19,840 --> 00:20:21,460 You can think of it as like a river. 468 00:20:21,460 --> 00:20:23,220 You know, you're running, running, running-- all of a 469 00:20:23,220 --> 00:20:28,010 sudden, you stop because you've got to ford the river. 470 00:20:28,010 --> 00:20:30,200 On the other hand, if you want high ductility-- 471 00:20:33,030 --> 00:20:34,370 why would you want ductility? 472 00:20:34,370 --> 00:20:37,410 For example, you want to make a beverage container. 473 00:20:37,410 --> 00:20:39,350 How do you make a beverage container? 474 00:20:39,350 --> 00:20:40,500 Not by casting. 475 00:20:40,500 --> 00:20:44,910 You take a sheet of aluminum and you punch it and you cause 476 00:20:44,910 --> 00:20:46,190 it to deep draw. 477 00:20:46,190 --> 00:20:48,610 That's atoms sliding over atoms. 478 00:20:48,610 --> 00:20:51,400 So do I want to facilitate that process or do I want to 479 00:20:51,400 --> 00:20:52,630 impede the process? 480 00:20:52,630 --> 00:20:55,210 Well, to facilitate the process, I want to make it as 481 00:20:55,210 --> 00:20:57,730 easy as possible for those atoms to 482 00:20:57,730 --> 00:20:59,320 glide over one another. 483 00:20:59,320 --> 00:21:01,820 So high ductility means coarse grain structure. 484 00:21:07,330 --> 00:21:12,970 Coarse grain means large, if you 485 00:21:12,970 --> 00:21:14,920 like, large grain diameter. 486 00:21:14,920 --> 00:21:21,330 Fine grain structure means small diameter. 487 00:21:21,330 --> 00:21:23,510 So there we go. 488 00:21:23,510 --> 00:21:24,190 That's the beginning. 489 00:21:24,190 --> 00:21:26,960 And there's a lot more to it, but I just wanted you to see 490 00:21:26,960 --> 00:21:27,730 that there is something. 491 00:21:27,730 --> 00:21:30,430 And David, may we cut back to the slides, please? 492 00:21:34,150 --> 00:21:35,660 OK, I think the next one shows. 493 00:21:35,660 --> 00:21:38,480 All right, so this is a-- 494 00:21:38,480 --> 00:21:39,500 oh, we don't want to hear that. 495 00:21:39,500 --> 00:21:41,630 Whoops! 496 00:21:41,630 --> 00:21:43,050 Well, I've got music embedded in this one. 497 00:21:43,050 --> 00:21:44,450 This is Philip Glass. 498 00:21:44,450 --> 00:21:45,170 [MUSIC PLAYING] 499 00:21:45,170 --> 00:21:47,430 PROFESSOR: Because we're going to talk about glasses later. 500 00:21:47,430 --> 00:21:48,660 Koyaanisqatsi. 501 00:21:48,660 --> 00:21:49,480 It's beautiful. 502 00:21:49,480 --> 00:21:50,540 Can you feel the bass? 503 00:21:50,540 --> 00:21:52,020 There's the subwoofer right here. 504 00:21:52,020 --> 00:21:53,652 You stand right here. 505 00:21:53,652 --> 00:21:56,780 It's like a message. 506 00:21:56,780 --> 00:21:58,290 Low frequency, of course. 507 00:21:58,290 --> 00:21:59,260 All right, so here's this. 508 00:21:59,260 --> 00:22:01,430 But this is a piece of copper. 509 00:22:01,430 --> 00:22:05,090 Now, this was the advent of modern materials 510 00:22:05,090 --> 00:22:08,810 characterization when Sorby, in the late 1800s, figured out 511 00:22:08,810 --> 00:22:12,750 that if you polish the piece of metal supersmooth-- 512 00:22:12,750 --> 00:22:14,500 that's good, huh? 513 00:22:14,500 --> 00:22:16,330 Maybe we better turn the volume down. 514 00:22:16,330 --> 00:22:17,230 I can't compete with these. 515 00:22:17,230 --> 00:22:18,340 There's more of them than me. 516 00:22:18,340 --> 00:22:19,900 I can't compete. 517 00:22:19,900 --> 00:22:22,090 That's called the mute button. 518 00:22:22,090 --> 00:22:22,550 [MUSIC ENDS] 519 00:22:22,550 --> 00:22:23,570 PROFESSOR: So what did he do? 520 00:22:23,570 --> 00:22:28,160 He polished the copper and then he etched it. 521 00:22:28,160 --> 00:22:30,910 And what happens with an acid etch? 522 00:22:30,910 --> 00:22:33,540 It will etch at different rates because the different 523 00:22:33,540 --> 00:22:35,830 grains have different atom densities. 524 00:22:35,830 --> 00:22:39,460 You see, if I take a piece of metal and I polish it super, 525 00:22:39,460 --> 00:22:42,470 super bright and I shine a light on it and look at it in 526 00:22:42,470 --> 00:22:43,980 a microscope, what am I going to see? 527 00:22:43,980 --> 00:22:45,900 I'm going to see my eyeball, right? 528 00:22:45,900 --> 00:22:46,910 I'll blind myself. 529 00:22:46,910 --> 00:22:48,930 So the key was to etch. 530 00:22:48,930 --> 00:22:50,330 And then when you etch, you differentiate 531 00:22:50,330 --> 00:22:52,120 the different grains. 532 00:22:52,120 --> 00:22:53,970 So that's what you're looking at-- the grain boundaries. 533 00:22:53,970 --> 00:22:56,740 And this is now the same thing, only under a field ion 534 00:22:56,740 --> 00:22:57,280 microscope. 535 00:22:57,280 --> 00:22:59,130 This is a bicrystal of tungsten. 536 00:22:59,130 --> 00:23:01,290 It's hard to see, but this is all one. 537 00:23:01,290 --> 00:23:03,150 This looks like a lolly pattern, doesn't it? 538 00:23:03,150 --> 00:23:04,620 You can see the symmetry here. 539 00:23:04,620 --> 00:23:05,750 I don't know if you can see right here. 540 00:23:05,750 --> 00:23:08,690 There's a line, sort of v-shaped here. 541 00:23:08,690 --> 00:23:09,990 And that's the second crystal. 542 00:23:09,990 --> 00:23:12,940 So there's one crystal here, a second crystal here. 543 00:23:12,940 --> 00:23:15,115 So this two-dimensional defect is now characterized. 544 00:23:18,600 --> 00:23:20,550 And we'll get to that later. 545 00:23:20,550 --> 00:23:20,820 OK. 546 00:23:20,820 --> 00:23:23,760 So now we want to do three-dimensional defects. 547 00:23:23,760 --> 00:23:25,420 What are the three-dimensional defects? 548 00:23:25,420 --> 00:23:31,140 Three-dimensional defects are important. 549 00:23:31,140 --> 00:23:37,190 And they have beneficial and they have harmful 550 00:23:37,190 --> 00:23:38,580 consequences. 551 00:23:38,580 --> 00:23:40,760 Three-dimensional defects. 552 00:23:40,760 --> 00:23:44,430 The dominant mechanism here is coalescence. 553 00:23:44,430 --> 00:23:48,580 So three-dimensional defects formed by coalescence. 554 00:23:51,800 --> 00:23:53,340 And you can coalesce two things. 555 00:23:53,340 --> 00:23:59,982 You can coalesce voids, or you can coalesce-- 556 00:23:59,982 --> 00:24:04,240 actually, you can coalesce void, and you can coalesce-- 557 00:24:04,240 --> 00:24:06,520 I'm going to use Democritus talk here. 558 00:24:06,520 --> 00:24:09,815 You can coalesce void, or you can coalesce being. 559 00:24:12,870 --> 00:24:13,930 What do I mean by that? 560 00:24:13,930 --> 00:24:18,560 Well, void, this could be a vacancy cluster. 561 00:24:18,560 --> 00:24:22,550 So if you have a large number of vacancies coalescing, 562 00:24:22,550 --> 00:24:25,200 you'll actually end up with a hole, a blow 563 00:24:25,200 --> 00:24:26,520 hole inside the material. 564 00:24:26,520 --> 00:24:28,580 And as you can imagine, that has the 565 00:24:28,580 --> 00:24:30,960 mechanical strength of nothing. 566 00:24:30,960 --> 00:24:33,310 That's bad. 567 00:24:33,310 --> 00:24:34,560 And being? 568 00:24:36,760 --> 00:24:38,457 This could be impurity clusters. 569 00:24:41,800 --> 00:24:44,070 And there's two types of impurities, as we've learned. 570 00:24:44,070 --> 00:24:46,880 There are good impurities, such as dopants, and there are 571 00:24:46,880 --> 00:24:52,220 bad impurities such as contaminants. 572 00:24:52,220 --> 00:24:54,330 And what can they do to the mechanical 573 00:24:54,330 --> 00:24:57,550 properties if they are bad? 574 00:24:57,550 --> 00:25:00,620 So what I like to say is impurity clusters-- 575 00:25:00,620 --> 00:25:03,410 so we've got, for example, there are good 576 00:25:03,410 --> 00:25:05,580 ones that are managed. 577 00:25:05,580 --> 00:25:09,260 The ones that are managed can be used to our advantage. 578 00:25:09,260 --> 00:25:11,430 So I'm going to say the managed ones get a smiley 579 00:25:11,430 --> 00:25:14,770 face, and the ones that are uncontrolled-- 580 00:25:14,770 --> 00:25:16,440 I'll give you a vivid example of that at 581 00:25:16,440 --> 00:25:17,680 the end of the lecture. 582 00:25:17,680 --> 00:25:21,700 Uncontrolled, they get a frowny face, and they can lead 583 00:25:21,700 --> 00:25:26,020 to major disasters. 584 00:25:26,020 --> 00:25:30,930 So for example, you're really talking about clusters that 585 00:25:30,930 --> 00:25:32,980 exsolve as a separate phase. 586 00:25:32,980 --> 00:25:36,110 So these things exist as a separate phase. 587 00:25:44,170 --> 00:25:46,160 So they're no longer dissolved. 588 00:25:46,160 --> 00:25:52,000 And these precipitates, some of these impurity clusters, if 589 00:25:52,000 --> 00:25:54,050 they're managed, we can call them precipitates. 590 00:25:58,880 --> 00:26:01,350 i'll give you an example of precipitates. 591 00:26:01,350 --> 00:26:04,860 Some of you might be going home at some point in the not 592 00:26:04,860 --> 00:26:07,230 too distant future, maybe for Thanksgiving. 593 00:26:07,230 --> 00:26:10,740 And if you're flying on an airplane, the airplane is made 594 00:26:10,740 --> 00:26:12,240 of an aluminum alloy. 595 00:26:12,240 --> 00:26:13,550 Aluminum copper. 596 00:26:13,550 --> 00:26:17,560 And one of the precipitates that you can form is various 597 00:26:17,560 --> 00:26:21,290 copper-aluminum compounds. 598 00:26:21,290 --> 00:26:27,240 And these form precipitates that the volume of 599 00:26:27,240 --> 00:26:33,680 copper-aluminum 2 is greater than the volume of the 600 00:26:33,680 --> 00:26:35,450 constituents. 601 00:26:35,450 --> 00:26:38,700 So if you take a copper atom and two aluminum atoms in the 602 00:26:38,700 --> 00:26:41,940 lattice and they react to form copper-aluminum 2, there's a 603 00:26:41,940 --> 00:26:43,120 volume increase. 604 00:26:43,120 --> 00:26:47,120 And so that works to give you constituents. 605 00:26:47,120 --> 00:26:47,720 Isn't that great? 606 00:26:47,720 --> 00:26:50,560 I left you in suspense there as to rest of the word. 607 00:26:50,560 --> 00:26:51,480 So what happens? 608 00:26:51,480 --> 00:26:54,460 This works a little bit the way carbon does in iron, where 609 00:26:54,460 --> 00:26:57,530 carbon atom is bigger than the interstitial void space in 610 00:26:57,530 --> 00:27:02,570 iron, and that force fit leads to a strengthening. 611 00:27:02,570 --> 00:27:05,000 This leads to a strengthening, oK? 612 00:27:05,000 --> 00:27:06,250 So that's good. 613 00:27:08,520 --> 00:27:11,400 So this is called precipitation hardening. 614 00:27:11,400 --> 00:27:13,790 I'm just going write precipitation pptn, 615 00:27:13,790 --> 00:27:16,300 precipitation hardening. 616 00:27:16,300 --> 00:27:20,060 Very important in metallurgy. 617 00:27:20,060 --> 00:27:26,140 Whereas carbon in iron is called solution hardening. 618 00:27:26,140 --> 00:27:28,680 Because it doesn't exist as a separate phase. 619 00:27:28,680 --> 00:27:32,310 The carbon atom is sitting on an interstitial site so it's a 620 00:27:32,310 --> 00:27:34,760 force fit, but it's still within the lattice, whereas 621 00:27:34,760 --> 00:27:38,880 the copper-aluminum actually exists as a precipitate 622 00:27:38,880 --> 00:27:41,390 outside the lattice. 623 00:27:41,390 --> 00:27:43,940 So there we go. 624 00:27:43,940 --> 00:27:46,027 In order to give you a little bit more, I said we're going 625 00:27:46,027 --> 00:27:49,380 to talk about the chemical origins 626 00:27:49,380 --> 00:27:50,860 of mechanical behavior. 627 00:27:50,860 --> 00:27:55,350 And I want to show you how this all leads to 628 00:27:55,350 --> 00:27:57,990 strengthening, strengthening in terms of the yield. 629 00:27:57,990 --> 00:28:00,080 So let's talk about deformation and the 630 00:28:00,080 --> 00:28:02,260 relationship to chemistry. 631 00:28:02,260 --> 00:28:03,510 There's two types of deformation. 632 00:28:06,840 --> 00:28:10,900 And this really accounts for the importance of metals in 633 00:28:10,900 --> 00:28:12,640 the history of man. 634 00:28:12,640 --> 00:28:14,150 Why? 635 00:28:14,150 --> 00:28:16,660 Because they have this unique property. 636 00:28:16,660 --> 00:28:18,930 Until the modern era, when we discovered plastics. 637 00:28:18,930 --> 00:28:23,060 But until modern era, metals are deformable. 638 00:28:23,060 --> 00:28:26,700 They can deform without breaking. 639 00:28:26,700 --> 00:28:30,740 That's what made them so desirable as materials of 640 00:28:30,740 --> 00:28:32,240 construction. 641 00:28:32,240 --> 00:28:34,820 So I'm going to talk about deformation, 642 00:28:34,820 --> 00:28:35,750 how we deform them. 643 00:28:35,750 --> 00:28:39,950 So really, metallurgy consists of-- 644 00:28:39,950 --> 00:28:44,230 really, there's two major divisions of metallurgy. 645 00:28:44,230 --> 00:28:48,380 The first part is chemical, chemical metallurgy, and 646 00:28:48,380 --> 00:28:52,630 that's called dirt to metal. 647 00:28:52,630 --> 00:28:53,520 That's the conversion. 648 00:28:53,520 --> 00:28:55,670 This is the intensive chemistry. 649 00:28:55,670 --> 00:28:59,140 And then the second part is called physical metallurgy, 650 00:28:59,140 --> 00:29:01,130 which is what I'm going to talk about next. 651 00:29:01,130 --> 00:29:02,950 Physical, which is change of shape. 652 00:29:07,590 --> 00:29:09,690 That relies on the ductility. 653 00:29:09,690 --> 00:29:10,520 So deformation. 654 00:29:10,520 --> 00:29:12,290 There's two types of deformation. 655 00:29:12,290 --> 00:29:14,760 The first one is called elastic deformation. 656 00:29:17,720 --> 00:29:18,970 And it is reversible. 657 00:29:21,570 --> 00:29:24,055 So it is strain only under stress. 658 00:29:30,600 --> 00:29:34,820 Or if you like, displacement only under applied force. 659 00:29:34,820 --> 00:29:37,690 So this is Hooke's Law. 660 00:29:37,690 --> 00:29:38,940 Hooke's Law applies. 661 00:29:42,390 --> 00:29:44,520 So let's take a look. 662 00:29:44,520 --> 00:29:49,190 I'm going to draw a little curve here. 663 00:29:49,190 --> 00:29:50,460 You've seen this before. 664 00:29:50,460 --> 00:29:54,120 I'm going to draw one of these energy curves. 665 00:29:54,120 --> 00:30:01,230 So this is interatomic separation, which we might use 666 00:30:01,230 --> 00:30:03,050 the lower case r. 667 00:30:03,050 --> 00:30:06,210 And this is the potential energy that's stored between 668 00:30:06,210 --> 00:30:08,620 two atoms. Remember, when they're far apart, they want 669 00:30:08,620 --> 00:30:09,040 to attract. 670 00:30:09,040 --> 00:30:11,420 When they get too close together, their electronic 671 00:30:11,420 --> 00:30:12,250 shells repel. 672 00:30:12,250 --> 00:30:14,010 So we've got-- 673 00:30:14,010 --> 00:30:15,260 time for colored chalk-- 674 00:30:20,620 --> 00:30:22,790 we have the attractive component, 675 00:30:22,790 --> 00:30:26,350 which looks like this. 676 00:30:26,350 --> 00:30:28,770 And then we have the repulsive component, which looks 677 00:30:28,770 --> 00:30:31,090 something like this. 678 00:30:31,090 --> 00:30:33,090 And then we put the two of them together, and I think we 679 00:30:33,090 --> 00:30:37,060 did this for ions, but there's an analogous one for other 680 00:30:37,060 --> 00:30:40,340 materials, and so you add the two of these, and you 681 00:30:40,340 --> 00:30:44,550 eventually end up like this, where this is r naught. 682 00:30:44,550 --> 00:30:46,356 r naught, the optimum separation. 683 00:30:49,250 --> 00:30:52,310 Here's attraction, this is repulsion, 684 00:30:52,310 --> 00:30:53,500 et cetera, et cetera. 685 00:30:53,500 --> 00:30:56,230 So this is e minimum. 686 00:30:56,230 --> 00:30:57,450 We've seen all of that before. 687 00:30:57,450 --> 00:31:00,590 Now what's this have to do with mechanical behavior? 688 00:31:00,590 --> 00:31:03,660 Well, I'll take it just a little bit farther. 689 00:31:03,660 --> 00:31:05,110 And so I'm going to take the derivative of that 690 00:31:05,110 --> 00:31:06,700 and look at the force. 691 00:31:06,700 --> 00:31:08,510 All right, so now I'm going to take the first 692 00:31:08,510 --> 00:31:09,640 derivative of that. 693 00:31:09,640 --> 00:31:18,470 So this is going to be force, which is equal to de dr. Force 694 00:31:18,470 --> 00:31:21,150 is the derivative of energy. 695 00:31:21,150 --> 00:31:22,540 And what do I find? 696 00:31:22,540 --> 00:31:23,570 Well, look. 697 00:31:23,570 --> 00:31:27,270 If I take this derivative, below r equals r naught. 698 00:31:27,270 --> 00:31:28,490 I've got a negative slope. 699 00:31:28,490 --> 00:31:30,250 Above r equals r naught-- 700 00:31:30,250 --> 00:31:31,270 I have a positive slope. 701 00:31:31,270 --> 00:31:34,290 And at r equals r naught, zero slope. 702 00:31:34,290 --> 00:31:35,930 So I'm want to put that down here. 703 00:31:35,930 --> 00:31:41,780 So it's zero right at r equals r naught, and above r equals r 704 00:31:41,780 --> 00:31:43,470 naught it's positive, and below r equals 705 00:31:43,470 --> 00:31:47,110 r naught it's negative. 706 00:31:47,110 --> 00:31:50,410 Not to scale. 707 00:31:50,410 --> 00:31:52,510 But one thing is certain. 708 00:31:52,510 --> 00:31:55,330 It is positive above r equals r naught, negative below r 709 00:31:55,330 --> 00:31:58,010 equals r naught, and to a first approximation, I can 710 00:31:58,010 --> 00:32:07,270 linearize about r equals r naught, Or Emin. 711 00:32:07,270 --> 00:32:09,410 So what's the real shape of this thing? 712 00:32:09,410 --> 00:32:11,770 You could use a Taylor series if you want. 713 00:32:11,770 --> 00:32:13,820 And just take the first-- what's the first term of a 714 00:32:13,820 --> 00:32:14,410 Taylor series? 715 00:32:14,410 --> 00:32:14,960 Constant. 716 00:32:14,960 --> 00:32:16,360 Second term, linear. 717 00:32:16,360 --> 00:32:18,780 Third term is squared, da, da, da, da. 718 00:32:18,780 --> 00:32:22,270 So neglect higher order terms. You get a straight line. 719 00:32:22,270 --> 00:32:23,960 And what does this mean? 720 00:32:23,960 --> 00:32:29,020 It means that if I try to disturb the atoms from one 721 00:32:29,020 --> 00:32:33,120 another and move them away from their rest position, 722 00:32:33,120 --> 00:32:36,260 there's a force that pulls them back, and the force is 723 00:32:36,260 --> 00:32:38,300 proportional to the displacement. 724 00:32:38,300 --> 00:32:42,990 If I move the atoms farther apart by a distance r1, I get 725 00:32:42,990 --> 00:32:44,010 a certain force. 726 00:32:44,010 --> 00:32:45,800 If I move them apart by r2-- 727 00:32:45,800 --> 00:32:47,010 2 times r1-- 728 00:32:47,010 --> 00:32:50,060 I get twice the force. 729 00:32:50,060 --> 00:32:50,960 It's linear. 730 00:32:50,960 --> 00:32:53,200 Now let's go over here. 731 00:32:53,200 --> 00:32:56,020 Now let's draw another analogy. 732 00:32:56,020 --> 00:33:01,880 So here I've got something that's pegged. 733 00:33:01,880 --> 00:33:05,500 And now I'm going to put a spring onto this secure wall. 734 00:33:05,500 --> 00:33:09,620 So here's my spring, and I'm going to hang 735 00:33:09,620 --> 00:33:12,050 a mass on the spring. 736 00:33:12,050 --> 00:33:13,550 Now I'm going to bring this into Hooke's Law. 737 00:33:13,550 --> 00:33:15,140 I'm going to show you that what you know to be Hooke's 738 00:33:15,140 --> 00:33:17,780 Law is a direct consequence of this. 739 00:33:17,780 --> 00:33:19,750 The atomic origin. 740 00:33:19,750 --> 00:33:20,970 So what's the force on this? 741 00:33:20,970 --> 00:33:23,620 There's a force on this, and that's equal to product of the 742 00:33:23,620 --> 00:33:26,580 mass times the gravitational constant. 743 00:33:26,580 --> 00:33:28,590 And if there were no mass, this spring would be 744 00:33:28,590 --> 00:33:30,820 compressed and it might be sitting here. 745 00:33:30,820 --> 00:33:32,710 I will call this x naught. 746 00:33:32,710 --> 00:33:35,660 And now that I put the spring here I'll 747 00:33:35,660 --> 00:33:37,835 measures, say, this point. 748 00:33:37,835 --> 00:33:41,250 And this point here is now at some value x. 749 00:33:41,250 --> 00:33:44,610 So this is the displacement, isn't it? 750 00:33:44,610 --> 00:33:46,140 This is the delta x. 751 00:33:46,140 --> 00:33:52,310 So Hooke's Law is simply f equals k delta x, isn't it? 752 00:33:52,310 --> 00:33:55,505 If I double the delta x, requires double the force. 753 00:33:55,505 --> 00:33:58,370 Well, that's this. 754 00:33:58,370 --> 00:34:00,310 This analogy goes right down. 755 00:34:00,310 --> 00:34:03,910 And if I remove the mass it springs back, which is what I 756 00:34:03,910 --> 00:34:05,620 meant when I said it's reversible. 757 00:34:05,620 --> 00:34:07,170 This is not permanent. 758 00:34:07,170 --> 00:34:08,990 No stress, no strain. 759 00:34:08,990 --> 00:34:10,330 Strain is the deformation. 760 00:34:10,330 --> 00:34:12,494 No deformation, no force. 761 00:34:12,494 --> 00:34:16,130 If I put a force, non-zero force, non-zero deformation. 762 00:34:16,130 --> 00:34:17,900 By the way, Hooke-- 763 00:34:17,900 --> 00:34:20,400 little bit of culture-- 764 00:34:20,400 --> 00:34:26,940 Hooke announced Hooke's Law in 1676. 765 00:34:26,940 --> 00:34:28,789 Here's how Hooke's Law was first published. 766 00:34:37,000 --> 00:34:41,020 It's an anagram and it's in Latin. 767 00:34:41,020 --> 00:34:45,000 And it was in a book entitled A Decimate of the Centesms of 768 00:34:45,000 --> 00:34:50,070 the Inventions I Intend to Reveal, which is English for, 769 00:34:50,070 --> 00:34:53,090 This is a Tenth of the Hundreds of the Inventions I 770 00:34:53,090 --> 00:34:53,650 Intend to Reveal. 771 00:34:53,650 --> 00:34:57,150 He did not suffer from an overabundance of modesty. 772 00:34:57,150 --> 00:35:01,240 Actually, Hooke and Newton sparred. 773 00:35:01,240 --> 00:35:02,780 They hated each other's guts. 774 00:35:02,780 --> 00:35:05,260 They fought bitterly. 775 00:35:05,260 --> 00:35:06,260 Two giant egos. 776 00:35:06,260 --> 00:35:07,540 Anyway, so here's the thing. 777 00:35:07,540 --> 00:35:15,380 So in 1679 he published a book called De Restitutiva. 778 00:35:15,380 --> 00:35:17,430 On The Spring. 779 00:35:17,430 --> 00:35:18,580 Very presumptuous. 780 00:35:18,580 --> 00:35:20,020 On The Spring. 781 00:35:20,020 --> 00:35:27,970 And here it is in its unraveled, ut tensio, sic vis. 782 00:35:27,970 --> 00:35:31,820 As the extension, so the force. 783 00:35:31,820 --> 00:35:32,670 Nice, huh? 784 00:35:32,670 --> 00:35:34,120 This is u. 785 00:35:34,120 --> 00:35:36,450 That's why the u, but it's really v. 786 00:35:36,450 --> 00:35:38,470 Vis. 787 00:35:38,470 --> 00:35:40,240 We get the English word vim from this. 788 00:35:40,240 --> 00:35:43,550 This is the accusative form of vis. 789 00:35:43,550 --> 00:35:46,910 The Romans didn't care between the u and v. 790 00:35:46,910 --> 00:35:51,090 In fact, if you go on the steps of 77 and you come up, 791 00:35:51,090 --> 00:35:55,330 it says Massachusetts Institute of Technology, you 792 00:35:55,330 --> 00:35:56,160 ever notice this? 793 00:35:56,160 --> 00:35:57,360 Yeah. 794 00:35:57,360 --> 00:35:58,710 I always thought that that's because the 795 00:35:58,710 --> 00:35:59,800 Romans, they couldn't-- 796 00:35:59,800 --> 00:36:00,110 no. 797 00:36:00,110 --> 00:36:02,560 And I thought, well, maybe it's because it's hard to make 798 00:36:02,560 --> 00:36:05,170 a u, but then it says Institute of-- 799 00:36:05,170 --> 00:36:07,020 I figure if you can make one of these, you should be able 800 00:36:07,020 --> 00:36:07,780 to make one of these. 801 00:36:07,780 --> 00:36:11,280 So if you can tell me why they do it that way, I might be 802 00:36:11,280 --> 00:36:13,530 able to find another Periodic Table beach towel. 803 00:36:13,530 --> 00:36:15,420 So that's another thing. 804 00:36:17,970 --> 00:36:18,270 All right. 805 00:36:18,270 --> 00:36:22,100 So that's the elastic deformation. 806 00:36:22,100 --> 00:36:24,770 And now we want to look at the other type of deformation, and 807 00:36:24,770 --> 00:36:26,373 that's called plastic deformation. 808 00:36:29,070 --> 00:36:30,320 And that's permanent. 809 00:36:35,200 --> 00:36:36,735 It's a permanent shape change. 810 00:36:39,240 --> 00:36:41,420 So let's get that up here. 811 00:36:41,420 --> 00:36:44,970 Permanent shape change. 812 00:36:44,970 --> 00:36:46,560 And this requires ductility. 813 00:36:46,560 --> 00:36:48,050 Because otherwise you'll have fracture. 814 00:36:48,050 --> 00:36:50,790 If you take something that has no ductility and you apply a 815 00:36:50,790 --> 00:36:53,640 super critical force, you just crack everything. 816 00:36:53,640 --> 00:36:56,670 So ductility allows for the atoms to 817 00:36:56,670 --> 00:36:59,670 glide over one another. 818 00:36:59,670 --> 00:37:00,920 So what is the mechanism? 819 00:37:05,620 --> 00:37:09,435 The mechanism for plastic deformation? 820 00:37:17,920 --> 00:37:20,700 Plastic deformation in crystals, we're talking about 821 00:37:20,700 --> 00:37:23,080 here, not liquids. 822 00:37:23,080 --> 00:37:25,280 It's called slip. 823 00:37:25,280 --> 00:37:27,230 Atom's slip over one another. 824 00:37:27,230 --> 00:37:30,780 So time for one more cartoon. 825 00:37:30,780 --> 00:37:33,270 So I'm going to say, well, what happens if I 826 00:37:33,270 --> 00:37:36,770 start again with this? 827 00:37:36,770 --> 00:37:40,170 I'm going to put a thin wire, a thin wire of metal. 828 00:37:40,170 --> 00:37:43,020 Make it an FCC metal, let's say it's copper, and I'm going 829 00:37:43,020 --> 00:37:44,730 to put a mass here-- 830 00:37:44,730 --> 00:37:46,180 a honking big mass-- 831 00:37:46,180 --> 00:37:49,250 it's going to give me a force, and the force is great enough 832 00:37:49,250 --> 00:37:52,820 that it is actually going to cause the wire to elongate. 833 00:37:52,820 --> 00:37:54,970 That is permanent shape change. 834 00:37:54,970 --> 00:37:56,430 So what's going on? 835 00:37:56,430 --> 00:37:58,790 Well, let's take this and blow it up. 836 00:37:58,790 --> 00:38:03,190 When we blow it up, we have what's on the screen. 837 00:38:03,190 --> 00:38:07,260 We have grains of different size. 838 00:38:07,260 --> 00:38:09,100 And I'm just going to show atomic planes. 839 00:38:09,100 --> 00:38:10,470 And that's why we have grains, right? 840 00:38:10,470 --> 00:38:13,510 Because the atomic planes don't line up. 841 00:38:13,510 --> 00:38:15,430 There's a misregistry along here. 842 00:38:20,160 --> 00:38:22,720 So now I want to go down to the atomic level. 843 00:38:22,720 --> 00:38:25,590 So now I'm going to take this and blow it up. 844 00:38:25,590 --> 00:38:26,970 And what do I see here? 845 00:38:26,970 --> 00:38:30,010 I see atoms like so. 846 00:38:30,010 --> 00:38:31,920 I'm going to use that hard-sphere, 847 00:38:31,920 --> 00:38:34,630 close-packed model. 848 00:38:34,630 --> 00:38:36,030 So here's the force. 849 00:38:36,030 --> 00:38:37,970 The force is vertical, agreed? 850 00:38:37,970 --> 00:38:39,960 We've got the mass and it's pulling straight down 851 00:38:39,960 --> 00:38:41,110 according to gravity. 852 00:38:41,110 --> 00:38:43,330 So what's going on at the atomic dimension? 853 00:38:43,330 --> 00:38:47,210 Because ultimately, this is what we're working with. 854 00:38:47,210 --> 00:38:48,830 So what happens? 855 00:38:48,830 --> 00:38:51,370 One possibility, and don't laugh-- this was actually 856 00:38:51,370 --> 00:38:52,180 suggested-- 857 00:38:52,180 --> 00:38:56,100 when you cause extension in this manner, you actually take 858 00:38:56,100 --> 00:38:58,600 some of these and you can turn them into 859 00:38:58,600 --> 00:39:02,070 elongated atoms. No, no. 860 00:39:02,070 --> 00:39:03,710 That's no good. 861 00:39:03,710 --> 00:39:06,610 What in fact happens is slip. 862 00:39:06,610 --> 00:39:12,820 So the force-- in fact, let me be more specific-- 863 00:39:18,720 --> 00:39:25,850 the applied force is resolved at atomic level. 864 00:39:30,080 --> 00:39:34,380 So what happens is that the atoms slip over one another 865 00:39:34,380 --> 00:39:38,770 because they can slip along the planes that have the least 866 00:39:38,770 --> 00:39:40,400 bonding between them, right? 867 00:39:40,400 --> 00:39:42,820 The chain is as strong as its weakest link. 868 00:39:42,820 --> 00:39:47,130 So what will happen here is that in order to affect the 869 00:39:47,130 --> 00:39:52,380 elongation, these will move relative to one another along 870 00:39:52,380 --> 00:39:54,030 this slip plane. 871 00:39:54,030 --> 00:39:58,655 This is resolved at the atomic level along slip planes. 872 00:40:01,610 --> 00:40:04,140 I'll write that larger for the people way, 873 00:40:04,140 --> 00:40:05,510 way up in the back. 874 00:40:05,510 --> 00:40:06,760 I haven't forgotten about you. 875 00:40:13,870 --> 00:40:15,190 And what's the slip plane? 876 00:40:15,190 --> 00:40:17,620 How do I determine which is the slip plane? 877 00:40:17,620 --> 00:40:20,080 The slip plane it's going to be the plane that's strongest 878 00:40:20,080 --> 00:40:22,680 because it retains its integrity. 879 00:40:22,680 --> 00:40:25,180 So which plane will be the strongest? 880 00:40:25,180 --> 00:40:26,780 The one with the most bonds. 881 00:40:26,780 --> 00:40:28,730 And which plane has the most bonds? 882 00:40:28,730 --> 00:40:32,430 The plane with the highest number of atoms per unit area. 883 00:40:32,430 --> 00:40:34,480 And that's why we study this stuff. 884 00:40:34,480 --> 00:40:37,280 Because now we know, in an FCC crystal, 885 00:40:37,280 --> 00:40:41,720 which plane will slide. 886 00:40:41,720 --> 00:40:46,570 So in FCC, the high-intensity plane is 1 1 1. 887 00:40:46,570 --> 00:40:49,980 So the 1 1 1 planes do the sliding one over another. 888 00:40:49,980 --> 00:40:53,420 And they'll zigzag the way you saw in the bubble wrap movie. 889 00:40:53,420 --> 00:40:59,890 They'll zigzag down, across, across, across, But from a 890 00:40:59,890 --> 00:41:02,560 distance, it appears as the thing is elongating. 891 00:41:02,560 --> 00:41:06,590 But at the atomic level, it's zigzagging along the 892 00:41:06,590 --> 00:41:07,440 close-packed planes. 893 00:41:07,440 --> 00:41:09,240 Now I'm in a close-packed plane. 894 00:41:09,240 --> 00:41:11,930 By the way, if I have the highest density in the plane 895 00:41:11,930 --> 00:41:16,470 of the floor, can you understand that orthogonal to 896 00:41:16,470 --> 00:41:19,132 the plane on the floor, I must have the weakest density? 897 00:41:19,132 --> 00:41:20,880 All right, now I'm in the plane. 898 00:41:20,880 --> 00:41:22,150 Which direction in the plane? 899 00:41:22,150 --> 00:41:23,820 Any direction? 900 00:41:23,820 --> 00:41:26,330 I'm going to push, I'm going to push some pasta. 901 00:41:26,330 --> 00:41:29,990 I'm going to push uncooked pasta or cooked pasta? 902 00:41:29,990 --> 00:41:31,740 Do you want to push on a rope? 903 00:41:31,740 --> 00:41:34,150 Do you want to push on a broom handle? 904 00:41:34,150 --> 00:41:35,320 The stiff. 905 00:41:35,320 --> 00:41:38,460 So how do I determine, within the plane, which direction is 906 00:41:38,460 --> 00:41:41,230 the stiffest direction? 907 00:41:41,230 --> 00:41:44,430 The one with the most atoms, which is the close-packed 908 00:41:44,430 --> 00:41:45,900 direction when I'm in the plane. 909 00:41:45,900 --> 00:41:48,670 So if I'm in the 1 1 1 plane, which direction? 910 00:41:48,670 --> 00:41:50,250 The 0 1 1 direction. 911 00:41:50,250 --> 00:41:54,480 So this is direct line of sight from the original 912 00:41:54,480 --> 00:41:55,790 crystallography. 913 00:41:55,790 --> 00:41:59,390 So that's how we get the slip. 914 00:41:59,390 --> 00:42:03,640 And in BCC the highest density plane is 0 1 1 and so on. 915 00:42:03,640 --> 00:42:07,830 And the close-packed plane simply means 1 1 1, because 916 00:42:07,830 --> 00:42:11,140 FCC is the closest-packed structure, so that's a 917 00:42:11,140 --> 00:42:12,010 close-packed plane. 918 00:42:12,010 --> 00:42:14,910 Otherwise, they're planes of highest density. 919 00:42:14,910 --> 00:42:15,860 It's a trivial-- 920 00:42:15,860 --> 00:42:17,930 forget the last column-- it's pedantry. 921 00:42:17,930 --> 00:42:18,940 Forget it. 922 00:42:18,940 --> 00:42:21,050 I'm sorry I have it up there. 923 00:42:21,050 --> 00:42:23,370 So this is the slip system. 924 00:42:23,370 --> 00:42:30,270 So the slip system is the combination of 925 00:42:30,270 --> 00:42:32,700 close-packed plane-- 926 00:42:32,700 --> 00:42:38,370 or closest-packed plane-- close-packed plane and the 927 00:42:38,370 --> 00:42:41,160 close-packed direction. 928 00:42:41,160 --> 00:42:43,020 They all have close-packed directions because we've got 929 00:42:43,020 --> 00:42:44,250 atoms touching. 930 00:42:44,250 --> 00:42:49,570 Close-packed direction. 931 00:42:49,570 --> 00:42:52,060 That's how it deforms. And then if I get a dislocation in 932 00:42:52,060 --> 00:42:53,435 a close-packed plane, voom! 933 00:42:53,435 --> 00:42:55,180 Away they go. 934 00:42:55,180 --> 00:42:57,330 1/10 of the applied sheer stress theoretical. 935 00:43:02,440 --> 00:43:07,770 So if you want to get it down to a simple phrase, you can 936 00:43:07,770 --> 00:43:11,560 say, what causes slip? 937 00:43:11,560 --> 00:43:15,680 Atoms slip, dislocations glide. 938 00:43:20,340 --> 00:43:22,480 But please don't think for one minute-- listen to me 939 00:43:22,480 --> 00:43:24,410 carefully-- a lot of students come away from this and they 940 00:43:24,410 --> 00:43:28,770 say, oh, I know why we have deformation. 941 00:43:28,770 --> 00:43:30,220 Because of dislocations. 942 00:43:30,220 --> 00:43:32,680 No, no, no, no. 943 00:43:32,680 --> 00:43:34,600 Atoms will slip no matter what. 944 00:43:34,600 --> 00:43:37,280 It's just that you're going to pay a lot more to cause the 945 00:43:37,280 --> 00:43:38,450 deformation. 946 00:43:38,450 --> 00:43:46,760 The dislocations allow you to have slip at lower cost. 947 00:43:46,760 --> 00:43:48,190 Yeah, this is good. 948 00:43:48,190 --> 00:43:53,260 And I think we're probably at the point where I can show you 949 00:43:53,260 --> 00:43:56,620 the enormous consequences of a three-dimensional defect. 950 00:43:56,620 --> 00:43:58,880 Why did the Titanic sink? 951 00:43:58,880 --> 00:44:02,030 It's a story of three-dimensional defects and 952 00:44:02,030 --> 00:44:03,550 human greed. 953 00:44:03,550 --> 00:44:06,710 So this Tim Fecke at the National Institutes of 954 00:44:06,710 --> 00:44:10,900 Standards and Technology with an optical microscope and a 955 00:44:10,900 --> 00:44:12,430 rivet from the Titanic. 956 00:44:12,430 --> 00:44:14,710 And what I'm going to show you in the rivet is a 957 00:44:14,710 --> 00:44:18,520 three-dimensional defect that took the boat down. 958 00:44:18,520 --> 00:44:22,620 So this is the microstructure and what they're doing is 959 00:44:22,620 --> 00:44:25,950 they're showing you a blow up of this section of the rivet. 960 00:44:25,950 --> 00:44:28,450 Now, the rivet is made of steel. 961 00:44:28,450 --> 00:44:31,130 Before I can explain to you what's going on there, I have 962 00:44:31,130 --> 00:44:31,510 to show you-- 963 00:44:31,510 --> 00:44:31,845 [MUSIC STARTS] 964 00:44:31,845 --> 00:44:32,900 PROFESSOR: Oh, shut up. 965 00:44:32,900 --> 00:44:34,300 [MUSIC ENDS] 966 00:44:34,300 --> 00:44:35,950 PROFESSOR: All right, so this is how they made steel. 967 00:44:35,950 --> 00:44:39,470 Imagine this area the front of 10-250 as an open-hearth 968 00:44:39,470 --> 00:44:43,120 furnace, and I'm up to about my knees in liquid iron. 969 00:44:43,120 --> 00:44:45,880 And on top of the liquid iron is a slag made of silica, 970 00:44:45,880 --> 00:44:47,590 calcia, and alumina. 971 00:44:47,590 --> 00:44:50,380 It's the stuff when it solidifies it makes something 972 00:44:50,380 --> 00:44:52,940 not too different from window glass. 973 00:44:52,940 --> 00:44:55,800 But we use it for refining to get some of the impurities out 974 00:44:55,800 --> 00:44:56,200 of the metal. 975 00:44:56,200 --> 00:44:59,180 And those impurities go up into the slag phase. 976 00:44:59,180 --> 00:45:01,665 And to keep this thing it about 1,300 degrees 977 00:45:01,665 --> 00:45:03,380 Centigrade, you've got burners. 978 00:45:03,380 --> 00:45:03,970 Two. 979 00:45:03,970 --> 00:45:05,413 One at each end like dragons-- 980 00:45:05,413 --> 00:45:06,400 [SOUND EFFECT] 981 00:45:06,400 --> 00:45:10,320 PROFESSOR: --blowing flame into here for about 12 hours. 982 00:45:10,320 --> 00:45:11,510 12 hours. 983 00:45:11,510 --> 00:45:13,480 And that's what it took to make a heat of 984 00:45:13,480 --> 00:45:16,060 steel back in 1910. 985 00:45:16,060 --> 00:45:18,690 This was made in Ireland, which was, at that time, part 986 00:45:18,690 --> 00:45:21,460 of the United Kingdom. 987 00:45:21,460 --> 00:45:25,690 So on that day that they made the heat of steel that 988 00:45:25,690 --> 00:45:28,550 ultimately was shaped into rivets, evidently somebody 989 00:45:28,550 --> 00:45:32,320 became greedy, and instead of waiting long enough for the 990 00:45:32,320 --> 00:45:37,120 slag to phase separate and form a film on the surface of 991 00:45:37,120 --> 00:45:41,220 the metals, much like oil and water don't mix, but you can 992 00:45:41,220 --> 00:45:44,880 shake them up in your salad dressing application tool 993 00:45:44,880 --> 00:45:47,010 device and then pour it on quickly. 994 00:45:47,010 --> 00:45:50,120 But if you let it sit they phase separate. 995 00:45:50,120 --> 00:45:52,340 Well, somebody didn't allow this to phase separate. 996 00:45:52,340 --> 00:45:54,350 They were told, pour the heat anyways. 997 00:45:54,350 --> 00:45:58,680 So now you have globs of what is the precursor to silicate 998 00:45:58,680 --> 00:46:00,620 glass in the metal. 999 00:46:00,620 --> 00:46:03,870 And now we take the metal and we cut it into little billets 1000 00:46:03,870 --> 00:46:06,750 and the billets are extruded to form rivets. 1001 00:46:06,750 --> 00:46:08,850 And then the rivets look like this, where 1002 00:46:08,850 --> 00:46:10,460 you have glass stringers. 1003 00:46:10,460 --> 00:46:13,570 Three-dimensional defects, impurity clusters, 1004 00:46:13,570 --> 00:46:14,730 uncontrolled. 1005 00:46:14,730 --> 00:46:16,960 What are the mechanical properties of steel? 1006 00:46:16,960 --> 00:46:17,930 Strong. 1007 00:46:17,930 --> 00:46:18,770 Ductile. 1008 00:46:18,770 --> 00:46:19,220 Tough. 1009 00:46:19,220 --> 00:46:20,560 What does toughness mean? 1010 00:46:20,560 --> 00:46:22,360 Impactability. 1011 00:46:22,360 --> 00:46:24,510 When you say someone is tough, it means they know how to take 1012 00:46:24,510 --> 00:46:29,110 a hit, whereas hardness means it takes enormous strength to 1013 00:46:29,110 --> 00:46:30,440 cause deformation. 1014 00:46:30,440 --> 00:46:31,850 They're very different. 1015 00:46:31,850 --> 00:46:32,380 You know? 1016 00:46:32,380 --> 00:46:34,010 You say someone is tough, you mean one thing. 1017 00:46:34,010 --> 00:46:35,780 You say they're strong, it's different. 1018 00:46:35,780 --> 00:46:37,920 You can be strong and yet not tough. 1019 00:46:37,920 --> 00:46:41,180 You can be strong and brittle, so you can't take a hit. 1020 00:46:41,180 --> 00:46:42,670 I know a lot of people like that. 1021 00:46:42,670 --> 00:46:43,840 That can't take a hit. 1022 00:46:43,840 --> 00:46:46,100 Anyway, so enough about the people. 1023 00:46:46,100 --> 00:46:48,050 So here are the stringers. 1024 00:46:48,050 --> 00:46:49,020 So what happened? 1025 00:46:49,020 --> 00:46:50,150 What do you think the mechanical 1026 00:46:50,150 --> 00:46:51,260 strength of this is? 1027 00:46:51,260 --> 00:46:54,190 If you have an impact like so, instead of having the 1028 00:46:54,190 --> 00:46:57,300 toughness to absorb the impact, these things broke. 1029 00:46:57,300 --> 00:47:00,450 This is like perforations on a sheet of postage stamps. 1030 00:47:00,450 --> 00:47:03,890 And so these rivets were on the hull. 1031 00:47:03,890 --> 00:47:06,090 And when the ship hit the iceberg, what should have 1032 00:47:06,090 --> 00:47:09,400 happened is there should have an a small hole, the water 1033 00:47:09,400 --> 00:47:13,760 would've taken, who knows, a day or two to fill up, and 1034 00:47:13,760 --> 00:47:15,740 there was plenty of time to get rescue vessels. 1035 00:47:15,740 --> 00:47:18,940 Instead, these rivets were brittle, thanks to this. 1036 00:47:18,940 --> 00:47:20,600 And so they just unzipped. 1037 00:47:20,600 --> 00:47:21,930 Just pop, pop, pop, pop, pop, pop, pop. 1038 00:47:21,930 --> 00:47:24,970 Opened up a giant hole and then took on the water. 1039 00:47:24,970 --> 00:47:27,040 Now, did nobody check? 1040 00:47:29,570 --> 00:47:32,310 Along the way, no inspection of the steel? 1041 00:47:32,310 --> 00:47:33,680 Nobody looked? 1042 00:47:33,680 --> 00:47:36,130 The guys that we're doing the riveting, they must have known 1043 00:47:36,130 --> 00:47:38,310 the rivets were acting strange. 1044 00:47:38,310 --> 00:47:41,490 They must have broken a lot of them just putting them in. 1045 00:47:41,490 --> 00:47:42,770 But hey, it's not my job. 1046 00:47:42,770 --> 00:47:43,480 Not my job. 1047 00:47:43,480 --> 00:47:44,170 Not my job. 1048 00:47:44,170 --> 00:47:48,370 No testing anywhere along the way. 1049 00:47:48,370 --> 00:47:50,840 What's shocking is not human greed. 1050 00:47:50,840 --> 00:47:52,110 That's as old as humanity. 1051 00:47:52,110 --> 00:47:54,860 What's shocking is there was no checks. 1052 00:47:54,860 --> 00:47:59,020 So we have a different way to make vessels like this today. 1053 00:47:59,020 --> 00:48:01,400 But that's the story, right there.