1 00:00:16,983 --> 00:00:17,817 Let's get started. 2 00:00:17,817 --> 00:00:18,518 How is everyone? 3 00:00:18,518 --> 00:00:19,185 [CLASS RESPONDS] 4 00:00:19,185 --> 00:00:20,320 Whoo. 5 00:00:20,320 --> 00:00:21,988 You know why you're so excited? 6 00:00:21,988 --> 00:00:24,124 Because it's a goody bag day. 7 00:00:24,124 --> 00:00:31,297 And I'm not going to deny you a weekend of goodie bag 8 00:00:31,297 --> 00:00:34,300 action, which is why you're getting it today. 9 00:00:34,300 --> 00:00:39,706 Even though the topic in the goody bag is crystallography, 10 00:00:39,706 --> 00:00:45,845 we will not start talking about crystallography until Monday. 11 00:00:45,845 --> 00:00:47,180 But I didn't want to wait. 12 00:00:47,180 --> 00:00:48,982 I know you didn't want to wait to have 13 00:00:48,982 --> 00:00:53,319 these models in your hands because it's 14 00:00:53,319 --> 00:00:55,889 an enhancement of your weekend activities. 15 00:00:55,889 --> 00:00:57,891 So the goody bag, again, just sort of 16 00:00:57,891 --> 00:01:00,360 like last time, I'm giving it out to you today, 17 00:01:00,360 --> 00:01:05,632 but the topic will start on Monday. 18 00:01:05,632 --> 00:01:07,333 Today, instead, we're going to talk 19 00:01:07,333 --> 00:01:09,769 about metals and metallic bonding, 20 00:01:09,769 --> 00:01:11,670 and the properties of metals that 21 00:01:11,670 --> 00:01:14,441 are related to the kind of bond that you get in metals. 22 00:01:17,710 --> 00:01:23,917 And you know, we kind of motivated band theory 23 00:01:23,917 --> 00:01:27,920 of solids with conductivity and we talked about conductivity. 24 00:01:27,920 --> 00:01:30,990 There is a chart of conductivity and there's 25 00:01:30,990 --> 00:01:35,595 some elements in there, some elements and some materials 26 00:01:35,595 --> 00:01:38,164 that are more complicated, right, like glass 27 00:01:38,164 --> 00:01:40,800 isn't necessarily one element or silica. 28 00:01:40,800 --> 00:01:43,402 There's diamond, silicon, germanium, copper. 29 00:01:43,402 --> 00:01:46,940 And we talked about insulators, semiconductors. 30 00:01:46,940 --> 00:01:50,210 And I've mentioned metals and that's 31 00:01:50,210 --> 00:01:52,145 what I want to focus on today. 32 00:01:52,145 --> 00:01:54,848 We did this in the context of the bands, right? 33 00:01:54,848 --> 00:02:01,087 So remember, here you've got your conduction band, 34 00:02:01,087 --> 00:02:02,889 and here you've got your valence band, 35 00:02:02,889 --> 00:02:04,891 and the valence band is filled. 36 00:02:04,891 --> 00:02:07,393 And so if there's a large gap, that's 37 00:02:07,393 --> 00:02:11,698 the gap, if it's large like, you know, over 3 and 1/2 38 00:02:11,698 --> 00:02:14,167 EV then it's an insulator. 39 00:02:14,167 --> 00:02:22,609 And then the one in between we talked about a lot on Wednesday 40 00:02:22,609 --> 00:02:25,578 that, you know, if this is your gap, 41 00:02:25,578 --> 00:02:32,051 and it's say between 0 to 3.5 EV, 42 00:02:32,051 --> 00:02:33,586 then that's a semiconductor. 43 00:02:33,586 --> 00:02:35,522 And so, you know, that's what we talked about. 44 00:02:35,522 --> 00:02:36,555 That's in your goody bag. 45 00:02:36,555 --> 00:02:38,625 We talked a lot about semiconductors. 46 00:02:38,625 --> 00:02:40,894 And then we talked about how, well, 47 00:02:40,894 --> 00:02:46,733 if you have some kind of band that is filled in the middle 48 00:02:46,733 --> 00:02:47,233 there. 49 00:02:47,233 --> 00:02:49,002 So it doesn't have to be filled in the middle. 50 00:02:49,002 --> 00:02:49,936 It can be filled here. 51 00:02:49,936 --> 00:02:51,371 It can be filled up here. 52 00:02:51,371 --> 00:02:53,973 But the point is that the filling of electrons 53 00:02:53,973 --> 00:02:58,378 does not stop where there is a forbidden zone of states, 54 00:02:58,378 --> 00:03:00,780 right, where there is no states. 55 00:03:00,780 --> 00:03:01,614 That's what this is. 56 00:03:01,614 --> 00:03:02,549 That's what a gap is. 57 00:03:02,549 --> 00:03:06,686 It's a gap of electron freedom, right. 58 00:03:06,686 --> 00:03:08,955 Where there's metal, there is no such thing 59 00:03:08,955 --> 00:03:10,890 because you fill up to a point where 60 00:03:10,890 --> 00:03:13,993 then right above that infinitesimally tiny bit 61 00:03:13,993 --> 00:03:16,863 of energy away, there is a free state right? 62 00:03:16,863 --> 00:03:19,532 There's a free state, so you're in the middle of a band 63 00:03:19,532 --> 00:03:22,502 and that's a metal. 64 00:03:22,502 --> 00:03:24,837 Well, I mean, this is you know-- 65 00:03:24,837 --> 00:03:26,406 so we should say that the gap here 66 00:03:26,406 --> 00:03:27,974 has to be greater than zero, here 67 00:03:27,974 --> 00:03:29,943 the gap would be equal to zero. 68 00:03:29,943 --> 00:03:30,677 There is no gap. 69 00:03:30,677 --> 00:03:34,414 You can't define a gap in a metal. 70 00:03:34,414 --> 00:03:36,249 And we talked about semi-conductor problems. 71 00:03:36,249 --> 00:03:40,286 I looked up, just for fun, you know, I mean, why not? 72 00:03:40,286 --> 00:03:42,622 Because what else do you do late at night? 73 00:03:42,622 --> 00:03:45,692 You look up old exam problems and you play with them. 74 00:03:45,692 --> 00:03:48,695 And you know, OK, so from last exam, all right, 75 00:03:48,695 --> 00:03:51,764 so this is for the semiconductors, we had-- 76 00:03:51,764 --> 00:03:53,633 oh, here's a good question. 77 00:03:53,633 --> 00:04:02,041 2.8 centimeters cubed of pure germanium. 78 00:04:02,041 --> 00:04:03,876 Now I want to highlight this because there's 79 00:04:03,876 --> 00:04:07,146 one more thing I want to say about semiconductors before I 80 00:04:07,146 --> 00:04:08,881 move on. 81 00:04:08,881 --> 00:04:10,583 Now, it's doped. 82 00:04:10,583 --> 00:04:12,252 And that's what we spent a lot of time 83 00:04:12,252 --> 00:04:13,386 talking about on Wednesday. 84 00:04:13,386 --> 00:04:22,895 It's doped with 50 micrograms, OK, of selenium. 85 00:04:22,895 --> 00:04:25,565 That was the problem. 86 00:04:25,565 --> 00:04:26,933 And the first part of the problem 87 00:04:26,933 --> 00:04:31,871 is, how many carriers are produced? 88 00:04:38,745 --> 00:04:42,048 And in the same question, it's like, are they n-type 89 00:04:42,048 --> 00:04:43,883 or are they p-type? 90 00:04:43,883 --> 00:04:44,884 What type of carriers? 91 00:04:44,884 --> 00:04:47,287 Those are things we can answer based on what 92 00:04:47,287 --> 00:04:49,589 we learned on Wednesday. 93 00:04:49,589 --> 00:04:52,692 And so, you know, oh, then you have this. 94 00:04:52,692 --> 00:04:55,528 And you say, aha, I know where to start because everything 95 00:04:55,528 --> 00:04:57,930 starts here, right? 96 00:04:57,930 --> 00:05:00,767 And so pure germanium is doped. 97 00:05:00,767 --> 00:05:02,735 Well, first of all, where am I? 98 00:05:02,735 --> 00:05:04,537 This is my map, right? 99 00:05:04,537 --> 00:05:06,406 Germanium is there. 100 00:05:06,406 --> 00:05:08,675 Now, it's doped with selenium. 101 00:05:08,675 --> 00:05:11,778 Is selenium to the right or to the left of the period? 102 00:05:11,778 --> 00:05:13,579 It's to the right. 103 00:05:13,579 --> 00:05:14,180 Right? 104 00:05:14,180 --> 00:05:18,618 And so right away you know, if you put a selenium in there 105 00:05:18,618 --> 00:05:21,788 instead of germanium, so if you take a germanium atom 106 00:05:21,788 --> 00:05:24,090 and you put a selenium atom in, it's 107 00:05:24,090 --> 00:05:25,625 going to-- if it's a doping, it's 108 00:05:25,625 --> 00:05:27,860 going to be in the bonding network 109 00:05:27,860 --> 00:05:30,997 that germanium was, but add electrons to it, 110 00:05:30,997 --> 00:05:32,031 if it's to the right. 111 00:05:32,031 --> 00:05:32,765 Right? 112 00:05:32,765 --> 00:05:37,103 And so you know that it's going to be n-type material. 113 00:05:37,103 --> 00:05:45,244 And if you do the math, the number of carriers 114 00:05:45,244 --> 00:05:51,017 is equal to 7.6 times 10 to the 20th per centimeter cubed. 115 00:05:51,017 --> 00:05:55,488 Now, here's something important. 116 00:05:55,488 --> 00:05:58,791 That is twice as many selenium atoms, 117 00:05:58,791 --> 00:06:03,629 twice as many because it's two over from germanium. 118 00:06:03,629 --> 00:06:08,034 So it had two extra electrons for each dopant atom, right? 119 00:06:08,034 --> 00:06:09,535 So the way you solve these problems, 120 00:06:09,535 --> 00:06:12,171 you figure out how many selenium atoms are there per centimeter 121 00:06:12,171 --> 00:06:14,741 cubed and how many electrons for each of those 122 00:06:14,741 --> 00:06:17,210 acted as a free carrier dope. 123 00:06:17,210 --> 00:06:21,047 As a dopant, remember, dopant simply 124 00:06:21,047 --> 00:06:25,451 give you carriers either of their-- if it's n-type, 125 00:06:25,451 --> 00:06:28,054 or down here, if it's p-type. 126 00:06:28,054 --> 00:06:29,522 OK? 127 00:06:29,522 --> 00:06:31,290 And this is n-type. 128 00:06:31,290 --> 00:06:33,126 N-type. 129 00:06:33,126 --> 00:06:33,626 OK. 130 00:06:33,626 --> 00:06:37,063 So that's nice-- now the reason I want to do this is 131 00:06:37,063 --> 00:06:38,698 because, again, it is-- 132 00:06:38,698 --> 00:06:42,502 you can never have enough fun doing problems like this 133 00:06:42,502 --> 00:06:44,704 and looking up old exams and stuff. 134 00:06:44,704 --> 00:06:46,472 But I also want to go back to this picture 135 00:06:46,472 --> 00:06:49,308 that I drew for you on Wednesday, OK? 136 00:06:49,308 --> 00:06:57,617 So this picture was of the number of carriers, 137 00:06:57,617 --> 00:07:02,755 and remember these are electrons that carry current, right? 138 00:07:02,755 --> 00:07:06,058 And we sort of drew something that looked like this. 139 00:07:06,058 --> 00:07:11,831 Now remember, this is, right, these are thermally activated 140 00:07:11,831 --> 00:07:20,206 and this is thermally activated, and these are from dopants. 141 00:07:24,577 --> 00:07:30,283 Now, if I put dopants in, and then I 142 00:07:30,283 --> 00:07:32,852 can get you a constant number of carriers 143 00:07:32,852 --> 00:07:35,621 because it's just defined by how much of the impurity 144 00:07:35,621 --> 00:07:37,056 I've mixed in. 145 00:07:37,056 --> 00:07:39,959 How much impurity and I can control that really carefully, 146 00:07:39,959 --> 00:07:41,994 which means I can control the number of carriers, 147 00:07:41,994 --> 00:07:45,264 and then eventually, thermally excited carriers 148 00:07:45,264 --> 00:07:47,332 will just start to dominate. 149 00:07:47,332 --> 00:07:51,237 But this ability to dope with chemistry 150 00:07:51,237 --> 00:07:53,339 is what enabled the semiconductor revolution. 151 00:07:53,339 --> 00:07:57,977 Now, you say, OK, what's going on over here? 152 00:07:57,977 --> 00:08:00,046 What's going on in this part here? 153 00:08:00,046 --> 00:08:00,713 All right. 154 00:08:00,713 --> 00:08:03,649 Well, you know what's going on there because we 155 00:08:03,649 --> 00:08:06,519 drew this picture on Wednesday. 156 00:08:06,519 --> 00:08:10,890 Because if I have an n-type, if that's my VBN 157 00:08:10,890 --> 00:08:14,026 and that's my CBN, the way this works 158 00:08:14,026 --> 00:08:18,097 is you introduce a donor level. 159 00:08:18,097 --> 00:08:20,132 Right? 160 00:08:20,132 --> 00:08:22,668 That's how doping works, right? 161 00:08:22,668 --> 00:08:26,939 The electrons from selenium go into here and then 162 00:08:26,939 --> 00:08:30,176 you have enough thermal energy to get them up to there 163 00:08:30,176 --> 00:08:32,211 and that's where they're free carriers. 164 00:08:32,211 --> 00:08:34,981 That's where they can carry electricity. 165 00:08:34,981 --> 00:08:39,719 And so at a certain temperature below which, right, 166 00:08:39,719 --> 00:08:42,488 at a certain temperature, if you're lower than that, 167 00:08:42,488 --> 00:08:44,757 well there's not even enough thermal energy 168 00:08:44,757 --> 00:08:46,759 to get from here to here. 169 00:08:46,759 --> 00:08:47,660 All right. 170 00:08:47,660 --> 00:08:48,995 Not even enough to do that. 171 00:08:48,995 --> 00:08:50,396 So it's got to go down eventually. 172 00:08:50,396 --> 00:08:52,298 That's what that part is. 173 00:08:52,298 --> 00:08:55,801 And then the one other thing I want to say about this plot 174 00:08:55,801 --> 00:08:57,703 is that we have names for this. 175 00:08:57,703 --> 00:09:03,209 These are called intrinsic carriers, intrinsic, 176 00:09:03,209 --> 00:09:07,113 and these are called extrinsic. 177 00:09:07,113 --> 00:09:07,613 Why? 178 00:09:07,613 --> 00:09:09,048 I mean, that kind of makes sense. 179 00:09:09,048 --> 00:09:11,617 That's actually a pretty good way to name them. 180 00:09:11,617 --> 00:09:13,786 Because, you know, intrinsic means 181 00:09:13,786 --> 00:09:15,021 I didn't need to do anything. 182 00:09:15,021 --> 00:09:19,825 It's pure germanium, pure germanium, intrinsic. 183 00:09:19,825 --> 00:09:23,029 I didn't do anything to the material. 184 00:09:23,029 --> 00:09:24,830 But it's still-- you can get carriers 185 00:09:24,830 --> 00:09:27,233 from thermal activation above the gap. 186 00:09:27,233 --> 00:09:30,169 Whereas if it's extrinsic, it means I did something external. 187 00:09:30,169 --> 00:09:31,237 I added dopants. 188 00:09:31,237 --> 00:09:34,140 Those are extrinsically doped. 189 00:09:34,140 --> 00:09:37,843 So those are just important distinguishing factors. 190 00:09:37,843 --> 00:09:40,413 Now, I'm going to come back to this plot later. 191 00:09:40,413 --> 00:09:41,581 I want to talk about metals. 192 00:09:41,581 --> 00:09:43,182 Metals are all the way over here. 193 00:09:43,182 --> 00:09:45,184 Those are semiconductors and doping them 194 00:09:45,184 --> 00:09:47,753 or thermal activation gets me carriers, 195 00:09:47,753 --> 00:09:49,989 which gets me this connectivity range, 196 00:09:49,989 --> 00:09:53,359 but metals are much, much, much higher. 197 00:09:53,359 --> 00:09:54,794 Metals are much, much, much higher. 198 00:09:54,794 --> 00:09:55,628 Why? 199 00:09:55,628 --> 00:09:59,465 What is going on in metals that's so special? 200 00:09:59,465 --> 00:10:00,399 OK. 201 00:10:00,399 --> 00:10:05,171 Well, the way we understand everything is from the bonds. 202 00:10:05,171 --> 00:10:07,006 So what is happening in a metal? 203 00:10:07,006 --> 00:10:08,608 There's aluminum. 204 00:10:08,608 --> 00:10:09,875 There's aluminum. 205 00:10:09,875 --> 00:10:11,344 There's aluminum. 206 00:10:11,344 --> 00:10:12,345 And there is aluminum. 207 00:10:12,345 --> 00:10:14,814 For us, this is all we see now. 208 00:10:14,814 --> 00:10:16,549 We don't see any of this anymore. 209 00:10:16,549 --> 00:10:20,019 We only see atoms and electrons because those are the building 210 00:10:20,019 --> 00:10:22,788 blocks, right? 211 00:10:22,788 --> 00:10:24,423 Those are the building blocks. 212 00:10:24,423 --> 00:10:28,594 And the thing is that, if we write down 213 00:10:28,594 --> 00:10:31,030 all the orbitals of an aluminum atom, there's the core, 214 00:10:31,030 --> 00:10:32,665 there's a shell, there's another shell, 215 00:10:32,665 --> 00:10:36,802 there's these ones out here, way out here, right, 216 00:10:36,802 --> 00:10:39,271 in the case of aluminum, three of them that are really, 217 00:10:39,271 --> 00:10:41,107 really, kind of weakly bonded. 218 00:10:41,107 --> 00:10:41,607 Right? 219 00:10:41,607 --> 00:10:42,540 They're way out there. 220 00:10:42,540 --> 00:10:44,343 They're loose. 221 00:10:44,343 --> 00:10:48,080 They have the ability to come off easily. 222 00:10:48,080 --> 00:10:50,449 We talked about this in the context of other properties, 223 00:10:50,449 --> 00:10:52,018 right? 224 00:10:52,018 --> 00:10:57,456 You know, the polarizability, the electronegativity, right? 225 00:10:57,456 --> 00:10:58,758 All of this feeds in. 226 00:10:58,758 --> 00:11:04,030 Everything is determined by where these electrons are. 227 00:11:04,030 --> 00:11:07,633 And then also, as I mentioned, by how the atom's arranged. 228 00:11:07,633 --> 00:11:10,536 That comes next week. 229 00:11:10,536 --> 00:11:13,439 But if they're really, really kind of almost free, 230 00:11:13,439 --> 00:11:15,207 then you can kind of picture it like this. 231 00:11:15,207 --> 00:11:17,543 Let's dial it back to sodium. 232 00:11:17,543 --> 00:11:22,782 And you can kind of picture a metal as truly free electrons, 233 00:11:22,782 --> 00:11:23,282 right. 234 00:11:23,282 --> 00:11:25,284 They are truly free. 235 00:11:25,284 --> 00:11:27,586 They're not in-- they're in the middle of that band 236 00:11:27,586 --> 00:11:30,089 and they've got all this freedom because the states are free 237 00:11:30,089 --> 00:11:33,292 all around them, and they're basically not really 238 00:11:33,292 --> 00:11:36,696 that attached to any one atom or another. 239 00:11:36,696 --> 00:11:40,533 And this is really the picture of the metallic bond. 240 00:11:40,533 --> 00:11:42,935 So let's use-- let's go over here. 241 00:11:48,007 --> 00:11:51,811 They're so free when these atoms come together with those very, 242 00:11:51,811 --> 00:11:54,246 very loosely bound outer electrons, 243 00:11:54,246 --> 00:11:57,616 those electrons are so free we actually call it a sea. 244 00:11:57,616 --> 00:11:59,518 We call it the electron sea. 245 00:11:59,518 --> 00:12:01,887 It's a simplified way to think about it, 246 00:12:01,887 --> 00:12:05,091 but it's a good picture to start with. 247 00:12:05,091 --> 00:12:09,428 So in metals, you've got this electron sea. 248 00:12:09,428 --> 00:12:12,932 Electron sea, we'll call it a model 249 00:12:12,932 --> 00:12:15,101 because it's a way of thinking. 250 00:12:15,101 --> 00:12:25,344 And in this model, you've got a positive charge, nuclei, 251 00:12:25,344 --> 00:12:26,879 so you've got positively charged. 252 00:12:26,879 --> 00:12:27,379 Why? 253 00:12:27,379 --> 00:12:30,249 Because they lost an electron to the sea. 254 00:12:30,249 --> 00:12:31,383 They've lost it. 255 00:12:31,383 --> 00:12:32,985 Those outer ones have gone. 256 00:12:32,985 --> 00:12:35,521 Well, they're not gone because there are others around too, 257 00:12:35,521 --> 00:12:38,491 but they're all just kind of roaming free, 258 00:12:38,491 --> 00:12:43,529 and so you're left with these positive charges, right? 259 00:12:43,529 --> 00:12:45,564 And these are the cations. 260 00:12:45,564 --> 00:12:47,767 Positively charged nuclei are cations. 261 00:12:50,703 --> 00:12:51,203 Right. 262 00:12:51,203 --> 00:12:53,873 And they're in a sea of electrons 263 00:12:53,873 --> 00:13:02,047 and so this is because the valence electrons is not 264 00:13:02,047 --> 00:13:02,982 tightly bound. 265 00:13:02,982 --> 00:13:08,721 This is what I've been saying, but this is why you get it. 266 00:13:08,721 --> 00:13:10,756 Cations, so positive charge nuclei, 267 00:13:10,756 --> 00:13:13,492 these are cat islands in a sea of electrons. 268 00:13:18,798 --> 00:13:23,202 So if you think about a metal in this way, 269 00:13:23,202 --> 00:13:27,373 you understand a lot of the properties of metals. 270 00:13:27,373 --> 00:13:30,743 This is a very useful way to think about metals. 271 00:13:30,743 --> 00:13:34,079 And let's go back to our pictures of bonding. 272 00:13:34,079 --> 00:13:35,548 Let me use this board here. 273 00:13:35,548 --> 00:13:37,983 I'll put it right under here. 274 00:13:37,983 --> 00:13:41,220 And we're going to finish what we started. 275 00:13:41,220 --> 00:13:42,822 We're going to finish what we started. 276 00:13:42,822 --> 00:13:45,591 Because, remember, we talked about covalent. 277 00:13:45,591 --> 00:13:48,060 We talked about ionic. 278 00:13:48,060 --> 00:13:50,563 And then we did all these intermolecular forces 279 00:13:50,563 --> 00:13:53,098 and the bonding that comes about from those, 280 00:13:53,098 --> 00:13:54,366 but we didn't do metallic. 281 00:13:54,366 --> 00:14:02,875 So if I do covalent over here, and I do ionic over here. 282 00:14:02,875 --> 00:14:05,010 Well, OK, covalent we know, right. 283 00:14:05,010 --> 00:14:07,346 You have a maybe HH. 284 00:14:07,346 --> 00:14:08,314 That's a covalent bond. 285 00:14:08,314 --> 00:14:11,116 That's a non-polar kind of covalent bond, 286 00:14:11,116 --> 00:14:12,918 caring is sharing. 287 00:14:12,918 --> 00:14:14,753 Or we could have HF, right, where 288 00:14:14,753 --> 00:14:17,857 it's sort of like, you know, it's a little less sharing. 289 00:14:17,857 --> 00:14:20,292 But you know, it's still a covalent bond. 290 00:14:20,292 --> 00:14:23,028 It's a polar covalent bond, right? 291 00:14:23,028 --> 00:14:27,132 I mean, now in the ionic sense, you have sodium chloride. 292 00:14:27,132 --> 00:14:29,835 We did that example where you literally-- 293 00:14:29,835 --> 00:14:34,373 chlorine is like give me and sodium's like OK and that's it. 294 00:14:34,373 --> 00:14:36,141 That's the relationship. 295 00:14:36,141 --> 00:14:36,642 Right. 296 00:14:36,642 --> 00:14:39,945 But see now here, let's take sodium and let's 297 00:14:39,945 --> 00:14:42,147 just put a bunch of them around. 298 00:14:42,147 --> 00:14:45,184 Well, but see, if I've got an electron sea, 299 00:14:45,184 --> 00:14:53,325 then my electrons are simply wandering around in the sea. 300 00:14:53,325 --> 00:14:59,198 So every ion has this kind of ocean of electrons around it. 301 00:14:59,198 --> 00:15:00,799 They're not attached. 302 00:15:00,799 --> 00:15:04,637 It would be like if you say, how are you going to parent? 303 00:15:04,637 --> 00:15:07,373 Well, I'm going to parent them until, you know, 304 00:15:07,373 --> 00:15:10,709 you can only go into the backyard and play. 305 00:15:10,709 --> 00:15:12,011 That's It, right? 306 00:15:12,011 --> 00:15:13,979 You are confined to be in the backyard. 307 00:15:16,782 --> 00:15:19,985 And now you say, well, OK, but now if I'm a proton 308 00:15:19,985 --> 00:15:22,154 and I'm parenting an electron, I say, you know what? 309 00:15:22,154 --> 00:15:23,455 You can be in any yard. 310 00:15:23,455 --> 00:15:25,324 It doesn't matter. 311 00:15:25,324 --> 00:15:26,258 Don't even come home. 312 00:15:26,258 --> 00:15:28,294 [LAUGHTER] 313 00:15:28,294 --> 00:15:30,262 I don't care. 314 00:15:30,262 --> 00:15:33,399 Another kid's going to come into my backyard at some point, 315 00:15:33,399 --> 00:15:36,435 so it's all good. 316 00:15:36,435 --> 00:15:43,175 That is the relationship of a metal inside of a metal. 317 00:15:43,175 --> 00:15:46,111 Maybe here it's like the two houses switch kids. 318 00:15:46,111 --> 00:15:47,479 I don't know what's going on. 319 00:15:47,479 --> 00:15:47,980 No. 320 00:15:47,980 --> 00:15:49,214 One of them just took the kid. 321 00:15:49,214 --> 00:15:49,715 [LAUGHTER] 322 00:15:49,715 --> 00:15:50,749 But anyway. 323 00:15:50,749 --> 00:15:51,283 All right. 324 00:15:51,283 --> 00:15:52,284 I'm going too far. 325 00:15:52,284 --> 00:15:54,520 But here's the thing. 326 00:15:54,520 --> 00:15:56,488 I want to give you that sense that they're just 327 00:15:56,488 --> 00:15:58,724 roaming around in a sea. 328 00:15:58,724 --> 00:16:01,093 They're roaming around. 329 00:16:01,093 --> 00:16:02,061 They're roaming around. 330 00:16:02,061 --> 00:16:03,462 Now, here's the point. 331 00:16:03,462 --> 00:16:05,698 I've got a sea of electrons-- 332 00:16:05,698 --> 00:16:06,832 oh. 333 00:16:06,832 --> 00:16:10,736 Oh, huh, we can finish our table. 334 00:16:10,736 --> 00:16:12,738 I'm going to finish that table. 335 00:16:12,738 --> 00:16:13,639 We started the table. 336 00:16:13,639 --> 00:16:14,940 Let's finish the table. 337 00:16:14,940 --> 00:16:18,477 Because now, if I have metallic, all right, 338 00:16:18,477 --> 00:16:23,515 and I have this kind of, you know, this kind 339 00:16:23,515 --> 00:16:25,484 of set up here, right. 340 00:16:25,484 --> 00:16:26,618 That's the picture. 341 00:16:26,618 --> 00:16:27,720 That's the model. 342 00:16:27,720 --> 00:16:29,421 And here I have cation-- 343 00:16:29,421 --> 00:16:39,198 remember our table-- slash delocalize, delocalize 344 00:16:39,198 --> 00:16:40,332 electrons. 345 00:16:40,332 --> 00:16:43,669 And the bonding strength for this table in kilojoules 346 00:16:43,669 --> 00:16:46,972 per mole is 75 to 1,000. 347 00:16:46,972 --> 00:16:47,873 It's a big range. 348 00:16:47,873 --> 00:16:50,442 We'll talk about that. 349 00:16:50,442 --> 00:16:52,211 And there is an example, iron. 350 00:16:52,211 --> 00:16:53,579 We finished our table. 351 00:16:53,579 --> 00:16:54,079 That's it. 352 00:16:54,079 --> 00:16:55,014 That's the last entry. 353 00:16:55,014 --> 00:16:57,683 Now, remember, this part of the table 354 00:16:57,683 --> 00:17:02,021 was the basis of attraction. 355 00:17:02,021 --> 00:17:03,355 Remember that? 356 00:17:03,355 --> 00:17:06,959 And we filled this out for all the other types of bonds, 357 00:17:06,959 --> 00:17:10,329 the basis of attraction. 358 00:17:10,329 --> 00:17:13,464 I want to point out that every single basis we have covered 359 00:17:13,464 --> 00:17:16,835 involves the same thing, understanding 360 00:17:16,835 --> 00:17:20,239 what electrons are doing. 361 00:17:20,239 --> 00:17:25,109 What is the electronic structure? 362 00:17:25,109 --> 00:17:30,315 That's the fundamental principle of this class, right? 363 00:17:30,315 --> 00:17:33,285 That's the key component, the key ingredient, 364 00:17:33,285 --> 00:17:35,621 that's in all of our recipes. 365 00:17:35,621 --> 00:17:38,090 What are those electrons doing? 366 00:17:38,090 --> 00:17:42,428 That leads us to every single one of those kinds of bonds, 367 00:17:42,428 --> 00:17:44,496 including metallic. 368 00:17:44,496 --> 00:17:44,997 All right. 369 00:17:44,997 --> 00:17:50,502 So now, you can imagine how this controls the properties, right? 370 00:17:50,502 --> 00:17:52,771 But first you say, well, if I had a group one 371 00:17:52,771 --> 00:17:56,675 metal, if I had a group one metal, then I've got two-- 372 00:17:56,675 --> 00:17:58,510 I've got one, right, like sodium. 373 00:17:58,510 --> 00:18:00,212 But if I go over to magnesium, you 374 00:18:00,212 --> 00:18:03,415 can see that I've got a higher charge because both 375 00:18:03,415 --> 00:18:07,152 of those electrons are likely to leave and wander around 376 00:18:07,152 --> 00:18:10,089 in this sea of electrons. 377 00:18:10,089 --> 00:18:12,691 So that would be what magnesium looks like in terms 378 00:18:12,691 --> 00:18:17,296 of this electron sea model. 379 00:18:17,296 --> 00:18:23,235 But the thing is that this sea, this picture, 380 00:18:23,235 --> 00:18:26,705 is what helps us understand the properties of metals 381 00:18:26,705 --> 00:18:29,208 and that's what I want to talk about. 382 00:18:29,208 --> 00:18:30,576 That's what I want to talk about. 383 00:18:30,576 --> 00:18:32,411 And these are some of the properties, right? 384 00:18:32,411 --> 00:18:34,746 You can go through metals and there's 385 00:18:34,746 --> 00:18:37,182 a whole range of properties, but these 386 00:18:37,182 --> 00:18:40,819 are some of the ones that are pretty consistent. 387 00:18:40,819 --> 00:18:41,987 They are reflective. 388 00:18:41,987 --> 00:18:43,188 They're shiny. 389 00:18:43,188 --> 00:18:48,694 There are literally settings in like photo apps. 390 00:18:48,694 --> 00:18:51,430 Metallic, make it look metallic. 391 00:18:51,430 --> 00:18:52,631 Right? 392 00:18:52,631 --> 00:18:55,868 Because metals are shiny. 393 00:18:55,868 --> 00:18:58,036 They have luster. 394 00:18:58,036 --> 00:18:59,338 Why? 395 00:18:59,338 --> 00:19:00,939 They have high electrical conductivity. 396 00:19:00,939 --> 00:19:03,041 That's the thing we've talked about a lot already. 397 00:19:03,041 --> 00:19:05,077 They have a high thermal conductivity. 398 00:19:05,077 --> 00:19:05,911 I'll mention that. 399 00:19:05,911 --> 00:19:07,446 High heat capacity. 400 00:19:07,446 --> 00:19:09,681 They're malleable and ductile. 401 00:19:09,681 --> 00:19:13,218 All of these and many more properties of metals 402 00:19:13,218 --> 00:19:19,024 can be explained from this one simple picture of the electron 403 00:19:19,024 --> 00:19:19,691 sea. 404 00:19:19,691 --> 00:19:21,660 This one simple picture. 405 00:19:21,660 --> 00:19:23,529 OK. 406 00:19:23,529 --> 00:19:24,763 So let's start. 407 00:19:24,763 --> 00:19:27,566 So if I think about-- 408 00:19:27,566 --> 00:19:29,768 let's look at these top three, OK? 409 00:19:29,768 --> 00:19:33,138 So I'll start, why is a metal shiny? 410 00:19:33,138 --> 00:19:34,573 Why is a metal shiny? 411 00:19:34,573 --> 00:19:36,441 Well, it goes back to the thing we've 412 00:19:36,441 --> 00:19:38,911 been talking about all along, you 413 00:19:38,911 --> 00:19:41,680 know, or certainly in a lot of parts, right? 414 00:19:41,680 --> 00:19:45,450 The bohr model, and atoms, and electrons getting excited. 415 00:19:45,450 --> 00:19:50,389 The semiconductors and LEDs, right? 416 00:19:50,389 --> 00:19:54,226 It has to do with how photons interact with the material. 417 00:19:54,226 --> 00:19:57,829 But see, now I've got these electrons 418 00:19:57,829 --> 00:20:01,066 that are sitting out there at any energy 419 00:20:01,066 --> 00:20:04,870 level ready for the photon. 420 00:20:04,870 --> 00:20:06,538 There's no gap. 421 00:20:06,538 --> 00:20:07,339 Right? 422 00:20:07,339 --> 00:20:10,275 So I've got electrons sitting around in the sea 423 00:20:10,275 --> 00:20:13,445 and they're ready for anything, any kind of energy that 424 00:20:13,445 --> 00:20:16,348 hits them, well, they've got room to be excited. 425 00:20:16,348 --> 00:20:16,848 Right? 426 00:20:16,848 --> 00:20:18,684 They've got room to be excited. 427 00:20:18,684 --> 00:20:22,321 And it's that, combined with other things, 428 00:20:22,321 --> 00:20:24,556 but it's that, that is a big part of why 429 00:20:24,556 --> 00:20:26,658 metals have their shininess. 430 00:20:26,658 --> 00:20:30,762 Those electrons can be excited in almost any way, 431 00:20:30,762 --> 00:20:32,898 right, because there's an infinite number of states 432 00:20:32,898 --> 00:20:34,099 right there. 433 00:20:34,099 --> 00:20:35,200 There's no gap. 434 00:20:35,200 --> 00:20:35,934 Right? 435 00:20:35,934 --> 00:20:39,137 So the way they can respond to energy from photons 436 00:20:39,137 --> 00:20:42,574 is extremely diverse. 437 00:20:42,574 --> 00:20:44,076 And you can imagine, if I'm a photon 438 00:20:44,076 --> 00:20:45,644 and I excite an electron, it doesn't 439 00:20:45,644 --> 00:20:46,912 matter what the wavelength is. 440 00:20:46,912 --> 00:20:50,415 That electron can fall back down and re-emit the same energy 441 00:20:50,415 --> 00:20:52,451 photon. 442 00:20:52,451 --> 00:20:53,919 OK. 443 00:20:53,919 --> 00:20:57,556 So that's luster either way. 444 00:20:57,556 --> 00:21:01,760 But now you know and you really should do this. 445 00:21:01,760 --> 00:21:02,494 And look at. 446 00:21:02,494 --> 00:21:05,063 I just said, you know, you have this. 447 00:21:05,063 --> 00:21:06,832 I've got electrons. 448 00:21:06,832 --> 00:21:08,267 I shine photons on these. 449 00:21:08,267 --> 00:21:10,802 They might come up and go back down. 450 00:21:10,802 --> 00:21:14,539 There's all this room here for electrons to be excited. 451 00:21:14,539 --> 00:21:16,642 There's no gap. 452 00:21:16,642 --> 00:21:23,448 Whereas in diamond, in diamond I've got this huge gap, right? 453 00:21:23,448 --> 00:21:26,785 Remember, diamond is an insulator. 454 00:21:26,785 --> 00:21:31,423 Diamond has a gap of 5.5 electron volts, roughly. 455 00:21:35,127 --> 00:21:38,096 Now you know why diamonds are transparent. 456 00:21:38,096 --> 00:21:41,333 It's of course, the electrons. 457 00:21:41,333 --> 00:21:42,301 Of course. 458 00:21:42,301 --> 00:21:45,570 Because if I shine photons on this, 459 00:21:45,570 --> 00:21:48,740 and those photons are indivisible, 460 00:21:48,740 --> 00:21:52,577 you know that even if I go all the way up to purple photons, 461 00:21:52,577 --> 00:21:54,446 they're not that high. 462 00:21:54,446 --> 00:21:56,214 So any time I try to-- 463 00:21:56,214 --> 00:21:58,083 so I'm shining photons on my diamond 464 00:21:58,083 --> 00:21:59,918 and those electrons are like, can I go here? 465 00:21:59,918 --> 00:22:00,452 No. 466 00:22:00,452 --> 00:22:01,053 Can I go here? 467 00:22:01,053 --> 00:22:01,620 No. 468 00:22:01,620 --> 00:22:02,187 Can I go here? 469 00:22:02,187 --> 00:22:02,788 No. 470 00:22:02,788 --> 00:22:06,892 You have to shine a very high energy photon to excite 471 00:22:06,892 --> 00:22:08,393 an electron in diamond. 472 00:22:08,393 --> 00:22:11,596 That's why it's transparent, right? 473 00:22:11,596 --> 00:22:12,964 That's the reason. 474 00:22:12,964 --> 00:22:14,666 When you go to the store to buy diamonds, 475 00:22:14,666 --> 00:22:16,968 you should ask them about the electrons. 476 00:22:16,968 --> 00:22:20,305 That's what's making it all work. 477 00:22:20,305 --> 00:22:24,543 That's what explains the properties. 478 00:22:24,543 --> 00:22:25,444 But back to metals. 479 00:22:25,444 --> 00:22:28,046 Now, OK, so that's luster. 480 00:22:28,046 --> 00:22:30,682 What about electrical conductivity? 481 00:22:30,682 --> 00:22:32,617 Well, it's the same thing. 482 00:22:32,617 --> 00:22:34,820 It comes from the sea. 483 00:22:34,820 --> 00:22:36,388 It comes from the sea. 484 00:22:36,388 --> 00:22:42,094 If I take a wire of copper and I look 485 00:22:42,094 --> 00:22:47,999 at this as a sea of electrons, so I'm not drawing the ions, 486 00:22:47,999 --> 00:22:49,101 they're in there. 487 00:22:49,101 --> 00:22:50,535 I'm just drawing the fact that I've 488 00:22:50,535 --> 00:22:53,472 got this sort of ocean of electrons 489 00:22:53,472 --> 00:22:57,042 that are fairly free, right? 490 00:22:57,042 --> 00:23:04,649 Well, what is happening when I try to move them, 491 00:23:04,649 --> 00:23:10,355 it is with some kind of electromagnetic force, right? 492 00:23:10,355 --> 00:23:11,590 There's some kind of force. 493 00:23:11,590 --> 00:23:15,727 And what that means is that I have a charge 494 00:23:15,727 --> 00:23:17,062 that this doesn't like. 495 00:23:17,062 --> 00:23:19,598 So like it's a repulsive charge over here. 496 00:23:19,598 --> 00:23:22,868 It's going to push one of these into the other one. 497 00:23:22,868 --> 00:23:24,736 But then that's going to feel-- 498 00:23:24,736 --> 00:23:26,671 that's going to feel-- a force is going to move 499 00:23:26,671 --> 00:23:27,873 and then that's going to push this one, 500 00:23:27,873 --> 00:23:29,875 and that's going to push that one, and so forth. 501 00:23:29,875 --> 00:23:34,913 That's how electricity works, right? 502 00:23:34,913 --> 00:23:37,215 So the actual movement of the electrons 503 00:23:37,215 --> 00:23:42,287 could be slow in the material, but the current, right, you 504 00:23:42,287 --> 00:23:45,690 can push a lot of current through because these ones 505 00:23:45,690 --> 00:23:49,528 over here feel pretty quickly the forces you applied over 506 00:23:49,528 --> 00:23:50,028 there. 507 00:23:50,028 --> 00:23:53,899 But they only feel it, they only feel it 508 00:23:53,899 --> 00:23:56,768 if you can get this freedom. 509 00:23:56,768 --> 00:23:59,337 If those electrons are not free, they're 510 00:23:59,337 --> 00:24:01,339 going to feel this repulsion there and be like, 511 00:24:01,339 --> 00:24:01,940 you know what? 512 00:24:01,940 --> 00:24:04,109 I'm stuck in my state. 513 00:24:04,109 --> 00:24:06,678 I'm stuck in this full valence band. 514 00:24:06,678 --> 00:24:07,946 I got nowhere to go. 515 00:24:07,946 --> 00:24:10,282 Sorry. 516 00:24:10,282 --> 00:24:14,519 You know, put your energy into the atom or something else. 517 00:24:14,519 --> 00:24:16,054 I don't know, but I'm not moving. 518 00:24:16,054 --> 00:24:18,790 Ah, but if it's a sea, then you can push them 519 00:24:18,790 --> 00:24:20,592 and they can push each other. 520 00:24:20,592 --> 00:24:21,326 Right? 521 00:24:21,326 --> 00:24:22,227 That's the same thing. 522 00:24:22,227 --> 00:24:23,695 It's a conceptual picture, but it's 523 00:24:23,695 --> 00:24:27,466 the same thing as almost an infinite number of free states. 524 00:24:27,466 --> 00:24:29,868 That's what that means, right? 525 00:24:29,868 --> 00:24:30,936 That's what that means. 526 00:24:30,936 --> 00:24:35,373 Now, if you've got copper, we see copper 527 00:24:35,373 --> 00:24:42,848 now as something like argon with those d electrons filled, 528 00:24:42,848 --> 00:24:47,586 3d 10, and an s electron here. 529 00:24:47,586 --> 00:24:50,989 And so if it's a copper wire, those d 530 00:24:50,989 --> 00:24:53,692 electrons it's all filled up in there 531 00:24:53,692 --> 00:24:55,560 and they act as a way of shielding, 532 00:24:55,560 --> 00:24:57,562 it's a beautiful shielding, so that this 533 00:24:57,562 --> 00:25:02,367 is even more free and less interested in staying around. 534 00:25:02,367 --> 00:25:04,503 So copper's such a great conductor 535 00:25:04,503 --> 00:25:08,240 and that whole column is such a great conductor and this is, 536 00:25:08,240 --> 00:25:09,841 by the way-- 537 00:25:09,841 --> 00:25:12,544 oh, such a good thing to do on a Friday night. 538 00:25:12,544 --> 00:25:14,012 I'm so glad it's Friday. 539 00:25:14,012 --> 00:25:16,781 Look at this, ptable.com. 540 00:25:16,781 --> 00:25:17,682 Ha. 541 00:25:17,682 --> 00:25:20,886 You could spend hours on this. 542 00:25:20,886 --> 00:25:22,654 I do spend hours on this. 543 00:25:22,654 --> 00:25:24,422 [LAUGHTER] 544 00:25:24,422 --> 00:25:25,524 Property. 545 00:25:25,524 --> 00:25:29,127 Electrical conductivity And then it shows you dark green 546 00:25:29,127 --> 00:25:30,795 is high-- 547 00:25:30,795 --> 00:25:34,332 dark green is high-- and then no coloring is low. 548 00:25:34,332 --> 00:25:37,035 And then you can just click around. 549 00:25:37,035 --> 00:25:38,403 You just click around. 550 00:25:38,403 --> 00:25:41,740 I could do it now, but I would never leave. 551 00:25:41,740 --> 00:25:44,442 But you go there and you can click on different properties 552 00:25:44,442 --> 00:25:46,278 and see the trends in the periodic table, 553 00:25:46,278 --> 00:25:48,246 and it's a beautiful thing. 554 00:25:48,246 --> 00:25:51,917 And you now can understand them because of the ways 555 00:25:51,917 --> 00:25:54,886 in which electrons behave. 556 00:25:54,886 --> 00:25:56,154 So you can see-- look at this. 557 00:25:56,154 --> 00:25:57,489 There's copper, right? 558 00:25:57,489 --> 00:26:00,492 So there's copper, and below that, we've 559 00:26:00,492 --> 00:26:02,127 got silver and gold. 560 00:26:02,127 --> 00:26:06,431 And this is a really high set of elements. 561 00:26:06,431 --> 00:26:09,367 The electrical conductivity in these three elements 562 00:26:09,367 --> 00:26:13,138 is super high, and this is why. 563 00:26:13,138 --> 00:26:16,575 Because in each case, you're going down but you're filling 564 00:26:16,575 --> 00:26:17,576 the d's. 565 00:26:17,576 --> 00:26:21,146 Oh, and then you're even filling f's. 566 00:26:21,146 --> 00:26:22,614 Screening. 567 00:26:22,614 --> 00:26:24,449 Further away. 568 00:26:24,449 --> 00:26:27,519 Really free s-electrons. 569 00:26:27,519 --> 00:26:29,387 High conductivity. 570 00:26:29,387 --> 00:26:32,490 Electron sea, right? 571 00:26:32,490 --> 00:26:34,259 Very easy to push them around. 572 00:26:34,259 --> 00:26:34,759 Now. 573 00:26:34,759 --> 00:26:35,260 OK. 574 00:26:37,729 --> 00:26:42,901 This also goes back to this picture, because, remember, 575 00:26:42,901 --> 00:26:45,637 I snuck it in because it was on the graph, 576 00:26:45,637 --> 00:26:47,672 and I didn't take it out. 577 00:26:47,672 --> 00:26:50,342 But there was a picture of silicon, 578 00:26:50,342 --> 00:26:53,111 where I showed silicon increasing 579 00:26:53,111 --> 00:26:56,281 its intrinsic carrier concentration with temperature, 580 00:26:56,281 --> 00:26:57,882 and on top of that was a metal. 581 00:26:57,882 --> 00:26:59,651 I think was tungsten. 582 00:26:59,651 --> 00:27:03,321 Now if you draw the metal, it would be way up. 583 00:27:03,321 --> 00:27:06,491 It would be way up right here because this is higher, 584 00:27:06,491 --> 00:27:07,759 but it went this way. 585 00:27:10,595 --> 00:27:12,797 But now you know why. 586 00:27:12,797 --> 00:27:15,367 It's totally different. 587 00:27:15,367 --> 00:27:18,770 The reason is totally different than why this changes, 588 00:27:18,770 --> 00:27:22,540 but you can understand it for the same root, which is 589 00:27:22,540 --> 00:27:24,442 the behavior of the electrons. 590 00:27:24,442 --> 00:27:27,345 So, in a metal, in a semiconductor, 591 00:27:27,345 --> 00:27:30,382 this temperature dependence-- 592 00:27:30,382 --> 00:27:32,384 here, I've taken the temperature dependence away 593 00:27:32,384 --> 00:27:33,818 because I've doped it. 594 00:27:33,818 --> 00:27:36,921 But here, that's the thermal activation 595 00:27:36,921 --> 00:27:42,460 into a place of freedom, into a place where they can 596 00:27:42,460 --> 00:27:44,429 be free in the conduction band. 597 00:27:44,429 --> 00:27:46,731 Here, they're already totally free. 598 00:27:46,731 --> 00:27:47,565 So what's happening? 599 00:27:47,565 --> 00:27:49,434 Well, when I increase the temperature, 600 00:27:49,434 --> 00:27:53,104 I'm increasing the vibrations. 601 00:27:53,104 --> 00:27:55,774 You can imagine if these electrons are trying 602 00:27:55,774 --> 00:27:59,811 to do their thing, and they're in a sea of electrons, 603 00:27:59,811 --> 00:28:02,047 the last thing I want to do if I'm moving along 604 00:28:02,047 --> 00:28:06,818 is to see some big ion moving around. 605 00:28:06,818 --> 00:28:11,656 And if it moves more, then it's going to make me more upset 606 00:28:11,656 --> 00:28:14,726 and get in my way. 607 00:28:14,726 --> 00:28:17,128 That's temperature. 608 00:28:17,128 --> 00:28:19,998 That's why this goes down and not up. 609 00:28:19,998 --> 00:28:23,101 For metals, the more thermal energy you put in, 610 00:28:23,101 --> 00:28:24,235 the more those ions-- 611 00:28:24,235 --> 00:28:27,338 those positive charges-- they're positive-- 612 00:28:27,338 --> 00:28:30,175 are going to interfere with the electrons being free. 613 00:28:33,078 --> 00:28:35,714 Oh, we are understanding things. 614 00:28:35,714 --> 00:28:37,882 We understood why these have-- 615 00:28:37,882 --> 00:28:39,918 now, you might say, why are these different? 616 00:28:39,918 --> 00:28:42,087 That's complicated. 617 00:28:42,087 --> 00:28:44,089 Relativity. 618 00:28:44,089 --> 00:28:45,924 Not part of this class. 619 00:28:45,924 --> 00:28:48,326 But if you want to understand why these are different from 620 00:28:48,326 --> 00:28:50,595 a-- they're all really high-- 621 00:28:50,595 --> 00:28:53,531 why are they different, it goes beyond the scope of this class, 622 00:28:53,531 --> 00:28:55,100 but it's also a very interesting story 623 00:28:55,100 --> 00:29:00,538 that has to do with, on the one hand, relativistic effects. 624 00:29:00,538 --> 00:29:03,174 Now there's another thing, which is that if I go back 625 00:29:03,174 --> 00:29:05,510 to that table and I did this-- 626 00:29:05,510 --> 00:29:06,544 I really did this a lot-- 627 00:29:06,544 --> 00:29:12,217 I clicked back and forth between electrical-- now look up here-- 628 00:29:12,217 --> 00:29:15,186 thermal, electrical, thermal, electrical. 629 00:29:15,186 --> 00:29:18,389 And you can click-- you can go, mm, mm, mm, mm, and you can 630 00:29:18,389 --> 00:29:21,826 watch the table, and do that for like five minutes or so. 631 00:29:21,826 --> 00:29:26,531 And what you'll find is almost nothing changes. 632 00:29:26,531 --> 00:29:28,900 You can't do that with very many properties. 633 00:29:28,900 --> 00:29:31,536 But for metals, and those two properties, 634 00:29:31,536 --> 00:29:33,404 they're almost identical. 635 00:29:33,404 --> 00:29:36,541 Again, it goes back to the sea. 636 00:29:36,541 --> 00:29:42,914 It goes back to the sea, because if you have electrons that 637 00:29:42,914 --> 00:29:49,521 are free in a material, those can carry not just electricity, 638 00:29:49,521 --> 00:29:51,856 but those can be the dominant carriers 639 00:29:51,856 --> 00:29:53,158 of thermal energy as well. 640 00:29:53,158 --> 00:29:54,959 And I'm not going to go into those details. 641 00:29:54,959 --> 00:29:56,294 I just want to mention it. 642 00:29:56,294 --> 00:30:00,698 So this is actually called the Wiedemann-Franz law, 643 00:30:00,698 --> 00:30:11,910 and it basically says for metals, that the thermal-- 644 00:30:11,910 --> 00:30:12,844 let's see. 645 00:30:12,844 --> 00:30:14,479 OK, I'll just write it here. 646 00:30:14,479 --> 00:30:25,156 Thermal divided by electrical conductivity for both-- 647 00:30:25,156 --> 00:30:29,494 conductivities-- OK, I'm putting it in parentheses. 648 00:30:29,494 --> 00:30:31,696 It should be thermal conductivity divided 649 00:30:31,696 --> 00:30:37,735 by electoral conductivity goes as some constant times 650 00:30:37,735 --> 00:30:41,239 the temperature. 651 00:30:41,239 --> 00:30:44,409 So if you look at that-- 652 00:30:44,409 --> 00:30:46,411 so you can look at it by toggling back and forth 653 00:30:46,411 --> 00:30:48,213 and see how similar these are. 654 00:30:48,213 --> 00:30:50,949 You can also just plot stuff or find plots of stuff. 655 00:30:50,949 --> 00:30:51,749 Here's one. 656 00:30:51,749 --> 00:30:54,719 Electroconductivity-- this is at some fixed temperature-- 657 00:30:54,719 --> 00:30:57,589 orders of magnitude variation, orders of magnitude variation, 658 00:30:57,589 --> 00:30:59,457 tons and tons of different materials. 659 00:30:59,457 --> 00:31:01,793 This is the Wiedemann-Franz law. 660 00:31:01,793 --> 00:31:05,697 Now you know that law is simply a result of the fact 661 00:31:05,697 --> 00:31:09,868 that these free electrons can carry both electrical-- 662 00:31:09,868 --> 00:31:13,805 their charge-- as well as thermal energy, 663 00:31:13,805 --> 00:31:15,173 and that the way they carry those 664 00:31:15,173 --> 00:31:19,077 are dependent on the material, dependent on the number 665 00:31:19,077 --> 00:31:21,145 of electrons, and the way they bond and all that, 666 00:31:21,145 --> 00:31:23,081 but if they carry it in one way for one, 667 00:31:23,081 --> 00:31:26,551 it carries it the same way for the other. 668 00:31:26,551 --> 00:31:27,785 And look at all these things. 669 00:31:27,785 --> 00:31:32,190 Now notice here, this word that's used a lot-- alloy. 670 00:31:32,190 --> 00:31:33,491 Alloy. 671 00:31:33,491 --> 00:31:33,992 Alloy. 672 00:31:33,992 --> 00:31:36,995 These are all-- alloy. 673 00:31:36,995 --> 00:31:38,997 And I mentioned the word alloy on Wednesday, 674 00:31:38,997 --> 00:31:45,270 because I said if you wanted to make a good blue LED, 675 00:31:45,270 --> 00:31:47,238 you had gallium nitride but it was a little too 676 00:31:47,238 --> 00:31:51,476 high in its band gap, so they alloyed it with other-- 677 00:31:51,476 --> 00:31:53,778 then that meant mixing in. 678 00:31:53,778 --> 00:31:57,482 Well, that is done for metals. 679 00:31:57,482 --> 00:32:02,120 That is done for metals in a very wide range. 680 00:32:02,120 --> 00:32:02,887 Why? 681 00:32:02,887 --> 00:32:05,490 Because the metal properties that you have, 682 00:32:05,490 --> 00:32:10,428 you may like some of, but you may not like others. 683 00:32:10,428 --> 00:32:15,667 So like for copper, it's got this really high conductivity, 684 00:32:15,667 --> 00:32:18,703 but maybe you don't want it to be so malleable. 685 00:32:18,703 --> 00:32:20,004 What does that mean? 686 00:32:20,004 --> 00:32:22,073 We'll see in 10 minutes. 687 00:32:22,073 --> 00:32:24,842 Malleable, ductile. 688 00:32:24,842 --> 00:32:25,610 So what do you do? 689 00:32:25,610 --> 00:32:27,111 Well, you alloy it. 690 00:32:27,111 --> 00:32:28,613 And so here's an example. 691 00:32:28,613 --> 00:32:30,248 Brass. 692 00:32:30,248 --> 00:32:33,384 Well, we know brass, but now you know brass. 693 00:32:33,384 --> 00:32:34,652 Now you really know brass. 694 00:32:34,652 --> 00:32:35,586 You didn't know brass. 695 00:32:35,586 --> 00:32:38,323 You don't know anyone or anything 696 00:32:38,323 --> 00:32:40,959 until you see it as an atom and electrons. 697 00:32:40,959 --> 00:32:43,328 That is how you know someone. 698 00:32:43,328 --> 00:32:44,128 Copper? 699 00:32:44,128 --> 00:32:46,431 With zinc substituted in a two-to-one ratio-- 700 00:32:46,431 --> 00:32:47,398 copper to zinc-- 701 00:32:47,398 --> 00:32:49,067 the connectivity drops. 702 00:32:49,067 --> 00:32:53,071 Those electrons are not as free, but they're still pretty free. 703 00:32:53,071 --> 00:32:55,173 Maybe they're a little more tied up in the bonding, 704 00:32:55,173 --> 00:32:57,642 and maybe what you've done by alloying 705 00:32:57,642 --> 00:32:59,944 has changed its mechanical properties, 706 00:32:59,944 --> 00:33:02,246 because I kind of want something copper-like 707 00:33:02,246 --> 00:33:05,450 but I wanted to have different mechanical properties, 708 00:33:05,450 --> 00:33:07,151 so I alloyed it. 709 00:33:07,151 --> 00:33:11,823 And this is really how we think about materials design. 710 00:33:11,823 --> 00:33:14,225 I need something to have, let's say, 711 00:33:14,225 --> 00:33:15,393 a certain set of properties. 712 00:33:15,393 --> 00:33:17,395 Well, I don't have them all here, 713 00:33:17,395 --> 00:33:19,330 and I don't have them all here, but how can I 714 00:33:19,330 --> 00:33:22,300 use a combination? 715 00:33:22,300 --> 00:33:24,602 How can I use a combination to get what I want? 716 00:33:24,602 --> 00:33:26,604 Bronze is copper with tin-- 717 00:33:26,604 --> 00:33:28,139 four-to-one ratio of copper and tin. 718 00:33:28,139 --> 00:33:31,142 The conductivity drop even more. 719 00:33:31,142 --> 00:33:33,044 It's not so simple. 720 00:33:33,044 --> 00:33:35,580 It's not so simple as, oh, if it's four-to-one, 721 00:33:35,580 --> 00:33:36,981 then maybe it's like 20%. 722 00:33:36,981 --> 00:33:40,885 No, because it has to do with what 723 00:33:40,885 --> 00:33:44,255 happens to the freedom of these electrons. 724 00:33:44,255 --> 00:33:47,291 That's what it has to do with, and that's more complicated. 725 00:33:47,291 --> 00:33:49,460 But maybe I've changed the properties in another way 726 00:33:49,460 --> 00:33:51,396 that I really like. 727 00:33:51,396 --> 00:33:52,697 Well, those are substitutional. 728 00:33:52,697 --> 00:33:55,833 Substitutional alloys means I took one of the coppers out 729 00:33:55,833 --> 00:33:57,835 and I replaced it with something else. 730 00:33:57,835 --> 00:33:59,670 Here's brass with zinc in there. 731 00:33:59,670 --> 00:34:02,807 You can also have interstitial alloys, 732 00:34:02,807 --> 00:34:04,409 and interstitial alloys-- 733 00:34:04,409 --> 00:34:07,645 so if we-- we'll be coming back to this when we talk about 734 00:34:07,645 --> 00:34:08,846 crystals next week-- 735 00:34:08,846 --> 00:34:12,617 but alloys-- actually when we talk about defects. 736 00:34:12,617 --> 00:34:17,355 So you can have substitutional-- substitutional-- 737 00:34:17,355 --> 00:34:23,094 and you can have interstitial. 738 00:34:23,094 --> 00:34:25,429 This is just a preview. 739 00:34:25,429 --> 00:34:27,465 Interstitial. 740 00:34:27,465 --> 00:34:28,399 This is just a preview. 741 00:34:28,399 --> 00:34:32,937 We're not going to be testing on this 742 00:34:32,937 --> 00:34:34,472 or thinking about this much until we 743 00:34:34,472 --> 00:34:37,975 get to actually putting these things in to a crystal 744 00:34:37,975 --> 00:34:41,012 later as defects. 745 00:34:41,012 --> 00:34:44,415 But right now, I just want to make sure you see them 746 00:34:44,415 --> 00:34:45,183 for the first time. 747 00:34:45,183 --> 00:34:47,051 Substitution, interstitial. 748 00:34:47,051 --> 00:34:47,717 Why would you want one or the other? 749 00:34:47,717 --> 00:34:49,253 Well, it depends on what properties 750 00:34:49,253 --> 00:34:51,054 you're trying to change. 751 00:34:51,054 --> 00:34:54,058 In this case, I really like iron. 752 00:34:54,058 --> 00:34:55,626 It's really cheap. 753 00:34:55,626 --> 00:34:59,397 It's a cool material, but I need it to be stronger. 754 00:34:59,397 --> 00:35:00,631 And that's called steel. 755 00:35:00,631 --> 00:35:03,568 And if you just put a little bit of carbon-- really, not much, 756 00:35:03,568 --> 00:35:06,337 like a percent by weight-- 757 00:35:06,337 --> 00:35:09,607 it can dramatically change the mechanical properties of iron. 758 00:35:09,607 --> 00:35:11,709 You can make it a much stronger material. 759 00:35:11,709 --> 00:35:14,779 There is a massive, massive range of properties. 760 00:35:14,779 --> 00:35:19,450 And part of why metals are so tunable 761 00:35:19,450 --> 00:35:23,588 is because of the electron sea. 762 00:35:23,588 --> 00:35:25,490 I just came across this article actually, 763 00:35:25,490 --> 00:35:26,591 and I thought I'd show you. 764 00:35:26,591 --> 00:35:28,793 This was just literally yesterday. 765 00:35:28,793 --> 00:35:30,294 Was that yesterday? 766 00:35:30,294 --> 00:35:32,396 I thought it was an interesting example. 767 00:35:32,396 --> 00:35:34,132 Car Wars: Steel Getting Stronger, 768 00:35:34,132 --> 00:35:35,566 Lighter to Curb Aluminum Rise. 769 00:35:35,566 --> 00:35:39,237 Well, see the thing is that as you want cars to be lighter-- 770 00:35:39,237 --> 00:35:43,674 think fuel efficiency, or range, if it's electric-- 771 00:35:43,674 --> 00:35:45,042 you've got to use lighter metals. 772 00:35:45,042 --> 00:35:47,445 And aluminum is lighter, but aluminum is more than twice 773 00:35:47,445 --> 00:35:49,480 as much a steel. 774 00:35:49,480 --> 00:35:51,082 It's a lot lighter though. 775 00:35:51,082 --> 00:35:54,619 So there's a lot of interest in making steel-- 776 00:35:54,619 --> 00:35:56,954 that's just iron with carbon interstitial-- 777 00:35:56,954 --> 00:35:58,055 and making steel stronger. 778 00:35:58,055 --> 00:36:00,458 And you can see, "Newest alloy." 779 00:36:00,458 --> 00:36:01,926 That's what caught my attention. 780 00:36:01,926 --> 00:36:03,928 Newest alloy. 781 00:36:03,928 --> 00:36:05,663 They've come up with something to add 782 00:36:05,663 --> 00:36:10,401 to iron to make its mechanical properties really, 783 00:36:10,401 --> 00:36:14,405 really good at a very, very thin layer 784 00:36:14,405 --> 00:36:18,509 because they need steel to be even stronger in a much 785 00:36:18,509 --> 00:36:19,210 thinner layer. 786 00:36:19,210 --> 00:36:20,678 Otherwise, it's too heavy. 787 00:36:20,678 --> 00:36:23,014 And you've got to make it really thin and really strong. 788 00:36:23,014 --> 00:36:25,049 Those are going to be alloys. 789 00:36:25,049 --> 00:36:25,583 OK. 790 00:36:25,583 --> 00:36:26,651 Back to our property list. 791 00:36:26,651 --> 00:36:29,153 Now, malleability and ductility. 792 00:36:29,153 --> 00:36:32,890 Why are metals malleable and ductile? 793 00:36:32,890 --> 00:36:36,060 Well, I thought this was a good place for a video 794 00:36:36,060 --> 00:36:37,128 because I really like it. 795 00:36:37,128 --> 00:36:40,464 I think this is a really simple explanation of malleability 796 00:36:40,464 --> 00:36:43,801 and ductility as it relates to the electron sea. 797 00:36:43,801 --> 00:36:44,769 So let's watch this. 798 00:36:44,769 --> 00:36:46,137 This looks like a minute long. 799 00:36:46,137 --> 00:36:46,804 [VIDEO PLAYBACK] 800 00:36:46,804 --> 00:36:49,540 - [INAUDIBLE] shatters. 801 00:36:49,540 --> 00:36:52,944 And this is because the applied force pushes light ions 802 00:36:52,944 --> 00:36:54,412 close together. 803 00:36:54,412 --> 00:36:58,182 They violently repel each other, breaking the crystal apart. 804 00:36:58,182 --> 00:36:59,183 That's an ionic crystal. 805 00:36:59,183 --> 00:37:02,119 - In contrast, if you hit a metal with a hammer, 806 00:37:02,119 --> 00:37:03,187 it doesn't break. 807 00:37:03,187 --> 00:37:04,922 It just dents. 808 00:37:04,922 --> 00:37:07,091 Metals are able to deform form in response 809 00:37:07,091 --> 00:37:08,826 to an applied force. 810 00:37:08,826 --> 00:37:12,230 The mobile sea of electrons shields the cations 811 00:37:12,230 --> 00:37:15,399 from each other, preventing violent repulsion 812 00:37:15,399 --> 00:37:18,236 and allowing the metal to change shape. 813 00:37:18,236 --> 00:37:21,706 The most malleable metal is gold. 814 00:37:21,706 --> 00:37:24,942 A similar property to the malleability of metals 815 00:37:24,942 --> 00:37:29,080 is their ability to be pulled into long thin wires. 816 00:37:29,080 --> 00:37:31,882 We call this ductility. 817 00:37:31,882 --> 00:37:35,386 Ionic compounds are not ductile for the same reason they 818 00:37:35,386 --> 00:37:37,488 are not malleable in general. 819 00:37:37,488 --> 00:37:41,125 If an ionic compound is forced into a long cylinder, 820 00:37:41,125 --> 00:37:45,429 it breaks apart because of the repulsion of like ions. 821 00:37:45,429 --> 00:37:48,299 In contrast, a metal can be pulled 822 00:37:48,299 --> 00:37:52,036 into a long cylindrical shape because the cations can 823 00:37:52,036 --> 00:37:54,472 line up, shielded from each other, 824 00:37:54,472 --> 00:37:57,708 as the fluid-like like sea of electrons flows around them. 825 00:37:57,708 --> 00:37:58,709 That's my favorite part. 826 00:37:58,709 --> 00:37:59,910 - The most ductile metal-- 827 00:37:59,910 --> 00:38:00,478 [END PLAYBACK] 828 00:38:00,478 --> 00:38:02,079 Fluid-like sea. 829 00:38:02,079 --> 00:38:02,613 Oh. 830 00:38:02,613 --> 00:38:04,615 The most ductile metal. 831 00:38:04,615 --> 00:38:06,517 What is it? 832 00:38:06,517 --> 00:38:09,186 We may never know. 833 00:38:09,186 --> 00:38:11,622 We may-- it's platinum. 834 00:38:11,622 --> 00:38:12,990 But see, now, OK. 835 00:38:12,990 --> 00:38:13,491 OK. 836 00:38:13,491 --> 00:38:14,392 Now that's a-- 837 00:38:14,392 --> 00:38:15,526 I just gave it away. 838 00:38:15,526 --> 00:38:17,728 OK. 839 00:38:17,728 --> 00:38:21,299 Ductile, malleable, sea of electrons. 840 00:38:21,299 --> 00:38:23,167 Sea of electrons. 841 00:38:23,167 --> 00:38:25,336 Because did you see them flowing around? 842 00:38:25,336 --> 00:38:29,440 You're moving the atom-- that was like a dance thing. 843 00:38:29,440 --> 00:38:31,142 That can be like a new dance move 844 00:38:31,142 --> 00:38:33,644 that you try out tonight, the sea of electrons dance move. 845 00:38:33,644 --> 00:38:36,047 I'm just saying. 846 00:38:36,047 --> 00:38:37,248 I'm not going to do it again. 847 00:38:37,248 --> 00:38:42,119 But the sea of electrons is able to move around the ions 848 00:38:42,119 --> 00:38:44,455 as they're distorting because the metal bond is not 849 00:38:44,455 --> 00:38:46,157 so directional. 850 00:38:46,157 --> 00:38:48,359 The metal bond is not so directional. 851 00:38:48,359 --> 00:38:49,327 Because think about it. 852 00:38:49,327 --> 00:38:52,129 What is holding the metal together? 853 00:38:52,129 --> 00:38:55,232 It's these interactions between the house and the kids 854 00:38:55,232 --> 00:38:57,902 that are roaming all over the place. 855 00:38:57,902 --> 00:38:59,403 Is the kid over there or over there? 856 00:38:59,403 --> 00:39:00,671 It doesn't matter. 857 00:39:00,671 --> 00:39:05,076 Just give me a little bit of negative charge 858 00:39:05,076 --> 00:39:08,512 so I can feel an attraction. 859 00:39:08,512 --> 00:39:12,483 That's the metal-- that's why it is so able 860 00:39:12,483 --> 00:39:15,586 to deform in the way it does. 861 00:39:15,586 --> 00:39:17,254 Because those atoms are moving around, 862 00:39:17,254 --> 00:39:19,724 and the electrons are just kind of there as this happy sea, 863 00:39:19,724 --> 00:39:21,459 and the bonding remains. 864 00:39:21,459 --> 00:39:23,294 It doesn't break. 865 00:39:23,294 --> 00:39:24,095 That's the key. 866 00:39:24,095 --> 00:39:26,530 Otherwise, this thing would just crack. 867 00:39:26,530 --> 00:39:29,033 So wire-pulling-- check this one out. 868 00:39:29,033 --> 00:39:37,975 You can take a 10-centimeter by one-centimeter platinum rod, 869 00:39:37,975 --> 00:39:40,845 and you can spin that into a wire, and this is done-- 870 00:39:40,845 --> 00:39:43,714 this is a very thin case for effect. 871 00:39:43,714 --> 00:39:49,019 But you can make a 0.0006-millimeter diameter 872 00:39:49,019 --> 00:39:57,428 wire, and you get 2,777 kilometers of wire. 873 00:39:57,428 --> 00:40:00,097 Now that's because of ductility. 874 00:40:00,097 --> 00:40:01,732 The only reason I can get from point A 875 00:40:01,732 --> 00:40:04,435 to point B there is because I'm not breaking this apart, 876 00:40:04,435 --> 00:40:06,103 and that's how thin I can get-- 877 00:40:06,103 --> 00:40:12,543 27-millimeter diameter when I pull it. 878 00:40:12,543 --> 00:40:15,679 And I thought that was a really good example of why 879 00:40:15,679 --> 00:40:20,651 this matters, because maybe you've noticed, 880 00:40:20,651 --> 00:40:23,788 but wires are really important to us. 881 00:40:23,788 --> 00:40:25,689 We use them a lot. 882 00:40:25,689 --> 00:40:30,094 And so, I you just saw in a cartoon with electrons. 883 00:40:30,094 --> 00:40:33,964 Here is a cartoon that I thought was interesting that 884 00:40:33,964 --> 00:40:36,534 shows a wire-pulling setup. 885 00:40:36,534 --> 00:40:39,637 So, now this is-- 886 00:40:39,637 --> 00:40:41,372 Die, reducing the diameter. 887 00:40:41,372 --> 00:40:42,239 That's a die. 888 00:40:42,239 --> 00:40:46,043 Further reduction can take place using extra dies. 889 00:40:46,043 --> 00:40:49,814 The drawn wire is finally wound on a spool. 890 00:40:49,814 --> 00:40:53,117 This transformation elongates the wire. 891 00:40:53,117 --> 00:40:58,122 One meter of 5.5-millimeter wire rod can be drawn to 30 meters 892 00:40:58,122 --> 00:41:03,627 with one millimeter diameter or 484 meters with 0.25 893 00:41:03,627 --> 00:41:05,296 millimeters diameter. 894 00:41:05,296 --> 00:41:05,796 OK. 895 00:41:05,796 --> 00:41:11,869 Now, that is a cartoon, and I think it's always good. 896 00:41:11,869 --> 00:41:14,805 When you see cartoons like this, you don't know. 897 00:41:14,805 --> 00:41:17,475 Go look up what the real deal is. 898 00:41:17,475 --> 00:41:19,510 What does it really look like to draw wires? 899 00:41:19,510 --> 00:41:21,512 And I found it pretty cool. 900 00:41:21,512 --> 00:41:24,849 So this is an actual wire-drawing plant, 901 00:41:24,849 --> 00:41:26,350 and this is what it looks like. 902 00:41:26,350 --> 00:41:28,152 Now, there's no audio here, but I just 903 00:41:28,152 --> 00:41:29,553 wanted to show you the magnitude. 904 00:41:29,553 --> 00:41:32,890 Those are huge towers that are melting metals 905 00:41:32,890 --> 00:41:37,161 to give you this first rod, and then it goes through one 906 00:41:37,161 --> 00:41:37,895 after the other. 907 00:41:37,895 --> 00:41:39,430 And look at it being pulled-- 908 00:41:39,430 --> 00:41:41,131 being pulled in at some diameter, 909 00:41:41,131 --> 00:41:43,234 and it comes out in a different diameter. 910 00:41:43,234 --> 00:41:47,738 But I wanted to show you the scope and size of this. 911 00:41:47,738 --> 00:41:48,772 This is just one of them. 912 00:41:48,772 --> 00:41:53,344 There's a person, and so you get a sense of the size, 913 00:41:53,344 --> 00:41:54,879 and then you can also see something-- 914 00:41:54,879 --> 00:41:56,814 when you go visit these factories, 915 00:41:56,814 --> 00:41:58,549 and I have these factories, there's 916 00:41:58,549 --> 00:41:59,917 always a lot of this happening. 917 00:41:59,917 --> 00:42:00,417 Why? 918 00:42:00,417 --> 00:42:03,087 Things are getting really hot. 919 00:42:03,087 --> 00:42:06,390 When you're spinning things like a wire at a very high velocity, 920 00:42:06,390 --> 00:42:09,226 things heat up, so you get water all over the place. 921 00:42:09,226 --> 00:42:13,097 So there's water being sprayed in factories 922 00:42:13,097 --> 00:42:15,533 all over the place, because you've got to keep stuff cool, 923 00:42:15,533 --> 00:42:19,169 or there's water baths that you run these things through. 924 00:42:19,169 --> 00:42:20,871 And then you've got to think about, well, 925 00:42:20,871 --> 00:42:23,274 does this thing interact with water? 926 00:42:23,274 --> 00:42:24,775 How does the water play a role? 927 00:42:24,775 --> 00:42:27,278 It all comes down to the electrons. 928 00:42:27,278 --> 00:42:29,547 And once they've actually drawn the wire out 929 00:42:29,547 --> 00:42:32,116 over this huge factory, they can actually 930 00:42:32,116 --> 00:42:33,083 weave it back together. 931 00:42:33,083 --> 00:42:33,918 So I found this. 932 00:42:33,918 --> 00:42:35,486 This is the same factory. 933 00:42:35,486 --> 00:42:38,589 Now these things here are doing the opposite. 934 00:42:38,589 --> 00:42:41,725 So these are huge drums, about the size of a person, 935 00:42:41,725 --> 00:42:46,697 and each of these got a wire that was drawn. 936 00:42:46,697 --> 00:42:50,200 And now, again, because of the ductility, 937 00:42:50,200 --> 00:42:53,203 you can also move the wires, play with the wires, 938 00:42:53,203 --> 00:42:54,538 and you can weave them together. 939 00:42:54,538 --> 00:42:56,273 You can weave them right back together 940 00:42:56,273 --> 00:42:58,542 into a thread that looks like that, which we all have 941 00:42:58,542 --> 00:43:01,979 seen I think many, many times. 942 00:43:01,979 --> 00:43:05,482 All of this processing, all of this manufacturability, 943 00:43:05,482 --> 00:43:08,052 has to do with the electron sea. 944 00:43:08,052 --> 00:43:10,988 That's why we have wires 945 00:43:10,988 --> 00:43:11,689 OK. 946 00:43:11,689 --> 00:43:15,159 Now, a couple more small points. 947 00:43:15,159 --> 00:43:18,062 So we're going to go back to this picture 948 00:43:18,062 --> 00:43:19,930 because this is how we started. 949 00:43:22,933 --> 00:43:26,637 And this is the 1-D-- 950 00:43:26,637 --> 00:43:33,243 remember that 1-D model that we used to introduce band theory-- 951 00:43:33,243 --> 00:43:39,717 and I want to go back to this, because what you can see is 952 00:43:39,717 --> 00:43:47,424 that if I think about this as bonding and anti-bonding 953 00:43:47,424 --> 00:43:49,927 orbitals all kind of mixed in here, 954 00:43:49,927 --> 00:43:55,833 then you can also get a sense, just like in the dimers that we 955 00:43:55,833 --> 00:43:56,433 make-- 956 00:43:56,433 --> 00:44:01,238 N2, O2, remember NO? 957 00:44:01,238 --> 00:44:02,906 Bond order. 958 00:44:02,906 --> 00:44:06,910 It counts how many electrons are in an anti-bonding orbital. 959 00:44:06,910 --> 00:44:08,746 Just because it's in an anti-bonding orbital 960 00:44:08,746 --> 00:44:10,681 doesn't mean it's not there in the system. 961 00:44:10,681 --> 00:44:13,517 It's the same with these metal bands. 962 00:44:13,517 --> 00:44:15,386 Some of them may be good for bonding. 963 00:44:15,386 --> 00:44:17,287 Some of them may not. 964 00:44:17,287 --> 00:44:20,190 But just like in the dimers, the bond order 965 00:44:20,190 --> 00:44:23,594 is related to the strength of that bond. 966 00:44:23,594 --> 00:44:24,395 Remember? 967 00:44:24,395 --> 00:44:26,497 And in NO, it's like a bond order of 2 and 1/2, 968 00:44:26,497 --> 00:44:30,768 and then if I took an electron out, it actually got stronger. 969 00:44:30,768 --> 00:44:32,736 The bonding got stronger. 970 00:44:32,736 --> 00:44:34,505 It's the same thing. 971 00:44:34,505 --> 00:44:37,074 You can think about this the same way in metals. 972 00:44:37,074 --> 00:44:38,442 You have a band. 973 00:44:38,442 --> 00:44:42,312 Some of these orbitals are not going to be bonding orbitals, 974 00:44:42,312 --> 00:44:45,949 and some of them are going to be much more about the bonding. 975 00:44:45,949 --> 00:44:53,457 And so that's going to relate to things like boiling point. 976 00:44:53,457 --> 00:44:56,527 Metals have boiling points too. 977 00:44:56,527 --> 00:44:59,963 So if you look now, go back to the periodic table, 978 00:44:59,963 --> 00:45:03,167 remember the highest electrical connectivity was here. 979 00:45:03,167 --> 00:45:08,272 Well, that had to do with that right there, with the position, 980 00:45:08,272 --> 00:45:10,541 with the filling of the orbitals to give me 981 00:45:10,541 --> 00:45:13,043 the freest electron I can imagine, 982 00:45:13,043 --> 00:45:16,280 after those d-orbitals are filled, that s. 983 00:45:16,280 --> 00:45:18,115 But if I'm thinking about whether I filled 984 00:45:18,115 --> 00:45:20,017 anti-bondings orbitals or not, because now I'm 985 00:45:20,017 --> 00:45:22,486 thinking about the strength of the bonds, 986 00:45:22,486 --> 00:45:24,488 you see a different trend, and you see something 987 00:45:24,488 --> 00:45:26,090 that you would expect. 988 00:45:26,090 --> 00:45:27,991 First of all, you see a huge variability, 989 00:45:27,991 --> 00:45:29,893 but you see that the ones that are strongest-- 990 00:45:29,893 --> 00:45:31,462 the highest boiling points-- 991 00:45:31,462 --> 00:45:34,598 are going to be the ones where you fill that band-- 992 00:45:34,598 --> 00:45:36,834 those bands-- roughly halfway. 993 00:45:39,369 --> 00:45:43,440 And this is also why, in a metallic bond, 994 00:45:43,440 --> 00:45:49,146 in a metallic bond, you've got this enormous range. 995 00:45:49,146 --> 00:46:02,693 So you've got-- it's the weakest for elements 996 00:46:02,693 --> 00:46:13,837 with near-empty, near empty, valence 997 00:46:13,837 --> 00:46:17,975 subshells, valence subshells, and I 998 00:46:17,975 --> 00:46:24,515 would say, like OK, caesium is an example, 999 00:46:24,515 --> 00:46:31,255 or near-full, like, for example, in mercury. 1000 00:46:31,255 --> 00:46:34,458 Now mercury is actually a liquid at room 1001 00:46:34,458 --> 00:46:36,593 temperature because of this. 1002 00:46:36,593 --> 00:46:37,961 There it is. 1003 00:46:37,961 --> 00:46:39,463 There it is. 1004 00:46:39,463 --> 00:46:39,963 Why? 1005 00:46:39,963 --> 00:46:45,569 Because I-- remember the beryllium dimer. 1006 00:46:45,569 --> 00:46:48,372 I filled all these electrons in there, 1007 00:46:48,372 --> 00:46:53,277 and they're causing this really weak bonding, this really weak 1008 00:46:53,277 --> 00:46:54,978 bonding, because I had to put all of them 1009 00:46:54,978 --> 00:46:57,581 into the anti-bonding orbitals. 1010 00:46:57,581 --> 00:47:00,017 I couldn't do this trick that right over here, right 1011 00:47:00,017 --> 00:47:01,985 one column next to it, these guys 1012 00:47:01,985 --> 00:47:04,087 can have tricks, where they-- 1013 00:47:04,087 --> 00:47:05,689 now this is bonding strength. 1014 00:47:05,689 --> 00:47:08,158 This is not electroconductivity. 1015 00:47:08,158 --> 00:47:11,762 But here, they're filling the d, and then the s is free. 1016 00:47:11,762 --> 00:47:12,963 Not here. 1017 00:47:12,963 --> 00:47:15,599 Here they're all filled, bonding and anti-bonding. 1018 00:47:15,599 --> 00:47:17,534 No tricks. 1019 00:47:17,534 --> 00:47:21,171 Now, if you look at the melting temperature-- that's 1020 00:47:21,171 --> 00:47:23,173 one of the strongest elements would be tungsten. 1021 00:47:27,211 --> 00:47:33,350 The strongest would be example tungsten, where 1022 00:47:33,350 --> 00:47:36,954 you've got a range of melting-- 1023 00:47:36,954 --> 00:47:38,856 the melting point of tungsten-- 1024 00:47:38,856 --> 00:47:40,858 and this is not the same as the boiling point-- 1025 00:47:40,858 --> 00:47:46,396 the melting point of tungsten is 3,680 degrees C. 1026 00:47:46,396 --> 00:47:49,566 That's a liquid at room temperature. 1027 00:47:49,566 --> 00:47:55,405 And the melting point of cesium is 28 degrees 1028 00:47:55,405 --> 00:47:57,074 C. Look at that range. 1029 00:47:57,074 --> 00:47:59,109 And it all has to do with how these electrons are 1030 00:47:59,109 --> 00:48:02,012 filling the metallic bands. 1031 00:48:02,012 --> 00:48:05,549 And more than that, because it also has to do with the way 1032 00:48:05,549 --> 00:48:08,919 the atoms come together, and that is going 1033 00:48:08,919 --> 00:48:10,520 to be the topic of next week. 1034 00:48:10,520 --> 00:48:12,522 Now that would have been a perfect line 1035 00:48:12,522 --> 00:48:16,026 to end on because I said the words, "next week." 1036 00:48:16,026 --> 00:48:18,595 I just want to make one more point. 1037 00:48:18,595 --> 00:48:20,163 I can't stop because there is one more 1038 00:48:20,163 --> 00:48:25,602 thing I want to show very quickly in one minute. 1039 00:48:25,602 --> 00:48:31,441 And that is-- going back to this picture, 1040 00:48:31,441 --> 00:48:34,978 if you're thinking about filling, 1041 00:48:34,978 --> 00:48:36,446 and I've got like my 3s-- 1042 00:48:36,446 --> 00:48:40,250 remember, I've got like my 3s-- 1043 00:48:40,250 --> 00:48:47,457 and let's put 2p here and then 3s and 3p. 1044 00:48:47,457 --> 00:48:51,828 Now remember, for metals, for a lot of these metals, what 1045 00:48:51,828 --> 00:48:55,599 ends up happening is what I showed you before on Wednesday, 1046 00:48:55,599 --> 00:48:58,535 which is that you get actually an overlap of this, 1047 00:48:58,535 --> 00:49:05,776 so you get a band that would be the 3s/3p band. 1048 00:49:05,776 --> 00:49:09,012 Sodium, magnesium, aluminum-- these 1049 00:49:09,012 --> 00:49:13,583 all come together like this to form a single band. 1050 00:49:13,583 --> 00:49:16,620 Now remember, I don't need you to know how to do this. 1051 00:49:16,620 --> 00:49:19,056 We would tell you if it does this or not. 1052 00:49:19,056 --> 00:49:20,090 And we talked about that. 1053 00:49:20,090 --> 00:49:23,627 I'm not going to ask you to know how these come together, 1054 00:49:23,627 --> 00:49:25,829 do they form a continuous band or not? 1055 00:49:25,829 --> 00:49:28,665 But in this case, they do, for that row. 1056 00:49:28,665 --> 00:49:30,100 And so you know. 1057 00:49:30,100 --> 00:49:34,504 I've got eight electrons, eight-electron capacity 1058 00:49:34,504 --> 00:49:38,308 in that band per atom. 1059 00:49:38,308 --> 00:49:39,643 That's the capacity of the band. 1060 00:49:39,643 --> 00:49:41,878 So now I want to talk about, how is this band filled? 1061 00:49:41,878 --> 00:49:46,850 Well, for sodium, I'm going to fill it 1/8th, 1062 00:49:46,850 --> 00:49:48,752 because it's got just one electron that it's 1063 00:49:48,752 --> 00:49:50,620 putting into that band. 1064 00:49:50,620 --> 00:49:57,127 And for magnesium, I'm going to fill it with two electrons. 1065 00:49:57,127 --> 00:49:59,629 And aluminum would be three. 1066 00:50:03,000 --> 00:50:05,402 And so on. 1067 00:50:05,402 --> 00:50:07,304 So it goes back to the same picture as before. 1068 00:50:07,304 --> 00:50:09,439 We're filling the bands, but now we've 1069 00:50:09,439 --> 00:50:12,476 got 10 to the 23rd and 24th atoms, 1070 00:50:12,476 --> 00:50:14,311 and so we think about filling the bands 1071 00:50:14,311 --> 00:50:20,884 as what's the occupancy per atom you can put in there? 1072 00:50:20,884 --> 00:50:23,220 And so I could tell you if I had a mole of sodium, 1073 00:50:23,220 --> 00:50:25,422 how many electrons I have in this band, right? 1074 00:50:25,422 --> 00:50:27,024 It's a mole. 1075 00:50:27,024 --> 00:50:28,325 And how did you fill it? 1076 00:50:28,325 --> 00:50:30,627 And that ties into what I just talked about, 1077 00:50:30,627 --> 00:50:33,463 which is how that relates to bonding strength. 1078 00:50:33,463 --> 00:50:33,964 OK. 1079 00:50:33,964 --> 00:50:35,399 Now we can stop. 1080 00:50:35,399 --> 00:50:38,568 On Monday, we will start talking about crystals. 1081 00:50:38,568 --> 00:50:40,937 Have a very good weekend.