1 00:00:16,015 --> 00:00:16,649 Happy Friday. 2 00:00:16,649 --> 00:00:18,084 How is everyone? 3 00:00:18,084 --> 00:00:18,585 Woo! 4 00:00:18,585 --> 00:00:20,086 Woo! 5 00:00:20,086 --> 00:00:21,554 Woo! 6 00:00:21,554 --> 00:00:22,055 Cool. 7 00:00:22,055 --> 00:00:23,123 Cool. 8 00:00:23,123 --> 00:00:25,759 I am excited. 9 00:00:25,759 --> 00:00:28,595 We're going to keep talking about XRD today. 10 00:00:28,595 --> 00:00:30,330 We're going to pick up where we left off. 11 00:00:30,330 --> 00:00:31,931 So I filled in some numbers. 12 00:00:31,931 --> 00:00:33,933 And then, we're going to fill out this chart 13 00:00:33,933 --> 00:00:39,372 and really get to a deep understanding of XRD. 14 00:00:39,372 --> 00:00:41,975 I'll also talk about Moseley's law 15 00:00:41,975 --> 00:00:48,348 and a little bit about another type of XRD that is done. 16 00:00:48,348 --> 00:00:50,316 Now, where were we? 17 00:00:50,316 --> 00:00:51,284 Oh, OK. 18 00:00:51,284 --> 00:00:53,353 We were here. 19 00:00:53,353 --> 00:00:58,458 So on Wednesday-- and before we fill this chart out, 20 00:00:58,458 --> 00:01:01,494 I want to go back and make sure we, kind of, get this. 21 00:01:01,494 --> 00:01:02,562 Right? 22 00:01:02,562 --> 00:01:04,931 We talked about the Bragg condition. 23 00:01:04,931 --> 00:01:12,505 And we talked about how the unique thing about x-rays 24 00:01:12,505 --> 00:01:17,544 is that their wavelengths are right in that, 25 00:01:17,544 --> 00:01:21,648 sort of, precious distance regime of the spacing of atoms 26 00:01:21,648 --> 00:01:23,015 in a crystal. 27 00:01:23,015 --> 00:01:27,253 And so if I shine them on the crystal, 28 00:01:27,253 --> 00:01:29,389 then they can diffract. 29 00:01:29,389 --> 00:01:33,726 And they can have constructive and destructive interference, 30 00:01:33,726 --> 00:01:37,130 but only if they line up. 31 00:01:37,130 --> 00:01:39,699 And that's what the Bragg diffraction tells us. 32 00:01:39,699 --> 00:01:42,801 It tells us the the Bragg condition 33 00:01:42,801 --> 00:01:43,937 for when they line up. 34 00:01:43,937 --> 00:01:48,074 And in particular, this is a pretty nice image. 35 00:01:48,074 --> 00:01:53,446 So you can see here's one x-ray coming in. 36 00:01:53,446 --> 00:01:54,481 And it's a wave. 37 00:01:54,481 --> 00:01:55,381 It's a wave. 38 00:01:55,381 --> 00:01:56,850 So it's going to be a wave that goes like that, 39 00:01:56,850 --> 00:01:58,518 and then it bounces off of this surface. 40 00:01:58,518 --> 00:02:01,488 Now a second one doesn't bounce off that top surface. 41 00:02:01,488 --> 00:02:04,724 It bounces off of the one beneath it. 42 00:02:04,724 --> 00:02:05,225 OK? 43 00:02:05,225 --> 00:02:07,393 And they're separated by a distance D. 44 00:02:07,393 --> 00:02:10,196 So this could be any set of planes. 45 00:02:10,196 --> 00:02:11,598 Right? 46 00:02:11,598 --> 00:02:13,133 So here are my planes now. 47 00:02:13,133 --> 00:02:16,302 So these black atoms are one plane. 48 00:02:16,302 --> 00:02:16,870 Right? 49 00:02:16,870 --> 00:02:19,239 But these yellow ones are another one. 50 00:02:19,239 --> 00:02:21,808 That's another plane that you could see. 51 00:02:21,808 --> 00:02:24,377 Remember, one of the assumptions of the Bragg condition 52 00:02:24,377 --> 00:02:26,579 is that these planes are like mirrors. 53 00:02:26,579 --> 00:02:29,415 So we lose a sense of where the atoms are exactly, 54 00:02:29,415 --> 00:02:31,017 and we just write a mirror there. 55 00:02:31,017 --> 00:02:32,752 And we say it's reflecting off the mirror. 56 00:02:32,752 --> 00:02:33,753 So where's the next one? 57 00:02:33,753 --> 00:02:36,022 And you can take the orange ones. 58 00:02:36,022 --> 00:02:37,023 That's another plane. 59 00:02:37,023 --> 00:02:40,360 The red ones and so forth. 60 00:02:40,360 --> 00:02:43,129 Now you have a wave on top. 61 00:02:43,129 --> 00:02:43,930 OK? 62 00:02:43,930 --> 00:02:45,098 You've got a wave on top. 63 00:02:45,098 --> 00:02:47,634 And then, you got a wave coming down and bouncing off the one 64 00:02:47,634 --> 00:02:51,971 beneath it and for those to constructively interfere 65 00:02:51,971 --> 00:02:55,441 so that you pick up a signal in the detector. 66 00:02:55,441 --> 00:02:57,543 There's only one way for that to happen. 67 00:02:57,543 --> 00:03:00,513 And that's if this distance plus that distance 68 00:03:00,513 --> 00:03:03,283 is equal to a multiple of the wavelength. 69 00:03:03,283 --> 00:03:03,783 Right? 70 00:03:03,783 --> 00:03:08,121 And that is the Bragg condition. 71 00:03:08,121 --> 00:03:10,623 It has to come all the way down to here, which makes 72 00:03:10,623 --> 00:03:12,759 that theta equal to that theta. 73 00:03:12,759 --> 00:03:13,293 You see that? 74 00:03:13,293 --> 00:03:16,796 Because they've gone up to this point, up to that line. 75 00:03:16,796 --> 00:03:18,264 They've gone the same distance. 76 00:03:18,264 --> 00:03:20,466 So they're waving together. 77 00:03:20,466 --> 00:03:21,034 All right? 78 00:03:21,034 --> 00:03:23,536 And it's that point where now this 79 00:03:23,536 --> 00:03:26,339 is the extra that the one that bounces off 80 00:03:26,339 --> 00:03:30,176 of this plane, that's the extra distance it goes. 81 00:03:30,176 --> 00:03:31,778 That's the Bragg condition. 82 00:03:31,778 --> 00:03:32,545 OK? 83 00:03:32,545 --> 00:03:33,680 That's the Bragg condition. 84 00:03:33,680 --> 00:03:36,683 And remember, in this class, OK, so it could be any multiple. 85 00:03:36,683 --> 00:03:39,819 But here, we're just going to assume n equals 1 86 00:03:39,819 --> 00:03:42,121 because it's the easiest case. 87 00:03:42,121 --> 00:03:43,089 OK, good. 88 00:03:43,089 --> 00:03:45,625 That's the Bragg condition. 89 00:03:45,625 --> 00:03:50,096 Then, we did something beyond just 90 00:03:50,096 --> 00:03:54,767 that because that tells us what the wavelength has 91 00:03:54,767 --> 00:03:57,870 to be to get a spot, to get something 92 00:03:57,870 --> 00:04:02,041 the detector can see because it constructively interferes. 93 00:04:02,041 --> 00:04:03,610 Everything else is destructive. 94 00:04:03,610 --> 00:04:05,345 No signal. 95 00:04:05,345 --> 00:04:07,380 But we did one more thing. 96 00:04:07,380 --> 00:04:12,285 We also said that d for some set of planes. 97 00:04:12,285 --> 00:04:15,388 Remember, this HKL is just telling me which 98 00:04:15,388 --> 00:04:17,123 one of these I'm talking about. 99 00:04:17,123 --> 00:04:18,257 That's what HKL is. 100 00:04:18,257 --> 00:04:20,493 I'm going to pick one of these planes. 101 00:04:20,493 --> 00:04:23,129 And the distance between them is DHKL. 102 00:04:23,129 --> 00:04:24,731 OK, good. 103 00:04:24,731 --> 00:04:29,569 But we know from before, from our Miller times, 104 00:04:29,569 --> 00:04:33,172 we know that that is equal to the square root of a squared 105 00:04:33,172 --> 00:04:36,709 plus k squared plus l squared for the [INAUDIBLE] 106 00:04:36,709 --> 00:04:37,844 we're talking about. 107 00:04:37,844 --> 00:04:38,544 All right? 108 00:04:38,544 --> 00:04:41,948 So you see, it's kind of Bragg plus Miller. 109 00:04:41,948 --> 00:04:47,453 Bragg plus distance Miller. 110 00:04:47,453 --> 00:04:48,021 Right? 111 00:04:48,021 --> 00:04:49,389 Miller cubic. 112 00:04:49,389 --> 00:04:52,058 That's what we're really combining here. 113 00:04:52,058 --> 00:04:54,394 The distance given by this formula 114 00:04:54,394 --> 00:04:57,930 when we talk about Miller planes, that combined 115 00:04:57,930 --> 00:05:00,233 gave us this. 116 00:05:00,233 --> 00:05:07,040 Lambda over 2a squared equals sine 117 00:05:07,040 --> 00:05:15,014 squared theta HKL over h squared plus k squared plus elsewhere. 118 00:05:15,014 --> 00:05:17,850 And all I've done is substitute and square. 119 00:05:17,850 --> 00:05:19,118 OK? 120 00:05:19,118 --> 00:05:21,454 And we did one more thing on Wednesday. 121 00:05:21,454 --> 00:05:22,722 And we talked about constance. 122 00:05:22,722 --> 00:05:25,325 And we said, well, if something is equal to a constant, 123 00:05:25,325 --> 00:05:27,694 then it's a constant. 124 00:05:27,694 --> 00:05:28,328 All right? 125 00:05:28,328 --> 00:05:30,063 That's some good math. 126 00:05:30,063 --> 00:05:31,030 That's some good math. 127 00:05:31,030 --> 00:05:32,932 And so we said, well, that's the whole beauty 128 00:05:32,932 --> 00:05:35,368 of these characteristic x-rays because if you 129 00:05:35,368 --> 00:05:42,642 take a k alpha line from copper, it's always 1.54 angstroms. 130 00:05:42,642 --> 00:05:46,045 It's always lambda equals 1.54. 131 00:05:46,045 --> 00:05:47,347 That's what's so nice about it. 132 00:05:47,347 --> 00:05:48,681 Doesn't depend on anything else. 133 00:05:48,681 --> 00:05:51,818 Just the metal you put in there is the target. 134 00:05:51,818 --> 00:05:53,853 It's called a target because you're 135 00:05:53,853 --> 00:05:55,722 targeting it with electrons. 136 00:05:55,722 --> 00:05:59,225 So the copper target, k alpha, lambda constant. 137 00:05:59,225 --> 00:06:00,393 Lattice constant? 138 00:06:00,393 --> 00:06:02,662 That's built into the name. 139 00:06:02,662 --> 00:06:04,163 Constant. 140 00:06:04,163 --> 00:06:09,602 Constant equals the angle and the plane it's reflecting off. 141 00:06:09,602 --> 00:06:13,806 And so our job then in crystallography and doing 142 00:06:13,806 --> 00:06:17,443 x-ray diffraction, our job is to figure out how 143 00:06:17,443 --> 00:06:19,679 to keep this thing a constant. 144 00:06:19,679 --> 00:06:21,347 The same constant. 145 00:06:21,347 --> 00:06:21,848 All right? 146 00:06:21,848 --> 00:06:24,450 That's what constant means. 147 00:06:24,450 --> 00:06:25,284 OK? 148 00:06:25,284 --> 00:06:25,985 That's our job. 149 00:06:25,985 --> 00:06:27,286 And that's where we left off. 150 00:06:27,286 --> 00:06:29,889 And we say, OK, well let's take this to the next level. 151 00:06:29,889 --> 00:06:31,190 Let's do an actual experiment. 152 00:06:31,190 --> 00:06:33,393 Now how do you do experiments? 153 00:06:33,393 --> 00:06:35,094 Well you have equipment. 154 00:06:35,094 --> 00:06:37,730 And this is what a really cool XRD machine looks like. 155 00:06:37,730 --> 00:06:40,400 This is what happens when you don't have any money. 156 00:06:40,400 --> 00:06:41,467 [LAUGHTER] 157 00:06:41,467 --> 00:06:43,403 So this is what's in my lab. 158 00:06:43,403 --> 00:06:44,237 [LAUGHTER] 159 00:06:44,237 --> 00:06:45,638 It's true. 160 00:06:45,638 --> 00:06:46,706 You can come see it. 161 00:06:46,706 --> 00:06:49,842 But you see, the point is they knew the same thing. 162 00:06:49,842 --> 00:06:52,011 We don't need fancy equipment at MIT. 163 00:06:52,011 --> 00:06:54,547 No, it's the ideas that matter that you're 164 00:06:54,547 --> 00:06:55,982 putting into this thing. 165 00:06:55,982 --> 00:06:58,317 But that's kind of cool still. 166 00:06:58,317 --> 00:07:00,086 I like the way that looks. 167 00:07:00,086 --> 00:07:00,753 Same thing. 168 00:07:00,753 --> 00:07:01,254 Right? 169 00:07:01,254 --> 00:07:02,188 Source. 170 00:07:02,188 --> 00:07:03,289 Sample. 171 00:07:03,289 --> 00:07:04,323 Detector. 172 00:07:04,323 --> 00:07:05,124 That's hard to see. 173 00:07:05,124 --> 00:07:09,028 But source, sample, detector from the 60s-ish. 174 00:07:09,028 --> 00:07:09,762 OK. 175 00:07:09,762 --> 00:07:11,364 [LAUGHING] 176 00:07:11,364 --> 00:07:12,365 All right. 177 00:07:12,365 --> 00:07:14,000 So now it's easier. 178 00:07:14,000 --> 00:07:15,401 Of course, you can understand. 179 00:07:15,401 --> 00:07:17,570 I mean, some of these things have different ways 180 00:07:17,570 --> 00:07:17,804 of doing it. 181 00:07:17,804 --> 00:07:20,139 But you can understand changing the angle is going to be easier 182 00:07:20,139 --> 00:07:21,040 to move that sample. 183 00:07:21,040 --> 00:07:21,674 Right? 184 00:07:21,674 --> 00:07:23,142 And then, maybe the detector moves. 185 00:07:23,142 --> 00:07:26,312 But you might keep the source x-rays fixed. 186 00:07:26,312 --> 00:07:27,580 And what happens? 187 00:07:27,580 --> 00:07:30,582 Well, you do this, and you generate a spectrum. 188 00:07:30,582 --> 00:07:32,784 So you're changing the angle. 189 00:07:32,784 --> 00:07:35,054 You're keeping this fixed. 190 00:07:35,054 --> 00:07:38,357 And you're saying, what do I got? 191 00:07:38,357 --> 00:07:41,761 Well here, in this case, I'm telling you what I got. 192 00:07:41,761 --> 00:07:43,429 I got aluminum. 193 00:07:43,429 --> 00:07:45,264 I put aluminum in there. 194 00:07:45,264 --> 00:07:48,668 And I shot x-rays. 195 00:07:48,668 --> 00:07:50,536 If anybody gives you an XRD pattern, 196 00:07:50,536 --> 00:07:54,740 they got to tell you what kind of x-rays they used. 197 00:07:54,740 --> 00:07:55,241 Right? 198 00:07:55,241 --> 00:07:55,975 That's really important. 199 00:07:55,975 --> 00:07:57,376 At some point, you got to know this. 200 00:07:57,376 --> 00:07:58,411 This is pretty important. 201 00:07:58,411 --> 00:08:00,446 The lambda is from a copper target, 202 00:08:00,446 --> 00:08:03,249 and the k alpha lines is 1.54 angstroms. 203 00:08:03,249 --> 00:08:04,283 And this is the spectrum. 204 00:08:04,283 --> 00:08:07,687 And I'm being asked to get the crystal structure of aluminum 205 00:08:07,687 --> 00:08:08,955 and the lattice constant. 206 00:08:08,955 --> 00:08:10,556 And I can get that because, look, 207 00:08:10,556 --> 00:08:12,458 I can simply read off peaks. 208 00:08:12,458 --> 00:08:14,193 And those are the peaks, and I've kind of 209 00:08:14,193 --> 00:08:15,261 highlighted them there. 210 00:08:15,261 --> 00:08:15,862 2 theta. 211 00:08:19,131 --> 00:08:22,468 More for historical reasons, you take 2 theta measurements, 212 00:08:22,468 --> 00:08:25,071 even though, in the Bragg condition, it's just theta. 213 00:08:25,071 --> 00:08:27,073 OK, we can divide by 2. 214 00:08:27,073 --> 00:08:27,573 Right? 215 00:08:27,573 --> 00:08:29,408 And so here are those first 4 peaks. 216 00:08:29,408 --> 00:08:30,710 And I've just listed them here. 217 00:08:30,710 --> 00:08:33,212 Peak 1, 2, 3, 4. 218 00:08:33,212 --> 00:08:35,847 Sin squared of half of that. 219 00:08:35,847 --> 00:08:36,782 Gesundheit. 220 00:08:36,782 --> 00:08:38,116 OK, there it is. 221 00:08:38,116 --> 00:08:40,019 And then, we have our recipe. 222 00:08:40,019 --> 00:08:44,457 I gave you this recipe as a way to keep this constant. 223 00:08:44,457 --> 00:08:45,024 All right? 224 00:08:45,024 --> 00:08:49,662 It's an easier way to do it if you scale and clear fractions. 225 00:08:49,662 --> 00:08:50,963 It's just easier. 226 00:08:50,963 --> 00:08:52,899 So that's why I've given you that recipe. 227 00:08:52,899 --> 00:08:53,533 So let's do it. 228 00:08:53,533 --> 00:08:54,700 So first we normalize. 229 00:08:54,700 --> 00:08:55,535 What does that mean? 230 00:08:55,535 --> 00:08:57,904 Well, you have the smallest value of science course data. 231 00:08:57,904 --> 00:08:59,739 I'm just going to divide everything by that. 232 00:08:59,739 --> 00:09:00,239 OK? 233 00:09:00,239 --> 00:09:01,440 So that's where we left off. 234 00:09:01,440 --> 00:09:04,243 One because that's what I'm normalizing by. 235 00:09:04,243 --> 00:09:07,547 And then, this one would be 1.33. 236 00:09:07,547 --> 00:09:10,816 And this one would be 2.67. 237 00:09:10,816 --> 00:09:14,287 And this one would be 3.67. 238 00:09:14,287 --> 00:09:15,688 And so that's good. 239 00:09:15,688 --> 00:09:17,089 But I don't want fractions. 240 00:09:17,089 --> 00:09:18,691 It's going to be easier for me to think 241 00:09:18,691 --> 00:09:20,893 about this as integers. 242 00:09:20,893 --> 00:09:22,328 And so we clear fractions. 243 00:09:22,328 --> 00:09:24,697 What does clear fractions mean? 244 00:09:24,697 --> 00:09:25,565 That! 245 00:09:25,565 --> 00:09:26,699 Clear the fractions. 246 00:09:26,699 --> 00:09:27,700 Get rid of them. 247 00:09:27,700 --> 00:09:28,601 Make it integers. 248 00:09:28,601 --> 00:09:29,502 How do you do that? 249 00:09:29,502 --> 00:09:34,440 Find what you multiply this by so that they're all integers. 250 00:09:34,440 --> 00:09:35,575 OK, I got an idea. 251 00:09:35,575 --> 00:09:38,778 How about 3 times 3. 252 00:09:38,778 --> 00:09:41,981 In this case, times 3 equals 3. 253 00:09:41,981 --> 00:09:43,316 OK, good. 254 00:09:43,316 --> 00:09:46,285 And in this case, well, I don't mean-- 255 00:09:46,285 --> 00:09:50,289 OK, anyway, times 3 equals 4. 256 00:09:50,289 --> 00:09:52,124 Times 3. 257 00:09:52,124 --> 00:09:55,294 Don't multiply it by a different number. 258 00:09:55,294 --> 00:09:57,263 I'm clearing the fractions for the whole table. 259 00:09:57,263 --> 00:09:59,532 I'm multiplying by the same number. 260 00:09:59,532 --> 00:10:00,533 OK, good. 261 00:10:00,533 --> 00:10:01,434 8. 262 00:10:01,434 --> 00:10:05,471 And this is times 3 equals 11. 263 00:10:05,471 --> 00:10:07,740 So I've got 3, 4, 8, 11. 264 00:10:07,740 --> 00:10:10,943 And that's what I need to work with. 265 00:10:10,943 --> 00:10:13,679 That's what I need to work with because now, you see, 266 00:10:13,679 --> 00:10:14,680 it's now-- 267 00:10:14,680 --> 00:10:17,683 I hope it's kind of starting to make some sense-- 268 00:10:17,683 --> 00:10:22,588 if I can get this to be 8 squared 269 00:10:22,588 --> 00:10:27,593 plus k squared plus l squared, well then I've done my job. 270 00:10:27,593 --> 00:10:29,195 I've kept this constant. 271 00:10:29,195 --> 00:10:29,996 That's the trick. 272 00:10:29,996 --> 00:10:30,496 Right? 273 00:10:30,496 --> 00:10:31,297 I've done my job. 274 00:10:31,297 --> 00:10:32,999 I've just made the math easy. 275 00:10:32,999 --> 00:10:35,368 If I can get h squared plus k squared plus l 276 00:10:35,368 --> 00:10:39,238 squared to equal these things, then I'm keeping it constant. 277 00:10:39,238 --> 00:10:39,805 So let's see. 278 00:10:39,805 --> 00:10:41,040 What would that be? 279 00:10:43,743 --> 00:10:47,680 So this has to be h squared-- let me just write here-- 280 00:10:47,680 --> 00:10:50,549 plus k squared plus l squared. 281 00:10:50,549 --> 00:10:52,952 OK? 282 00:10:52,952 --> 00:10:55,287 I want those to be an h squared plus k. 283 00:10:55,287 --> 00:10:59,892 So if I do that, well, this looks a whole lot like 1 1 1. 284 00:10:59,892 --> 00:11:00,893 That works. 285 00:11:00,893 --> 00:11:04,530 And for 4, 2 0 0. 286 00:11:04,530 --> 00:11:08,234 OK, and for 8, 2 2 0. 287 00:11:08,234 --> 00:11:13,739 And finally, for 11, 3 1 1. 288 00:11:13,739 --> 00:11:16,342 Aw, it's a beautiful thing. 289 00:11:16,342 --> 00:11:20,846 I've gone from angles to planes. 290 00:11:20,846 --> 00:11:22,181 These are planes. 291 00:11:22,181 --> 00:11:26,485 H, k and l mean one of these. 292 00:11:26,485 --> 00:11:28,020 It means one of those. 293 00:11:28,020 --> 00:11:31,791 That's what it means, a set of those. 294 00:11:31,791 --> 00:11:38,330 And I have found now, literally, which ones give me each peak. 295 00:11:38,330 --> 00:11:41,267 This peak is the 1 1 1 plain. 296 00:11:41,267 --> 00:11:43,736 It's x-rays bouncing off of that, 297 00:11:43,736 --> 00:11:45,771 reflecting off of that, and the one below it, 298 00:11:45,771 --> 00:11:48,140 and the one below it, and seeing where 299 00:11:48,140 --> 00:11:50,976 it gives you constructive interference, 300 00:11:50,976 --> 00:11:52,411 and gives you the Bragg condition. 301 00:11:52,411 --> 00:11:53,813 And therefore, a peak. 302 00:11:53,813 --> 00:11:55,548 OK. 303 00:11:55,548 --> 00:11:56,315 All right. 304 00:11:56,315 --> 00:11:57,950 Now hold on. 305 00:11:57,950 --> 00:11:59,285 Hold on. 306 00:11:59,285 --> 00:12:08,060 Now, OK, have we determined the crystal structure? 307 00:12:08,060 --> 00:12:10,096 Have we determined the crystal structure? 308 00:12:10,096 --> 00:12:11,464 Can anybody? 309 00:12:11,464 --> 00:12:13,999 How do we get the crystal structure from this, 310 00:12:13,999 --> 00:12:17,069 from these peaks? 311 00:12:17,069 --> 00:12:17,636 How do we get? 312 00:12:17,636 --> 00:12:18,804 Well, let's see. 313 00:12:18,804 --> 00:12:19,305 OK. 314 00:12:21,974 --> 00:12:22,475 Let's see. 315 00:12:22,475 --> 00:12:26,178 Could it be bcc? 316 00:12:29,215 --> 00:12:31,417 What else did we learn on Wednesday? 317 00:12:31,417 --> 00:12:32,418 Right? 318 00:12:32,418 --> 00:12:33,919 What else did we learn on Wednesday? 319 00:12:33,919 --> 00:12:36,455 We learned about selection rules. 320 00:12:36,455 --> 00:12:38,557 You got to remember the selection rules. 321 00:12:38,557 --> 00:12:40,426 Those factor in. 322 00:12:40,426 --> 00:12:42,394 So let's write those down here. 323 00:12:42,394 --> 00:12:45,664 Let's remind ourselves of, OK, that's important. 324 00:12:45,664 --> 00:12:46,165 Right? 325 00:12:49,068 --> 00:12:52,338 Now I mentioned how this came about. 326 00:12:52,338 --> 00:12:58,043 I don't need you to know how to derive the selection rules. 327 00:12:58,043 --> 00:13:00,813 But I did talk about why they come about 328 00:13:00,813 --> 00:13:03,883 because, for some of these cuts, you 329 00:13:03,883 --> 00:13:07,386 could have a plane in between that 330 00:13:07,386 --> 00:13:13,392 destroys the signal, depending on which crystal structure it 331 00:13:13,392 --> 00:13:15,995 is and which plane you're talking about. 332 00:13:15,995 --> 00:13:20,099 And when it comes down to it, for a simple cubic, 333 00:13:20,099 --> 00:13:22,168 it's anything goes. 334 00:13:22,168 --> 00:13:24,336 Anything. 335 00:13:24,336 --> 00:13:25,671 Oh, polonium. 336 00:13:25,671 --> 00:13:33,779 And for bcc, it adds to an even number. 337 00:13:33,779 --> 00:13:37,917 And for FCC, no mixing. 338 00:13:40,953 --> 00:13:45,224 No mixing of odd and even. 339 00:13:45,224 --> 00:13:46,926 Those are the selection rules. 340 00:13:46,926 --> 00:13:48,894 You don't need to know how to divide them, 341 00:13:48,894 --> 00:13:51,297 but I do want you to know what they are. 342 00:13:51,297 --> 00:13:53,465 So now we can see, well OK, hold on. 343 00:13:53,465 --> 00:13:57,903 If this were a bcc crystal and they had to add to even 1 344 00:13:57,903 --> 00:14:00,973 plus 1 plus 1 is 3. 345 00:14:00,973 --> 00:14:02,141 Bam! 346 00:14:02,141 --> 00:14:04,009 It's not bcc. 347 00:14:04,009 --> 00:14:04,543 Right? 348 00:14:04,543 --> 00:14:05,044 Yeah? 349 00:14:05,044 --> 00:14:05,578 OK. 350 00:14:05,578 --> 00:14:07,179 Yeah, but now, hang on. 351 00:14:07,179 --> 00:14:10,783 If it's no mixing on even, did I handle that one OK? 352 00:14:10,783 --> 00:14:12,184 Yeah! 353 00:14:12,184 --> 00:14:13,185 Odd! 354 00:14:13,185 --> 00:14:13,853 Even! 355 00:14:13,853 --> 00:14:14,920 Even. 356 00:14:14,920 --> 00:14:15,554 Odd. 357 00:14:15,554 --> 00:14:17,957 This looks like an FCC crystal to me. 358 00:14:17,957 --> 00:14:19,258 Right? 359 00:14:19,258 --> 00:14:20,826 This looks like an FCC crystal. 360 00:14:20,826 --> 00:14:22,161 And I can go even further. 361 00:14:22,161 --> 00:14:25,130 I can calculate the lattice constant. 362 00:14:25,130 --> 00:14:28,434 I can calculate the lattice constant cause it's right here. 363 00:14:28,434 --> 00:14:30,536 It's right here. 364 00:14:30,536 --> 00:14:32,238 Right? 365 00:14:32,238 --> 00:14:34,240 So that's the lattice constant. 366 00:14:34,240 --> 00:14:37,009 That's a number that's a constant lambda. 367 00:14:37,009 --> 00:14:42,581 So I could take any one of those planes, any one of those, 368 00:14:42,581 --> 00:14:45,117 any one of these four peaks. 369 00:14:45,117 --> 00:14:50,389 And if I did this right, they better 370 00:14:50,389 --> 00:14:52,825 give me the same lattice constant. 371 00:14:52,825 --> 00:14:55,060 And that's actually the last step in the recipe. 372 00:14:55,060 --> 00:14:55,928 Did I put the recipe? 373 00:14:55,928 --> 00:14:56,629 Yes! 374 00:14:56,629 --> 00:14:57,129 All right. 375 00:14:57,129 --> 00:15:00,132 This is the recipe I gave you on Wednesday for you 376 00:15:00,132 --> 00:15:02,635 all to become crystallographers. 377 00:15:02,635 --> 00:15:06,272 X-ray defractioners. 378 00:15:06,272 --> 00:15:07,106 That's OK. 379 00:15:07,106 --> 00:15:08,073 We'll make it work. 380 00:15:08,073 --> 00:15:11,477 You're X-ray diffractioners. 381 00:15:11,477 --> 00:15:15,447 And the thing is, you got to remember how powerful this is. 382 00:15:15,447 --> 00:15:18,717 Yeah, how powerful this is because we've 383 00:15:18,717 --> 00:15:21,320 learned about perfect crystals. 384 00:15:21,320 --> 00:15:25,424 And now, we've just gotten the single most important way 385 00:15:25,424 --> 00:15:28,661 to figure out which one we have. 386 00:15:28,661 --> 00:15:32,998 We shine x-rays on it, and we look for diffraction peaks. 387 00:15:32,998 --> 00:15:33,699 That's it. 388 00:15:33,699 --> 00:15:35,968 This is a very powerful tool. 389 00:15:35,968 --> 00:15:41,106 And it is used all over the place in materials chemistry, 390 00:15:41,106 --> 00:15:41,607 physics. 391 00:15:41,607 --> 00:15:44,176 You name the field, x-ray diffraction 392 00:15:44,176 --> 00:15:47,913 is a starting point for characterizing the crystal. 393 00:15:47,913 --> 00:15:49,715 And so, the last sanity check that you 394 00:15:49,715 --> 00:15:53,519 want to do here because it'll help you make sure you did 395 00:15:53,519 --> 00:15:58,390 these points correctly, is compute these values 396 00:15:58,390 --> 00:16:00,492 because, you know, this is it. 397 00:16:00,492 --> 00:16:00,993 Right? 398 00:16:00,993 --> 00:16:03,429 Sine squared over a squared plus k squared plus l 399 00:16:03,429 --> 00:16:07,633 squared better be a constant. 400 00:16:07,633 --> 00:16:09,368 If it's not, then you've done something 401 00:16:09,368 --> 00:16:11,003 wrong in this analysis. 402 00:16:11,003 --> 00:16:12,271 Right? 403 00:16:12,271 --> 00:16:15,140 You could just calculate the lattice constant for each peak, 404 00:16:15,140 --> 00:16:17,910 and they also better agree. 405 00:16:17,910 --> 00:16:20,512 So I won't do that, but it turns out we did it right. 406 00:16:20,512 --> 00:16:23,248 For each one of these, that is indeed a constant. 407 00:16:23,248 --> 00:16:26,986 We have achieved our goal. 408 00:16:26,986 --> 00:16:30,155 With great power comes great responsibility. 409 00:16:30,155 --> 00:16:31,390 How you use XRD. 410 00:16:31,390 --> 00:16:33,492 How you use XRD. 411 00:16:33,492 --> 00:16:34,727 Well, let's see. 412 00:16:34,727 --> 00:16:39,898 Let's use it to figure out what phase of material we have. 413 00:16:39,898 --> 00:16:41,233 Why does this matter, right? 414 00:16:41,233 --> 00:16:45,204 Well I have a why this matters, but there's multiple reasons 415 00:16:45,204 --> 00:16:46,105 for why this matters. 416 00:16:49,842 --> 00:16:53,012 As I think we've talked about, the properties of a material 417 00:16:53,012 --> 00:16:54,680 depend on the chemistry in the material, 418 00:16:54,680 --> 00:16:58,250 but they also depend on the structure of the material. 419 00:16:58,250 --> 00:17:02,721 And we're making solids, so those structures are crystals, 420 00:17:02,721 --> 00:17:06,290 until next week when we destroy the crystals by putting defects 421 00:17:06,290 --> 00:17:07,792 in them! 422 00:17:07,792 --> 00:17:09,627 But for now, they're these perfect crystals. 423 00:17:09,627 --> 00:17:12,231 And they have this, kind of, repeating pattern. 424 00:17:12,231 --> 00:17:14,133 Worry about hcp. 425 00:17:14,133 --> 00:17:18,270 bcc, ah we're comfortable. fcc, comfortable. bcc. 426 00:17:18,270 --> 00:17:21,773 Now, this is called a phase diagram. 427 00:17:21,773 --> 00:17:23,742 This is called a phase diagram. 428 00:17:23,742 --> 00:17:26,011 Phase diagrams will be on the quiz next week. 429 00:17:26,011 --> 00:17:26,712 I'm kidding. 430 00:17:26,712 --> 00:17:27,713 They're not going to be on the quiz 431 00:17:27,713 --> 00:17:29,915 because this isn't a class about phase diagrams. 432 00:17:29,915 --> 00:17:36,321 But I want you to know what a phase diagram is. 433 00:17:36,321 --> 00:17:39,792 It is a map of materials. 434 00:17:39,792 --> 00:17:44,596 It is like a treasure map, literally 435 00:17:44,596 --> 00:17:47,833 because you find I need iron to have a different property. 436 00:17:47,833 --> 00:17:48,333 Oh! 437 00:17:48,333 --> 00:17:51,303 If I go to this pressure and that temperature, aha! 438 00:17:51,303 --> 00:17:52,771 It can have a different property. 439 00:17:52,771 --> 00:17:53,839 Why? 440 00:17:53,839 --> 00:17:56,542 Because it has a different crystal structure. 441 00:17:56,542 --> 00:17:59,044 So the crystal structure of something-- 442 00:17:59,044 --> 00:18:01,080 in this case, it's iron-- depends on the pressure 443 00:18:01,080 --> 00:18:02,414 and temperature. 444 00:18:02,414 --> 00:18:05,617 And the properties depend on the crystal structure. 445 00:18:05,617 --> 00:18:08,520 So we've got a way now to change materials. 446 00:18:08,520 --> 00:18:09,354 Same element. 447 00:18:09,354 --> 00:18:11,723 I'm just changing its structure. 448 00:18:11,723 --> 00:18:12,991 I love this one. 449 00:18:12,991 --> 00:18:13,826 This is water. 450 00:18:13,826 --> 00:18:16,462 Now don't worry about how complex this is. 451 00:18:16,462 --> 00:18:19,731 Actually, the whole point is it's complex. 452 00:18:19,731 --> 00:18:21,333 This is the phase diagram of water. 453 00:18:21,333 --> 00:18:22,835 Now this doesn't even have them all. 454 00:18:22,835 --> 00:18:25,604 There are 17 current phases of ice. 455 00:18:25,604 --> 00:18:30,342 17 different crystalline structures of ice. 456 00:18:30,342 --> 00:18:31,543 That is incredible. 457 00:18:31,543 --> 00:18:33,011 Right? 458 00:18:33,011 --> 00:18:35,714 You can actually imagine why, from your knowledge 459 00:18:35,714 --> 00:18:37,983 in this class already, those are hydrogen bonds. 460 00:18:37,983 --> 00:18:40,586 They're kind of strong, but they're not too strong. 461 00:18:40,586 --> 00:18:43,188 There's a lot of ways that those water molecules 462 00:18:43,188 --> 00:18:44,590 could form a solid. 463 00:18:44,590 --> 00:18:45,390 And they do. 464 00:18:45,390 --> 00:18:48,026 17 to date and counting. 465 00:18:48,026 --> 00:18:48,660 Let's see. 466 00:18:48,660 --> 00:18:50,362 And this tells you which one you have. 467 00:18:50,362 --> 00:18:52,931 Now Earth's operating conditions are right around here. 468 00:18:52,931 --> 00:18:54,433 And that's a really good thing because there 469 00:18:54,433 --> 00:18:55,567 is a liquid phase in there. 470 00:18:55,567 --> 00:18:59,138 Ice 1 is here. ih is ice one. 471 00:18:59,138 --> 00:19:02,674 And it's a really good thing because of the fish 472 00:19:02,674 --> 00:19:07,279 because if you weren't ice 1, then when it freezes, 473 00:19:07,279 --> 00:19:09,648 it wouldn't have a different density. 474 00:19:09,648 --> 00:19:11,550 And the ice wouldn't float to the top. 475 00:19:11,550 --> 00:19:14,987 And the fish could still live, which they do in the winter 476 00:19:14,987 --> 00:19:16,688 because you don't freeze from the bottom. 477 00:19:16,688 --> 00:19:17,823 You freeze from the top. 478 00:19:17,823 --> 00:19:21,293 That's because it's ice 1 and not ice 8. 479 00:19:21,293 --> 00:19:23,295 It would be terrible. 480 00:19:23,295 --> 00:19:24,663 But yet, we know about these. 481 00:19:24,663 --> 00:19:26,632 And how do we know? 482 00:19:26,632 --> 00:19:28,700 We know because of crystallography. 483 00:19:28,700 --> 00:19:31,403 We know because of XRD. 484 00:19:31,403 --> 00:19:33,472 We can figure out. 485 00:19:33,472 --> 00:19:36,175 Now if you're out and maybe it's a Friday night, 486 00:19:36,175 --> 00:19:38,610 so maybe this is a good idea-- it's a good time to mention 487 00:19:38,610 --> 00:19:39,111 it-- 488 00:19:39,111 --> 00:19:42,548 you might get ice in your water out at a restaurant. 489 00:19:42,548 --> 00:19:44,917 How do you know which kind of ice it is? 490 00:19:44,917 --> 00:19:46,218 Talk about XRD. 491 00:19:46,218 --> 00:19:49,021 It's the only real way to figure out which one of these 492 00:19:49,021 --> 00:19:50,756 you really have. 493 00:19:50,756 --> 00:19:52,024 OK. 494 00:19:52,024 --> 00:19:55,093 So for example, if I were to think 495 00:19:55,093 --> 00:19:56,795 of other types of problems you might get, 496 00:19:56,795 --> 00:19:58,697 well, here's a good one. 497 00:19:58,697 --> 00:20:00,032 OK, here's a good one. 498 00:20:00,032 --> 00:20:06,471 So this is an X-ray diffraction spectrum. 499 00:20:06,471 --> 00:20:10,275 And I give it to you, and I don't even tell you what it is. 500 00:20:10,275 --> 00:20:10,809 Why is that? 501 00:20:10,809 --> 00:20:13,512 Here's a pattern that I put something in there, 502 00:20:13,512 --> 00:20:16,148 and I measure these pics. 503 00:20:16,148 --> 00:20:17,549 And I tell you the source. 504 00:20:17,549 --> 00:20:19,318 It's the k alpha line of copper. 505 00:20:19,318 --> 00:20:21,186 So that's the wavelength of the source. 506 00:20:21,186 --> 00:20:28,393 First thing is what lattice, what symmetry, 507 00:20:28,393 --> 00:20:30,128 does this correspond to? 508 00:20:30,128 --> 00:20:32,030 Is it simple cubic, body centered 509 00:20:32,030 --> 00:20:33,365 cubic, or face centered cubic? 510 00:20:33,365 --> 00:20:36,435 Can we get that? 511 00:20:36,435 --> 00:20:40,472 We could get that because of the exact same thing 512 00:20:40,472 --> 00:20:41,974 that we just talked about. 513 00:20:41,974 --> 00:20:42,474 Right? 514 00:20:45,611 --> 00:20:47,512 This can not be. 515 00:20:47,512 --> 00:20:49,581 If it were simple cubic, you'd see the peaks. 516 00:20:49,581 --> 00:20:50,482 Mm! 517 00:20:50,482 --> 00:20:52,951 But know that some peaks are forbidden, 518 00:20:52,951 --> 00:20:55,254 so they don't show up. 519 00:20:55,254 --> 00:20:55,754 Right? 520 00:20:55,754 --> 00:20:59,157 And you only get peaks that look like an FCC, 521 00:20:59,157 --> 00:21:01,093 according to our selection rules. 522 00:21:01,093 --> 00:21:03,662 No mixing odd even at work. 523 00:21:03,662 --> 00:21:05,030 So this is an FCC crystal. 524 00:21:05,030 --> 00:21:06,465 So I've already learned that. 525 00:21:06,465 --> 00:21:07,933 And then to say, well, what's the-- 526 00:21:07,933 --> 00:21:12,638 OK, use the 1 1 1 peak to calculate the lattice constant. 527 00:21:12,638 --> 00:21:13,538 OK. 528 00:21:13,538 --> 00:21:15,007 Well, we can do that. 529 00:21:15,007 --> 00:21:15,507 Right? 530 00:21:19,344 --> 00:21:21,680 So the 1 1 1 peak is even labeled there. 531 00:21:21,680 --> 00:21:24,883 It's 38 degrees. 532 00:21:24,883 --> 00:21:27,152 38 degrees. 533 00:21:27,152 --> 00:21:30,889 So to theta is 38 degrees. 534 00:21:30,889 --> 00:21:33,992 So that means that theta-- 535 00:21:33,992 --> 00:21:37,296 OK, I can do this one-- is 19 degrees. 536 00:21:37,296 --> 00:21:38,196 OK. 537 00:21:38,196 --> 00:21:39,931 Oh, oh, oh, from Bragg. 538 00:21:39,931 --> 00:21:44,369 Lambda equals to d sine theta. 539 00:21:44,369 --> 00:21:49,308 But look, label, label the plane. 540 00:21:49,308 --> 00:21:51,743 This corresponds to a plane. 541 00:21:51,743 --> 00:21:55,147 So some distance between some planes 542 00:21:55,147 --> 00:21:57,749 corresponds to some angle that gave me 543 00:21:57,749 --> 00:22:00,085 constructive interference for those planes. 544 00:22:00,085 --> 00:22:03,922 Let's pass it around so you guys can look at these planes. 545 00:22:03,922 --> 00:22:05,957 They're beautiful things. 546 00:22:05,957 --> 00:22:11,229 Now that means that if I look at the first peek, 547 00:22:11,229 --> 00:22:13,832 I know what la-- well I labeled them here. 548 00:22:13,832 --> 00:22:15,133 In the last one, I didn't. 549 00:22:15,133 --> 00:22:16,301 And you want to find those. 550 00:22:16,301 --> 00:22:19,438 Here, I'm giving you the planes. 551 00:22:19,438 --> 00:22:26,411 So if I do that, then d 1 1 1 equals lambda 552 00:22:26,411 --> 00:22:36,621 over 2 sine theta 1 1 1, which equals 2.37 angstroms. 553 00:22:36,621 --> 00:22:37,122 OK. 554 00:22:37,122 --> 00:22:39,391 Have I answered the question? 555 00:22:39,391 --> 00:22:43,228 I haven't answered the question yet because, you see, 556 00:22:43,228 --> 00:22:47,099 the question says what's the lattice constant. 557 00:22:47,099 --> 00:22:48,233 But I'm very close. 558 00:22:48,233 --> 00:22:53,538 The lattice constant is related because of Miller. 559 00:22:53,538 --> 00:22:56,308 The Miller plains equation for lattice. 560 00:22:56,308 --> 00:22:57,376 Lattice constant. 561 00:22:57,376 --> 00:23:00,045 Distance between any planes. 562 00:23:00,045 --> 00:23:02,614 Oh, this is all just coming together. 563 00:23:02,614 --> 00:23:12,224 And so d 1 1 1 is equal to a over 3. 564 00:23:12,224 --> 00:23:16,495 And so a equals 4.1 angstroms. 565 00:23:16,495 --> 00:23:18,930 Oh, you could go even further. 566 00:23:18,930 --> 00:23:23,201 You could figure out, now that you know it's fcc-- 567 00:23:23,201 --> 00:23:25,570 it's a single atom base, it's fcc crystal, 568 00:23:25,570 --> 00:23:28,440 you could actually figure out the atomic radius. 569 00:23:28,440 --> 00:23:32,878 I got a, and I know the close pack direction. 570 00:23:32,878 --> 00:23:33,612 Right? 571 00:23:33,612 --> 00:23:35,547 I could actually figure out the atomic radius. 572 00:23:35,547 --> 00:23:37,482 And I could go into my periodic table 573 00:23:37,482 --> 00:23:42,053 and figure out what I have just from the atomic radii 574 00:23:42,053 --> 00:23:45,190 listed in the periodic table and the crystal structures. 575 00:23:45,190 --> 00:23:47,192 FCC. 576 00:23:47,192 --> 00:23:48,660 Automic radius. 577 00:23:48,660 --> 00:23:49,795 Which one is it? 578 00:23:49,795 --> 00:23:51,263 It's gold. 579 00:23:51,263 --> 00:23:53,765 It's gold. 580 00:23:53,765 --> 00:23:55,967 So this is the kind of thing that you guys now 581 00:23:55,967 --> 00:23:58,270 have the power to do. 582 00:23:58,270 --> 00:24:00,038 You have the power to do this. 583 00:24:00,038 --> 00:24:03,308 You can go back and forth between-- 584 00:24:03,308 --> 00:24:05,143 based on your knowledge of crystals 585 00:24:05,143 --> 00:24:07,646 and now your knowledge of x-rays and how x-rays interact 586 00:24:07,646 --> 00:24:11,750 with crystals you can do this. 587 00:24:11,750 --> 00:24:14,386 Oh, that went too far. 588 00:24:14,386 --> 00:24:20,392 OK, so now I'm going to get to the why this matters. 589 00:24:20,392 --> 00:24:24,296 So there's two different sources, two different targets. 590 00:24:24,296 --> 00:24:27,332 Remember, we can call them sources or targets. 591 00:24:27,332 --> 00:24:34,306 And notice they both have this continuous radiation. 592 00:24:34,306 --> 00:24:35,540 And I will talk about that. 593 00:24:35,540 --> 00:24:37,843 The [INAUDIBLE] will end with a discussion 594 00:24:37,843 --> 00:24:40,745 a little bit on what you can do with that. 595 00:24:40,745 --> 00:24:43,815 But for now, let's keep focused on these lines, 596 00:24:43,815 --> 00:24:45,517 these discrete characteristic lines. 597 00:24:45,517 --> 00:24:47,118 So there's the k alpha from molybdenum. 598 00:24:47,118 --> 00:24:48,987 There's the k alpha for copper. 599 00:24:48,987 --> 00:24:57,963 OK, now Moseley, Henry Moseley, was a brilliant scientist. 600 00:24:57,963 --> 00:25:02,267 And he was working with Rutherford and others. 601 00:25:02,267 --> 00:25:08,006 And he was really interested in looking at the trends. 602 00:25:08,006 --> 00:25:10,141 So he took all of these elements. 603 00:25:10,141 --> 00:25:12,844 So from calcium all the way to zinc. 604 00:25:12,844 --> 00:25:14,312 20 to 30. 605 00:25:14,312 --> 00:25:16,348 And he said I want to look at the k 606 00:25:16,348 --> 00:25:18,917 alpha lines of all of these. 607 00:25:18,917 --> 00:25:21,620 I want to look at the K alpha lines of all of these. 608 00:25:21,620 --> 00:25:25,757 And what he found was extraordinary. 609 00:25:25,757 --> 00:25:26,791 He did more. 610 00:25:26,791 --> 00:25:28,126 38 in total. 611 00:25:28,126 --> 00:25:30,896 But I'm just going to show you his data for these. 612 00:25:30,896 --> 00:25:31,630 OK? 613 00:25:31,630 --> 00:25:36,902 And what he did was absolutely profound because what 614 00:25:36,902 --> 00:25:37,836 he noticed-- 615 00:25:37,836 --> 00:25:38,703 there are the lines. 616 00:25:38,703 --> 00:25:40,171 These are actually his measurements. 617 00:25:40,171 --> 00:25:40,672 OK? 618 00:25:40,672 --> 00:25:43,642 These are his k alpha lines. 619 00:25:43,642 --> 00:25:47,512 And what he noticed in going from calcium down to-- 620 00:25:47,512 --> 00:25:49,281 ohh-- brass? 621 00:25:49,281 --> 00:25:51,583 OK, we'll talk about that in a minute. 622 00:25:51,583 --> 00:25:53,485 It's supposed to be zinc, isn't it? 623 00:25:53,485 --> 00:25:54,586 Why is it zinc? 624 00:25:54,586 --> 00:25:55,687 Well, why is it not zinc? 625 00:25:55,687 --> 00:25:57,822 Let's think about that later. 626 00:25:57,822 --> 00:26:02,861 For now he noticed that this has a square root relationship 627 00:26:02,861 --> 00:26:04,095 to the energy. 628 00:26:04,095 --> 00:26:06,998 So Moseley came up with-- 629 00:26:06,998 --> 00:26:09,834 he was working on this in 1912. 630 00:26:09,834 --> 00:26:11,703 OK? 631 00:26:11,703 --> 00:26:15,373 You got to remember 1913. 632 00:26:15,373 --> 00:26:20,645 1912 was when Rutherford did the gold foil experiments. 633 00:26:20,645 --> 00:26:24,149 It had been 44 years since Mendeleev 634 00:26:24,149 --> 00:26:27,552 put his periodic table to paper and published that. 635 00:26:27,552 --> 00:26:31,156 So for 44 years, we had a periodic table. 636 00:26:31,156 --> 00:26:33,792 But see, the thing is, there was a huge problem 637 00:26:33,792 --> 00:26:39,397 with the periodic table because Mendeleev 638 00:26:39,397 --> 00:26:44,436 had this, sort of, brilliant realization that periodicity-- 639 00:26:44,436 --> 00:26:50,942 periodicity-- was related to, both, the atomic mass-- 640 00:26:50,942 --> 00:26:52,877 and remember, we talked about this-- 641 00:26:52,877 --> 00:26:57,115 and the properties, the chemical properties. 642 00:26:57,115 --> 00:27:00,185 That chemical properties. 643 00:27:02,687 --> 00:27:07,926 That allowed him to create in ordering of the elements. 644 00:27:07,926 --> 00:27:09,594 In ordering of the elements. 645 00:27:09,594 --> 00:27:11,429 That is still the ordering, essentially, 646 00:27:11,429 --> 00:27:14,132 that we have today. 647 00:27:14,132 --> 00:27:18,970 But the problem is why did they have that ordering? 648 00:27:18,970 --> 00:27:22,774 I didn't really tell you why, sometimes, he was like, well, 649 00:27:22,774 --> 00:27:24,743 the properties win. 650 00:27:24,743 --> 00:27:26,277 OK, maybe the mass-- no, no. 651 00:27:26,277 --> 00:27:27,012 Properties win. 652 00:27:27,012 --> 00:27:29,280 Properties need to be aligned in this column, 653 00:27:29,280 --> 00:27:30,782 so I'm I'm going to move those over. 654 00:27:30,782 --> 00:27:33,351 Like, that's what he did. 655 00:27:33,351 --> 00:27:37,288 But he didn't know why, except that it made sense to him. 656 00:27:37,288 --> 00:27:39,724 Moseley's experiments told us. 657 00:27:39,724 --> 00:27:40,959 They gave us the why. 658 00:27:40,959 --> 00:27:42,994 Aw, it was so important. 659 00:27:42,994 --> 00:27:45,630 And Moseley's law-- 660 00:27:45,630 --> 00:27:49,734 Moseley's law-- was, essentially, 661 00:27:49,734 --> 00:27:52,270 him thinking about the Bohr model 662 00:27:52,270 --> 00:27:54,606 for these characteristic x-rays. 663 00:27:54,606 --> 00:27:58,510 So he said that h nu-- 664 00:27:58,510 --> 00:28:02,580 so that's the frequency for some k alpha line-- 665 00:28:02,580 --> 00:28:05,650 is equal to 13.6 ev. 666 00:28:05,650 --> 00:28:07,052 All that looks familiar. 667 00:28:07,052 --> 00:28:10,689 Times z minus 1 squared. 668 00:28:10,689 --> 00:28:14,359 And then, he did the difference in energy, 669 00:28:14,359 --> 00:28:18,496 just like we've done now a number of times in this class. 670 00:28:18,496 --> 00:28:19,764 That's what he did. 671 00:28:19,764 --> 00:28:22,233 And this is 3/4. 672 00:28:22,233 --> 00:28:23,034 Why this? 673 00:28:23,034 --> 00:28:24,903 Well, let's talk about that in a second. 674 00:28:24,903 --> 00:28:37,348 So 13.6 ev times 3/4 times z minus 1 squared. 675 00:28:37,348 --> 00:28:38,917 Two things about this, right? 676 00:28:38,917 --> 00:28:45,590 One is why is it 1 over 1 squared minus 1 over 2 squared? 677 00:28:45,590 --> 00:28:49,227 Well that's because they knew, or at least they 678 00:28:49,227 --> 00:28:52,464 were pretty confident, that you had this positive charge 679 00:28:52,464 --> 00:28:53,631 in the middle here. 680 00:28:53,631 --> 00:28:56,034 That's the protons and the nucleus. 681 00:28:56,034 --> 00:28:57,435 And then, you had these electrons. 682 00:28:57,435 --> 00:28:57,936 Right? 683 00:28:57,936 --> 00:29:00,772 So you had, like, the 1s electrons. 684 00:29:00,772 --> 00:29:03,908 And then, you had another shell out here. 685 00:29:03,908 --> 00:29:06,211 And so they knew, OK, 2s. 686 00:29:06,211 --> 00:29:10,682 Maybe that's combined with 2p, so it goes on. 687 00:29:10,682 --> 00:29:13,818 So what happens in the x-ray experiment? 688 00:29:13,818 --> 00:29:16,387 Well what happens is you shoot an electron in. 689 00:29:16,387 --> 00:29:19,357 Rank and just crank the voltage up 690 00:29:19,357 --> 00:29:23,261 so high that an electron could come and knock that out. 691 00:29:23,261 --> 00:29:23,762 Right? 692 00:29:23,762 --> 00:29:26,464 And so that's what did it. 693 00:29:26,464 --> 00:29:30,435 And so now one of these can cascade down there 694 00:29:30,435 --> 00:29:35,507 and give off a k alpha photon. 695 00:29:35,507 --> 00:29:36,040 Right? 696 00:29:36,040 --> 00:29:37,609 This is nothing new. 697 00:29:37,609 --> 00:29:39,344 We've talked about this. 698 00:29:39,344 --> 00:29:42,180 But you see it here in the equation. 699 00:29:42,180 --> 00:29:43,581 You see it in two ways. 700 00:29:43,581 --> 00:29:47,552 First, we're going from 2 to 1. 701 00:29:47,552 --> 00:29:49,521 1 squared minus 1/2 squared. 702 00:29:49,521 --> 00:29:50,955 3/4. 703 00:29:50,955 --> 00:29:51,723 Right? 704 00:29:51,723 --> 00:29:55,260 But second-- and this was critical-- 705 00:29:55,260 --> 00:29:56,628 the z minus. 706 00:29:56,628 --> 00:30:04,169 The z minus told us that all these positive charges 707 00:30:04,169 --> 00:30:06,571 in here, all these positive charges, 708 00:30:06,571 --> 00:30:09,874 are screened perfectly by one electron, this one that 709 00:30:09,874 --> 00:30:11,342 was left. 710 00:30:11,342 --> 00:30:13,178 And it works. 711 00:30:13,178 --> 00:30:15,880 He assumed perfect [INAUDIBLE]. 712 00:30:15,880 --> 00:30:17,782 So what do all these see? 713 00:30:17,782 --> 00:30:19,684 They see z minus 1. 714 00:30:19,684 --> 00:30:25,690 They see z minus 1 if z is related to the atomic number. 715 00:30:25,690 --> 00:30:28,660 Now here's where this was so powerful 716 00:30:28,660 --> 00:30:30,929 because when you-- and if you can't read this, 717 00:30:30,929 --> 00:30:31,896 don't worry about that. 718 00:30:31,896 --> 00:30:35,433 I just want to show you that it is a perfectly straight line. 719 00:30:35,433 --> 00:30:38,636 When you plot the K alpha transitions, 720 00:30:38,636 --> 00:30:40,872 these are different elements. 721 00:30:40,872 --> 00:30:43,074 These are his different elements. 722 00:30:43,074 --> 00:30:48,646 And if you plot the square root of the frequency 723 00:30:48,646 --> 00:30:54,485 versus element, it is a perfect line that holds. 724 00:30:54,485 --> 00:30:56,387 And so what Moseley wrote in the paper 725 00:30:56,387 --> 00:31:00,491 is we have your proof in 1930 that there is, in the atom, 726 00:31:00,491 --> 00:31:01,793 a fundamental quantity. 727 00:31:01,793 --> 00:31:05,463 A fundamental quantity, which increases by regular steps 728 00:31:05,463 --> 00:31:07,932 as one passes from one element to the next. 729 00:31:07,932 --> 00:31:10,368 This quantity can only be-- only be-- 730 00:31:10,368 --> 00:31:13,238 the charge on the central positive nucleus, 731 00:31:13,238 --> 00:31:15,607 of the existence of which we already have definite proof. 732 00:31:15,607 --> 00:31:16,641 Now we know about that. 733 00:31:16,641 --> 00:31:20,278 We know from experiments that Rutherford 734 00:31:20,278 --> 00:31:23,381 did that that nucleus had the positive charge. 735 00:31:23,381 --> 00:31:25,884 But they didn't know that it was connected 736 00:31:25,884 --> 00:31:27,852 to the position in the periodic table. 737 00:31:30,655 --> 00:31:35,059 In fact, years later, people talking about those 738 00:31:35,059 --> 00:31:35,593 experiences-- 739 00:31:35,593 --> 00:31:38,830 I mean, people didn't even take Rutherford's experiments 740 00:31:38,830 --> 00:31:44,135 as seriously until Moseley's work came along. 741 00:31:44,135 --> 00:31:48,706 44 years had come since Mendeleev. 742 00:31:48,706 --> 00:31:52,577 But Moseley gave it the foundation that it needed. 743 00:31:52,577 --> 00:31:57,682 Periodicity is because of atomic number. 744 00:31:57,682 --> 00:32:00,184 Periodicity is atomic number. 745 00:32:00,184 --> 00:32:03,288 That was not known. 746 00:32:03,288 --> 00:32:06,257 That z gives you the periodicity. 747 00:32:06,257 --> 00:32:06,758 Right? 748 00:32:06,758 --> 00:32:09,460 And that gives you, also, the number of protons. 749 00:32:11,663 --> 00:32:13,998 This was a time when they didn't know what was going on. 750 00:32:13,998 --> 00:32:17,502 Why did the mass change so much the neutron wasn't discovered 751 00:32:17,502 --> 00:32:21,239 till 1932, 20 years later? 752 00:32:21,239 --> 00:32:23,308 But this gave the grounding that was 753 00:32:23,308 --> 00:32:25,843 needed to the chemistry of the periodic table. 754 00:32:25,843 --> 00:32:28,146 It was a very important discovery. 755 00:32:28,146 --> 00:32:29,480 Very, very important discovery. 756 00:32:29,480 --> 00:32:30,949 So that's my why this matters. 757 00:32:30,949 --> 00:32:38,456 And it's really tragic because he died, tragically, 758 00:32:38,456 --> 00:32:41,292 in World War I at age 27. 759 00:32:41,292 --> 00:32:45,396 And the Nobel Prize was not given in 1916 760 00:32:45,396 --> 00:32:46,798 for either physics or chemistry. 761 00:32:46,798 --> 00:32:48,232 He died in 1915. 762 00:32:48,232 --> 00:32:50,435 And most people, at the time, believe that he 763 00:32:50,435 --> 00:32:53,071 would have won it at age 28. 764 00:32:53,071 --> 00:32:56,341 That's how important that discovery was. 765 00:32:56,341 --> 00:32:58,209 OK, let's go back to brass. 766 00:32:58,209 --> 00:32:59,610 I got to go to brass. 767 00:32:59,610 --> 00:33:01,446 What's going on here? 768 00:33:01,446 --> 00:33:04,015 What is going on with brass? 769 00:33:04,015 --> 00:33:04,849 Right? 770 00:33:04,849 --> 00:33:08,219 Any ideas? 771 00:33:08,219 --> 00:33:11,956 Why didn't he just put zinc there? 772 00:33:11,956 --> 00:33:14,325 It looked so good until brass! 773 00:33:14,325 --> 00:33:15,593 What is going on? 774 00:33:15,593 --> 00:33:19,664 Well, ha, here, I'll give you a hint. 775 00:33:19,664 --> 00:33:21,799 OK, the melting temperature. 776 00:33:21,799 --> 00:33:22,734 Let's see. 777 00:33:22,734 --> 00:33:24,035 Ah, brass. 778 00:33:24,035 --> 00:33:35,046 OK, zinc melts around 420 C. Brass, 779 00:33:35,046 --> 00:33:47,725 which equals zinc and copper, melts at around 900 C or more. 780 00:33:47,725 --> 00:33:50,028 Greater than 900 C. 781 00:33:50,028 --> 00:33:53,231 That's a hint because if we go back to the video-- 782 00:33:53,231 --> 00:33:54,766 let's go back. 783 00:33:54,766 --> 00:33:57,268 Oh, the sound is on. 784 00:33:57,268 --> 00:33:58,436 Those are the electrons! 785 00:33:58,436 --> 00:33:59,837 A small portion of the time. 786 00:33:59,837 --> 00:34:03,508 Let me set that up because I'm doing in the middle. 787 00:34:03,508 --> 00:34:05,676 The electrons are coming off of a cathode 788 00:34:05,676 --> 00:34:07,779 because Rankin has cranked the voltage way up, 789 00:34:07,779 --> 00:34:08,913 and pumped all the air out. 790 00:34:08,913 --> 00:34:10,281 So those electrons are coming off 791 00:34:10,281 --> 00:34:12,817 with thousands and thousands of KEV. 792 00:34:12,817 --> 00:34:13,351 OK? 793 00:34:13,351 --> 00:34:14,152 They're coming out. 794 00:34:14,152 --> 00:34:16,554 And that's what's on the right here. 795 00:34:16,554 --> 00:34:17,288 There they are. 796 00:34:17,288 --> 00:34:19,123 The cathode is shaped to focus the electrons 797 00:34:19,123 --> 00:34:21,125 onto a small portion of the target, which 798 00:34:21,125 --> 00:34:25,463 increases the intensity of the x-rays produced. 799 00:34:25,463 --> 00:34:27,065 The target is, typically, a piece 800 00:34:27,065 --> 00:34:29,132 of tungsten or molybdenum, which may 801 00:34:29,132 --> 00:34:32,603 be embedded in a stationary water or oil coiled rod, 802 00:34:32,603 --> 00:34:34,806 or on a rotating disk. 803 00:34:34,806 --> 00:34:37,408 The high speed electrons collide with the target 804 00:34:37,408 --> 00:34:40,011 and rapidly lose energy. 805 00:34:40,011 --> 00:34:41,946 There are two x-ray producing interactions 806 00:34:41,946 --> 00:34:44,449 between the incident electrons and the atom. 807 00:34:44,449 --> 00:34:45,149 Ah! 808 00:34:45,149 --> 00:34:47,118 Look at the power! 809 00:34:47,118 --> 00:34:50,855 You can feel the power coming into that tiny little piece 810 00:34:50,855 --> 00:34:53,091 of metal. 811 00:34:53,091 --> 00:34:57,395 Now some of the time, you get the transition 812 00:34:57,395 --> 00:34:58,596 that we talked about. 813 00:34:58,596 --> 00:35:02,900 You knock an electron out, and you emit a photon-- 814 00:35:02,900 --> 00:35:04,435 a k alpha photon-- 815 00:35:04,435 --> 00:35:07,105 or maybe an l beta photon. 816 00:35:07,105 --> 00:35:08,439 Right? 817 00:35:08,439 --> 00:35:10,641 And sometimes you slow the electron down 818 00:35:10,641 --> 00:35:12,677 so you get the Brahms fraulein. 819 00:35:12,677 --> 00:35:16,714 But there's so much energy being pumped into this material. 820 00:35:16,714 --> 00:35:20,051 And a lot of times, those electrons just collide and heat 821 00:35:20,051 --> 00:35:22,120 up the metal. 822 00:35:22,120 --> 00:35:25,423 That metal is getting extremely hot. 823 00:35:25,423 --> 00:35:28,392 And in these experiments, either you cooled it, 824 00:35:28,392 --> 00:35:32,930 or you might rotate it quickly so that it gets to cool down. 825 00:35:32,930 --> 00:35:35,199 It gets a little break. 826 00:35:35,199 --> 00:35:37,135 Or you do both. 827 00:35:37,135 --> 00:35:38,970 Or you just throw up your hands and you say, 828 00:35:38,970 --> 00:35:40,938 you know what, I'm just going to go for an aloy 829 00:35:40,938 --> 00:35:45,276 that's got some zinc in it, but won't melt every time. 830 00:35:45,276 --> 00:35:46,744 Yeah, that was a good idea. 831 00:35:46,744 --> 00:35:49,347 So you put brass in, OK, you're going to get the copper lines. 832 00:35:49,347 --> 00:35:51,282 But you'll get the zinc lines. 833 00:35:51,282 --> 00:35:53,784 You'll get the zinc lines. 834 00:35:53,784 --> 00:35:56,254 And that was why he used brass. 835 00:35:56,254 --> 00:35:58,723 And that's why you can see you get extra lines 836 00:35:58,723 --> 00:36:01,125 in the case of brass. 837 00:36:01,125 --> 00:36:02,059 Al right. 838 00:36:04,829 --> 00:36:05,830 Good! 839 00:36:05,830 --> 00:36:06,330 All right. 840 00:36:06,330 --> 00:36:12,236 Now I am very excited about Moseley. 841 00:36:12,236 --> 00:36:16,174 You know, it allowed us to actually understand this 842 00:36:16,174 --> 00:36:17,642 not just because. 843 00:36:17,642 --> 00:36:18,876 Look at this. 844 00:36:18,876 --> 00:36:22,313 Mendeleev was like, you know what, cobalt and nickel 845 00:36:22,313 --> 00:36:23,748 can't be swapped. 846 00:36:23,748 --> 00:36:26,918 Hey, all you people who just think about mass, 847 00:36:26,918 --> 00:36:29,120 you're not going to put them in the order you think. 848 00:36:29,120 --> 00:36:31,722 I'm changing that. 849 00:36:31,722 --> 00:36:34,192 I'm changing it because properties matter. 850 00:36:34,192 --> 00:36:36,594 Moseley said, no, you're changing it 851 00:36:36,594 --> 00:36:41,265 because it's the right order because of the blue numbers. 852 00:36:41,265 --> 00:36:44,168 You're changing it because there is an actual count here 853 00:36:44,168 --> 00:36:45,169 that matters. 854 00:36:45,169 --> 00:36:48,506 And that is why your periodic table is what it is. 855 00:36:48,506 --> 00:36:49,807 Absolutely critical. 856 00:36:49,807 --> 00:36:52,043 It put the lantinides in the right place. 857 00:36:52,043 --> 00:36:55,846 It allowed the prediction of elements-- 858 00:36:55,846 --> 00:36:59,083 like [INAUDIBLE] and a number of others that hadn't been 859 00:36:59,083 --> 00:37:01,085 discovered yet-- 860 00:37:01,085 --> 00:37:04,689 and it set it all on this much more solid grounding. 861 00:37:04,689 --> 00:37:07,124 So that is the contribution of Moseley. 862 00:37:07,124 --> 00:37:08,693 I can't help it! 863 00:37:08,693 --> 00:37:11,963 I'm very excited so I brought t-shirts. 864 00:37:11,963 --> 00:37:14,232 I knew I was talking about Moseley. 865 00:37:14,232 --> 00:37:14,732 Now-- 866 00:37:14,732 --> 00:37:15,333 Woo! 867 00:37:15,333 --> 00:37:16,901 I'm going. 868 00:37:16,901 --> 00:37:17,735 OK. 869 00:37:17,735 --> 00:37:18,336 All right. 870 00:37:18,336 --> 00:37:19,704 There. 871 00:37:19,704 --> 00:37:20,771 And in the middle. 872 00:37:20,771 --> 00:37:21,872 And over there. 873 00:37:21,872 --> 00:37:22,573 [CHEERING] 874 00:37:22,573 --> 00:37:23,507 And over there. 875 00:37:23,507 --> 00:37:24,308 [CHEERING] 876 00:37:24,308 --> 00:37:25,209 And over there. 877 00:37:25,209 --> 00:37:26,410 This way! 878 00:37:26,410 --> 00:37:27,878 And, oh! 879 00:37:27,878 --> 00:37:28,913 That's a bad arm. 880 00:37:28,913 --> 00:37:32,183 [CHEERING] 881 00:37:32,183 --> 00:37:33,684 And up there. 882 00:37:33,684 --> 00:37:35,286 [CHEERING] 883 00:37:35,286 --> 00:37:35,820 Hold on. 884 00:37:35,820 --> 00:37:36,654 Hold on now. 885 00:37:36,654 --> 00:37:37,688 OK, there. 886 00:37:37,688 --> 00:37:38,656 There. 887 00:37:38,656 --> 00:37:41,525 And this is all for Moseley. 888 00:37:41,525 --> 00:37:42,393 Ah! 889 00:37:42,393 --> 00:37:43,894 This is all for Mosley! 890 00:37:43,894 --> 00:37:45,763 [CHEERING] 891 00:37:48,566 --> 00:37:51,369 All right. 892 00:37:51,369 --> 00:37:54,138 Now, OK. 893 00:37:54,138 --> 00:37:56,073 [SIDE CONVERSATION] 894 00:37:59,443 --> 00:38:08,919 Now apart from me showing off-- 895 00:38:08,919 --> 00:38:10,121 I don't have much of an arm-- 896 00:38:10,121 --> 00:38:12,757 one thing I'd like to say is, if you did already get a t-shirt, 897 00:38:12,757 --> 00:38:14,792 please, just hand it off to a friend or somebody. 898 00:38:14,792 --> 00:38:15,793 You know, let's share. 899 00:38:15,793 --> 00:38:18,596 Sharing is always caring. 900 00:38:18,596 --> 00:38:22,366 Now here's another type of x-ray I want to talk about. 901 00:38:22,366 --> 00:38:30,141 And z, actually, this is much less used today. 902 00:38:30,141 --> 00:38:31,676 I hope you've gotten a sense of how 903 00:38:31,676 --> 00:38:34,578 powerful these characteristic x-rays are. 904 00:38:34,578 --> 00:38:37,081 You know exactly what the wavelength is. 905 00:38:37,081 --> 00:38:39,717 But in the very earliest XRD experiments, 906 00:38:39,717 --> 00:38:43,487 it was the Bremsstrahlung radiation that was used. 907 00:38:43,487 --> 00:38:44,989 And that was by Van Laway. 908 00:38:44,989 --> 00:38:46,891 So I want to just tell you about that. 909 00:38:46,891 --> 00:38:48,993 And so here's an example of an Mo target. 910 00:38:48,993 --> 00:38:52,763 Now let's remind ourselves what we're looking at. 911 00:38:52,763 --> 00:38:55,499 These are x-rays. 912 00:38:55,499 --> 00:38:59,170 These are x-ray intensities versus wavelength. 913 00:38:59,170 --> 00:39:02,740 And this corresponds as 5, 10, 15, 20. 914 00:39:02,740 --> 00:39:04,408 That corresponds to the [INAUDIBLE].. 915 00:39:04,408 --> 00:39:04,909 Electrons. 916 00:39:04,909 --> 00:39:08,946 That's thousands of electron volts of the incoming electron. 917 00:39:08,946 --> 00:39:13,317 That electron that came in here and knocked this out 918 00:39:13,317 --> 00:39:14,852 from the cathode. 919 00:39:14,852 --> 00:39:15,486 Right? 920 00:39:15,486 --> 00:39:15,986 OK. 921 00:39:15,986 --> 00:39:17,822 Now that electron-- if it comes in, 922 00:39:17,822 --> 00:39:19,256 and we talked about this already, 923 00:39:19,256 --> 00:39:22,026 but let me remind you-- if it comes in at, kind of, 924 00:39:22,026 --> 00:39:23,627 a low energy, well, you're still going 925 00:39:23,627 --> 00:39:27,698 to get this continuous spectrum. 926 00:39:27,698 --> 00:39:28,933 This continuous spectrum. 927 00:39:28,933 --> 00:39:29,433 Oh! 928 00:39:29,433 --> 00:39:31,035 Why does it look like that? 929 00:39:31,035 --> 00:39:33,237 Beyond the scope of what we need to know. 930 00:39:33,237 --> 00:39:34,772 But in case you're wondering, it has 931 00:39:34,772 --> 00:39:37,041 to do with very complicated effects that 932 00:39:37,041 --> 00:39:42,113 happen when x-rays come off and then are reabsorbed 933 00:39:42,113 --> 00:39:43,047 by the same material. 934 00:39:43,047 --> 00:39:44,548 You can imagine that that could lead 935 00:39:44,548 --> 00:39:47,518 to all sorts of interesting cascades of absorption 936 00:39:47,518 --> 00:39:48,285 and emission. 937 00:39:48,285 --> 00:39:49,620 That's what leads to this shape. 938 00:39:49,620 --> 00:39:52,590 But we don't need to know those details. 939 00:39:52,590 --> 00:39:54,592 What we need to know is that as you increase 940 00:39:54,592 --> 00:39:56,627 the power of those incident electrons, 941 00:39:56,627 --> 00:40:00,231 you're going to get more and more intensity of x-rays. 942 00:40:00,231 --> 00:40:03,067 And this goes down. 943 00:40:03,067 --> 00:40:05,936 The minimum wavelength or maximum energy 944 00:40:05,936 --> 00:40:07,671 of the continuous spectrum-- 945 00:40:07,671 --> 00:40:10,908 the maximum energy goes up because the maximum energy 946 00:40:10,908 --> 00:40:12,476 you can get in the continuous spectrum 947 00:40:12,476 --> 00:40:15,746 is equal to the incident electron itself. 948 00:40:15,746 --> 00:40:16,981 So it's set. 949 00:40:16,981 --> 00:40:18,349 Right? 950 00:40:18,349 --> 00:40:20,651 Remember the Duane something limit? 951 00:40:20,651 --> 00:40:21,752 Duane Hunt? 952 00:40:21,752 --> 00:40:25,556 OK, we talked about that already, how to get that value. 953 00:40:25,556 --> 00:40:27,425 Yeah, but then you get to this certain point! 954 00:40:27,425 --> 00:40:31,562 And look, all of a sudden, the characteristic lines appear. 955 00:40:31,562 --> 00:40:34,031 And those are the K alpha lines for molybdenum. 956 00:40:34,031 --> 00:40:34,865 Why all of a sudden? 957 00:40:34,865 --> 00:40:37,334 Well because you got over the amount 958 00:40:37,334 --> 00:40:42,840 of energy needed to kick out a 1s electron from molybdenum. 959 00:40:42,840 --> 00:40:44,141 That's exactly why. 960 00:40:44,141 --> 00:40:45,676 Before that, you had enough energy 961 00:40:45,676 --> 00:40:47,778 to produce x-rays, but not enough 962 00:40:47,778 --> 00:40:49,480 to kick out the 1s electron. 963 00:40:49,480 --> 00:40:51,048 It's kicking out the 1s electron that 964 00:40:51,048 --> 00:40:53,017 gives you characteristic peaks. 965 00:40:53,017 --> 00:40:53,918 OK, good. 966 00:40:53,918 --> 00:40:55,286 This is all reminder stuff, but I 967 00:40:55,286 --> 00:40:56,821 want to get back on that page. 968 00:40:56,821 --> 00:40:59,924 But see now, OK, this continuous part is also used. 969 00:40:59,924 --> 00:41:03,928 And it was used, like I said, by Von Laue. 970 00:41:03,928 --> 00:41:10,868 And Von Laue was, again, a really, really smart cookie. 971 00:41:10,868 --> 00:41:15,840 And he used the Bragg condition to prove 972 00:41:15,840 --> 00:41:19,543 that the x-rays and the space light of structure of crystals 973 00:41:19,543 --> 00:41:23,581 can be interfered with each other to make this diffraction. 974 00:41:23,581 --> 00:41:25,816 But what he did was different. 975 00:41:25,816 --> 00:41:28,385 OK, so the Nobel Prize was given for this epoch making 976 00:41:28,385 --> 00:41:29,320 discovery. 977 00:41:29,320 --> 00:41:32,723 And I'm actually very happy that the people that worked with him 978 00:41:32,723 --> 00:41:36,393 also shared the Nobel Prize. 979 00:41:36,393 --> 00:41:38,329 Walter and Paul. 980 00:41:38,329 --> 00:41:39,797 What they did was different though. 981 00:41:39,797 --> 00:41:42,132 They took this continuous spectrum. 982 00:41:42,132 --> 00:41:51,442 And instead of fixing the angle and the lambda-- 983 00:41:51,442 --> 00:41:53,210 I'm sorry, instead of varying the angle 984 00:41:53,210 --> 00:41:56,247 but having a fixed lambda, they did the opposite 985 00:41:56,247 --> 00:42:00,484 because the continuous spectrum has all lambdas. 986 00:42:00,484 --> 00:42:01,252 Right? 987 00:42:01,252 --> 00:42:03,521 And so you can imagine how this works. 988 00:42:03,521 --> 00:42:04,321 Right? 989 00:42:04,321 --> 00:42:05,623 You can imagine how this works. 990 00:42:05,623 --> 00:42:11,295 So in the Laue version of XRD, you 991 00:42:11,295 --> 00:42:15,933 shoot the x-rays, which have all the wavelengths in them, 992 00:42:15,933 --> 00:42:17,868 at a crystal that's fixed. 993 00:42:17,868 --> 00:42:19,570 I'm not changing the angle. 994 00:42:19,570 --> 00:42:20,538 OK? 995 00:42:20,538 --> 00:42:22,439 I'm not changing the angle. 996 00:42:22,439 --> 00:42:26,076 And what you get are still diffraction peaks. 997 00:42:26,076 --> 00:42:28,979 You get spots. 998 00:42:28,979 --> 00:42:38,756 So In Laue XRD, you have a single crystal. 999 00:42:38,756 --> 00:42:41,759 It's got to be the same everywhere, in this case. 1000 00:42:41,759 --> 00:42:43,961 You have a single crystal. 1001 00:42:43,961 --> 00:42:46,230 Theta is fixed. 1002 00:42:46,230 --> 00:42:48,198 You don't move it around. 1003 00:42:48,198 --> 00:42:53,871 But lambda varies continuously. 1004 00:42:57,308 --> 00:42:59,276 OK. 1005 00:42:59,276 --> 00:43:03,581 And the pattern that you get reflects the symmetry. 1006 00:43:03,581 --> 00:43:09,820 Pattern reflects the crystal symmetry. 1007 00:43:13,857 --> 00:43:14,792 How is that possible? 1008 00:43:14,792 --> 00:43:20,598 Well, you can actually see this by thinking about the-- 1009 00:43:20,598 --> 00:43:21,732 do I have another picture? 1010 00:43:21,732 --> 00:43:23,334 I just have his one. 1011 00:43:23,334 --> 00:43:26,437 You can see this by thinking about that model, which is 1012 00:43:26,437 --> 00:43:29,473 somewhere out there in the sea. 1013 00:43:29,473 --> 00:43:31,475 Where is the model? 1014 00:43:31,475 --> 00:43:32,710 I don't see it. 1015 00:43:32,710 --> 00:43:33,611 Ah! 1016 00:43:33,611 --> 00:43:35,446 All the way in the back waving around. 1017 00:43:38,282 --> 00:43:39,683 Let's see if I can draw this. 1018 00:43:39,683 --> 00:43:42,086 Let's see. 1019 00:43:42,086 --> 00:43:43,187 Ah, I'm not going to try. 1020 00:43:46,457 --> 00:43:49,793 If I shoot x-rays that have a fixed lambda in, 1021 00:43:49,793 --> 00:43:52,129 but I vary the angle, then as we've been talking about, 1022 00:43:52,129 --> 00:43:54,765 there's going to be certain angles where you 1023 00:43:54,765 --> 00:43:56,266 get constructive interference. 1024 00:43:56,266 --> 00:43:58,802 Now if I keep the thing fixed and I 1025 00:43:58,802 --> 00:44:03,974 shoot all lambdas into it, well, take a look at the crystal. 1026 00:44:03,974 --> 00:44:06,744 Imagine that I'm holding that structure right now. 1027 00:44:06,744 --> 00:44:07,544 OK? 1028 00:44:07,544 --> 00:44:11,115 Well I'm going to see this set of planes here. 1029 00:44:11,115 --> 00:44:12,583 So I'm to see this set of planes. 1030 00:44:12,583 --> 00:44:13,951 Maybe they're [INAUDIBLE] planes. 1031 00:44:13,951 --> 00:44:14,518 I don't know. 1032 00:44:14,518 --> 00:44:15,052 Right? 1033 00:44:15,052 --> 00:44:17,388 And I'm going to bounce off of that 1034 00:44:17,388 --> 00:44:19,423 and constructively interfere, maybe, 1035 00:44:19,423 --> 00:44:21,025 if I've got the right lambda. 1036 00:44:21,025 --> 00:44:23,794 But see, if I'm looking at the crystal and it's fixed, 1037 00:44:23,794 --> 00:44:26,230 I'm going to see also there's another set of planes 1038 00:44:26,230 --> 00:44:26,730 like that. 1039 00:44:26,730 --> 00:44:27,731 Do you see? 1040 00:44:27,731 --> 00:44:29,400 There's another set of planes like that. 1041 00:44:29,400 --> 00:44:31,602 And if I'm a different wavelength-- not the same one, 1042 00:44:31,602 --> 00:44:33,370 but a different one-- 1043 00:44:33,370 --> 00:44:35,773 I might constructively interfere with those. 1044 00:44:35,773 --> 00:44:39,643 But you can see that the angle that I make will be different. 1045 00:44:39,643 --> 00:44:42,079 And so I'll put a spot in a different place. 1046 00:44:42,079 --> 00:44:42,579 You see? 1047 00:44:45,449 --> 00:44:49,219 So I've got all the wavelengths there. 1048 00:44:49,219 --> 00:44:53,424 And as they constructively interfere with different planes 1049 00:44:53,424 --> 00:44:56,627 that they see, they make different spots. 1050 00:44:56,627 --> 00:44:58,395 They make different spots. 1051 00:44:58,395 --> 00:45:00,297 And that's what those are. 1052 00:45:00,297 --> 00:45:03,434 In those spots, it's more complicated to get crystal 1053 00:45:03,434 --> 00:45:06,537 structure from those spots. 1054 00:45:06,537 --> 00:45:07,738 It's more complicated. 1055 00:45:07,738 --> 00:45:12,643 You can get symmetry fairly easily. 1056 00:45:12,643 --> 00:45:15,345 But getting the structure itself is a little bit more 1057 00:45:15,345 --> 00:45:15,846 complicated. 1058 00:45:15,846 --> 00:45:18,549 It can be tricky. 1059 00:45:18,549 --> 00:45:21,452 And for that, another reason most work today 1060 00:45:21,452 --> 00:45:26,390 is done with characteristic peaks, XRD. 1061 00:45:26,390 --> 00:45:28,826 But this happened before. 1062 00:45:28,826 --> 00:45:30,260 And so I wanted to show it to you. 1063 00:45:30,260 --> 00:45:32,663 And this resolved, actually, in one 1064 00:45:32,663 --> 00:45:34,131 of Laue's very famous papers. 1065 00:45:34,131 --> 00:45:36,567 It resolved the structure of zinc sulfide. 1066 00:45:36,567 --> 00:45:38,235 It was very important work. 1067 00:45:38,235 --> 00:45:39,737 And those are the spots. 1068 00:45:39,737 --> 00:45:41,972 Look at that pattern there. 1069 00:45:41,972 --> 00:45:45,008 See, the thing that you could get is the symmetry. 1070 00:45:45,008 --> 00:45:49,546 Oh, by the way, by the way, I'm not going to test you on Laue. 1071 00:45:49,546 --> 00:45:52,483 I'm only talking about it for five minutes here. 1072 00:45:52,483 --> 00:45:54,284 So in this class, I want you to know 1073 00:45:54,284 --> 00:45:57,755 about using characteristic peaks, 1074 00:45:57,755 --> 00:45:59,723 and all the things we've been talking about. 1075 00:45:59,723 --> 00:46:03,227 Laue is just on the side for knowledge. 1076 00:46:03,227 --> 00:46:05,062 We won't test on this. 1077 00:46:05,062 --> 00:46:09,066 But I want to end by telling you a story. 1078 00:46:09,066 --> 00:46:11,635 This tells you something about crystal symmetry. 1079 00:46:11,635 --> 00:46:14,104 What is symmetry? 1080 00:46:14,104 --> 00:46:17,441 Well it just means, if I rotate it, is it the same? 1081 00:46:17,441 --> 00:46:19,276 Or if I translate it, is it the same? 1082 00:46:19,276 --> 00:46:22,346 Give me just one minute because this is actually 1083 00:46:22,346 --> 00:46:24,481 a really interesting story. 1084 00:46:24,481 --> 00:46:27,284 That's translational symmetry. 1085 00:46:27,284 --> 00:46:29,753 We looked at this picture already. 1086 00:46:29,753 --> 00:46:31,121 There's no rotational symmetry. 1087 00:46:31,121 --> 00:46:33,724 To get back to this picture, I'd have to rotate the whole thing 1088 00:46:33,724 --> 00:46:36,493 by 360 degrees. 1089 00:46:36,493 --> 00:46:39,530 But see, there are crystals that actually 1090 00:46:39,530 --> 00:46:44,768 have only rotational symmetry and no translational symmetry. 1091 00:46:44,768 --> 00:46:46,937 And Dan Shechtman was the one who 1092 00:46:46,937 --> 00:46:49,206 discovered these in the 1980s. 1093 00:46:49,206 --> 00:46:51,508 Nobody believed him. 1094 00:46:51,508 --> 00:46:54,978 His advisor told him to go back and read the book. 1095 00:46:54,978 --> 00:46:57,114 And you know who wrote the book? 1096 00:46:57,114 --> 00:46:58,549 Linus Pauling. 1097 00:46:58,549 --> 00:47:01,285 Linus Pauling wrote the book on chemical bonds. 1098 00:47:01,285 --> 00:47:05,088 Literally, the book was called The Chemical Bond. 1099 00:47:05,088 --> 00:47:07,524 And Linus Pauling took the lead. 1100 00:47:07,524 --> 00:47:09,293 He won two Nobel prizes, not one. 1101 00:47:09,293 --> 00:47:13,130 He took the lead in attacking Shechtman. 1102 00:47:13,130 --> 00:47:16,099 Shechtman had discovered quasi crystals. 1103 00:47:16,099 --> 00:47:18,735 Shechtman had discovered quasi crystals, but nobody-- 1104 00:47:18,735 --> 00:47:20,003 he was fired his papers. 1105 00:47:20,003 --> 00:47:21,205 His papers weren't published. 1106 00:47:21,205 --> 00:47:23,340 And for 10 years, nobody believed him. 1107 00:47:23,340 --> 00:47:24,942 Linus Pauling said famously, "There 1108 00:47:24,942 --> 00:47:27,144 are no such things as quasi crystals, only 1109 00:47:27,144 --> 00:47:28,478 quasi scientists." 1110 00:47:28,478 --> 00:47:30,113 That's how bad it was. 1111 00:47:30,113 --> 00:47:31,915 Oh! 1112 00:47:31,915 --> 00:47:33,984 But Shechtman had his day. 1113 00:47:33,984 --> 00:47:36,386 He won the Nobel Prize. 1114 00:47:36,386 --> 00:47:37,721 And he had his day. 1115 00:47:37,721 --> 00:47:39,122 And he was proven right. 1116 00:47:39,122 --> 00:47:42,326 And these quasi crystals are absolutely fascinating. 1117 00:47:42,326 --> 00:47:45,329 Rotational, but no translational symmetry. 1118 00:47:45,329 --> 00:47:46,763 Have a great weekend!