1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,810 Commons License. 3 00:00:03,810 --> 00:00:06,850 Your support will help MIT OpenCourseWare continue to 4 00:00:06,850 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:21,440 --> 00:00:23,470 PROFESSOR: OK, Let's get down to business. 9 00:00:23,470 --> 00:00:26,890 Last day we started study crystallography. 10 00:00:26,890 --> 00:00:29,300 And we were looking at ordered solids. 11 00:00:29,300 --> 00:00:32,990 And we recognized the crystal structure is the sum of the 12 00:00:32,990 --> 00:00:36,880 combination of a Bravais lattice, which is the way that 13 00:00:36,880 --> 00:00:40,650 points are identified in space, plus the basis. 14 00:00:40,650 --> 00:00:44,670 And we saw that we could put a variety of elements at the 15 00:00:44,670 --> 00:00:46,950 corners of the Bravais lattice. 16 00:00:46,950 --> 00:00:49,800 And this is taken from the archival notes where we see 17 00:00:49,800 --> 00:00:54,220 the simple, single atoms at the various lattice points. 18 00:00:54,220 --> 00:00:58,070 And we recognized last day that we could put clusters of 19 00:00:58,070 --> 00:01:00,370 atoms and so on, and even proteins will 20 00:01:00,370 --> 00:01:01,580 crystallize in this form. 21 00:01:01,580 --> 00:01:05,650 And actually, to make a point, about five years ago, a group 22 00:01:05,650 --> 00:01:09,110 of students came to my office after the final exam, and 23 00:01:09,110 --> 00:01:13,740 recognizing that I drink Fresca during the lectures, 24 00:01:13,740 --> 00:01:15,590 they came to me with this 25 00:01:15,590 --> 00:01:19,610 body-centered Fresca unit cell. 26 00:01:19,610 --> 00:01:24,570 So this just makes the point that you can put anything at 27 00:01:24,570 --> 00:01:25,310 the lattice point. 28 00:01:25,310 --> 00:01:29,260 So there it is. 29 00:01:29,260 --> 00:01:30,400 Oh, here's the point. 30 00:01:30,400 --> 00:01:33,120 This is me at a conference in Copenhagen. 31 00:01:33,120 --> 00:01:35,480 This is outside the Admiral Hotel. 32 00:01:35,480 --> 00:01:38,370 And just to show you I'm always thinking about 3.091, I 33 00:01:38,370 --> 00:01:40,400 came outside-- 34 00:01:40,400 --> 00:01:42,500 and this is a colleague of mine from France, Marcelle 35 00:01:42,500 --> 00:01:43,620 Gaune-Escard. 36 00:01:43,620 --> 00:01:45,150 How do we know she's French? 37 00:01:45,150 --> 00:01:47,330 She's got a cigarette. 38 00:01:47,330 --> 00:01:48,950 She's a scientist. She's a woman. 39 00:01:48,950 --> 00:01:49,850 And she smoking. 40 00:01:49,850 --> 00:01:50,720 And it's fantastic. 41 00:01:50,720 --> 00:01:52,290 And she's a great gal. 42 00:01:52,290 --> 00:01:55,330 Anyways, so there we are out in front of the Admiral Hotel. 43 00:01:55,330 --> 00:01:56,990 And I notice these cannon balls. 44 00:01:56,990 --> 00:01:59,050 And what do you notice about the cannon balls? 45 00:01:59,050 --> 00:02:02,420 They are sitting in one of the Bravais lattices. 46 00:02:02,420 --> 00:02:04,970 So I couldn't resist having my wife take this picture. 47 00:02:04,970 --> 00:02:08,240 Because I knew that this would come back to 3.091. 48 00:02:08,240 --> 00:02:13,690 So here we are with the individual cubic lattices 49 00:02:13,690 --> 00:02:15,040 where we're going to focus. 50 00:02:15,040 --> 00:02:18,190 And we started looking at the properties of cubic lattices. 51 00:02:18,190 --> 00:02:22,620 And I started working through this table. 52 00:02:22,620 --> 00:02:26,140 And we got down to nearest neighbors, and so on, and this 53 00:02:26,140 --> 00:02:28,260 relationship between the lattice 54 00:02:28,260 --> 00:02:29,770 constant and the radius. 55 00:02:29,770 --> 00:02:32,320 And I just wanted to show this last point here 56 00:02:32,320 --> 00:02:33,580 about packing density. 57 00:02:33,580 --> 00:02:40,340 Because it comes up considerations of properties 58 00:02:40,340 --> 00:02:41,460 of elements. 59 00:02:41,460 --> 00:02:43,570 And so I wanted to go through the packing density 60 00:02:43,570 --> 00:02:44,770 calculation. 61 00:02:44,770 --> 00:02:47,570 And so the way we handle the packing density, remember 62 00:02:47,570 --> 00:02:49,890 we're looking at a unit cell here. 63 00:02:49,890 --> 00:02:52,820 This is the cube that's the repeat unit. 64 00:02:52,820 --> 00:02:55,870 And it has a lattice constant of dimension a. 65 00:02:55,870 --> 00:02:59,000 And then depending on where we put atoms, I want to show that 66 00:02:59,000 --> 00:03:02,040 we've got three different options here, simple cubic, 67 00:03:02,040 --> 00:03:04,350 body-centered cubic, and face-centered cubic. 68 00:03:04,350 --> 00:03:07,870 And the last line of that slide shows that the densest 69 00:03:07,870 --> 00:03:09,555 packing of atoms-- this is hard 70 00:03:09,555 --> 00:03:11,490 spheres, the cannon balls-- 71 00:03:11,490 --> 00:03:13,450 the densest packing is face-centered cubic. 72 00:03:13,450 --> 00:03:16,760 And I wanted to show the derivation of that where if we 73 00:03:16,760 --> 00:03:19,940 face-centered cubic where the atoms are big enough to touch. 74 00:03:19,940 --> 00:03:23,310 If we have 4 atoms at the corner touching on the face 75 00:03:23,310 --> 00:03:26,950 diagonal and then continuing through the cell, we want to 76 00:03:26,950 --> 00:03:34,680 get packing density as the ratio of the volume occupied 77 00:03:34,680 --> 00:03:36,640 by the atoms-- and here we're modeling the 78 00:03:36,640 --> 00:03:38,240 atoms as hard spheres-- 79 00:03:38,240 --> 00:03:41,610 divided by the volume of the cell itself. 80 00:03:41,610 --> 00:03:44,680 And so that's pretty straightforward calculation. 81 00:03:44,680 --> 00:03:47,290 We're modeling the atoms as hard spheres. 82 00:03:47,290 --> 00:03:51,570 And we saw last day that if we take the fraction of the atom, 83 00:03:51,570 --> 00:03:55,970 1/8 times 1/8, and 6 times 1/2, we have 4 atom 84 00:03:55,970 --> 00:03:57,510 equivalents per unit cell. 85 00:03:57,510 --> 00:04:01,910 And each of these has a volume of 4/3 pi r cubed. 86 00:04:01,910 --> 00:04:04,360 And then we divide that by a cubed. 87 00:04:04,360 --> 00:04:07,460 And then we know the relationship between a and r. 88 00:04:07,460 --> 00:04:09,540 This is 4r and that's root 2 a. 89 00:04:09,540 --> 00:04:13,260 So we can say root 2 a equals 4r. 90 00:04:13,260 --> 00:04:15,800 Either eliminate a or eliminate r. 91 00:04:15,800 --> 00:04:18,310 We eventually end up with this dimensionless group, which is 92 00:04:18,310 --> 00:04:21,510 pi divided by 3 roots of 2. 93 00:04:21,510 --> 00:04:25,040 And that is 74%. 94 00:04:25,040 --> 00:04:26,405 And that's the densest package. 95 00:04:26,405 --> 00:04:28,740 If you go through the same calculation for body-centered 96 00:04:28,740 --> 00:04:32,160 packing, you'll find it's 68% packing. 97 00:04:32,160 --> 00:04:35,120 And for simple cubic it's 52% packing. 98 00:04:35,120 --> 00:04:39,130 That's the highest density that you can have. So I urge 99 00:04:39,130 --> 00:04:40,140 you to spend some time. 100 00:04:40,140 --> 00:04:42,900 If you work the homework, you'll work your way through 101 00:04:42,900 --> 00:04:44,110 that chart. 102 00:04:44,110 --> 00:04:47,130 So now I wanted to take a few minutes and talk about 103 00:04:47,130 --> 00:04:48,660 crystallographic notation. 104 00:04:48,660 --> 00:04:52,040 Because we need to know this in order to describe various 105 00:04:52,040 --> 00:04:53,060 features of a cell. 106 00:04:53,060 --> 00:04:57,950 So I'm going to start with a Cartesian coordinate system 107 00:04:57,950 --> 00:04:59,600 that obeys the right-hand rule. 108 00:04:59,600 --> 00:05:02,310 So we'll put down x, y and z. 109 00:05:02,310 --> 00:05:07,010 And then we'll put up a unit cell here with edge a. 110 00:05:07,010 --> 00:05:12,280 So we have a on the x, y and z coordinate. 111 00:05:12,280 --> 00:05:16,010 And we know that a equals b equals c. 112 00:05:16,010 --> 00:05:17,420 That's the unit vectors here. 113 00:05:17,420 --> 00:05:19,810 There's a little a here, a little b here, 114 00:05:19,810 --> 00:05:20,970 and a little c here. 115 00:05:20,970 --> 00:05:25,160 These are all equal to the lattice constant value a. 116 00:05:25,160 --> 00:05:27,240 And all of the angles are 90 degrees. 117 00:05:27,240 --> 00:05:29,430 This is what defines the cubic system. 118 00:05:29,430 --> 00:05:32,150 So I'm going to put several positions here. 119 00:05:32,150 --> 00:05:34,150 So here is the origin. 120 00:05:34,150 --> 00:05:38,710 And the origin we designate as 0, 0, 0. 121 00:05:38,710 --> 00:05:41,170 I'm going to put a position up here, a. 122 00:05:41,170 --> 00:05:44,050 And you just use the same notation as you'd use 123 00:05:44,050 --> 00:05:44,810 mathematics. 124 00:05:44,810 --> 00:05:48,150 Only crystallographers don't put parentheses around it. 125 00:05:48,150 --> 00:05:49,990 So what I'm really teaching is notation. 126 00:05:49,990 --> 00:05:51,630 You already know the math. 127 00:05:51,630 --> 00:05:54,230 So a up here is what? 128 00:05:54,230 --> 00:05:56,130 It's 0 units on the x-axis. 129 00:05:56,130 --> 00:05:59,150 It's 1 unit on the y-axis, and 1 unit on a z-axis. 130 00:05:59,150 --> 00:06:01,820 So that would make it 0, 1, 1. 131 00:06:01,820 --> 00:06:04,550 And I'm going to put a b out here. 132 00:06:04,550 --> 00:06:07,700 B is out 1 unit on the x-axis. 133 00:06:07,700 --> 00:06:10,350 It's 0 units on the y-axis. 134 00:06:10,350 --> 00:06:14,890 And it looks like it's up at about 1/2 unit on the z-axis. 135 00:06:14,890 --> 00:06:18,390 So that makes 1, 0, and 1/2. 136 00:06:18,390 --> 00:06:21,810 And so now what I want to do is show you how we designate 137 00:06:21,810 --> 00:06:24,275 directions and planes. 138 00:06:24,275 --> 00:06:26,690 You use a slightly different notation from what 139 00:06:26,690 --> 00:06:27,910 you used to in math. 140 00:06:27,910 --> 00:06:31,650 So this chart will be posted at the website. 141 00:06:31,650 --> 00:06:34,480 Move the coordinate axes so the line passes through the 142 00:06:34,480 --> 00:06:38,400 origin, define a vector from the origin to the point on the 143 00:06:38,400 --> 00:06:40,580 line, and choose the smaller set of integers. 144 00:06:40,580 --> 00:06:42,440 So let's do a simple one here. 145 00:06:42,440 --> 00:06:46,020 Let's do from origin to b. 146 00:06:46,020 --> 00:06:47,720 So o to b. 147 00:06:47,720 --> 00:06:49,500 That's this vector here. 148 00:06:49,500 --> 00:06:50,620 So how would we do that one? 149 00:06:50,620 --> 00:06:52,640 Well we're already at the origin. 150 00:06:52,640 --> 00:06:53,310 So that's trivial. 151 00:06:53,310 --> 00:06:56,410 o to b, so we're going from here out to here. 152 00:06:56,410 --> 00:06:57,820 And then what does it say? 153 00:06:57,820 --> 00:07:02,140 It says choose the smallest set of integers, no commas, 154 00:07:02,140 --> 00:07:03,100 clear fractions. 155 00:07:03,100 --> 00:07:06,980 So that's going to take us out to 1 0 1/2. 156 00:07:06,980 --> 00:07:09,725 But the crystallographers don't like fractions. 157 00:07:09,725 --> 00:07:11,610 So you're supposed to clear the fractions. 158 00:07:11,610 --> 00:07:14,140 You clear the fractions by multiplying through. 159 00:07:14,140 --> 00:07:17,410 So make that 2 0 1. 160 00:07:17,410 --> 00:07:18,650 It's the same direction. 161 00:07:18,650 --> 00:07:20,980 See if I came out two units here, I'd end up 162 00:07:20,980 --> 00:07:21,970 being one unit here. 163 00:07:21,970 --> 00:07:24,850 So it's the same direction. 164 00:07:24,850 --> 00:07:26,400 It really is the same direction. 165 00:07:26,400 --> 00:07:27,780 Don't put any commas. 166 00:07:27,780 --> 00:07:29,090 And put brackets around it. 167 00:07:29,090 --> 00:07:33,640 So that's the 2, 0, 1 direction, which is o b. 168 00:07:33,640 --> 00:07:34,800 And I want to do a different one. 169 00:07:34,800 --> 00:07:37,690 I'm going to go this way, a to o. 170 00:07:37,690 --> 00:07:41,240 So let's look at that one, a o. 171 00:07:41,240 --> 00:07:42,620 And what happens on a o? 172 00:07:42,620 --> 00:07:44,720 Well now I'm going to put the origin at a. 173 00:07:44,720 --> 00:07:48,590 I'm going to go to 0 in the x-axis. 174 00:07:48,590 --> 00:07:51,350 I'm going to go minus 1 in the z-axis, and 175 00:07:51,350 --> 00:07:52,790 minus 1 in the y-axis. 176 00:07:52,790 --> 00:07:56,510 So that gives me 0 minus 1 minus 1. 177 00:07:56,510 --> 00:07:58,290 But see they don't use commas. 178 00:07:58,290 --> 00:07:59,940 And so this looks kind of goofy. 179 00:07:59,940 --> 00:08:01,440 Because you get these minus signs in here. 180 00:08:01,440 --> 00:08:04,090 So what the crystallographers do is they put the minus sign 181 00:08:04,090 --> 00:08:05,340 on top of the number. 182 00:08:05,340 --> 00:08:09,000 So this becomes 0 1 with a macron it. 183 00:08:11,530 --> 00:08:14,780 If you'd studied Latin, you'd know this thing is a macron, a 184 00:08:14,780 --> 00:08:16,800 line over a vowel. 185 00:08:16,800 --> 00:08:19,490 So 0 1 bar 1 bar. 186 00:08:19,490 --> 00:08:21,760 And that's the direction a o. 187 00:08:21,760 --> 00:08:25,430 So that's the macron acting as the minus sign. 188 00:08:25,430 --> 00:08:28,790 So that's the a o direction 189 00:08:28,790 --> 00:08:32,200 And then furthermore, we can designate families. 190 00:08:32,200 --> 00:08:35,780 This is just the 0 1 bar 1 bar. 191 00:08:35,780 --> 00:08:38,200 If you want to be a hipster with crystallography, 192 00:08:38,200 --> 00:08:39,380 you call this 0. 193 00:08:39,380 --> 00:08:41,870 You say it's 0 1 bar 1 bar. 194 00:08:41,870 --> 00:08:44,690 But if you're a nice chemistry student, you'll say zero, 195 00:08:44,690 --> 00:08:46,510 minus 1 minus 1. 196 00:08:46,510 --> 00:08:49,710 No we don't do that in 3.091, 0 1 bar 1 bar. 197 00:08:49,710 --> 00:08:54,250 Now suppose I wanted to describe all of the faces, 198 00:08:54,250 --> 00:08:55,560 every face. 199 00:08:55,560 --> 00:08:58,210 So what I could do, is I could say I want the 200 00:08:58,210 --> 00:09:02,158 set of all face diagonals. 201 00:09:05,750 --> 00:09:07,480 Well, that's a face diagonal. 202 00:09:07,480 --> 00:09:11,200 But what I can do is in a compact notation, I could 203 00:09:11,200 --> 00:09:17,180 write 0 1 1 and use the carat. 204 00:09:17,180 --> 00:09:20,300 This is called the carat. 205 00:09:20,300 --> 00:09:24,560 So if I enclose in carats, this means the set up all 0 1 206 00:09:24,560 --> 00:09:26,410 1 type planes. 207 00:09:26,410 --> 00:09:30,320 And so what that means is I can unpack that, and write 0 1 208 00:09:30,320 --> 00:09:37,790 1, 0 1 1 bar, 0 1 bar 1, et cetera. 209 00:09:37,790 --> 00:09:40,420 And what I'll end up doing is describing the 210 00:09:40,420 --> 00:09:42,780 set up all face diagonals. 211 00:09:42,780 --> 00:09:45,470 So if I want to talk to you later when we're studying 212 00:09:45,470 --> 00:09:48,600 x-ray diffraction, I want to talk about face diagonals, I 213 00:09:48,600 --> 00:09:49,530 don't use that word. 214 00:09:49,530 --> 00:09:50,950 We're quantitative here at MIT. 215 00:09:50,950 --> 00:09:53,970 I say look at the 0 1 1 planes. 216 00:09:53,970 --> 00:09:55,780 So you go face diagonals. 217 00:09:55,780 --> 00:09:57,850 That's the compact notation. 218 00:09:57,850 --> 00:10:05,130 If we want to look at all cell edges, what's the cell edge? 219 00:10:05,130 --> 00:10:07,090 Here's the cell edge. 220 00:10:07,090 --> 00:10:08,910 This is an edge here, isn't it? 221 00:10:08,910 --> 00:10:10,060 It's right on the edge of the cell. 222 00:10:10,060 --> 00:10:12,880 So it's 0 on the y, 0 in the z. 223 00:10:12,880 --> 00:10:14,290 It's 1 in the x. 224 00:10:14,290 --> 00:10:19,620 So the set of all cell edges would be 0 0 1. 225 00:10:19,620 --> 00:10:22,210 And you could write 1 0 0, that's OK too. 226 00:10:22,210 --> 00:10:23,540 Or you could write 0 1 0. 227 00:10:23,540 --> 00:10:24,460 That's OK. 228 00:10:24,460 --> 00:10:27,050 But if you want to be a hipster in crystallography, 229 00:10:27,050 --> 00:10:28,710 put the zeroes out in front. 230 00:10:28,710 --> 00:10:33,710 So the set of 0 0 1 directions is all the cube edges. 231 00:10:33,710 --> 00:10:37,400 And then lastly, if we wanted to get all the diagonals that 232 00:10:37,400 --> 00:10:42,540 starts from here and goes up, we'll have all cell diagonals, 233 00:10:42,540 --> 00:10:45,430 all, if you want to call it, body diagonals, not face 234 00:10:45,430 --> 00:10:48,890 diagonals, body diagonals. 235 00:10:48,890 --> 00:10:51,250 Body diagonals is 1 1 1. 236 00:10:51,250 --> 00:10:53,130 And the mathematics imitates reality. 237 00:10:53,130 --> 00:10:55,240 How many combinations are there here? 238 00:10:55,240 --> 00:10:58,380 I've got 0 1, and I've got minus 1. 239 00:10:58,380 --> 00:11:03,510 So I have 0 0 1, 0 0 1 bar, 0 1 0, 0 1 bar 0, 240 00:11:03,510 --> 00:11:04,695 1 0 0, 1 bar 0. 241 00:11:04,695 --> 00:11:07,020 There's 6 And how many edges are there? 242 00:11:07,020 --> 00:11:08,070 6. 243 00:11:08,070 --> 00:11:10,990 Mathematics imitating reality, what a concept. 244 00:11:10,990 --> 00:11:11,930 That's great. 245 00:11:11,930 --> 00:11:12,870 OK. 246 00:11:12,870 --> 00:11:13,510 So that's good. 247 00:11:13,510 --> 00:11:15,630 Now we want to look at planes. 248 00:11:15,630 --> 00:11:17,010 Let's look at planes. 249 00:11:17,010 --> 00:11:18,550 Now planes are a little bit different. 250 00:11:18,550 --> 00:11:21,250 This is basically what you know from math with a little 251 00:11:21,250 --> 00:11:24,600 bit of notation It's basically the same thing. 252 00:11:24,600 --> 00:11:25,700 Planes are quite different. 253 00:11:25,700 --> 00:11:27,540 So let's go to the planes. 254 00:11:27,540 --> 00:11:29,170 So you know the equation of a plane. 255 00:11:29,170 --> 00:11:34,870 It's x over a plus y over b plus z over c equals 1. 256 00:11:34,870 --> 00:11:39,530 And a b and c are the intercepts at the x, y z axes. 257 00:11:39,530 --> 00:11:44,950 Well, in order to make this notation compatible to what we 258 00:11:44,950 --> 00:11:48,430 have here for lines, a British meteorologist by the name of 259 00:11:48,430 --> 00:11:53,550 William Hallowes Miller in 1839 said let's define h, k, 260 00:11:53,550 --> 00:11:56,880 and l as the reciprocals of these intercepts. 261 00:11:56,880 --> 00:12:01,960 And now we'll write the equation of a plane as hx plus 262 00:12:01,960 --> 00:12:04,580 ky plus lz equals 1. 263 00:12:04,580 --> 00:12:09,440 And we'll use those values of h, k, and l as the indicators 264 00:12:09,440 --> 00:12:09,940 of a plane. 265 00:12:09,940 --> 00:12:12,640 So here's an example. 266 00:12:12,640 --> 00:12:17,110 So again, I've got the right-handed rule coordinates. 267 00:12:17,110 --> 00:12:18,550 And here's the plane. 268 00:12:18,550 --> 00:12:21,360 And you can see that it cuts the x-axis and a. 269 00:12:21,360 --> 00:12:23,310 It cuts the y-axis at b. 270 00:12:23,310 --> 00:12:24,710 And it's parallel to the z-axis. 271 00:12:27,840 --> 00:12:30,810 So if we were just to use the old mathematics notation, and 272 00:12:30,810 --> 00:12:34,350 put the a, b and c, you'd have 1/2 here. 273 00:12:34,350 --> 00:12:35,220 You'd have 1 here. 274 00:12:35,220 --> 00:12:36,420 And you'd have infinity here. 275 00:12:36,420 --> 00:12:38,080 And that looks goofy. 276 00:12:38,080 --> 00:12:41,150 So instead what we want to do is use the Miller indices, 277 00:12:41,150 --> 00:12:43,170 which are the reciprocals. 278 00:12:43,170 --> 00:12:46,150 So now the reciprocal of 1/2 is 2. 279 00:12:46,150 --> 00:12:48,330 The reciprocal of 1 trivially is 1. 280 00:12:48,330 --> 00:12:51,100 And the reciprocal of infinity is 0. 281 00:12:51,100 --> 00:12:53,060 And so now you have something that makes sense. 282 00:12:53,060 --> 00:12:55,430 And you put no commas in between. 283 00:12:55,430 --> 00:12:57,800 And you put the whole thing in parentheses. 284 00:12:57,800 --> 00:13:01,110 So that's the 2 1 0 plane. 285 00:13:01,110 --> 00:13:03,430 And there's a really cool property here. 286 00:13:03,430 --> 00:13:07,810 And that is, using this same formulation I just showed you 287 00:13:07,810 --> 00:13:11,560 for directions, the 2 1 0 directions-- you see 2 1 0 288 00:13:11,560 --> 00:13:13,880 with square brackets, that's a direction. 289 00:13:13,880 --> 00:13:16,140 2 1 0 with parentheses is a plane. 290 00:13:16,140 --> 00:13:19,390 The 2 1 0 direction is perpendicular 291 00:13:19,390 --> 00:13:21,320 to the 2 1 0 plane. 292 00:13:21,320 --> 00:13:23,430 And that's one of the advantages of using Miller 293 00:13:23,430 --> 00:13:26,030 indices notation with the classical 294 00:13:26,030 --> 00:13:28,710 notation for direction. 295 00:13:28,710 --> 00:13:29,460 Here's another one. 296 00:13:29,460 --> 00:13:31,120 This is 0 1 0. 297 00:13:31,120 --> 00:13:33,150 This is the x, y, and the z. 298 00:13:33,150 --> 00:13:35,760 So this cuts at 1, 0 1 0. 299 00:13:35,760 --> 00:13:38,230 This is 0 2 0. 300 00:13:38,230 --> 00:13:41,580 An 0 1 0 directions are perpendicular to 0 1 0 plane. 301 00:13:41,580 --> 00:13:45,100 0 2 0 directions are perpendicular to 0 2 0 plane. 302 00:13:45,100 --> 00:13:47,520 Oh here's 1 1 1. 303 00:13:47,520 --> 00:13:48,020 That's cool. 304 00:13:48,020 --> 00:13:50,690 See it cuts it at 1 1 and 1. 305 00:13:50,690 --> 00:13:55,730 And 1 1 1 direction cuts through the 1 1 1 plane 306 00:13:55,730 --> 00:13:57,830 perpendicular. 307 00:13:57,830 --> 00:13:58,850 This is an interesting one. 308 00:13:58,850 --> 00:14:00,290 See the origin. 309 00:14:00,290 --> 00:14:01,940 The plane cuts through the origin. 310 00:14:01,940 --> 00:14:03,740 Now what do you do? 311 00:14:03,740 --> 00:14:04,780 What do you do? 312 00:14:04,780 --> 00:14:08,000 You move the origin. 313 00:14:08,000 --> 00:14:09,900 Because we don't know where the origin of the universe is. 314 00:14:09,900 --> 00:14:10,840 It's just a unit cell. 315 00:14:10,840 --> 00:14:11,360 It doesn't matter. 316 00:14:11,360 --> 00:14:12,645 So we move the origin up here. 317 00:14:12,645 --> 00:14:13,760 And now what do we have? 318 00:14:13,760 --> 00:14:16,420 We have 1 1 and minus 1. 319 00:14:16,420 --> 00:14:19,250 And just as before, we put 1 with a macron over it. 320 00:14:19,250 --> 00:14:21,490 That's 1 1 1 bar plane. 321 00:14:21,490 --> 00:14:23,860 And there is the 1 1 1 bar direction. 322 00:14:23,860 --> 00:14:24,700 It doesn't matter. 323 00:14:24,700 --> 00:14:27,920 It'll always give you perpendicular. 324 00:14:27,920 --> 00:14:29,810 It's really cool. 325 00:14:29,810 --> 00:14:30,420 All right. 326 00:14:30,420 --> 00:14:33,340 And we can also specify a set of planes. 327 00:14:33,340 --> 00:14:35,360 So instead of using parentheses, 328 00:14:35,360 --> 00:14:36,700 we use brace brackets. 329 00:14:36,700 --> 00:14:40,080 And if we use brae brackets, we get families of planes. 330 00:14:40,080 --> 00:14:45,000 So for example, we could say if we wanted a particular face 331 00:14:45,000 --> 00:14:54,170 so that the face in the xy plane, facing the xy plane 332 00:14:54,170 --> 00:14:55,720 would be 0 0 1. 333 00:14:55,720 --> 00:14:57,400 Right, because it cuts the z. 334 00:14:57,400 --> 00:14:58,610 So this is 0 0 1. 335 00:14:58,610 --> 00:15:02,360 But what if I wanted to say in a compact way, all faces of 336 00:15:02,360 --> 00:15:04,710 the unit cell, all of the faces. 337 00:15:04,710 --> 00:15:06,450 So this is the particular plane. 338 00:15:06,450 --> 00:15:11,665 If I wanted to say all faces I would write 0 0 1. 339 00:15:11,665 --> 00:15:15,005 But I can't use any of these containers. 340 00:15:15,005 --> 00:15:16,560 So I'll use brace brackets. 341 00:15:16,560 --> 00:15:21,140 So 0 0 1 in brace brackets means the whole setup, 0 0 1, 342 00:15:21,140 --> 00:15:30,950 0 0 1 bar, 0 1 0, 0 1 bar 0, 1 0 0, and 1 bar 0 0. 343 00:15:30,950 --> 00:15:32,040 So there's only 6. 344 00:15:32,040 --> 00:15:33,270 And there's 6 faces. 345 00:15:33,270 --> 00:15:36,200 Again mathematics imitating reality. 346 00:15:36,200 --> 00:15:36,960 What a concept. 347 00:15:36,960 --> 00:15:38,140 Make the math work for you. 348 00:15:38,140 --> 00:15:39,600 You don't work for the math. 349 00:15:39,600 --> 00:15:43,740 All right and just to make the point about the h k l plane, 350 00:15:43,740 --> 00:15:48,610 is perpendicular to the h k l direction. 351 00:15:48,610 --> 00:15:49,730 So that's good. 352 00:15:49,730 --> 00:15:51,960 And the last thing I want to show you that comes out of the 353 00:15:51,960 --> 00:15:58,200 use of the Miller indices for planes, is that another 354 00:15:58,200 --> 00:16:00,530 property that we'd like to know is 355 00:16:00,530 --> 00:16:02,150 the interplanar spacing. 356 00:16:02,150 --> 00:16:05,360 What's the spacing between like planes. 357 00:16:05,360 --> 00:16:15,810 So interplanar spacing, that is to say the distance between 358 00:16:15,810 --> 00:16:27,426 like planes, adjacent planes identical index. 359 00:16:33,470 --> 00:16:40,620 I'm going to write it to be specific to say Miller index, 360 00:16:40,620 --> 00:16:43,710 h k l in parentheses. 361 00:16:43,710 --> 00:16:45,760 And the property that comes out of this-- and you don't 362 00:16:45,760 --> 00:16:46,500 have to derive it. 363 00:16:46,500 --> 00:16:49,530 Somebody worked this out for you about a 150 years ago-- 364 00:16:49,530 --> 00:16:53,420 is that the distance between adjacent planes with the index 365 00:16:53,420 --> 00:16:58,040 h k l is given by the ratio of a, which is the lattice 366 00:16:58,040 --> 00:17:05,670 constant, this is the cubed edge, divided by the sum of 367 00:17:05,670 --> 00:17:13,710 the squares of h, k, and l taken to the power of 1/2, So 368 00:17:13,710 --> 00:17:16,520 the square root of h squared plus k squared plus l squared 369 00:17:16,520 --> 00:17:22,430 divided into the lattice constant, gives you the value 370 00:17:22,430 --> 00:17:25,010 of the spacing in between. 371 00:17:25,010 --> 00:17:28,280 And this is the a just to be clear about it. 372 00:17:28,280 --> 00:17:32,686 So for example, I think I've got some cartoons up 373 00:17:32,686 --> 00:17:33,900 here that show this. 374 00:17:33,900 --> 00:17:35,080 So here's 0 1 0. 375 00:17:35,080 --> 00:17:35,720 It's trivial. 376 00:17:35,720 --> 00:17:37,860 What's the distance here? 377 00:17:37,860 --> 00:17:40,780 The d 0 1 0 is just day. 378 00:17:40,780 --> 00:17:41,370 How about here? 379 00:17:41,370 --> 00:17:44,490 This is 0 squared, 2 squared. 380 00:17:44,490 --> 00:17:46,290 0 squared, this is d over 2. 381 00:17:46,290 --> 00:17:48,320 So this is a 0 2 0 plane. 382 00:17:48,320 --> 00:17:53,270 But if the distance between 0 2 0 planes is 1/2 a, well, 383 00:17:53,270 --> 00:17:54,970 then that's an 0 2 0 plane. 384 00:17:54,970 --> 00:17:56,980 Then this is an 0 2 0 plane. 385 00:17:56,980 --> 00:18:00,960 So point of fact, every 0 1 0 plane is an 0 2 0 plane. 386 00:18:00,960 --> 00:18:03,740 But every 0 2 0 plane isn't an 0 1 0 plane. 387 00:18:03,740 --> 00:18:07,660 You can see that some planes have multiple names. 388 00:18:07,660 --> 00:18:08,090 Here's another one. 389 00:18:08,090 --> 00:18:11,650 Look, this is the distance between adjacent 1 1 1 planes. 390 00:18:11,650 --> 00:18:12,910 It's a over root 3. 391 00:18:12,910 --> 00:18:16,620 So as the index goes up, as h k l goes up, the distance 392 00:18:16,620 --> 00:18:18,590 between successive planes goes down. 393 00:18:18,590 --> 00:18:22,150 And the angle between the planes goes up. 394 00:18:22,150 --> 00:18:24,240 The easiest one is orthogonal. 395 00:18:24,240 --> 00:18:26,520 OK, that's good. 396 00:18:26,520 --> 00:18:27,740 That's good. 397 00:18:27,740 --> 00:18:28,200 All right. 398 00:18:28,200 --> 00:18:31,700 I think that's a good place to stop. 399 00:18:31,700 --> 00:18:33,920 I dread these kinds of lessons. 400 00:18:33,920 --> 00:18:35,620 And I'm sorry that the parents ended up here 401 00:18:35,620 --> 00:18:36,390 on a day like today. 402 00:18:36,390 --> 00:18:39,500 But there's a little bit of this notation and taxonomy 403 00:18:39,500 --> 00:18:40,650 that they have to know. 404 00:18:40,650 --> 00:18:41,795 And so we suffer through it. 405 00:18:41,795 --> 00:18:43,600 And then we get on to the meat. 406 00:18:43,600 --> 00:18:45,520 Now we're ready for some meat. 407 00:18:45,520 --> 00:18:49,050 Now that we can describe crystal structure, we're ready 408 00:18:49,050 --> 00:18:51,270 for physical measurement of crystal structure. 409 00:18:51,270 --> 00:18:55,180 So what I want to start today is the characterization of 410 00:18:55,180 --> 00:18:56,555 crystal structure by x-rays. 411 00:19:01,540 --> 00:19:02,400 How do we measure? 412 00:19:02,400 --> 00:19:05,820 How do we know that gold is fcc. 413 00:19:05,820 --> 00:19:07,070 We use x-rays. 414 00:19:18,700 --> 00:19:22,660 So today what I want to do is start as I always do on new 415 00:19:22,660 --> 00:19:24,470 unit with history lesson. 416 00:19:24,470 --> 00:19:26,720 We'll start with the discovery of x-rays. 417 00:19:26,720 --> 00:19:28,580 And we'll get into the underlying physics. 418 00:19:28,580 --> 00:19:31,620 And the next day we'll look at applications including x-ray 419 00:19:31,620 --> 00:19:32,340 diffraction. 420 00:19:32,340 --> 00:19:35,330 So first of all, what are x-rays? 421 00:19:35,330 --> 00:19:38,642 They're a form of electromagnetic radiation. 422 00:19:43,680 --> 00:19:45,040 And they have the property of that. 423 00:19:45,040 --> 00:19:50,490 They have very short wavelength. 424 00:19:50,490 --> 00:19:51,230 How short? 425 00:19:51,230 --> 00:19:56,820 It's on the order of about angstroms. So strictly 426 00:19:56,820 --> 00:20:04,260 speaking, it goes from about 1/100 to 100 angstroms. So 427 00:20:04,260 --> 00:20:09,480 centered at about 1 angstrom is the center of the x region 428 00:20:09,480 --> 00:20:10,960 of the spectrum. 429 00:20:10,960 --> 00:20:14,270 And because they're a form of electromagnetic radiation, 430 00:20:14,270 --> 00:20:20,000 their energy is given by these equations, hu equals hc over 431 00:20:20,000 --> 00:20:23,540 lambda or hc u bar. 432 00:20:23,540 --> 00:20:26,900 Those equations that you've seen over and over again apply 433 00:20:26,900 --> 00:20:31,390 for the energy of an x-ray, because an x-ray is identical 434 00:20:31,390 --> 00:20:35,120 to a photon of wavelength somewhere down at this level. 435 00:20:35,120 --> 00:20:36,240 Why do we care about this? 436 00:20:36,240 --> 00:20:38,540 Because this is atomic dimensions. 437 00:20:38,540 --> 00:20:41,020 If I want to measure the dimension of the human hair, I 438 00:20:41,020 --> 00:20:42,110 don't use a yard stick. 439 00:20:42,110 --> 00:20:44,980 I use something that is of the human hair dimension. 440 00:20:44,980 --> 00:20:47,580 If we want to get into the characterization of atomic 441 00:20:47,580 --> 00:20:51,330 structure, we need a measurement tool that is on 442 00:20:51,330 --> 00:20:53,120 the order of that blank scale. 443 00:20:53,120 --> 00:20:56,150 And that's why we're going to use x-rays. 444 00:20:56,150 --> 00:21:00,410 Now other property, I said very, very short wavelength. 445 00:21:00,410 --> 00:21:02,650 But because of this inverse relationship between 446 00:21:02,650 --> 00:21:05,320 wavelength and energy, I want to draw attention to these 447 00:21:05,320 --> 00:21:08,770 superbly high value of energy. 448 00:21:08,770 --> 00:21:14,930 So let's plug in the energy for lambda equals 1 angstrom. 449 00:21:14,930 --> 00:21:22,540 When lambda equals 1 angstrom, we end up with 12,400 electron 450 00:21:22,540 --> 00:21:23,920 volts per photon. 451 00:21:28,710 --> 00:21:31,400 Now what's that mean, just to put it in perspective? 452 00:21:31,400 --> 00:21:33,640 Look up here at the table I've shown. 453 00:21:33,640 --> 00:21:38,320 We know the ionization energy, the lone electron in hydrogen 454 00:21:38,320 --> 00:21:41,570 is 13.6 electron volts, which is 14 to 455 00:21:41,570 --> 00:21:43,440 2 significant figures. 456 00:21:43,440 --> 00:21:46,200 And then we go to helium. 457 00:21:46,200 --> 00:21:47,950 You pull these off the periodic table. 458 00:21:47,950 --> 00:21:49,630 This is the first ionization energy. 459 00:21:49,630 --> 00:21:52,210 And they're down around somewhere 460 00:21:52,210 --> 00:21:54,100 about 10 electron volts. 461 00:21:54,100 --> 00:21:54,610 Look at. 462 00:21:54,610 --> 00:21:56,560 This is 12,400. 463 00:21:56,560 --> 00:21:58,740 So let's go down to the 1 electron atom. 464 00:21:58,740 --> 00:22:00,100 So this is helium plus. 465 00:22:00,100 --> 00:22:01,770 This is lithium 2 plus. 466 00:22:01,770 --> 00:22:07,220 And we see a set of numbers here that follow this sequence 467 00:22:07,220 --> 00:22:11,480 1 4 9 16, which is nothing more than the sequence you 468 00:22:11,480 --> 00:22:15,200 would expect for a series of 1 electron atoms. It's K, which 469 00:22:15,200 --> 00:22:20,590 is 13.6 times the square of z/ So z here is 2, z here is 3, z 470 00:22:20,590 --> 00:22:21,790 here is 4, and so on. 471 00:22:21,790 --> 00:22:25,360 But even so, this is the last electron of nitrogen. 472 00:22:25,360 --> 00:22:29,110 The most tightly bound electron of nitrogen, 668 473 00:22:29,110 --> 00:22:29,940 electron volts. 474 00:22:29,940 --> 00:22:31,290 That's a huge amount of energy. 475 00:22:31,290 --> 00:22:35,540 But that pales in comparison to 12,400 electron volts. 476 00:22:35,540 --> 00:22:41,820 So this is clearly ionizing radiation writ large. 477 00:22:41,820 --> 00:22:43,810 What do I mean by ionizing radiation? 478 00:22:43,810 --> 00:22:47,070 It has the capacity to ionize everything. 479 00:22:47,070 --> 00:22:51,560 Every electron will be blown away. 480 00:22:51,560 --> 00:22:54,140 This is called knocking the stuffing out of 481 00:22:54,140 --> 00:22:56,500 the electron structure. 482 00:22:56,500 --> 00:22:59,790 So that's what we're dealing with. 483 00:22:59,790 --> 00:23:03,030 So now let's go to the origin of x-rays. 484 00:23:03,030 --> 00:23:06,410 So how did we discover x-rays? 485 00:23:06,410 --> 00:23:10,080 Well, it was a dark and stormy night, not unlike the weather 486 00:23:10,080 --> 00:23:12,132 today, apropos of the lesson. 487 00:23:12,132 --> 00:23:18,450 It was November 8, 1895. 488 00:23:18,450 --> 00:23:22,600 And it was at the home and laboratory of a professor. 489 00:23:22,600 --> 00:23:25,800 Of course it's a professor, Professor Wilhelm Roentgen. 490 00:23:32,970 --> 00:23:38,780 And he was a professor of physics at the University of 491 00:23:38,780 --> 00:23:50,470 Wurzburg in Bavaria, now part of Germany. 492 00:23:50,470 --> 00:23:53,790 And he was doing research, as many people were in the 1890s, 493 00:23:53,790 --> 00:23:57,880 on the properties of gas discharge tubes. 494 00:23:57,880 --> 00:24:01,350 He was studying gas discharge tubes. 495 00:24:01,350 --> 00:24:05,130 And he had a special interest in gas discharge tubes. 496 00:24:05,130 --> 00:24:05,910 Remember Lorentz? 497 00:24:05,910 --> 00:24:07,820 He like to put the gas discharge tubes 498 00:24:07,820 --> 00:24:08,870 in a magnetic field. 499 00:24:08,870 --> 00:24:11,400 Stark liked the put them in an electric field. 500 00:24:11,400 --> 00:24:13,990 And what was Roentgen's pet project? 501 00:24:13,990 --> 00:24:16,390 Roentgen loved high voltage. 502 00:24:16,390 --> 00:24:18,510 He loved high voltage an low pressure. 503 00:24:18,510 --> 00:24:29,240 He was focused high voltage, low pressure, near vacuum. 504 00:24:29,240 --> 00:24:35,410 And so let's have a drawing of what he used. 505 00:24:35,410 --> 00:24:41,040 And here's an image of the museum that is literally in 506 00:24:41,040 --> 00:24:43,170 the house that was occupied by him. 507 00:24:43,170 --> 00:24:45,990 So the apparatus is sitting right there on the table. 508 00:24:45,990 --> 00:24:47,710 And here's the heart of the apparatus. 509 00:24:47,710 --> 00:24:50,040 I'm going to go to a fresh board because I need a little 510 00:24:50,040 --> 00:24:51,480 extra room here. 511 00:24:51,480 --> 00:24:54,230 So we know what the gas discharge tube looks like. 512 00:24:54,230 --> 00:24:57,590 It's a glass tube, sealed. 513 00:24:57,590 --> 00:25:02,990 And we've got feedthroughs for electrodes at both ends. 514 00:25:02,990 --> 00:25:06,280 And this goes down to a power supply. 515 00:25:06,280 --> 00:25:09,460 And the power supply that he used was 516 00:25:09,460 --> 00:25:12,540 batteries of chromic acid. 517 00:25:12,540 --> 00:25:14,140 And they were open beakers. 518 00:25:14,140 --> 00:25:16,310 And they were down in the basement two floors below. 519 00:25:16,310 --> 00:25:18,270 And he had wires going from the basement up 520 00:25:18,270 --> 00:25:19,550 to the second floor. 521 00:25:19,550 --> 00:25:21,810 And he was able to generate about 20 volts. 522 00:25:21,810 --> 00:25:23,300 So he had a number of these in series. 523 00:25:23,300 --> 00:25:24,790 Because this is roughly a 1-volt system. 524 00:25:24,790 --> 00:25:27,130 So round numbers, you got about two dozen of these 525 00:25:27,130 --> 00:25:28,305 things in series. 526 00:25:28,305 --> 00:25:32,210 And I'm going to write here, in the cellar. 527 00:25:32,210 --> 00:25:33,560 Now how did he get the high voltage? 528 00:25:33,560 --> 00:25:37,070 He put in here something that we wouldn't recognize today as 529 00:25:37,070 --> 00:25:37,680 an inductor. 530 00:25:37,680 --> 00:25:40,960 He called it a choke coil. 531 00:25:40,960 --> 00:25:44,630 And what the choke coil did, is it would charge up until it 532 00:25:44,630 --> 00:25:47,840 got to 35,000 volts. 533 00:25:47,840 --> 00:25:51,620 When it got to 35,000 volts, it would discharge and send a 534 00:25:51,620 --> 00:25:55,480 current at 35,000 volts to the cathode here. 535 00:25:58,410 --> 00:26:04,540 And with 35,000 volts, the cathode would send electrons 536 00:26:04,540 --> 00:26:08,230 boiling off the cathode, heading towards the anode with 537 00:26:08,230 --> 00:26:12,490 the kinetic energy associated with 35,000 volts. 538 00:26:12,490 --> 00:26:14,800 And this discharged at about eight times a second. 539 00:26:14,800 --> 00:26:16,640 So I'm going to write 8 hertz here. 540 00:26:16,640 --> 00:26:19,960 So eight times a second this thing, bam, bam, bam, bam. 541 00:26:19,960 --> 00:26:22,650 And the electrons go firing off here. 542 00:26:22,650 --> 00:26:25,480 And this to make sure he had really low pressure, he had 543 00:26:25,480 --> 00:26:26,960 the cell open actually. 544 00:26:26,960 --> 00:26:29,060 And this went to a vacuum pump. 545 00:26:32,820 --> 00:26:36,610 He had almost no gas molecules in here. 546 00:26:36,610 --> 00:26:39,700 Now, the way he did the experiment is, he'd set this 547 00:26:39,700 --> 00:26:43,320 thing up, started it going, and this was after dinner. 548 00:26:43,320 --> 00:26:46,690 So on a Friday night after dinner, he was upstairs. 549 00:26:46,690 --> 00:26:48,925 And he wanted to measure emissions here. 550 00:26:48,925 --> 00:26:52,490 And so what he had, you either get graduate students to sit 551 00:26:52,490 --> 00:26:57,300 there and you exploit their labor, or what you do is you 552 00:26:57,300 --> 00:27:00,340 put up a detector here which was a screen. 553 00:27:00,340 --> 00:27:05,680 So this is either a sheet of paper or a sheet of cloth. 554 00:27:05,680 --> 00:27:09,460 So we call this a screen. 555 00:27:09,460 --> 00:27:12,480 And so you're going to look here. 556 00:27:12,480 --> 00:27:15,070 All right you're looking at this, seeing what's coming out 557 00:27:15,070 --> 00:27:17,160 of this gas discharge tube. 558 00:27:17,160 --> 00:27:19,845 And it was a screen up paper or fabric. 559 00:27:23,340 --> 00:27:26,220 And it had been painted with a chemical that would glow if it 560 00:27:26,220 --> 00:27:31,420 were struck by a particle, or by a photon of a given energy. 561 00:27:31,420 --> 00:27:35,800 And they used in this case, coated with the chemical 562 00:27:35,800 --> 00:27:42,840 barium platinocyanide, so cyanide four times. 563 00:27:42,840 --> 00:27:45,170 So you make an aqueous paste of this stuff. 564 00:27:45,170 --> 00:27:46,910 And you gob it on to the screen. 565 00:27:46,910 --> 00:27:50,790 And when the screen is hit by something, it sparks. 566 00:27:50,790 --> 00:27:52,750 And the latin word for spark is scintilla. 567 00:27:52,750 --> 00:27:54,470 Have you ever heard of someone being described as a 568 00:27:54,470 --> 00:27:56,030 scintillating conversationalist? 569 00:27:56,030 --> 00:27:59,040 It means they are a sparkling conversationalist. So this is 570 00:27:59,040 --> 00:28:03,060 called a scintillation screen, a scintillation screen. 571 00:28:03,060 --> 00:28:04,440 And so presumably, every time there's an 572 00:28:04,440 --> 00:28:06,750 event, the screen glows. 573 00:28:06,750 --> 00:28:11,670 And so Roentgen starts the experiment. 574 00:28:11,670 --> 00:28:14,400 And it's raining outside. 575 00:28:14,400 --> 00:28:14,950 There's thunder. 576 00:28:14,950 --> 00:28:15,570 There's lightning. 577 00:28:15,570 --> 00:28:17,670 There's a street light as you can see right there. 578 00:28:17,670 --> 00:28:18,870 There's windows. 579 00:28:18,870 --> 00:28:21,150 And the thing is glowing. 580 00:28:21,150 --> 00:28:24,330 And he really can't detect what's going on here. 581 00:28:24,330 --> 00:28:30,090 So he decides to cover the tube. 582 00:28:30,090 --> 00:28:36,140 So he puts a wooden box around the gas discharge tube. 583 00:28:36,140 --> 00:28:40,050 So now the gas discharge tube is enclosed in a box. 584 00:28:40,050 --> 00:28:43,170 And he continues the experiment. 585 00:28:43,170 --> 00:28:48,844 And what he sees is glowing on this scintillation screen. 586 00:28:48,844 --> 00:28:53,780 The scintillation screen is glowing even though the gas 587 00:28:53,780 --> 00:28:55,090 discharge tube is in a box. 588 00:28:55,090 --> 00:28:56,930 There was another observation he made. 589 00:28:56,930 --> 00:28:59,500 The student earlier in the day, who had painted the 590 00:28:59,500 --> 00:29:02,250 screen with the barium platinocyanide. 591 00:29:02,250 --> 00:29:05,060 I guess he was practicing his calligraphy. 592 00:29:05,060 --> 00:29:08,150 And he left a paper towel on the edge of the bench. 593 00:29:08,150 --> 00:29:10,855 And he painted the letter A on the paper towel. 594 00:29:10,855 --> 00:29:14,310 And the paper towel was glowing with the letter A. 595 00:29:14,310 --> 00:29:17,170 And this thing is enclosed in a box. 596 00:29:17,170 --> 00:29:20,930 So he's saying what's going on here. 597 00:29:20,930 --> 00:29:24,600 So he decides that there's some kind of an interaction 598 00:29:24,600 --> 00:29:27,560 between the screen and something going on in here. 599 00:29:27,560 --> 00:29:31,030 So the first thing he does is he says, well maybe it's 600 00:29:31,030 --> 00:29:32,510 electromagnetic. 601 00:29:32,510 --> 00:29:34,160 Maybe it's charged particles. 602 00:29:34,160 --> 00:29:35,610 So he takes a magnet. 603 00:29:35,610 --> 00:29:37,300 And he moves a magnet around. 604 00:29:37,300 --> 00:29:39,040 And nothing changes. 605 00:29:39,040 --> 00:29:43,050 He kills the power to the gas discharge tube. 606 00:29:43,050 --> 00:29:44,100 Everything stops. 607 00:29:44,100 --> 00:29:48,570 So it's definitely inspired by 35,000 volts of energy going 608 00:29:48,570 --> 00:29:49,930 into the tube. 609 00:29:49,930 --> 00:29:53,405 So then he says, OK I'll take a piece of black paper. 610 00:29:53,405 --> 00:29:55,910 And he puts the black paper in between. 611 00:29:55,910 --> 00:29:58,210 And the screen continues to glow. 612 00:29:58,210 --> 00:30:00,110 So then he takes a book. 613 00:30:00,110 --> 00:30:01,580 And he puts the book in front. 614 00:30:01,580 --> 00:30:03,420 And he sees the shadow of the book. 615 00:30:03,420 --> 00:30:04,950 And he's standing here like this. 616 00:30:04,950 --> 00:30:06,750 He sees the shadow of the book. 617 00:30:06,750 --> 00:30:08,920 And he can see the shadow of the bones of his hand. 618 00:30:15,390 --> 00:30:20,150 So he says, you know I don't think it's particles. 619 00:30:20,150 --> 00:30:21,770 I think it's radiation. 620 00:30:21,770 --> 00:30:23,230 I think it's radiation. 621 00:30:23,230 --> 00:30:25,920 And maybe it's something like that radiation that Hertz has 622 00:30:25,920 --> 00:30:27,140 been talking about. 623 00:30:27,140 --> 00:30:28,690 It's some kind of radiation. 624 00:30:28,690 --> 00:30:30,650 But I don't know exactly what it is. 625 00:30:30,650 --> 00:30:31,710 It's mysterious. 626 00:30:31,710 --> 00:30:33,830 And x is the letter of mystery. 627 00:30:33,830 --> 00:30:35,080 I'm going to call it x-radiation. 628 00:30:38,750 --> 00:30:42,070 So he's discovered this mysterious form of radiation. 629 00:30:42,070 --> 00:30:43,220 Does he rush to publish? 630 00:30:43,220 --> 00:30:44,230 No. 631 00:30:44,230 --> 00:30:46,830 He's not going to risk his scientific career by 632 00:30:46,830 --> 00:30:49,420 announcing that he's discovered a form of radiation 633 00:30:49,420 --> 00:30:52,220 that can see inside the human body. 634 00:30:52,220 --> 00:30:54,800 That would be professional suicide. 635 00:30:54,800 --> 00:30:58,030 So he continues to repeat the experiments through November 636 00:30:58,030 --> 00:31:00,350 and December of 1895. 637 00:31:00,350 --> 00:31:03,460 And in January of 1896, he finally publishers. 638 00:31:03,460 --> 00:31:07,960 And it takes the world by storm. 639 00:31:07,960 --> 00:31:10,220 By the way, how did he record this stuff? 640 00:31:10,220 --> 00:31:11,990 He used photographic plates. 641 00:31:11,990 --> 00:31:15,330 And he stored the photographic plates in his lab in a wooden 642 00:31:15,330 --> 00:31:16,560 file cabinet. 643 00:31:16,560 --> 00:31:19,510 And so many of the plates were fogged even before he got them 644 00:31:19,510 --> 00:31:20,390 to the experiment. 645 00:31:20,390 --> 00:31:21,780 Because of the x-ray, they were going 646 00:31:21,780 --> 00:31:23,040 everywhere in the lab. 647 00:31:23,040 --> 00:31:26,850 And he was working there the whole time. 648 00:31:26,850 --> 00:31:29,700 So what happens? 649 00:31:29,700 --> 00:31:31,630 What's the world's reaction? 650 00:31:31,630 --> 00:31:36,730 January 16, 1896, New York Times reports radiation that 651 00:31:36,730 --> 00:31:41,800 can see through matter and peer inside the human body. 652 00:31:41,800 --> 00:31:43,300 Peer inside the human body, you say. 653 00:31:43,300 --> 00:31:44,630 Well, why is that? 654 00:31:44,630 --> 00:31:46,290 What's the big deal? 655 00:31:46,290 --> 00:31:50,740 Well, in London, immediately there was a market response. 656 00:31:50,740 --> 00:31:54,620 A manufacturer claimed to be a purveyor of x-ray proof lady's 657 00:31:54,620 --> 00:31:56,400 undergarments. 658 00:31:56,400 --> 00:31:58,020 I mean if you can see inside the human body, 659 00:31:58,020 --> 00:31:59,820 it's Victorian England. 660 00:31:59,820 --> 00:32:02,130 How modest can you be? 661 00:32:02,130 --> 00:32:04,220 This is a calamity. 662 00:32:04,220 --> 00:32:06,360 In France, of course, they don't care about such things. 663 00:32:06,360 --> 00:32:08,920 So they had a different response. 664 00:32:08,920 --> 00:32:11,000 Remember this is where Daguerre invented halide 665 00:32:11,000 --> 00:32:11,610 photography. 666 00:32:11,610 --> 00:32:13,310 So there it's very deep. 667 00:32:13,310 --> 00:32:14,620 It's very existential. 668 00:32:14,620 --> 00:32:18,740 Somebody claimed that with x-rays he could irradiate and 669 00:32:18,740 --> 00:32:21,240 get a picture of the human soul. 670 00:32:21,240 --> 00:32:23,230 How French. 671 00:32:23,230 --> 00:32:25,340 But I'm sorry to say it, the wackiest 672 00:32:25,340 --> 00:32:27,000 comes from guess where? 673 00:32:27,000 --> 00:32:28,300 The United States. 674 00:32:28,300 --> 00:32:32,110 No lesser an institution than the New York City College of 675 00:32:32,110 --> 00:32:34,070 Physicians and Surgeons. 676 00:32:34,070 --> 00:32:38,660 They proposed to use x-rays to project drawings from text 677 00:32:38,660 --> 00:32:43,680 books of anatomy onto the brains of students thereby 678 00:32:43,680 --> 00:32:46,105 creating, and I quote, an enduring impression. 679 00:32:48,820 --> 00:32:51,370 In Iowa, we plumb new depths. 680 00:32:51,370 --> 00:32:53,620 There was a group out there claiming that they could turn 681 00:32:53,620 --> 00:32:56,030 copper pennies into gold. 682 00:32:56,030 --> 00:32:57,800 So this was the response. 683 00:32:57,800 --> 00:33:03,480 But the thing that makes it so fantastic is we take it for 684 00:33:03,480 --> 00:33:08,120 granted that if I want to exercise power and exert a 685 00:33:08,120 --> 00:33:11,910 force on that can, I don't necessarily have to make 686 00:33:11,910 --> 00:33:13,900 physical contact with it. 687 00:33:13,900 --> 00:33:17,690 We accept this as given that you an either have direct 688 00:33:17,690 --> 00:33:21,390 mechanical contact, or indirect contact, magnetics, 689 00:33:21,390 --> 00:33:22,280 what have you. 690 00:33:22,280 --> 00:33:25,280 But in 1896, this wasn't given. 691 00:33:25,280 --> 00:33:29,890 So the notion that I could exert a force on something 692 00:33:29,890 --> 00:33:32,250 from a distance was very fresh. 693 00:33:32,250 --> 00:33:33,600 It wasn't so easy. 694 00:33:33,600 --> 00:33:38,350 But there were benefits of the x-radiation already 695 00:33:38,350 --> 00:33:41,030 in middle of 1896. 696 00:33:41,030 --> 00:33:43,860 There was a seamstress who had a broken needle in an 697 00:33:43,860 --> 00:33:47,510 industrial accident in Scotland buried into her hand. 698 00:33:47,510 --> 00:33:48,270 This is trivial. 699 00:33:48,270 --> 00:33:54,090 Look, all you need is low pressure in a gas tube, and 700 00:33:54,090 --> 00:33:56,340 you can set this up in high school. 701 00:33:56,340 --> 00:33:57,360 It's nothing. 702 00:33:57,360 --> 00:33:59,430 People had this set up in dentist offices. 703 00:33:59,430 --> 00:34:00,770 It's nothing. 704 00:34:00,770 --> 00:34:03,710 So this surgeon was able to find where the needle was, and 705 00:34:03,710 --> 00:34:06,880 then use precision to go in and take the needle out of the 706 00:34:06,880 --> 00:34:09,350 injured person's hand. 707 00:34:09,350 --> 00:34:12,040 In eighteen 1899 they were already using radiation in 708 00:34:12,040 --> 00:34:13,510 treatment of cancer. 709 00:34:13,510 --> 00:34:15,420 So what is the relevant physics? 710 00:34:15,420 --> 00:34:17,110 what's the relevant physics here? 711 00:34:17,110 --> 00:34:18,890 Let's look at the relevant physics. 712 00:34:18,890 --> 00:34:25,280 Well, when we're talking about 35,000 volts, and we're 713 00:34:25,280 --> 00:34:28,720 talking about energies in the vicinity of tens of thousands 714 00:34:28,720 --> 00:34:32,510 of electron volts, you know that this can't come from 715 00:34:32,510 --> 00:34:37,140 emission from an excited electron in a gas molecule. 716 00:34:37,140 --> 00:34:40,470 The gas binding energies are way lower than that. 717 00:34:40,470 --> 00:34:43,000 This must come from the solid. 718 00:34:43,000 --> 00:34:45,180 The electron leaves the cathode, and it 719 00:34:45,180 --> 00:34:46,750 crashes into the anode. 720 00:34:46,750 --> 00:34:48,190 Here's the smoking gun. 721 00:34:48,190 --> 00:34:51,370 There's something going on here when the electron crashes 722 00:34:51,370 --> 00:34:54,190 into the anode and then gives rise to the radiation. 723 00:34:54,190 --> 00:34:56,660 So let's look inside the anode. 724 00:35:01,060 --> 00:35:04,680 So what's the energy level diagram? 725 00:35:04,680 --> 00:35:07,070 Let's say the anode is made of copper. 726 00:35:07,070 --> 00:35:09,630 So what's the energy level diagram look like? 727 00:35:09,630 --> 00:35:12,940 So we know up here we're going to have energy is 0. 728 00:35:12,940 --> 00:35:17,730 And the energy quantum state is infinity. 729 00:35:17,730 --> 00:35:19,650 Down here is the ground state. 730 00:35:19,650 --> 00:35:22,310 And the energy is the ground state energy. 731 00:35:22,310 --> 00:35:25,040 And we know this is up in the tens of 732 00:35:25,040 --> 00:35:26,780 thousands of electron volts. 733 00:35:26,780 --> 00:35:31,520 And then up here there's an E2 for state 2. 734 00:35:31,520 --> 00:35:35,242 And up here is an E3, energy 3. 735 00:35:35,242 --> 00:35:38,970 Then maybe an E4 for energy 4, et cetera. 736 00:35:38,970 --> 00:35:40,760 And I'm going to write not to scale. 737 00:35:40,760 --> 00:35:45,110 This is just to give you a sense. 738 00:35:45,110 --> 00:35:49,610 And so the ballistic electron with, in this case, 35,000 739 00:35:49,610 --> 00:35:53,110 volts of energy, comes crashing in to the anode. 740 00:35:53,110 --> 00:35:54,640 And this is one of these mixed metaphors. 741 00:35:54,640 --> 00:35:58,030 So this is a Cartesian drawing of an electron. 742 00:35:58,030 --> 00:35:58,350 All right? 743 00:35:58,350 --> 00:36:00,460 This is the incident electron. 744 00:36:00,460 --> 00:36:04,560 And its energy is given by the charge on the electron, which 745 00:36:04,560 --> 00:36:07,960 is E, and the plate voltage, which is 35,000. 746 00:36:07,960 --> 00:36:10,470 So it's got 35,000 electron volts, which 747 00:36:10,470 --> 00:36:12,410 turns into 1/2 mv squared. 748 00:36:12,410 --> 00:36:14,270 It goes crashing into this thing. 749 00:36:14,270 --> 00:36:17,730 And it's got enough energy it can kick out top level 750 00:36:17,730 --> 00:36:20,460 electrons, mid-level electrons, and in the extreme, 751 00:36:20,460 --> 00:36:26,570 it an eject ground state electrons in 1s. 752 00:36:26,570 --> 00:36:28,670 By the way, the spectroscopists, they don't 753 00:36:28,670 --> 00:36:29,220 like numbers. 754 00:36:29,220 --> 00:36:30,820 Remember, this is K. 755 00:36:30,820 --> 00:36:32,150 This is L. 756 00:36:32,150 --> 00:36:33,500 This is M. 757 00:36:33,500 --> 00:36:34,220 This is N. 758 00:36:34,220 --> 00:36:37,650 So we can eject K shell electrons. 759 00:36:37,650 --> 00:36:40,630 What happens if we create a vacancy down here? 760 00:36:40,630 --> 00:36:40,870 all? 761 00:36:40,870 --> 00:36:42,970 Of these electrons above are unstable. 762 00:36:42,970 --> 00:36:44,970 If its copper, there's 29 of them. 763 00:36:44,970 --> 00:36:47,160 Now there's 28 with a vacancy. 764 00:36:47,160 --> 00:36:48,960 And they fall down. 765 00:36:48,960 --> 00:36:51,760 And when they fall down from N equals 2 to N equals 1, 766 00:36:51,760 --> 00:36:53,510 there's a photon emitted. 767 00:36:53,510 --> 00:36:57,810 And that photon emission is in the x region of the spectrum. 768 00:36:57,810 --> 00:37:00,330 But we don't just get one wavelength. 769 00:37:00,330 --> 00:37:02,400 We get a plurality of wavelengths. 770 00:37:02,400 --> 00:37:06,260 n equals 2 to n equals 1, we get a photon. 771 00:37:06,260 --> 00:37:09,260 There's a possibility to go for n equals 3 to n equals 1. 772 00:37:09,260 --> 00:37:11,840 We'll get a photon of even higher energy or a lower 773 00:37:11,840 --> 00:37:12,810 wavelength. 774 00:37:12,810 --> 00:37:15,260 Well, heck, if you've got enough energy to kick out an 775 00:37:15,260 --> 00:37:17,830 electron from n equals 1, you've certainly got enough 776 00:37:17,830 --> 00:37:20,210 energy to kick out an electron from n equals 2. 777 00:37:20,210 --> 00:37:24,010 So you can get a cascade from 3 to 2, which gives us a 778 00:37:24,010 --> 00:37:27,990 photon, or from 4 to 2, which gives us a photon. 779 00:37:27,990 --> 00:37:30,775 Can you see that you're going to get an entire set of lines? 780 00:37:33,830 --> 00:37:35,610 We're going to label them because we don't 781 00:37:35,610 --> 00:37:36,880 have a single line. 782 00:37:36,880 --> 00:37:38,190 So what do we label them? 783 00:37:38,190 --> 00:37:42,540 We label them on the basis of the destination shell and how 784 00:37:42,540 --> 00:37:43,440 far they traveled. 785 00:37:43,440 --> 00:37:47,010 So this line here is known as a K alpha line. 786 00:37:47,010 --> 00:37:48,650 Why is it a K? 787 00:37:48,650 --> 00:37:52,320 Because that's the nf. 788 00:37:52,320 --> 00:37:55,440 That's the n number of the final state. 789 00:37:55,440 --> 00:37:56,890 And why is it alpha? 790 00:37:56,890 --> 00:37:59,540 Because the delta n equals 1. 791 00:37:59,540 --> 00:38:02,530 It came from 1 shell away. 792 00:38:02,530 --> 00:38:03,640 What's this one? 793 00:38:03,640 --> 00:38:05,430 It's gotta be a K line, because we 794 00:38:05,430 --> 00:38:06,810 ended at n equals 1. 795 00:38:06,810 --> 00:38:08,500 But the delta is 2. 796 00:38:08,500 --> 00:38:10,690 It went from n equals 3 to n equals 1. 797 00:38:10,690 --> 00:38:13,030 So this is called K beta. 798 00:38:13,030 --> 00:38:15,400 So there's a K beta line and a K alpha line. 799 00:38:15,400 --> 00:38:20,330 This ends at n equals 2, which the spectroscopists call L. 800 00:38:20,330 --> 00:38:22,560 So we call this L. 801 00:38:22,560 --> 00:38:24,190 Delta is 1 L alpha. 802 00:38:24,190 --> 00:38:26,520 This is L, but delta is 2. 803 00:38:26,520 --> 00:38:28,730 So this is L beta. 804 00:38:28,730 --> 00:38:32,830 And what I can do, is I can plot all of this on a curve 805 00:38:32,830 --> 00:38:36,980 showing the spectrum of this particular element. 806 00:38:36,980 --> 00:38:38,900 And what do I expect to see? 807 00:38:38,900 --> 00:38:45,850 I expect to see a spectrum that plots intensity versus 808 00:38:45,850 --> 00:38:47,120 some energy coordinate. 809 00:38:47,120 --> 00:38:50,050 It could be wavelength in this direction, which means that 810 00:38:50,050 --> 00:38:52,140 energy increases in that direction. 811 00:38:52,140 --> 00:38:53,830 And which has the highest energy? 812 00:38:53,830 --> 00:38:56,890 The highest energy up here is K beta, n equals 813 00:38:56,890 --> 00:38:58,580 3 to n equals 1. 814 00:38:58,580 --> 00:39:00,520 So there's K beta. 815 00:39:00,520 --> 00:39:05,370 And then close to it is K alpha. 816 00:39:05,370 --> 00:39:07,580 And why do I put the K alpha line higher 817 00:39:07,580 --> 00:39:08,610 than the K beta line? 818 00:39:08,610 --> 00:39:11,390 I don't know what the relative amounts should be. 819 00:39:11,390 --> 00:39:13,280 But I suspect that if there's a vacancy, it's 820 00:39:13,280 --> 00:39:14,760 like musical chairs. 821 00:39:14,760 --> 00:39:18,480 If there's a vacancy in n equals 1, and an electron only 822 00:39:18,480 --> 00:39:22,790 has to go from n equals 2 versus n equals 3, the chances 823 00:39:22,790 --> 00:39:27,150 are the journey from n equals 2 to N equals 1 is easier, and 824 00:39:27,150 --> 00:39:29,750 therefore more frequent than the journey from n equals 3, 825 00:39:29,750 --> 00:39:33,600 even though n equals 3 to 1 is greater energy. 826 00:39:33,600 --> 00:39:35,170 But 2 to 1 is more likely. 827 00:39:35,170 --> 00:39:37,990 And intensity reflects frequency. 828 00:39:37,990 --> 00:39:41,540 The wavelength reflects the energy. 829 00:39:41,540 --> 00:39:45,500 And then over here is L alpha L beta. 830 00:39:48,480 --> 00:39:50,560 Now there's one more piece here. 831 00:39:53,340 --> 00:39:57,690 The precise value here is determined by the identity of 832 00:39:57,690 --> 00:40:00,110 the element in the anode. 833 00:40:00,110 --> 00:40:01,430 If it's copper-- 834 00:40:01,430 --> 00:40:03,080 and I had to do this as a junior at the 835 00:40:03,080 --> 00:40:04,030 University of Toronto. 836 00:40:04,030 --> 00:40:07,790 I spent a whole year doing x-ray crystallography. 837 00:40:07,790 --> 00:40:13,700 And I will know on my death bed the wavelength of copper K 838 00:40:13,700 --> 00:40:19,730 alpha radiation is to five significant figures, 1.5418 839 00:40:19,730 --> 00:40:21,330 angstroms. 840 00:40:21,330 --> 00:40:24,790 Now if someone had fallen asleep in this lecture and 841 00:40:24,790 --> 00:40:29,170 open their eyes right now, and looked at the wavelength of 842 00:40:29,170 --> 00:40:35,450 this line as 1.5418 angstroms. And I erase the letters Cu. 843 00:40:35,450 --> 00:40:38,970 You take one look at that, and you say copper. 844 00:40:38,970 --> 00:40:43,710 Because only copper has a K alpha wavelength of 1.5418, 845 00:40:43,710 --> 00:40:47,070 which means I can use x-ray analysis to determine the 846 00:40:47,070 --> 00:40:50,220 identity of a unknown specimen. 847 00:40:50,220 --> 00:40:51,960 And furthermore it's additive. 848 00:40:51,960 --> 00:40:56,490 So if I had a brass, which is copper and zinc, the zinc K 849 00:40:56,490 --> 00:40:58,500 alpha line is over here. 850 00:40:58,500 --> 00:41:00,790 And I will have both lines. 851 00:41:00,790 --> 00:41:05,590 And the relative intensities of the lines are related to 852 00:41:05,590 --> 00:41:09,490 the relative concentrations of the copper in zinc. So now I 853 00:41:09,490 --> 00:41:13,280 have a tool for chemical analysis. 854 00:41:13,280 --> 00:41:17,440 All of this from going upstairs after dinner and 855 00:41:17,440 --> 00:41:20,000 horsing around with the gas discharge tube. 856 00:41:20,000 --> 00:41:22,520 OK, so we're going to end the formal lesson here. 857 00:41:22,520 --> 00:41:23,710 But we have a few more minutes. 858 00:41:23,710 --> 00:41:27,000 So everybody is instructed to not make a lot of noise and 859 00:41:27,000 --> 00:41:28,510 just sit quietly. 860 00:41:28,510 --> 00:41:29,440 So let's take a look. 861 00:41:29,440 --> 00:41:32,370 This is an image. 862 00:41:32,370 --> 00:41:35,520 This is an image of Bertha. 863 00:41:35,520 --> 00:41:38,750 This is Roentgen's wife. 864 00:41:38,750 --> 00:41:39,670 This is her hand. 865 00:41:39,670 --> 00:41:42,070 He invited her into the lab. 866 00:41:42,070 --> 00:41:48,760 And she stood for a full 15 minutes in front of this tube. 867 00:41:48,760 --> 00:41:53,140 And in that 15 minutes, got a lifetime's worth of radiation. 868 00:41:53,140 --> 00:41:55,980 But what we're looking at here, and what I'm going to 869 00:41:55,980 --> 00:41:59,440 point out to you in the last several minutes here, Roentgen 870 00:41:59,440 --> 00:42:03,190 was a prissy physicist, a really prissy guy. 871 00:42:03,190 --> 00:42:06,930 And he was German, which meant that the German academics had 872 00:42:06,930 --> 00:42:09,320 no contact with industry whatsoever. 873 00:42:09,320 --> 00:42:14,220 On the night of November 8, 1895, he invented three modern 874 00:42:14,220 --> 00:42:16,100 technologies. 875 00:42:16,100 --> 00:42:19,050 This is Bertha's hand. 876 00:42:19,050 --> 00:42:22,320 It represents the birth of medical radiography. 877 00:42:22,320 --> 00:42:25,580 Is there anybody in this auditorium who has never had 878 00:42:25,580 --> 00:42:30,180 an x-ray, a dental or body x-ray? 879 00:42:30,180 --> 00:42:31,620 It's very rare. 880 00:42:31,620 --> 00:42:33,140 We see them all the time. 881 00:42:33,140 --> 00:42:34,730 We use them all the time. 882 00:42:34,730 --> 00:42:39,610 This morning I had one taken about 9:10, right here. 883 00:42:39,610 --> 00:42:42,400 And I'm OK. 884 00:42:42,400 --> 00:42:45,220 So that's radiography, medical radiography. 885 00:42:45,220 --> 00:42:49,210 Roentgen had a balance in his laboratory. 886 00:42:49,210 --> 00:42:51,675 The justice, and she's got the torsion balance. 887 00:42:51,675 --> 00:42:55,280 So you put the unknown on one side, and then you put weights 888 00:42:55,280 --> 00:42:56,150 that are calibrated. 889 00:42:56,150 --> 00:42:57,480 These are made of brass. 890 00:42:57,480 --> 00:42:59,000 And they're in a wooden box. 891 00:42:59,000 --> 00:43:01,740 And so Roentgen has already covered the tube 892 00:43:01,740 --> 00:43:02,840 with a wooden box. 893 00:43:02,840 --> 00:43:05,920 And so he took the emission from this, and he radiating 894 00:43:05,920 --> 00:43:07,440 his box of weights. 895 00:43:07,440 --> 00:43:08,520 And what he see? 896 00:43:08,520 --> 00:43:11,510 He saw dark regions where the weights were. 897 00:43:11,510 --> 00:43:14,780 Because metals have a different electron density, 898 00:43:14,780 --> 00:43:17,430 because they've got a greater atom density than wood. 899 00:43:17,430 --> 00:43:19,060 Wood is a more open structure. 900 00:43:19,060 --> 00:43:22,280 And so by contrast, he could see inside the box. 901 00:43:22,280 --> 00:43:24,305 This is the basis for airport security. 902 00:43:27,770 --> 00:43:30,640 Roentgen had a gun. 903 00:43:30,640 --> 00:43:32,650 He was not holding up convenience stores. 904 00:43:32,650 --> 00:43:33,730 He was a hunter. 905 00:43:33,730 --> 00:43:35,760 He went into the woods. 906 00:43:35,760 --> 00:43:37,460 And he x-rayed the gun. 907 00:43:37,460 --> 00:43:38,990 Now why did he x-ray the gun? 908 00:43:38,990 --> 00:43:41,880 Now the gun is made of steel. 909 00:43:41,880 --> 00:43:45,100 But deep inside the steel, there could be a flaw. 910 00:43:45,100 --> 00:43:46,220 There could be a crack. 911 00:43:46,220 --> 00:43:47,830 There could be a blowhole. 912 00:43:47,830 --> 00:43:49,840 The surface of the steel looks beautiful. 913 00:43:49,840 --> 00:43:51,960 But inside is a crack. 914 00:43:51,960 --> 00:43:55,370 And that crack could lead to failure under pressure. 915 00:43:55,370 --> 00:43:56,655 So Roentgen irradiates. 916 00:43:56,655 --> 00:43:59,440 And we already know from this that different electron 917 00:43:59,440 --> 00:44:02,340 densities give different shading, which means if there 918 00:44:02,340 --> 00:44:04,730 were a crack right here, you might see it in the 919 00:44:04,730 --> 00:44:05,700 radiograph. 920 00:44:05,700 --> 00:44:09,450 And this we use for certification of pressure 921 00:44:09,450 --> 00:44:10,770 vessels today. 922 00:44:10,770 --> 00:44:13,650 Certain pressure vessels that have to be welded, have a 923 00:44:13,650 --> 00:44:17,810 specification that requires that every inch of the weld be 924 00:44:17,810 --> 00:44:21,860 inspected by radiation, to be certain that there are no 925 00:44:21,860 --> 00:44:24,530 cracks deep inside the weld that under high pressure could 926 00:44:24,530 --> 00:44:29,510 open up, have an explosion, and cause injury, or in the 927 00:44:29,510 --> 00:44:32,070 worst case, death. 928 00:44:32,070 --> 00:44:34,700 So what's the outcome of it all? 929 00:44:34,700 --> 00:44:37,820 In 1901 when the Nobel Prizes were offered for the first 930 00:44:37,820 --> 00:44:40,970 time, Roentgen by unanimous vote of the selection 931 00:44:40,970 --> 00:44:44,550 committee was the first recipient of the Nobel Prize 932 00:44:44,550 --> 00:44:45,510 in Physics. 933 00:44:45,510 --> 00:44:49,460 So on that occasion, he was invited to come from Wurzburg 934 00:44:49,460 --> 00:44:51,660 and to deliver a lecture in Stockholm. 935 00:44:51,660 --> 00:44:55,060 I've been to the place, it's a spectacular hall, gilded, 936 00:44:55,060 --> 00:44:57,980 beautiful champagne reception, elegant dinner. 937 00:44:57,980 --> 00:45:00,090 And he gives a lecture. 938 00:45:00,090 --> 00:45:01,310 And what's his lecture on? 939 00:45:01,310 --> 00:45:03,100 The discovery of x-rays. 940 00:45:03,100 --> 00:45:05,460 He received a huge amount of money at the 941 00:45:05,460 --> 00:45:07,460 time in prize money. 942 00:45:07,460 --> 00:45:10,610 And he returned to Wurzburg What did he do 943 00:45:10,610 --> 00:45:11,940 with the prize money? 944 00:45:11,940 --> 00:45:12,130 he? 945 00:45:12,130 --> 00:45:16,020 Donated it to the University to be used for scholarships 946 00:45:16,020 --> 00:45:18,490 for students studying physics. 947 00:45:18,490 --> 00:45:21,100 And to this day, students who study physics at the 948 00:45:21,100 --> 00:45:24,120 University of Wurzburg are beneficiaries of the 949 00:45:24,120 --> 00:45:28,260 generosity of the first winner of the Nobel Prize in Physics. 950 00:45:28,260 --> 00:45:30,400 Such was his humanity. 951 00:45:30,400 --> 00:45:32,110 I hope you have a great weekend. 952 00:45:32,110 --> 00:45:34,760 We'll see the students back here on Monday.