1 00:00:00,995 --> 00:00:03,320 The following content is provided under a Creative 2 00:00:03,320 --> 00:00:04,710 Commons license. 3 00:00:04,710 --> 00:00:06,920 Your support will help MIT OpenCourseWare 4 00:00:06,920 --> 00:00:11,010 continue to offer high-quality educational resources for free. 5 00:00:11,010 --> 00:00:13,580 To make a donation or to view additional materials 6 00:00:13,580 --> 00:00:17,540 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,540 --> 00:00:18,420 at ocw.mit.edu. 8 00:00:22,023 --> 00:00:22,940 MIKE SHORT: All right. 9 00:00:22,940 --> 00:00:25,040 So I am super excited about today 10 00:00:25,040 --> 00:00:26,870 because this is, in my opinion, the highest 11 00:00:26,870 --> 00:00:29,060 point of the apex of the course where we're 12 00:00:29,060 --> 00:00:31,640 going to put together everything you've done so far 13 00:00:31,640 --> 00:00:34,400 and start to explain things like Bremsstrahlung, radiation 14 00:00:34,400 --> 00:00:37,430 damage, X-ray spectra that you get in a scanning electron 15 00:00:37,430 --> 00:00:40,700 microscope, and actually find a way where cross-sections 16 00:00:40,700 --> 00:00:42,558 are areas. 17 00:00:42,558 --> 00:00:44,600 Remember before, I told you guys cross-section is 18 00:00:44,600 --> 00:00:46,910 measured in barns, in centimeters squared? 19 00:00:46,910 --> 00:00:48,425 Think of it kind of like an area. 20 00:00:48,425 --> 00:00:50,300 We'll actually be able to show mathematically 21 00:00:50,300 --> 00:00:52,820 that some of them do derive from actual areas. 22 00:00:52,820 --> 00:00:54,900 So it will make a lot more sense. 23 00:00:54,900 --> 00:00:57,630 It's not just an abstract concept. 24 00:00:57,630 --> 00:00:59,990 What I want to do is a quick review 25 00:00:59,990 --> 00:01:04,010 of the ionization and excitation collisions 26 00:01:04,010 --> 00:01:05,000 that we did last time. 27 00:01:05,000 --> 00:01:13,070 Remember we had this imaginary hollow cylinder where 28 00:01:13,070 --> 00:01:15,440 we said that there is some ion traveling 29 00:01:15,440 --> 00:01:18,590 in this direction with charge, let's say, 30 00:01:18,590 --> 00:01:21,800 z times the electron charge and it's colliding, 31 00:01:21,800 --> 00:01:26,810 kind of, with an electron somewhere else separated 32 00:01:26,810 --> 00:01:29,840 by some impact parameter b. 33 00:01:29,840 --> 00:01:31,730 And let's say this hollow cylinder 34 00:01:31,730 --> 00:01:35,780 head a shell of thickness db. 35 00:01:35,780 --> 00:01:37,820 And we started off with this situation 36 00:01:37,820 --> 00:01:39,680 where we wanted to say-- 37 00:01:39,680 --> 00:01:44,570 we can find the y momentum as the integral of the y force. 38 00:01:44,570 --> 00:01:47,450 We did something. 39 00:01:47,450 --> 00:01:48,830 And one of the intermediate steps 40 00:01:48,830 --> 00:01:53,270 we came up with was that our energy in part of the electron 41 00:01:53,270 --> 00:01:57,740 is p squared over 2 times mass of the electron, which came out 42 00:01:57,740 --> 00:02:05,360 to 2z squared e to the 4th over the mass of the electron 43 00:02:05,360 --> 00:02:09,050 impact parameter squared velocity squared. 44 00:02:09,050 --> 00:02:13,220 Then we multiplied by the electron density 45 00:02:13,220 --> 00:02:18,770 in the material, which was the number density of atoms times 46 00:02:18,770 --> 00:02:21,740 z, the number of electrons per atom, 47 00:02:21,740 --> 00:02:25,580 times the area, the cross-sectional area 48 00:02:25,580 --> 00:02:27,710 of this hollow cylindrical shell, which came out 49 00:02:27,710 --> 00:02:33,740 to 2 pi b, which is the circumference of that circle 50 00:02:33,740 --> 00:02:39,270 right there, times db dx. 51 00:02:39,270 --> 00:02:42,150 I'm just going to leave that there for now, 52 00:02:42,150 --> 00:02:44,723 and we'll come back to it in a second. 53 00:02:44,723 --> 00:02:46,390 I will mention, though, that at the end, 54 00:02:46,390 --> 00:02:50,940 we came up with our stopping power expression. 55 00:02:50,940 --> 00:02:55,500 Let's call this ionizations that came out 56 00:02:55,500 --> 00:03:00,360 to 4 pi, this constant k0 squared, which 57 00:03:00,360 --> 00:03:05,940 comes from the Coulomb force law, little z squared, big Z, e 58 00:03:05,940 --> 00:03:11,796 to the 4th over mass of the electron velocity squared-- 59 00:03:11,796 --> 00:03:13,500 I'm running out of room-- 60 00:03:13,500 --> 00:03:20,730 times log of mass of the electron v squared 61 00:03:20,730 --> 00:03:27,680 over this mean excitation energy, which 62 00:03:27,680 --> 00:03:29,840 comes out to around, let's say, 10 63 00:03:29,840 --> 00:03:34,780 to 19 electron volts times z. 64 00:03:34,780 --> 00:03:38,320 And what this meant was that if we graph stopping power 65 00:03:38,320 --> 00:03:47,380 as a function of energy, there's a couple components to it. 66 00:03:47,380 --> 00:03:51,400 One of them is this roughly 1 over energy component. 67 00:03:51,400 --> 00:03:53,550 So let's say there's a component of it-- 68 00:03:53,550 --> 00:03:55,260 yes, I love when I can do that-- 69 00:03:55,260 --> 00:03:58,260 that actually-- that follows 1 over e. 70 00:03:58,260 --> 00:04:04,060 And there's this logarithmic component that goes that way. 71 00:04:04,060 --> 00:04:10,350 And if we sum them together, we ended up with a much higher 72 00:04:10,350 --> 00:04:11,910 stopping power at low energies. 73 00:04:11,910 --> 00:04:16,029 But around this local minimum of about 3 times 74 00:04:16,029 --> 00:04:18,240 the mass of the electron c squared, 75 00:04:18,240 --> 00:04:20,279 it starts to increase again. 76 00:04:20,279 --> 00:04:22,180 And that's due to this. 77 00:04:22,180 --> 00:04:25,870 How many excitations can you make as a function of energy? 78 00:04:25,870 --> 00:04:29,070 So if you think about it, this is kind of like an energy term. 79 00:04:29,070 --> 00:04:32,850 How much energy do you have divided by how many ionizations 80 00:04:32,850 --> 00:04:34,380 can you make? 81 00:04:34,380 --> 00:04:36,853 So it's kind of an intuitive result in that it's 82 00:04:36,853 --> 00:04:39,270 how much energy you've got versus how much energy it takes 83 00:04:39,270 --> 00:04:41,220 for a single unit process. 84 00:04:41,220 --> 00:04:44,083 And that's all mediated by this 1 over e term. 85 00:04:44,083 --> 00:04:45,750 The last thing that we said is that this 86 00:04:45,750 --> 00:04:49,170 curves back down here. 87 00:04:49,170 --> 00:04:56,320 And that's because at around 500 times this mean excitation 88 00:04:56,320 --> 00:05:01,280 energy, which as you can see is around 1 keV times z-- 89 00:05:01,280 --> 00:05:03,250 it's not a very high energy-- 90 00:05:03,250 --> 00:05:06,834 you start to get charged neutralization. 91 00:05:12,410 --> 00:05:15,410 The reason for that is that for-- in order for this formula 92 00:05:15,410 --> 00:05:19,920 to work, we have to assume that the deflection is really, 93 00:05:19,920 --> 00:05:23,010 really, really small, infinitesimally small. 94 00:05:23,010 --> 00:05:27,560 If it's not, and if the ion manages to catch that electron, 95 00:05:27,560 --> 00:05:32,720 it's not going to lose energy by undergoing a Coulomb 96 00:05:32,720 --> 00:05:33,283 interaction. 97 00:05:33,283 --> 00:05:35,450 It's going to lose energy by absorbing that electron 98 00:05:35,450 --> 00:05:36,710 and neutralizing. 99 00:05:36,710 --> 00:05:39,260 And so for really low energy, the ions 100 00:05:39,260 --> 00:05:41,200 are moving so slowly that they can capture 101 00:05:41,200 --> 00:05:42,200 some of those electrons. 102 00:05:42,200 --> 00:05:45,560 And it gets less and less effective at stopping 103 00:05:45,560 --> 00:05:47,960 the material. 104 00:05:47,960 --> 00:05:49,190 And this led to-- 105 00:05:49,190 --> 00:05:52,210 let's see-- this, we're distance, 106 00:05:52,210 --> 00:05:58,550 and this, we're dt dx times the energy required 107 00:05:58,550 --> 00:06:01,980 to make an ion pair, which we'll just call this i. 108 00:06:01,980 --> 00:06:07,393 We ended up with a curve that looked something like this. 109 00:06:07,393 --> 00:06:08,810 This right here we call the range. 110 00:06:11,460 --> 00:06:14,400 We just gave that the symbol r. 111 00:06:14,400 --> 00:06:15,840 So that's the review of last time, 112 00:06:15,840 --> 00:06:18,870 but I left some extra space for some reasons which will become 113 00:06:18,870 --> 00:06:22,560 clear in about half an hour. 114 00:06:22,560 --> 00:06:25,200 Right now I want to take you through a little bit 115 00:06:25,200 --> 00:06:27,030 of a whirlwind in terms of Bremsstrahlung. 116 00:06:27,030 --> 00:06:29,040 I'm not going to derive anything about it. 117 00:06:29,040 --> 00:06:32,310 We're just going to go over what the cross-sections and stopping 118 00:06:32,310 --> 00:06:35,470 powers look like, why they take that form intuitively. 119 00:06:35,470 --> 00:06:38,160 But we're not going to go through a rigorous derivation 120 00:06:38,160 --> 00:06:40,920 because, well, we simply don't have time. 121 00:06:40,920 --> 00:06:43,350 But I do want you to know what sort of things exist. 122 00:06:43,350 --> 00:06:46,786 So for Bremsstrahlung, better known as braking radiation-- 123 00:06:52,250 --> 00:06:55,170 who's actually heard of this before? 124 00:06:55,170 --> 00:06:57,440 Does anyone know roughly-- 125 00:06:57,440 --> 00:07:03,120 let's say if we were to say some cross-section 126 00:07:03,120 --> 00:07:04,140 for Bremsstrahlung. 127 00:07:04,140 --> 00:07:07,290 Let's call it cross-section radiative. 128 00:07:07,290 --> 00:07:09,210 Because in this case, we're actually 129 00:07:09,210 --> 00:07:12,570 talking about the charged particle radiating away 130 00:07:12,570 --> 00:07:13,240 photons. 131 00:07:13,240 --> 00:07:18,060 So let's say we had some nucleus of charge big Z, 132 00:07:18,060 --> 00:07:20,990 and we had some ion-- 133 00:07:20,990 --> 00:07:23,430 we'll look at a different color-- 134 00:07:23,430 --> 00:07:27,950 some ion of charge little Z moving towards it. 135 00:07:27,950 --> 00:07:30,330 It will either be attracted or repelled 136 00:07:30,330 --> 00:07:32,760 depending on what the sign looks like. 137 00:07:32,760 --> 00:07:36,405 And sometimes you might get radiation of a photon. 138 00:07:39,150 --> 00:07:44,650 Let's call it of energy E equals hc over lambda. 139 00:07:44,650 --> 00:07:47,500 That'll become important in a sec. 140 00:07:47,500 --> 00:07:49,688 So this radiative cross-section-- 141 00:07:51,997 --> 00:07:53,580 I don't care about-- particularly care 142 00:07:53,580 --> 00:07:56,700 about the exact form, but what is it proportional to? 143 00:07:56,700 --> 00:07:58,140 What sort of factors do you think 144 00:07:58,140 --> 00:08:02,370 would make the emission of that photon more or less likely? 145 00:08:02,370 --> 00:08:03,200 Yeah? 146 00:08:03,200 --> 00:08:05,320 AUDIENCE: The energy of the charged particle. 147 00:08:05,320 --> 00:08:07,528 MIKE SHORT: Sure, the energy of the charged particle. 148 00:08:07,528 --> 00:08:09,870 So you can-- there's one expression I like you. 149 00:08:09,870 --> 00:08:12,060 Can only take my money until you take it all. 150 00:08:12,060 --> 00:08:14,340 Well, the same thing goes for the energy of a photon. 151 00:08:14,340 --> 00:08:18,198 You can't radiate any more than the energy 152 00:08:18,198 --> 00:08:19,740 of the particle coming in, so there's 153 00:08:19,740 --> 00:08:24,760 going to be some maximum energy which 154 00:08:24,760 --> 00:08:29,020 is going to correspond to some minimum wavelength, which 155 00:08:29,020 --> 00:08:32,380 is-- let's say if we just put our initial energy in here, 156 00:08:32,380 --> 00:08:36,090 that gives us our minimum wavelength right there. 157 00:08:42,010 --> 00:08:43,179 That's true. 158 00:08:43,179 --> 00:08:46,810 And it can radiate at any energy smaller than that 159 00:08:46,810 --> 00:08:48,700 or any wavelength larger than that. 160 00:08:48,700 --> 00:08:50,710 I'm basically saying the same thing. 161 00:08:50,710 --> 00:08:53,170 Because if this particle started off further away 162 00:08:53,170 --> 00:08:58,450 and felt less of a deflection, it could still emit a photon, 163 00:08:58,450 --> 00:09:00,918 but of a longer wavelength. 164 00:09:00,918 --> 00:09:02,710 Don't have room to draw enough wavelengths, 165 00:09:02,710 --> 00:09:05,660 but I want to make sure that's physically accurate. 166 00:09:05,660 --> 00:09:07,600 So it's actually going to be also proportional 167 00:09:07,600 --> 00:09:10,990 to z of the large nucleus. 168 00:09:10,990 --> 00:09:14,027 The stronger the pull, the more of that breaking radiation 169 00:09:14,027 --> 00:09:14,860 you're going to see. 170 00:09:14,860 --> 00:09:18,370 It's actually proportional to z squared. 171 00:09:18,370 --> 00:09:22,360 What this says is that heavier z materials produce a lot more 172 00:09:22,360 --> 00:09:24,560 of this breaking radiation. 173 00:09:24,560 --> 00:09:28,120 And it's also proportional to the inverse 174 00:09:28,120 --> 00:09:29,950 of the mass squared. 175 00:09:29,950 --> 00:09:33,220 What this says intuitively is a heavier particle deflects 176 00:09:33,220 --> 00:09:37,390 less and emits less of this breaking radiation. 177 00:09:37,390 --> 00:09:40,480 Hopefully this makes a lot of sense to you guys, 178 00:09:40,480 --> 00:09:42,672 that the stronger the pull of the nucleus, the more 179 00:09:42,672 --> 00:09:45,130 deflection you're going to get, and the more Bremsstrahlung 180 00:09:45,130 --> 00:09:46,330 you'll get. 181 00:09:46,330 --> 00:09:48,490 The larger the mass of the incoming ion-- 182 00:09:48,490 --> 00:09:51,000 let's say that's mass m-- 183 00:09:51,000 --> 00:09:54,290 the less deflection you'll get because the less-- 184 00:09:54,290 --> 00:09:54,790 what is it? 185 00:09:54,790 --> 00:09:58,270 The less momentum transfer you can apply with the same force 186 00:09:58,270 --> 00:10:01,582 if you've got a heavier particle. 187 00:10:01,582 --> 00:10:04,040 Does this make sense to everybody? 188 00:10:04,040 --> 00:10:11,270 So what this says is it's really important for high z materials. 189 00:10:14,208 --> 00:10:15,500 And we'll see a little bit why. 190 00:10:15,500 --> 00:10:19,963 If I actually write the full expression for stopping power-- 191 00:10:19,963 --> 00:10:21,380 and I promise to you I'm not going 192 00:10:21,380 --> 00:10:26,270 to derive it because we don't really have the time for that. 193 00:10:26,270 --> 00:10:28,880 It's proportional to the number density. 194 00:10:28,880 --> 00:10:31,130 You should always think there will be a number density 195 00:10:31,130 --> 00:10:33,347 and stopping power, because the more atoms there are, 196 00:10:33,347 --> 00:10:34,430 the more they stop things. 197 00:10:34,430 --> 00:10:36,410 It's just directly proportional. 198 00:10:36,410 --> 00:10:40,860 Times that kinetic energy plus mec squared. 199 00:10:40,860 --> 00:10:43,400 And again, this is not something I want you to memorize, 200 00:10:43,400 --> 00:10:44,900 but it is something I want you to be 201 00:10:44,900 --> 00:10:49,040 able to decompose and explain why the parts are there. 202 00:10:49,040 --> 00:10:49,580 Let's see. 203 00:10:49,580 --> 00:10:56,320 Times some radiative cross-section 204 00:10:56,320 --> 00:11:04,550 where this sigma radiative is some constant cross-section. 205 00:11:04,550 --> 00:11:12,730 This ends up being about 1/500 barns times z squared 206 00:11:12,730 --> 00:11:16,570 times this parameter b, which if you see in the reading 207 00:11:16,570 --> 00:11:18,340 is actually given just-- 208 00:11:18,340 --> 00:11:22,810 this b scales roughly with the atomic-- 209 00:11:22,810 --> 00:11:26,500 I'm sorry-- yeah, with the proton number of the material. 210 00:11:26,500 --> 00:11:29,500 So you can see that in here, in the stopping power 211 00:11:29,500 --> 00:11:32,090 is actually directly the cross-section. 212 00:11:32,090 --> 00:11:35,140 So the components of a stopping power-- 213 00:11:35,140 --> 00:11:44,320 there's going to be some probability of interaction, 214 00:11:44,320 --> 00:11:48,190 and there's going to be some energy transfer part. 215 00:11:51,680 --> 00:11:53,612 This is an interesting result to show. 216 00:11:53,612 --> 00:11:55,820 This is why I wanted to just write the Bremsstrahlung 217 00:11:55,820 --> 00:11:57,050 stopping power. 218 00:11:57,050 --> 00:11:59,360 Because in here, actually, is the cross-section 219 00:11:59,360 --> 00:12:01,940 times some other stuff. 220 00:12:01,940 --> 00:12:04,400 Pretty neat result. And so now I want 221 00:12:04,400 --> 00:12:06,860 to show you how our cross-section is actually 222 00:12:06,860 --> 00:12:10,233 contained in the ionization stopping power. 223 00:12:10,233 --> 00:12:11,900 So let's bring this back down for a sec. 224 00:12:14,510 --> 00:12:18,080 You can think of the likelihood that the ion comes off 225 00:12:18,080 --> 00:12:22,070 with any particular energy to be directly related 226 00:12:22,070 --> 00:12:23,810 to this impact parameter. 227 00:12:23,810 --> 00:12:27,170 Because as we saw, the final expression for stopping power 228 00:12:27,170 --> 00:12:30,200 is directly related to this parameter b. 229 00:12:30,200 --> 00:12:32,990 We ended up integrating over all possible b 230 00:12:32,990 --> 00:12:36,020 to get the total stopping power in the material. 231 00:12:36,020 --> 00:12:37,640 But if we didn't do that integral-- 232 00:12:37,640 --> 00:12:40,940 if we stopped, let's say, at this stage in the game, 233 00:12:40,940 --> 00:12:43,610 and we said, all right, well, the stopping power 234 00:12:43,610 --> 00:12:49,070 at some fixed b actually depends on the probability 235 00:12:49,070 --> 00:12:53,630 that that particle enters into this cross-sectional area right 236 00:12:53,630 --> 00:13:00,200 here, this 2 pi b db, that right there is 237 00:13:00,200 --> 00:13:02,720 the cross-section for scattering as a function 238 00:13:02,720 --> 00:13:06,990 of the incoming energy and the outgoing energy. 239 00:13:06,990 --> 00:13:08,740 This is one of the coolest parts, I think, 240 00:13:08,740 --> 00:13:10,540 is that there is an actual area right here. 241 00:13:10,540 --> 00:13:15,250 It's the area of a hollow circle is the actual cross-section 242 00:13:15,250 --> 00:13:18,995 for scattering with a given ingoing and outgoing, 243 00:13:18,995 --> 00:13:21,150 outcoming energy. 244 00:13:21,150 --> 00:13:24,090 And then the rest of this stuff-- 245 00:13:24,090 --> 00:13:27,210 if you pull all this together, if you take a microscopic 246 00:13:27,210 --> 00:13:30,420 cross-section times the number of particles that are there-- 247 00:13:30,420 --> 00:13:39,720 because this is your atomic number density, 248 00:13:39,720 --> 00:13:45,810 and these two together are your electron number density. 249 00:13:45,810 --> 00:13:48,000 Like we talked about before with reaction rates 250 00:13:48,000 --> 00:13:49,800 and cross-sections, this thing right 251 00:13:49,800 --> 00:13:54,630 here is your macroscopic cross-section for an incoming 252 00:13:54,630 --> 00:13:59,500 and an outgoing energy contained directly in the stopping power 253 00:13:59,500 --> 00:14:01,420 formula, because then we integrated 254 00:14:01,420 --> 00:14:04,240 over all possible cross sections, which 255 00:14:04,240 --> 00:14:07,960 means all possible outgoing energies for a given 256 00:14:07,960 --> 00:14:10,270 incoming energy. 257 00:14:10,270 --> 00:14:13,660 And so the last bit, the way to link these two together, 258 00:14:13,660 --> 00:14:17,860 which is why I left a little bit of space right here-- 259 00:14:17,860 --> 00:14:20,805 we know right now, because I wrote it up there, 260 00:14:20,805 --> 00:14:22,180 that the scattering cross-section 261 00:14:22,180 --> 00:14:29,890 as a function of the ingoing an outgoing energy per unit energy 262 00:14:29,890 --> 00:14:34,555 is just the area of that hollow circle. 263 00:14:34,555 --> 00:14:38,500 So let's divide everything by dt. 264 00:14:38,500 --> 00:14:41,230 We end up with the total formula for cross-- 265 00:14:41,230 --> 00:14:44,050 for the scattering cross-section. 266 00:14:44,050 --> 00:14:46,970 We don't know what this b db dt is. 267 00:14:46,970 --> 00:14:49,810 What's the differential probability 268 00:14:49,810 --> 00:14:52,240 between impact parameter and outgoing energy? 269 00:14:52,240 --> 00:14:56,020 We don't quite know, but we can express this 270 00:14:56,020 --> 00:14:58,930 as a change of variables that we do know. 271 00:14:58,930 --> 00:15:04,480 We do know-- if we have a certain impact parameter, 272 00:15:04,480 --> 00:15:06,670 we know what the scattering angle is going to be. 273 00:15:06,670 --> 00:15:08,860 There is a well-known relation for that. 274 00:15:08,860 --> 00:15:11,290 And there's a derivation in the book 275 00:15:11,290 --> 00:15:14,290 and in another book that I want to point out to you 276 00:15:14,290 --> 00:15:19,810 guys by Gary Was called Fundamentals of Radiation 277 00:15:19,810 --> 00:15:27,360 Material Science on page 32. 278 00:15:27,360 --> 00:15:29,700 If anyone wants to see the derivation from which 279 00:15:29,700 --> 00:15:32,940 this result came from, you can head right there, 280 00:15:32,940 --> 00:15:35,490 and it's free on MIT Libraries. 281 00:15:35,490 --> 00:15:39,060 Meanwhile, we do know our relation between this impact 282 00:15:39,060 --> 00:15:41,490 parameter and the angle, and we do 283 00:15:41,490 --> 00:15:46,855 know a relation between this angle and the outgoing energy. 284 00:15:46,855 --> 00:15:49,230 And this is where some of the hard sphere collision stuff 285 00:15:49,230 --> 00:15:51,640 comes in. 286 00:15:51,640 --> 00:15:54,790 What's the maximum amount of energy 287 00:15:54,790 --> 00:15:57,580 that a particle can impart to another particle 288 00:15:57,580 --> 00:16:01,690 in some sort of a hard, sphere-like collision? 289 00:16:01,690 --> 00:16:02,900 Let's take the easy example. 290 00:16:02,900 --> 00:16:05,680 If the two particles have equal mass, 291 00:16:05,680 --> 00:16:09,617 how much energy can one particle impart to another? 292 00:16:09,617 --> 00:16:10,450 AUDIENCE: All of it. 293 00:16:10,450 --> 00:16:11,658 MIKE SHORT: All of it, right? 294 00:16:11,658 --> 00:16:13,390 It can impart a maximum of, let's say, 295 00:16:13,390 --> 00:16:16,150 this incoming energy ei. 296 00:16:16,150 --> 00:16:21,730 As those mass ratios change, you can impart a maximum-- 297 00:16:21,730 --> 00:16:25,400 let's say your maximum becomes what's 298 00:16:25,400 --> 00:16:30,880 called gamma ei where this gamma right here 299 00:16:30,880 --> 00:16:35,950 is 4 times those two masses multiplied 300 00:16:35,950 --> 00:16:40,360 over the sum squared. 301 00:16:40,360 --> 00:16:43,240 The full expression-- I'm going to use a different color 302 00:16:43,240 --> 00:16:45,010 because I'm running out of space here. 303 00:16:45,010 --> 00:16:51,700 The full expression for t is actually gamma ei over 2 times 304 00:16:51,700 --> 00:16:57,110 1 minus cosine theta. 305 00:16:57,110 --> 00:17:03,250 The two intuitive limits from this is if theta equals pi, 306 00:17:03,250 --> 00:17:06,940 then this here equals 2, and t is our t maximum, 307 00:17:06,940 --> 00:17:09,730 just gamma times ei. 308 00:17:09,730 --> 00:17:15,510 If theta equals 0, that whole thing equals 0. 309 00:17:15,510 --> 00:17:17,910 And in our case of forward scattering, 310 00:17:17,910 --> 00:17:22,204 no interaction occurs, and the energy imparted is 0. 311 00:17:22,204 --> 00:17:23,579 But the important part here is we 312 00:17:23,579 --> 00:17:27,630 have a direct relation between t and theta 313 00:17:27,630 --> 00:17:30,750 and the angle, which we can put in here. 314 00:17:30,750 --> 00:17:33,643 And we actually have a direct relation between b and theta, 315 00:17:33,643 --> 00:17:35,310 which I wrote down so I wouldn't forget. 316 00:17:39,510 --> 00:17:41,260 So we actually have-- our impact parameter 317 00:17:41,260 --> 00:17:44,500 is classical radius of the electron times 318 00:17:44,500 --> 00:17:46,795 cosine of angle over 2. 319 00:17:46,795 --> 00:17:48,670 You don't have to know where these came from, 320 00:17:48,670 --> 00:17:50,680 but the point is we have a relation between B 321 00:17:50,680 --> 00:17:51,820 and the angle. 322 00:17:51,820 --> 00:17:54,400 We have a relation between angle and energy. 323 00:17:54,400 --> 00:17:56,290 So we can just do a change of variables 324 00:17:56,290 --> 00:17:59,233 to get our final cross-section. 325 00:18:02,410 --> 00:18:06,210 And it ends up being, I think, pi times radius of the electron 326 00:18:06,210 --> 00:18:08,715 squared over gamma. 327 00:18:11,220 --> 00:18:14,220 So in this way, we can go from known relations between each 328 00:18:14,220 --> 00:18:18,120 of the variables and an actual physical cross-section 329 00:18:18,120 --> 00:18:24,240 that has units of real area down to an energy-dependent form 330 00:18:24,240 --> 00:18:27,485 for this cross-section, which I think is pretty cool. 331 00:18:27,485 --> 00:18:28,860 And then this is the one that you 332 00:18:28,860 --> 00:18:31,440 would see tabulated in the JANIS tables, 333 00:18:31,440 --> 00:18:34,590 like the energy-dependent cross-section for the S 334 00:18:34,590 --> 00:18:36,995 reaction or the scattering. 335 00:18:36,995 --> 00:18:39,120 So this is one of my favorite parts of this course, 336 00:18:39,120 --> 00:18:42,360 because you can see how cross-sections really 337 00:18:42,360 --> 00:18:46,290 do follow directly from areas. 338 00:18:46,290 --> 00:18:49,870 So now for the other part, now that we've 339 00:18:49,870 --> 00:18:53,880 got this Bremsstrahlung stopping power 340 00:18:53,880 --> 00:18:56,460 and we've got our ionization stopping power, 341 00:18:56,460 --> 00:18:59,970 it's useful to find out which one is more important when. 342 00:18:59,970 --> 00:19:02,550 To do that, we just look at their ratios. 343 00:19:02,550 --> 00:19:13,180 So if we look at the dt dx from ionizations over the dx dx 344 00:19:13,180 --> 00:19:17,980 from radiative energy transfer or Bremsstrahlung-- 345 00:19:17,980 --> 00:19:20,020 let me make sure I get this one right. 346 00:19:20,020 --> 00:19:26,540 It's proportional to z times mass of the electron over m 347 00:19:26,540 --> 00:19:35,760 squared times t over 1,400 rest mass of the electron. 348 00:19:35,760 --> 00:19:38,200 So what this tells you here is that-- 349 00:19:38,200 --> 00:19:38,700 I'm sorry. 350 00:19:38,700 --> 00:19:41,910 I think I have those backwards, because radiative 351 00:19:41,910 --> 00:19:45,545 should get more important at higher energies. 352 00:19:49,790 --> 00:19:52,550 So what this tells you is for higher z materials, 353 00:19:52,550 --> 00:19:54,790 Bremsstrahlung becomes more dominant, 354 00:19:54,790 --> 00:19:56,830 and for higher energies, Bremsstrahlung 355 00:19:56,830 --> 00:19:59,270 becomes more dominant. 356 00:19:59,270 --> 00:20:04,460 So if we want to generalize our stopping power curve from just 357 00:20:04,460 --> 00:20:07,580 ionization to everything-- 358 00:20:07,580 --> 00:20:09,200 so I know I had another color. 359 00:20:09,200 --> 00:20:09,700 No. 360 00:20:09,700 --> 00:20:10,857 I ran out of colors. 361 00:20:10,857 --> 00:20:11,690 I need a fourth one. 362 00:20:15,500 --> 00:20:19,520 There's going to be some Bremsstrahlung component that 363 00:20:19,520 --> 00:20:21,380 starts to get more and more important 364 00:20:21,380 --> 00:20:23,300 with increasing energy. 365 00:20:23,300 --> 00:20:26,203 And so then if you extend this curve, 366 00:20:26,203 --> 00:20:28,370 you're going to radiate more and more and more power 367 00:20:28,370 --> 00:20:30,110 the higher energy you go-- 368 00:20:30,110 --> 00:20:35,790 not from this component or that component of ionization, 369 00:20:35,790 --> 00:20:39,060 but from radiation or Bremsstrahlung. 370 00:20:39,060 --> 00:20:42,180 So this has some pretty serious implications 371 00:20:42,180 --> 00:20:46,335 to answer questions like, how do you shield beta rays? 372 00:20:46,335 --> 00:20:48,230 Does anyone have any idea? 373 00:20:48,230 --> 00:20:50,900 Based on this formula right here, 374 00:20:50,900 --> 00:20:53,240 what would you use to shield beta particles 375 00:20:53,240 --> 00:20:56,780 and not irradiate the person standing behind the shield? 376 00:21:01,150 --> 00:21:02,650 Let's ask a question everyone knows. 377 00:21:02,650 --> 00:21:06,550 What do you use to shield photons really well? 378 00:21:06,550 --> 00:21:10,090 Lead, tungsten, something with high z. 379 00:21:10,090 --> 00:21:11,425 Because as we saw from before-- 380 00:21:11,425 --> 00:21:15,160 I'm going to steal a little bit of the Rutherford stuff. 381 00:21:15,160 --> 00:21:19,870 If you graph the energy versus the mass attenuation 382 00:21:19,870 --> 00:21:25,120 coefficient, you get a curve that looks like this, 383 00:21:25,120 --> 00:21:29,920 but everything increases with increasing z. 384 00:21:29,920 --> 00:21:32,260 You get more mass attenuation with increasing z. 385 00:21:32,260 --> 00:21:35,470 And also, denser materials tend to be higher z. 386 00:21:35,470 --> 00:21:37,960 Is that what you want to do for beta particles? 387 00:21:40,667 --> 00:21:42,250 You say-- so Monica, you're saying no. 388 00:21:42,250 --> 00:21:42,903 How come? 389 00:21:42,903 --> 00:21:44,528 AUDIENCE: Don't you just want something 390 00:21:44,528 --> 00:21:46,858 with a low cross-section? 391 00:21:46,858 --> 00:21:47,900 MIKE SHORT: That's right. 392 00:21:47,900 --> 00:21:50,120 Well, you don't necessarily want something 393 00:21:50,120 --> 00:21:51,620 with a low cross-section, or else it 394 00:21:51,620 --> 00:21:54,415 might not shield at all, but you are on the right track. 395 00:21:54,415 --> 00:21:56,040 You can actually look at the difference 396 00:21:56,040 --> 00:21:58,973 between these stopping powers, and cross-sections 397 00:21:58,973 --> 00:21:59,890 are embedded in there. 398 00:21:59,890 --> 00:22:02,200 So I think that answer is pretty much correct. 399 00:22:02,200 --> 00:22:04,870 But also, you're going to get more Bremsstrahlung 400 00:22:04,870 --> 00:22:08,150 or more breaking radiation in higher z materials. 401 00:22:08,150 --> 00:22:10,990 So if we actually look at what thresholds does this become 402 00:22:10,990 --> 00:22:21,490 important in lead, this ratio is about 1 at around 10 MeV, 403 00:22:21,490 --> 00:22:23,710 which means that you lose an equal amount of energy 404 00:22:23,710 --> 00:22:28,930 to Bremsstrahlung as ionization at 10 MeV for electrons. 405 00:22:33,000 --> 00:22:41,370 In water, this ratio is about 1 at 100 MeV. 406 00:22:41,370 --> 00:22:45,640 So what this says is if you want to shield electrons or beta 407 00:22:45,640 --> 00:22:47,400 particles safely, you actually have 408 00:22:47,400 --> 00:22:49,560 to use lower Z materials because they 409 00:22:49,560 --> 00:22:51,360 won't make much Bremsstrahlung. 410 00:22:51,360 --> 00:22:53,910 But because, like Monica said, then the cross-section 411 00:22:53,910 --> 00:22:56,780 is lower, you actually have to use more. 412 00:22:56,780 --> 00:22:58,300 So you don't have a choice. 413 00:22:58,300 --> 00:23:01,950 You can't just use less high z material. 414 00:23:01,950 --> 00:23:04,410 Because while you will stop more of the electrons, 415 00:23:04,410 --> 00:23:07,110 they will create more x-rays in the process. 416 00:23:07,110 --> 00:23:09,630 And those x-rays are highly penetrating, 417 00:23:09,630 --> 00:23:12,480 as we know from these mass attenuation curves. 418 00:23:12,480 --> 00:23:14,880 Once you get to high energy, this is-- 419 00:23:14,880 --> 00:23:16,440 these are logarithmic scales, so let 420 00:23:16,440 --> 00:23:22,190 me correct those and say these are log of e 421 00:23:22,190 --> 00:23:24,030 and log of mu over p. 422 00:23:24,030 --> 00:23:26,580 It gets millions of times less effective 423 00:23:26,580 --> 00:23:30,630 at shielding high energy photons. 424 00:23:30,630 --> 00:23:32,880 So that's one of those really important things to note 425 00:23:32,880 --> 00:23:34,838 is if you're designing shielding for something, 426 00:23:34,838 --> 00:23:38,440 and there are electrons involved that are even around 1 MeV 427 00:23:38,440 --> 00:23:42,460 or so, you can't just use high z materials to shield them, 428 00:23:42,460 --> 00:23:46,490 or you will create more problems than you solve. 429 00:23:46,490 --> 00:23:48,350 That's a pretty important implication. 430 00:23:48,350 --> 00:23:52,757 It's quite important for what's called betavoltaic devices. 431 00:23:52,757 --> 00:23:54,340 It's kind of a sidetrack, so I'm going 432 00:23:54,340 --> 00:23:57,380 to stick it on a board that'll be hidden soon. 433 00:23:57,380 --> 00:23:59,205 Has anyone heard of a betavoltaic device? 434 00:24:02,630 --> 00:24:03,770 Anyone? 435 00:24:03,770 --> 00:24:05,286 What are they? 436 00:24:05,286 --> 00:24:06,770 AUDIENCE: It's like a beta source 437 00:24:06,770 --> 00:24:11,320 that emits electrons onto a semiconductor [INAUDIBLE].. 438 00:24:11,320 --> 00:24:13,110 MIKE SHORT: Yeah, it's a beta battery. 439 00:24:13,110 --> 00:24:19,940 All it is is, let's say, some pieces of silicon, 440 00:24:19,940 --> 00:24:26,060 some circuit that grabs the power, and a beta emitter. 441 00:24:26,060 --> 00:24:29,300 And these beta particles directly hit the silicon, 442 00:24:29,300 --> 00:24:32,930 and the movement of those betas constitutes a charge. 443 00:24:32,930 --> 00:24:36,680 And it's direct-- it's direct conversion of radiation 444 00:24:36,680 --> 00:24:38,240 to electrical energy. 445 00:24:38,240 --> 00:24:42,180 They're not very high power, but they last for a very long time. 446 00:24:42,180 --> 00:24:43,430 How long? 447 00:24:43,430 --> 00:24:46,515 Around a few half lives of that beta decay. 448 00:24:46,515 --> 00:24:48,140 So for most of these beta emitters that 449 00:24:48,140 --> 00:24:51,530 have half lives in the realm of, like, 10 to 1,000 years, 450 00:24:51,530 --> 00:24:55,490 you can make a microwatt battery that could last for millennia. 451 00:24:55,490 --> 00:24:57,320 This could be pretty useful. 452 00:24:57,320 --> 00:24:59,810 Let's say if you wanted to have some secret sensors 453 00:24:59,810 --> 00:25:02,570 in a naughty country like North Korea, 454 00:25:02,570 --> 00:25:05,060 you could drop these tiny little beta particles that would 455 00:25:05,060 --> 00:25:09,330 just-- betavoltaics that would just trickle charge a battery, 456 00:25:09,330 --> 00:25:10,310 make a measurement of-- 457 00:25:10,310 --> 00:25:13,430 I don't know-- radiation level, or weight of the dictator, 458 00:25:13,430 --> 00:25:16,010 or whatever you happen to want to measure, 459 00:25:16,010 --> 00:25:19,160 and send that off once a month or once a year 460 00:25:19,160 --> 00:25:21,620 with no need for external monitoring. 461 00:25:21,620 --> 00:25:25,280 Or let's say you're designing a mission to land on a comet, 462 00:25:25,280 --> 00:25:29,420 like the Rosetta Philae Lander, and your radiothermal isotope 463 00:25:29,420 --> 00:25:32,180 generator is going to burn out in, let's say, 10 or 20 years. 464 00:25:32,180 --> 00:25:33,890 You might not need that much power just 465 00:25:33,890 --> 00:25:35,600 to measure temperature, or light levels, 466 00:25:35,600 --> 00:25:37,370 or something else, or a gas that you might 467 00:25:37,370 --> 00:25:39,280 want to know what's there. 468 00:25:39,280 --> 00:25:42,765 But you have to choose your beta isotope wisely. 469 00:25:42,765 --> 00:25:44,890 If you want to make these things in a little chip-- 470 00:25:44,890 --> 00:25:47,890 and they actually have been commercialized in a chip 471 00:25:47,890 --> 00:25:50,470 that's about that actual size using 472 00:25:50,470 --> 00:25:53,160 about two curies of tritium. 473 00:25:53,160 --> 00:25:55,425 Anyone have any idea why one would choose tritium? 474 00:26:01,178 --> 00:26:02,720 AUDIENCE: It's got a short half-life. 475 00:26:02,720 --> 00:26:03,860 MIKE SHORT: Yeah, it's got a short half-life, 476 00:26:03,860 --> 00:26:06,080 so you can get a lot of power out of it. 477 00:26:06,080 --> 00:26:08,210 That's one of the two correct reasons. 478 00:26:08,210 --> 00:26:10,210 And what is the other one? 479 00:26:10,210 --> 00:26:14,960 Lets see who's memorized there KAERI table of nuclides. 480 00:26:14,960 --> 00:26:17,000 What do you think its beta decay energy 481 00:26:17,000 --> 00:26:20,549 would have to be for this not to blast anyone in the vicinity? 482 00:26:24,461 --> 00:26:25,165 AUDIENCE: Low. 483 00:26:25,165 --> 00:26:26,040 MIKE SHORT: Very low. 484 00:26:26,040 --> 00:26:28,210 Why do you say that? 485 00:26:28,210 --> 00:26:33,540 AUDIENCE: [INAUDIBLE] they don't penetrate all the way 486 00:26:33,540 --> 00:26:34,540 through the [INAUDIBLE]. 487 00:26:34,540 --> 00:26:35,540 MIKE SHORT: That's true. 488 00:26:35,540 --> 00:26:37,120 Their range is much smaller. 489 00:26:37,120 --> 00:26:40,320 But the range of all betas is pretty low in materials. 490 00:26:40,320 --> 00:26:43,030 But the answer lies right here-- 491 00:26:43,030 --> 00:26:44,800 less Bremsstrahlung. 492 00:26:44,800 --> 00:26:48,250 Lower energy betas give most of their energy 493 00:26:48,250 --> 00:26:53,020 off in ionization rather than by radiating Bremsstrahlung. 494 00:26:53,020 --> 00:26:56,060 So you can have a device with two curies of tritium, 495 00:26:56,060 --> 00:26:59,590 which if that's released to the outside world, that's bad news. 496 00:26:59,590 --> 00:27:01,990 That's something that you might have to report. 497 00:27:01,990 --> 00:27:05,180 But as long as it stays contained in this device, 498 00:27:05,180 --> 00:27:08,710 it does not have enough energy to produce many x-rays 499 00:27:08,710 --> 00:27:10,030 from Bremsstrahlung. 500 00:27:10,030 --> 00:27:12,430 And therefore, it does not require an enormous amount 501 00:27:12,430 --> 00:27:13,420 of shielding. 502 00:27:13,420 --> 00:27:15,120 So you can't just pick a 1 MeV beta 503 00:27:15,120 --> 00:27:16,870 emitter which you might get a lot of power 504 00:27:16,870 --> 00:27:19,420 out of, because it's also going to be a big, crazy X-ray 505 00:27:19,420 --> 00:27:22,480 source that you wouldn't want in a cell phone or a sensor 506 00:27:22,480 --> 00:27:25,000 or some other device you might put in your pocket, 507 00:27:25,000 --> 00:27:28,402 or even 20 feet from you. 508 00:27:28,402 --> 00:27:30,220 Cool. 509 00:27:30,220 --> 00:27:33,385 So that's the idea behind Bremsstrahlung. 510 00:27:33,385 --> 00:27:35,510 There's a little bit more I want to tell you about, 511 00:27:35,510 --> 00:27:39,020 and I'll save that for the sidetrack board. 512 00:27:39,020 --> 00:27:41,420 We use Bremsstrahlung in a lot of really interesting 513 00:27:41,420 --> 00:27:47,000 applications, including cyclotron, one of which 514 00:27:47,000 --> 00:27:50,990 we just took delivery of here at MIT, or a synchrotron. 515 00:27:54,970 --> 00:27:57,470 And I'll just briefly explain how these work. 516 00:27:57,470 --> 00:28:01,070 In a cyclotron, you've got two D-shaped magnets. 517 00:28:01,070 --> 00:28:04,580 They actually call them dees because we're 518 00:28:04,580 --> 00:28:07,520 so creative in naming these things. 519 00:28:07,520 --> 00:28:11,890 You inject some source of charged particles, 520 00:28:11,890 --> 00:28:19,130 and there is some electric field lines across these two dee 521 00:28:19,130 --> 00:28:20,180 magnets. 522 00:28:20,180 --> 00:28:23,510 And what this says is that in between the magnets, 523 00:28:23,510 --> 00:28:25,280 the particle accelerates. 524 00:28:25,280 --> 00:28:29,180 And inside each magnet, the path curves. 525 00:28:29,180 --> 00:28:31,190 And it accelerates some more. 526 00:28:31,190 --> 00:28:34,420 And it's moving even faster, so it takes longer to curve. 527 00:28:34,420 --> 00:28:37,520 Than it moves even faster, and it takes longer to curve, 528 00:28:37,520 --> 00:28:44,920 and so on and so on, until it finally shoots out the side. 529 00:28:44,920 --> 00:28:47,830 And so this is one way that you can have an extremely compact-- 530 00:28:47,830 --> 00:28:50,320 and I'm talking like garbage-can-sized-- 531 00:28:50,320 --> 00:28:54,490 accelerator that brings things up to about 13 MeV. 532 00:28:54,490 --> 00:28:57,370 That's the one that we've got in the basement of Northwest 13. 533 00:28:57,370 --> 00:28:59,710 The problem is every time these particles 534 00:28:59,710 --> 00:29:07,260 bend, they send off photons, what's 535 00:29:07,260 --> 00:29:09,240 known as cyclotron radiation. 536 00:29:09,240 --> 00:29:12,690 And the higher energy that is, the more intense 537 00:29:12,690 --> 00:29:14,850 that cyclotron radiation gets. 538 00:29:14,850 --> 00:29:18,480 So you've got this garbage-can-sized device with 539 00:29:18,480 --> 00:29:23,040 a little hole right here, and it's just blasting out photons 540 00:29:23,040 --> 00:29:25,140 in all directions in this one plane-- 541 00:29:25,140 --> 00:29:27,120 let's just call it the plane of death-- 542 00:29:27,120 --> 00:29:28,770 which you don't want to be in, which 543 00:29:28,770 --> 00:29:31,860 is why this the thing is behind 4 feet of concrete shielding, 544 00:29:31,860 --> 00:29:34,110 and in the middle of a room, to help-- 545 00:29:34,110 --> 00:29:37,080 that 1 over r squared keeps your dose down. 546 00:29:37,080 --> 00:29:42,330 But we actually use this plane of death in a synchrotron. 547 00:29:42,330 --> 00:29:44,680 What it is is it's a circular accelerator. 548 00:29:44,680 --> 00:29:47,280 It's not quite circular, so let me correct 549 00:29:47,280 --> 00:29:48,870 my drawing a little bit. 550 00:29:48,870 --> 00:29:51,780 There are straight segments, and there are slightly 551 00:29:51,780 --> 00:29:52,650 curved segments. 552 00:29:56,670 --> 00:29:59,490 But it pretty much looks like a circle 553 00:29:59,490 --> 00:30:01,200 if you look at it from high up enough. 554 00:30:01,200 --> 00:30:04,200 In each of these curved segments, 555 00:30:04,200 --> 00:30:05,520 there is a bending magnet. 556 00:30:08,610 --> 00:30:10,300 That's my best drawing for a magnet. 557 00:30:13,110 --> 00:30:15,960 And what this does is it continuously 558 00:30:15,960 --> 00:30:21,480 changes the path of these charged particles going through 559 00:30:21,480 --> 00:30:23,010 usually electrons. 560 00:30:23,010 --> 00:30:25,410 And you end up with intense beams. 561 00:30:25,410 --> 00:30:26,910 Let me use a different color. 562 00:30:26,910 --> 00:30:30,690 You end up with intense beams perpendicular 563 00:30:30,690 --> 00:30:34,650 to the original path before it went in that bending magnet 564 00:30:34,650 --> 00:30:38,700 of synchrotron radiation. 565 00:30:38,700 --> 00:30:42,420 So it's kind of like a gigaelectron volt 566 00:30:42,420 --> 00:30:44,790 spinning ninja star of death, except at the end 567 00:30:44,790 --> 00:30:47,700 of every one of these stations, you have 568 00:30:47,700 --> 00:30:50,780 what's called a beam line. 569 00:30:50,780 --> 00:30:55,040 Because there's 60 or 80-odd of these beam lines 570 00:30:55,040 --> 00:30:56,930 coming off with, let's say, 80 kv 571 00:30:56,930 --> 00:30:59,720 and below Bremsstrahlung x-rays, you 572 00:30:59,720 --> 00:31:02,760 can use those for a whole lot of different analysis techniques. 573 00:31:02,760 --> 00:31:04,820 You can simply irradiate things. 574 00:31:04,820 --> 00:31:09,140 You can send those x-rays through a monochromator 575 00:31:09,140 --> 00:31:12,260 to select only one wavelength, and then use that wavelength 576 00:31:12,260 --> 00:31:15,310 to probe the structure of matter down to the atomic level. 577 00:31:15,310 --> 00:31:17,810 There's actually one of these just down in Long Island. 578 00:31:17,810 --> 00:31:19,490 About a 2-and-1/2-hour drive from here, 579 00:31:19,490 --> 00:31:21,530 there's Brookhaven National Lab. 580 00:31:21,530 --> 00:31:23,780 And they just opened up the National Synchrotron Light 581 00:31:23,780 --> 00:31:27,260 Source, or NSLS version 2, where they can actually 582 00:31:27,260 --> 00:31:32,150 measure distances with single nanometer precision. 583 00:31:32,150 --> 00:31:35,840 So inside this beam line is a bigger room 584 00:31:35,840 --> 00:31:37,850 which is encased in another room which 585 00:31:37,850 --> 00:31:39,710 is encased in another room. 586 00:31:39,710 --> 00:31:42,230 And the whole point of that is for vibration and temperature 587 00:31:42,230 --> 00:31:43,280 isolation. 588 00:31:43,280 --> 00:31:45,540 So they maintain this entire room 589 00:31:45,540 --> 00:31:49,400 to within a speck of 0.1 Celsius. 590 00:31:49,400 --> 00:31:52,375 And it's the least vibrating place, probably, in the US. 591 00:31:52,375 --> 00:31:53,750 I don't know about on the planet. 592 00:31:53,750 --> 00:31:56,750 But it's got basically no vibration. 593 00:31:56,750 --> 00:31:58,550 So the atoms are effectively standing 594 00:31:58,550 --> 00:32:01,860 still except for their normal vibrations in the material. 595 00:32:01,860 --> 00:32:04,017 But there's no source of external vibration. 596 00:32:04,017 --> 00:32:05,600 And the cooling has to come in through 597 00:32:05,600 --> 00:32:09,500 these convoluted channels so as not to blow on the sample, 598 00:32:09,500 --> 00:32:12,450 so as not to make any convection currents or temperature 599 00:32:12,450 --> 00:32:12,950 changes. 600 00:32:12,950 --> 00:32:15,075 And they can actually probe the structure of matter 601 00:32:15,075 --> 00:32:19,370 with single-nanometer precision using these synchrotron x-rays 602 00:32:19,370 --> 00:32:23,240 all produced by Bremsstrahlung. 603 00:32:23,240 --> 00:32:24,360 So it's not all bad. 604 00:32:24,360 --> 00:32:27,535 You can use Bremsstrahlung for good. 605 00:32:27,535 --> 00:32:28,660 Then there's a little bit-- 606 00:32:28,660 --> 00:32:30,790 I have to hijack a little more area 607 00:32:30,790 --> 00:32:32,805 from Rutherford scattering. 608 00:32:32,805 --> 00:32:34,180 You might think about, well, what 609 00:32:34,180 --> 00:32:37,300 is the actual spectrum of this Bremsstrahlung. 610 00:32:37,300 --> 00:32:39,610 Well, you can look to see what's the probability 611 00:32:39,610 --> 00:32:45,580 that an atom enters into any of these concentric, hollow 612 00:32:45,580 --> 00:32:46,870 circles. 613 00:32:46,870 --> 00:32:49,510 It looks to be less and less likely that you're 614 00:32:49,510 --> 00:32:51,520 going to enter through one of the center rings 615 00:32:51,520 --> 00:32:53,020 and more and more likely that you're 616 00:32:53,020 --> 00:32:55,190 going to enter through one of the outer rings. 617 00:32:55,190 --> 00:32:58,600 If you start farther away, there's less of a pull 618 00:32:58,600 --> 00:33:01,180 to change the path of that ion or electron, 619 00:33:01,180 --> 00:33:05,000 and the Bremsstrahlung is going to be lower in energy. 620 00:33:05,000 --> 00:33:06,580 This is actually described by what's 621 00:33:06,580 --> 00:33:15,618 called Cramer's law, which says that the intensity 622 00:33:15,618 --> 00:33:17,660 of the Bremsstrahlung as a function of wavelength 623 00:33:17,660 --> 00:33:21,890 scales with some constant k, and that constant scales with-- 624 00:33:21,890 --> 00:33:23,900 surprise, surprise-- the atomic number 625 00:33:23,900 --> 00:33:29,240 of the material times some lambda 626 00:33:29,240 --> 00:33:36,273 over lambda minimum minus 1 times 1 over lambda squared. 627 00:33:36,273 --> 00:33:37,690 And what this says is that there's 628 00:33:37,690 --> 00:33:43,110 some minimum lambda or some maximum energy 629 00:33:43,110 --> 00:33:45,330 that you can impart to this Bremsstrahlung, which 630 00:33:45,330 --> 00:33:48,610 again, you can only take some energy before you take it all. 631 00:33:48,610 --> 00:33:52,440 And there's going to be some sort of a fixed minimum lambda 632 00:33:52,440 --> 00:33:54,840 if we draw this intensity. 633 00:33:54,840 --> 00:33:57,120 And I graphed this on Desmos just before coming here, 634 00:33:57,120 --> 00:34:00,390 so I know it looks something like this where that 635 00:34:00,390 --> 00:34:05,190 right there is lambda minimum. 636 00:34:05,190 --> 00:34:06,910 It's taking more area. 637 00:34:06,910 --> 00:34:14,190 If you then change variables from lambda to the angular 638 00:34:14,190 --> 00:34:16,110 frequency where, if you remember, 639 00:34:16,110 --> 00:34:22,830 the energy of the photon is just h bar times that frequency-- so 640 00:34:22,830 --> 00:34:27,420 it's kind of like converting into energy with just a tiny, 641 00:34:27,420 --> 00:34:28,679 little constant in front. 642 00:34:28,679 --> 00:34:31,170 And I mean really, really tiny little constant. 643 00:34:31,170 --> 00:34:35,370 You end up with an energy relation 644 00:34:35,370 --> 00:34:40,719 that looks like some maximum angular frequency 645 00:34:40,719 --> 00:34:44,380 or some maximum energy. 646 00:34:44,380 --> 00:34:47,909 And this is kind of a simple, linear-looking relation, this 1 647 00:34:47,909 --> 00:34:52,000 over energy relation minus 1. 648 00:34:52,000 --> 00:34:54,760 So if we graph energy versus the intensity 649 00:34:54,760 --> 00:34:56,679 of the Bremsstrahlung, you end up 650 00:34:56,679 --> 00:35:02,170 with a curve something like this where 651 00:35:02,170 --> 00:35:07,960 your max energy is the same as your incoming particle energy. 652 00:35:07,960 --> 00:35:11,470 Now, who here has done any sort of X-ray or SCM analysis 653 00:35:11,470 --> 00:35:12,650 before? 654 00:35:12,650 --> 00:35:13,150 You have. 655 00:35:13,150 --> 00:35:15,520 So can you tell me, is this the Bremsstrahlung spectrum 656 00:35:15,520 --> 00:35:17,605 that you tend to see? 657 00:35:17,605 --> 00:35:19,522 AUDIENCE: Well, I've done [INAUDIBLE] analysis 658 00:35:19,522 --> 00:35:20,250 with imaging. 659 00:35:20,250 --> 00:35:22,347 MIKE SHORT: OK. 660 00:35:22,347 --> 00:35:24,430 Have you ever gotten a regular, old X-ray spectrum 661 00:35:24,430 --> 00:35:26,770 to see what elements are there? 662 00:35:26,770 --> 00:35:28,623 Can you draw what one looks like? 663 00:35:28,623 --> 00:35:29,290 AUDIENCE: Maybe. 664 00:35:29,290 --> 00:35:31,965 MIKE SHORT: You want to try? 665 00:35:31,965 --> 00:35:32,840 They're all the same. 666 00:35:32,840 --> 00:35:35,090 So if you remember any particular one, you're correct. 667 00:35:39,700 --> 00:35:41,110 Yep. 668 00:35:41,110 --> 00:35:42,015 There's some peaks. 669 00:35:42,015 --> 00:35:44,140 And then what does this background stuff look like? 670 00:35:48,250 --> 00:35:49,400 Yeah. 671 00:35:49,400 --> 00:35:52,070 There's some noise and junk on the back of it, right? 672 00:35:52,070 --> 00:35:53,950 So this is actually correct. 673 00:35:53,950 --> 00:35:55,100 Thank you. 674 00:35:55,100 --> 00:35:58,220 And what you actually see here is a bunch 675 00:35:58,220 --> 00:35:59,690 of characteristic peaks. 676 00:35:59,690 --> 00:36:03,350 These will maybe be like the L lines and the K lines 677 00:36:03,350 --> 00:36:06,560 for one element or another, these characteristic X-ray 678 00:36:06,560 --> 00:36:10,090 peaks, on top of the Bremsstrahlung, 679 00:36:10,090 --> 00:36:11,840 the breaking radiation which constitutes 680 00:36:11,840 --> 00:36:13,040 the background here. 681 00:36:13,040 --> 00:36:14,300 And what you actually see-- 682 00:36:14,300 --> 00:36:16,130 I'm just going to draw the background curve 683 00:36:16,130 --> 00:36:18,440 under Julia's curve here-- 684 00:36:18,440 --> 00:36:20,960 looks something like this. 685 00:36:20,960 --> 00:36:23,300 What happened to the real spectrum? 686 00:36:23,300 --> 00:36:27,540 Why don't we observe what actually exists? 687 00:36:27,540 --> 00:36:28,790 There are a couple of reasons. 688 00:36:28,790 --> 00:36:30,376 Does anybody have an idea? 689 00:36:36,300 --> 00:36:38,220 So let's take this to the extreme. 690 00:36:38,220 --> 00:36:40,590 Why don't you think you would observe physically-- 691 00:36:40,590 --> 00:36:42,840 and this is when we actually get into the real world-- 692 00:36:42,840 --> 00:36:45,600 any x-rays with energy in, let's say, the eV 693 00:36:45,600 --> 00:36:52,150 range if you were to try and observe any x-rays at all? 694 00:36:58,470 --> 00:37:01,020 This is where we actually get into what 695 00:37:01,020 --> 00:37:03,510 do these detectors look like. 696 00:37:03,510 --> 00:37:07,570 So there will be some active piece of your material 697 00:37:07,570 --> 00:37:10,080 if this is your detector. 698 00:37:10,080 --> 00:37:15,210 This is most definitely not Rutherford scattering anymore. 699 00:37:15,210 --> 00:37:17,790 And there's got to be some window. 700 00:37:17,790 --> 00:37:20,560 We can make it as thin as we possibly can. 701 00:37:20,560 --> 00:37:23,910 And they make it out of the most X-ray-transparent structural 702 00:37:23,910 --> 00:37:27,720 material that they can, which tends to be beryllium. 703 00:37:27,720 --> 00:37:31,460 So beryllium has got an atomic number 4. 704 00:37:31,460 --> 00:37:33,470 It's the first and lightest element 705 00:37:33,470 --> 00:37:36,230 that you can make structural anythings out of. 706 00:37:36,230 --> 00:37:39,830 So if you want to protect your detector from, let's say, 707 00:37:39,830 --> 00:37:41,945 air or something-- if this were full of air, 708 00:37:41,945 --> 00:37:43,820 it would absorb the x-rays, so you want there 709 00:37:43,820 --> 00:37:45,680 to be pretty much nothing. 710 00:37:45,680 --> 00:37:50,030 You can put a very thin, seven-micron beryllium 711 00:37:50,030 --> 00:37:51,440 window in front. 712 00:37:51,440 --> 00:37:53,520 But the problem is we've already got 713 00:37:53,520 --> 00:37:55,100 one of these mass attenuation curves. 714 00:37:55,100 --> 00:37:57,980 And when you get down to these energy levels, 715 00:37:57,980 --> 00:37:59,990 you attenuate everything. 716 00:37:59,990 --> 00:38:03,175 So the lower energy your Bremsstrahlung is, 717 00:38:03,175 --> 00:38:04,800 the less likely you're going to see it. 718 00:38:04,800 --> 00:38:14,560 So even though this is the actual Bremsstrahlung spectrum, 719 00:38:14,560 --> 00:38:15,560 this is what we observe. 720 00:38:20,040 --> 00:38:22,070 And I haven't finished grading the tests yet. 721 00:38:22,070 --> 00:38:25,095 But I like I promised, for the two folks who do the best, 722 00:38:25,095 --> 00:38:26,720 I'm going to ask you to bring something 723 00:38:26,720 --> 00:38:28,790 in for elemental analysis. 724 00:38:28,790 --> 00:38:31,640 This is precisely what we're going to see. 725 00:38:31,640 --> 00:38:35,000 You're going to see this Bremsstrahlung which is not 726 00:38:35,000 --> 00:38:37,640 the actual spectrum coming out, but this 727 00:38:37,640 --> 00:38:39,530 has to do with the absorption of x-rays 728 00:38:39,530 --> 00:38:43,910 in the detector window, as well as some self-shielding. 729 00:38:43,910 --> 00:38:46,430 If we're using a scanning electron microscope, which 730 00:38:46,430 --> 00:38:49,760 is nothing more than an electron gun, 731 00:38:49,760 --> 00:38:53,060 and you're firing electrons to some distance in the material 732 00:38:53,060 --> 00:38:59,540 where they'll then interact and send off x-rays, 733 00:38:59,540 --> 00:39:03,830 you've also got this part of the material to contend with, 734 00:39:03,830 --> 00:39:05,300 some self-shielding. 735 00:39:07,850 --> 00:39:10,310 So not only do the x-rays all have to get through 736 00:39:10,310 --> 00:39:12,680 the detector window to be counted-- 737 00:39:12,680 --> 00:39:15,560 so the high-energy ones, which we'll 738 00:39:15,560 --> 00:39:17,640 have with small wavelength, get through, 739 00:39:17,640 --> 00:39:20,090 but the low-energy or long-wavelength ones 740 00:39:20,090 --> 00:39:21,530 might get stopped. 741 00:39:21,530 --> 00:39:24,020 You also have to get out of the material itself. 742 00:39:24,020 --> 00:39:25,910 The electrons don't just produce x-rays 743 00:39:25,910 --> 00:39:28,130 in the outer atoms of the material. 744 00:39:28,130 --> 00:39:30,050 They go down a micron or two. 745 00:39:30,050 --> 00:39:33,680 And then the x-rays that are produced in those interactions 746 00:39:33,680 --> 00:39:36,827 have to get back out again. 747 00:39:36,827 --> 00:39:37,660 So it's interesting. 748 00:39:37,660 --> 00:39:40,520 It's kind of like the inverse photoelectric effect, right? 749 00:39:40,520 --> 00:39:43,140 In the photoelectric effect, photon comes in, 750 00:39:43,140 --> 00:39:44,850 electrons come out. 751 00:39:44,850 --> 00:39:47,910 In a scanning electron microscope, electrons come in. 752 00:39:47,910 --> 00:39:49,380 Photons come out. 753 00:39:49,380 --> 00:39:53,010 Many of them are these characteristic x-rays. 754 00:39:53,010 --> 00:39:54,810 Because now if we start to review 755 00:39:54,810 --> 00:39:58,230 what sort of interactions are possible when we fire electrons 756 00:39:58,230 --> 00:40:01,465 into material, we've just gone over Bremsstrahlung. 757 00:40:01,465 --> 00:40:03,840 And we know that with higher and higher energy electrons, 758 00:40:03,840 --> 00:40:05,910 you're going to get more and more Bremsstrahlung. 759 00:40:05,910 --> 00:40:09,300 But you're not going to see the actual x-rays produced 760 00:40:09,300 --> 00:40:12,810 at low energies no matter what, because this isn't just 761 00:40:12,810 --> 00:40:13,710 a system on paper. 762 00:40:13,710 --> 00:40:15,210 It's real life. 763 00:40:15,210 --> 00:40:19,140 And you're going to get characteristic x-rays that 764 00:40:19,140 --> 00:40:23,220 come from energy transitions. 765 00:40:23,220 --> 00:40:25,380 So if you fire in an electron, and you 766 00:40:25,380 --> 00:40:29,910 happen to undergo one of these ionization collisions, 767 00:40:29,910 --> 00:40:33,375 you might just knock an electron out. 768 00:40:33,375 --> 00:40:38,250 So let's say an electron comes in, knocks an electron out. 769 00:40:38,250 --> 00:40:43,610 Then another electron fills that shell, 770 00:40:43,610 --> 00:40:47,840 giving off-- in this case, it would be a k alpha or a shell 2 771 00:40:47,840 --> 00:40:50,150 to a shell 1 X-ray the way I've drawn 772 00:40:50,150 --> 00:40:52,490 it, which is why Julia has got everything 773 00:40:52,490 --> 00:40:54,050 right on the spectrum here. 774 00:40:54,050 --> 00:40:56,120 There's the Bremsstrahlung, and then there's 775 00:40:56,120 --> 00:40:58,460 these characteristic peaks. 776 00:40:58,460 --> 00:41:01,740 The background is due to radiative stopping power, 777 00:41:01,740 --> 00:41:03,500 and these characteristic peaks give away 778 00:41:03,500 --> 00:41:06,980 some of the ionization stopping power. 779 00:41:06,980 --> 00:41:10,310 And so all in one spectrum, you can see just about everything 780 00:41:10,310 --> 00:41:12,930 going on in this material. 781 00:41:12,930 --> 00:41:17,150 The last thing that you can't see that I would be remiss 782 00:41:17,150 --> 00:41:21,860 if I didn't talk about it as a radiation material scientist 783 00:41:21,860 --> 00:41:24,590 is radiation material science, which 784 00:41:24,590 --> 00:41:29,090 really is concerned with mostly Rutherford scattering, 785 00:41:29,090 --> 00:41:31,547 Rutherford or hard sphere scattering. 786 00:41:37,760 --> 00:41:41,420 This is the last of the major interactions 787 00:41:41,420 --> 00:41:45,230 between charged particles and matter that concern us. 788 00:41:45,230 --> 00:41:47,630 It's not really in your reading except for, I think, 789 00:41:47,630 --> 00:41:51,282 being mentioned once, because they didn't 790 00:41:51,282 --> 00:41:52,490 seem to think it's important. 791 00:41:52,490 --> 00:41:54,620 But I happen to think it's extremely important, 792 00:41:54,620 --> 00:41:56,960 because this is the basis behind radiation damage. 793 00:42:03,400 --> 00:42:05,200 In all of these collisions right here, 794 00:42:05,200 --> 00:42:08,320 you have some sort of displacement of electrons. 795 00:42:08,320 --> 00:42:09,872 And those electrons can get ionized, 796 00:42:09,872 --> 00:42:11,830 and other ones will fill them back in the holes 797 00:42:11,830 --> 00:42:13,250 and whatever they'll do. 798 00:42:13,250 --> 00:42:17,200 But at no point were nuclei displaced. 799 00:42:17,200 --> 00:42:20,770 You can transfer a lot of energy without moving any atoms 800 00:42:20,770 --> 00:42:21,760 around. 801 00:42:21,760 --> 00:42:24,580 But when your energy starts to get lower, 802 00:42:24,580 --> 00:42:29,097 you end up with a new kind of stopping power-- 803 00:42:29,097 --> 00:42:30,055 let's call it nuclear-- 804 00:42:32,810 --> 00:42:39,350 which scales with, as always, a number density times pi. 805 00:42:39,350 --> 00:42:40,640 Let's see. 806 00:42:40,640 --> 00:42:42,740 Little z, big z, e the 4th-- 807 00:42:42,740 --> 00:42:46,310 everything looks pretty similar so far, except for now 808 00:42:46,310 --> 00:42:49,220 we've got the energy of the incoming material, 809 00:42:49,220 --> 00:42:54,208 and now we have a mass ratio. 810 00:42:54,208 --> 00:42:55,750 Because in this case, you're actually 811 00:42:55,750 --> 00:42:57,370 undergoing some sort of a hard sphere 812 00:42:57,370 --> 00:43:02,020 collision between one atom and the other times 813 00:43:02,020 --> 00:43:03,020 the natural log. 814 00:43:03,020 --> 00:43:06,310 This is going to look awfully familiar. 815 00:43:06,310 --> 00:43:10,980 It ends up being some energy term over-- 816 00:43:10,980 --> 00:43:14,200 actually, let's just go with-- yeah, 817 00:43:14,200 --> 00:43:18,280 gamma ei over some new energy. 818 00:43:18,280 --> 00:43:22,550 This thing right here is called the displacement threshold 819 00:43:22,550 --> 00:43:23,050 energy. 820 00:43:28,120 --> 00:43:35,730 And it ranges from about 25 to 90 eV, but it's usually 40 eV. 821 00:43:35,730 --> 00:43:37,360 And what that is-- it's the max-- 822 00:43:37,360 --> 00:43:39,130 the minimum amount of energy that 823 00:43:39,130 --> 00:43:43,300 has to be imparted to a nucleus smack head on in order for it 824 00:43:43,300 --> 00:43:46,090 to move from its original atomic position. 825 00:43:46,090 --> 00:43:48,990 And that's what's known as a hard sphere type collision. 826 00:43:48,990 --> 00:43:52,120 Or in this case, it's just like all 827 00:43:52,120 --> 00:43:56,230 the other q-equation-looking scenarios 828 00:43:56,230 --> 00:43:59,730 that we looked at before. 829 00:43:59,730 --> 00:44:02,770 So let's say the little nucleus goes off, 830 00:44:02,770 --> 00:44:05,395 and the big nucleus goes off. 831 00:44:05,395 --> 00:44:07,270 This should look familiar by now because I've 832 00:44:07,270 --> 00:44:09,610 harped on it probably too much. 833 00:44:09,610 --> 00:44:13,960 Now what I want you to consider is this big nucleus 834 00:44:13,960 --> 00:44:14,950 had a position. 835 00:44:14,950 --> 00:44:18,570 It liked where it was, and now it's been knocked away. 836 00:44:18,570 --> 00:44:21,610 What's left over is an atomic vacancy, 837 00:44:21,610 --> 00:44:25,810 which is the most basic building block of radiation damage. 838 00:44:25,810 --> 00:44:28,360 So sometimes it's neat to look at the ratio of-- 839 00:44:31,010 --> 00:44:31,570 let's see. 840 00:44:31,570 --> 00:44:33,280 Make sure I get this ratio right. 841 00:44:33,280 --> 00:44:34,510 Ionization on top. 842 00:44:41,310 --> 00:44:44,970 To look and see when is ionization versus radiation 843 00:44:44,970 --> 00:44:46,910 damage actually important. 844 00:44:46,910 --> 00:44:53,010 And the ratio scales with 2 times the mass of the nucleus 845 00:44:53,010 --> 00:44:59,145 over MeZ times their respective natural log threshold things. 846 00:45:02,060 --> 00:45:06,450 And that's the ionization potential and log gamma 847 00:45:06,450 --> 00:45:10,110 ei over ed. 848 00:45:10,110 --> 00:45:15,000 So what this says is that for higher energies, 849 00:45:15,000 --> 00:45:18,270 ionization is more important, and for lower energies, 850 00:45:18,270 --> 00:45:20,610 nuclear stopping power or radiation damage 851 00:45:20,610 --> 00:45:22,560 is more important. 852 00:45:22,560 --> 00:45:28,290 If we graph these two, let's say, on a log e graph-- 853 00:45:28,290 --> 00:45:30,450 and let's say we have our nuclear stopping 854 00:45:30,450 --> 00:45:36,750 power in blue and our ionization stopping power in green-- 855 00:45:36,750 --> 00:45:40,760 we end up with curves that look something like this. 856 00:45:44,483 --> 00:45:45,275 That's our nuclear. 857 00:45:48,140 --> 00:45:51,470 That's our electronic or ionic. 858 00:45:51,470 --> 00:45:55,490 So what this actually says is if you fire high-energy neutrons 859 00:45:55,490 --> 00:45:58,760 or high-energy protons into a material, 860 00:45:58,760 --> 00:46:02,450 it's ionization that does most of the damage at high energies 861 00:46:02,450 --> 00:46:08,720 until you slow down to around like 10 to 100 keV 862 00:46:08,720 --> 00:46:15,470 level, curiously very similar to this 500 times i bar, 863 00:46:15,470 --> 00:46:19,430 the mean ionization potential, at which point Rutherford 864 00:46:19,430 --> 00:46:21,590 scattering or hard sphere scattering becomes 865 00:46:21,590 --> 00:46:23,518 the dominant mechanism. 866 00:46:23,518 --> 00:46:26,060 And so what this says is if we want to draw a picture of what 867 00:46:26,060 --> 00:46:28,120 radiation damage looks like-- 868 00:46:28,120 --> 00:46:32,450 let's say we had a proton that we're firing into a material, 869 00:46:32,450 --> 00:46:36,450 and it hits some atom that we're going 870 00:46:36,450 --> 00:46:40,550 to call the PKA or Primary Knock-on Atom. 871 00:46:40,550 --> 00:46:43,270 That PKA then becomes-- 872 00:46:43,270 --> 00:46:45,830 let's say it was nickel. 873 00:46:45,830 --> 00:46:48,920 It's like a nickel plus 26 ion because you've 874 00:46:48,920 --> 00:46:52,350 knocked the nucleus out of its electron cloud, effectively, 875 00:46:52,350 --> 00:46:54,590 and it's now flying out through the material. 876 00:46:54,590 --> 00:46:59,720 That proton might go off to do more damage somewhere else, 877 00:46:59,720 --> 00:47:02,410 but it's not actually the protons 878 00:47:02,410 --> 00:47:04,310 or the incoming particles that do the bulk 879 00:47:04,310 --> 00:47:05,840 of the final radiation damage. 880 00:47:05,840 --> 00:47:12,830 The radiation damage is mostly self-ion radiation. 881 00:47:12,830 --> 00:47:15,200 Even though it all starts with the incoming particle, 882 00:47:15,200 --> 00:47:17,840 nothing would happen if the incoming particle didn't 883 00:47:17,840 --> 00:47:18,860 show up. 884 00:47:18,860 --> 00:47:20,930 Most of the final results of the damage 885 00:47:20,930 --> 00:47:24,590 are from these heavy ion collisions. 886 00:47:24,590 --> 00:47:27,680 And so we actually talked a little bit about-- 887 00:47:27,680 --> 00:47:30,590 I think we talked about when this ionization starts 888 00:47:30,590 --> 00:47:33,890 to pick up for electrons versus heavy ions. 889 00:47:33,890 --> 00:47:37,273 If you think about when electrons start to radiate away 890 00:47:37,273 --> 00:47:39,440 most of their energy, taking it away from radiation, 891 00:47:39,440 --> 00:47:42,980 it's like 10 to 100 MeV. 892 00:47:42,980 --> 00:47:45,860 What would be the case for a heavy ion, like even a proton? 893 00:47:50,270 --> 00:47:53,060 Well, what's the only thing that changes 894 00:47:53,060 --> 00:47:58,586 when you change from an electron to a proton here? 895 00:47:58,586 --> 00:48:00,297 AUDIENCE: The charge. 896 00:48:00,297 --> 00:48:02,630 MIKE SHORT: Well, yeah, the charge is the opposite sign, 897 00:48:02,630 --> 00:48:04,200 but of equal strength. 898 00:48:04,200 --> 00:48:07,121 But what else in this formula? 899 00:48:07,121 --> 00:48:08,488 AUDIENCE: [INAUDIBLE] 900 00:48:08,488 --> 00:48:09,530 MIKE SHORT: That's right. 901 00:48:12,180 --> 00:48:15,900 So for heavy ions, for even things like protons, 902 00:48:15,900 --> 00:48:21,600 you need to go at approximately 1,837 903 00:48:21,600 --> 00:48:26,160 squared more energy than the electron. 904 00:48:26,160 --> 00:48:29,010 So we're talking in the gigaelectron volt 905 00:48:29,010 --> 00:48:33,670 to teraelectron volt range for ions. 906 00:48:33,670 --> 00:48:35,910 So this is why Bremsstrahlung is not 907 00:48:35,910 --> 00:48:39,600 important for any sort of ion interactions 908 00:48:39,600 --> 00:48:41,910 unless you are a high-energy physicist 909 00:48:41,910 --> 00:48:44,040 and you're working in the GeV or gigaelectron 910 00:48:44,040 --> 00:48:46,540 volt in the upper range. 911 00:48:46,540 --> 00:48:48,520 So we like to say in the radiation damage field 912 00:48:48,520 --> 00:48:50,140 if you want to know the total stopping 913 00:48:50,140 --> 00:48:55,230 power from all interactions, you have 914 00:48:55,230 --> 00:49:00,920 to take into account the ionizations. 915 00:49:04,590 --> 00:49:07,480 I'll just make that a minus sign for the symbols. 916 00:49:07,480 --> 00:49:14,760 The nuclear and the radiative. 917 00:49:14,760 --> 00:49:16,890 For most radiation damage processes 918 00:49:16,890 --> 00:49:21,660 except for high-energy electron radiation, we neglect that. 919 00:49:21,660 --> 00:49:25,680 The reason is that the radiative to ionization stopping 920 00:49:25,680 --> 00:49:28,140 power is pretty close to zero. 921 00:49:28,140 --> 00:49:33,610 It's like-- even at 10 NeV, it's like 1 over 2,000 squared-- 922 00:49:33,610 --> 00:49:35,845 or 1 over, I guess, 4,000,000. 923 00:49:35,845 --> 00:49:37,840 It doesn't matter at all. 924 00:49:37,840 --> 00:49:40,690 With heavier ions, it becomes even less of an issue 925 00:49:40,690 --> 00:49:43,600 because you can deflect a heavier ion less 926 00:49:43,600 --> 00:49:46,350 with the same Coulomb. 927 00:49:46,350 --> 00:49:48,510 And so what ends up only mattering 928 00:49:48,510 --> 00:49:53,280 is the ionization stopping power and the nuclear stopping power. 929 00:49:53,280 --> 00:49:57,540 It's this nuclear stopping power that leads to collisions. 930 00:49:57,540 --> 00:50:00,190 And it's like two of five of. 931 00:50:00,190 --> 00:50:02,760 So I want to stop here and answer any questions. 932 00:50:02,760 --> 00:50:05,760 And I'll hijack a bit of the neutron discussion on Thursday 933 00:50:05,760 --> 00:50:07,290 with some review of this and filling 934 00:50:07,290 --> 00:50:09,090 in the last gaps of radiation damage. 935 00:50:11,680 --> 00:50:15,170 So anyone have any questions from today? 936 00:50:15,170 --> 00:50:15,670 Yeah? 937 00:50:15,670 --> 00:50:17,253 AUDIENCE: Can you repeat what you just 938 00:50:17,253 --> 00:50:19,180 said about why the radiation term goes away? 939 00:50:19,180 --> 00:50:19,888 MIKE SHORT: Yeah. 940 00:50:19,888 --> 00:50:23,367 The radiation term goes away because of that. 941 00:50:23,367 --> 00:50:25,700 AUDIENCE: And that's under the assumption you're working 942 00:50:25,700 --> 00:50:28,340 with a proton or a heavier-- 943 00:50:28,340 --> 00:50:29,330 MIKE SHORT: Yeah. 944 00:50:29,330 --> 00:50:31,520 If you're working with an electron, 945 00:50:31,520 --> 00:50:32,840 then it actually does matter. 946 00:50:32,840 --> 00:50:35,570 If you're firing 10 MeV electrons into something, 947 00:50:35,570 --> 00:50:38,270 you must account for the radiative stopping power, 948 00:50:38,270 --> 00:50:39,500 because there's a lot of it. 949 00:50:39,500 --> 00:50:42,880 At 10 MeV, there's as much radiative as ionizing, 950 00:50:42,880 --> 00:50:45,520 and there's basically no nuclear yet. 951 00:50:45,520 --> 00:50:46,870 But for anything heavier-- 952 00:50:46,870 --> 00:50:50,500 even muons, which are approximately 237 times 953 00:50:50,500 --> 00:50:55,030 heavier, or protons, which are approximately 1,837 times 954 00:50:55,030 --> 00:50:57,490 heavier, it totally doesn't matter because it scales 955 00:50:57,490 --> 00:51:00,205 with the mass ratio squared. 956 00:51:00,205 --> 00:51:02,320 It might be 267 for muons. 957 00:51:02,320 --> 00:51:04,960 I forget that middle number. 958 00:51:04,960 --> 00:51:08,387 But still, 267 squared is a pretty big number. 959 00:51:08,387 --> 00:51:09,720 Was there another question here? 960 00:51:09,720 --> 00:51:13,160 I thought I had seen a hand. 961 00:51:13,160 --> 00:51:14,740 So remember, you guys had said you 962 00:51:14,740 --> 00:51:17,290 want to see some radiation material science or radiation 963 00:51:17,290 --> 00:51:18,040 damage. 964 00:51:18,040 --> 00:51:19,570 This is where it comes from. 965 00:51:19,570 --> 00:51:22,120 This is why I love teaching graduate radiation 966 00:51:22,120 --> 00:51:24,240 damage and 22.01 at the same time-- 967 00:51:24,240 --> 00:51:25,930 because they're the same thing. 968 00:51:25,930 --> 00:51:27,430 Except you guys get the derivations, 969 00:51:27,430 --> 00:51:30,040 and in the grad class, I say I assume they know it. 970 00:51:30,040 --> 00:51:32,040 And then in the homework, I find out they don't. 971 00:51:32,040 --> 00:51:34,640 But it doesn't matter because they're supposed to. 972 00:51:34,640 --> 00:51:37,310 At least you guys will, so you've got the power. 973 00:51:37,310 --> 00:51:39,190 And knowledge brings fear, as I like to say. 974 00:51:41,880 --> 00:51:43,063 OK. 975 00:51:43,063 --> 00:51:44,480 I'll see you guys on Thursday when 976 00:51:44,480 --> 00:51:46,190 we'll wrap up a little bit more radiation 977 00:51:46,190 --> 00:51:47,590 damage, because I can't resist. 978 00:51:47,590 --> 00:51:50,090 And then we'll start moving into neutron interactions, which 979 00:51:50,090 --> 00:51:52,160 is kind of taking a step down from here, 980 00:51:52,160 --> 00:51:55,220 because there aren't really any electronic interactions. 981 00:51:55,220 --> 00:51:57,800 But because we can deal with enormous populations 982 00:51:57,800 --> 00:52:01,846 of neutrons, things are going to get messy. 983 00:52:01,846 --> 00:52:03,530 Have you seen the equation shirts 984 00:52:03,530 --> 00:52:07,160 that we have here, the neutron transport equation shirts? 985 00:52:07,160 --> 00:52:07,660 Yeah. 986 00:52:07,660 --> 00:52:11,100 We're going to derive that on Thursday.