WEBVTT 00:00:00.000 --> 00:00:16.305 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:16.305 --> 00:00:17.180 align:middle line:90% PROFESSOR: All right. 00:00:17.180 --> 00:00:20.615 align:middle line:84% So in the last lecture, we discussed about essentially-- 00:00:20.615 --> 00:00:22.240 align:middle line:84% give you an overview of different kinds 00:00:22.240 --> 00:00:25.400 align:middle line:90% of inorganic network glasses. 00:00:25.400 --> 00:00:27.417 align:middle line:84% What we'll focus on in this lecture-- 00:00:27.417 --> 00:00:29.000 align:middle line:84% we'll start by essentially wrapping up 00:00:29.000 --> 00:00:31.640 align:middle line:84% the introduction of different glass categories. 00:00:31.640 --> 00:00:34.600 align:middle line:84% And then we'll move on to actually my favorite part 00:00:34.600 --> 00:00:37.560 align:middle line:84% of this class, which is talking about glass-forming theories 00:00:37.560 --> 00:00:42.200 align:middle line:84% and how topology actually impacts glass network stability. 00:00:42.200 --> 00:00:42.840 align:middle line:90% All right. 00:00:42.840 --> 00:00:48.740 align:middle line:84% So the next class I'm going to discuss here, 00:00:48.740 --> 00:00:51.040 align:middle line:84% these are essentially amorphous semiconductors. 00:00:51.040 --> 00:00:53.800 align:middle line:84% In particular, we are mostly talking about group four 00:00:53.800 --> 00:00:56.640 align:middle line:84% elements, so amorphous silicon, amorphous germanium, 00:00:56.640 --> 00:00:58.760 align:middle line:90% amorphous carbon. 00:00:58.760 --> 00:01:01.440 align:middle line:84% If you look at some literature, people sometimes call it 00:01:01.440 --> 00:01:03.200 align:middle line:90% tetrahedral "glasses." 00:01:03.200 --> 00:01:05.519 align:middle line:84% I put a quotation mark there because these are really 00:01:05.519 --> 00:01:06.760 align:middle line:90% not glasses. 00:01:06.760 --> 00:01:09.800 align:middle line:84% So we talk about what constitutes glass. 00:01:09.800 --> 00:01:12.860 align:middle line:84% A glass needs to have a metastable disordered structure. 00:01:12.860 --> 00:01:16.480 align:middle line:84% And then you also need to have glass transition. 00:01:16.480 --> 00:01:18.800 align:middle line:84% So for these amorphous semiconductors, 00:01:18.800 --> 00:01:20.600 align:middle line:90% they are definitely amorphous. 00:01:20.600 --> 00:01:23.760 align:middle line:90% But they lack glass transition. 00:01:23.760 --> 00:01:26.600 align:middle line:84% In fact, in order to form these semiconductors, 00:01:26.600 --> 00:01:29.540 align:middle line:84% unlike conventional glass where you start from a melt, 00:01:29.540 --> 00:01:30.782 align:middle line:90% you then cool down. 00:01:30.782 --> 00:01:32.240 align:middle line:84% And then a supercooled liquid, then 00:01:32.240 --> 00:01:34.860 align:middle line:84% go through glass transition, and then become the glassy state. 00:01:34.860 --> 00:01:39.360 align:middle line:84% For these materials, the way to prepare them 00:01:39.360 --> 00:01:41.580 align:middle line:84% is to usually go directly from the gas phase. 00:01:41.580 --> 00:01:44.080 align:middle line:84% You do a vapor phase deposition, whether it's physical vapor 00:01:44.080 --> 00:01:47.000 align:middle line:84% deposition or chemical vapor deposition to directly form 00:01:47.000 --> 00:01:48.020 align:middle line:90% amorphous-thin film. 00:01:48.020 --> 00:01:51.600 align:middle line:84% You simply skip that glass transition step, 00:01:51.600 --> 00:01:54.800 align:middle line:84% Also, when you heat them up, if it's traditional glass, when 00:01:54.800 --> 00:01:57.770 align:middle line:84% you heat it up, it's going to soften, 00:01:57.770 --> 00:02:00.170 align:middle line:84% and then eventually goes back into essentially 00:02:00.170 --> 00:02:01.190 align:middle line:90% a supercooled liquid. 00:02:01.190 --> 00:02:04.770 align:middle line:84% Whereas for these amorphous semiconductors, when 00:02:04.770 --> 00:02:08.050 align:middle line:84% you heat them up, they crystallize well 00:02:08.050 --> 00:02:11.370 align:middle line:84% before they exhibit any signature of glass transition. 00:02:11.370 --> 00:02:14.510 align:middle line:84% And that's why they are considered as amorphous. 00:02:14.510 --> 00:02:16.850 align:middle line:84% But they are not the glass, at least not 00:02:16.850 --> 00:02:20.430 align:middle line:90% in the traditional sense. 00:02:20.430 --> 00:02:22.290 align:middle line:84% So now if you look at the structure 00:02:22.290 --> 00:02:26.288 align:middle line:84% for this kind of amorphous group for semiconductors, silicon-- 00:02:26.288 --> 00:02:28.830 align:middle line:84% if you think about silicon, you have diamond cubic structure. 00:02:28.830 --> 00:02:30.410 align:middle line:84% Each silicon for four coordinated 00:02:30.410 --> 00:02:34.170 align:middle line:84% form this kind of periodic network. 00:02:34.170 --> 00:02:36.410 align:middle line:84% When it becomes amorphous, you still 00:02:36.410 --> 00:02:38.690 align:middle line:84% get a little bit of distortion of the bond angles. 00:02:38.690 --> 00:02:42.530 align:middle line:84% And you also change local coordination structure. 00:02:42.530 --> 00:02:44.290 align:middle line:84% One of the key structure signatures 00:02:44.290 --> 00:02:46.490 align:middle line:84% in this amorphous semiconductor is 00:02:46.490 --> 00:02:49.410 align:middle line:84% that you tend to have some silicon with what's 00:02:49.410 --> 00:02:52.530 align:middle line:90% called a dangling bond. 00:02:52.530 --> 00:02:55.570 align:middle line:84% A dangling bond basically means that you 00:02:55.570 --> 00:02:59.130 align:middle line:84% have essentially your one electron that does not 00:02:59.130 --> 00:03:00.970 align:middle line:90% pair with other electrons. 00:03:00.970 --> 00:03:02.890 align:middle line:84% So the silicon becomes basically three or four 00:03:02.890 --> 00:03:05.910 align:middle line:84% coordinated with one lone electron sitting there. 00:03:05.910 --> 00:03:09.120 align:middle line:90% 00:03:09.120 --> 00:03:12.930 align:middle line:84% So these dangling bonds actually has a profound impact 00:03:12.930 --> 00:03:17.290 align:middle line:84% on the electronic properties of these amorphous semiconductors. 00:03:17.290 --> 00:03:20.070 align:middle line:84% If you look at the density of states-- 00:03:20.070 --> 00:03:22.070 align:middle line:84% so this is the density of states-- 00:03:22.070 --> 00:03:29.290 align:middle line:90% 00:03:29.290 --> 00:03:32.330 align:middle line:90% so this is basically the energy. 00:03:32.330 --> 00:03:36.970 align:middle line:84% And then this will be the density of states. 00:03:36.970 --> 00:03:39.850 align:middle line:84% So what's going to happen there is that if it's 00:03:39.850 --> 00:03:42.207 align:middle line:84% a conventional semiconductor, then you 00:03:42.207 --> 00:03:44.290 align:middle line:84% will have your valence band, your conduction band. 00:03:44.290 --> 00:03:46.930 align:middle line:84% Inside the band gap, there's nothing. 00:03:46.930 --> 00:03:49.770 align:middle line:84% But with the introduction of these dangling bonds, 00:03:49.770 --> 00:03:54.730 align:middle line:84% they tend to form what's called a mid gap defect. 00:03:54.730 --> 00:03:57.730 align:middle line:84% So close to the middle of the end gap, 00:03:57.730 --> 00:04:00.850 align:middle line:84% you then have a number of states that actually correspond 00:04:00.850 --> 00:04:03.170 align:middle line:90% to these dangling bonds. 00:04:03.170 --> 00:04:08.650 align:middle line:84% Now this is very harmful in terms of electronic properties 00:04:08.650 --> 00:04:12.490 align:middle line:84% or semiconductors, because if you have some states in there-- 00:04:12.490 --> 00:04:13.850 align:middle line:90% so this is EC. 00:04:13.850 --> 00:04:15.370 align:middle line:90% This is EV. 00:04:15.370 --> 00:04:18.690 align:middle line:84% Suppose you have some electrons excited into the conduction 00:04:18.690 --> 00:04:19.410 align:middle line:90% band. 00:04:19.410 --> 00:04:23.890 align:middle line:84% It can then very quickly relax into these mid-gap states, 00:04:23.890 --> 00:04:29.570 align:middle line:84% and then recombine with a hole in the valence band. 00:04:29.570 --> 00:04:31.410 align:middle line:84% So you quickly annihilate, essentially, 00:04:31.410 --> 00:04:34.270 align:middle line:84% any kind of excited electrons in the conduction band. 00:04:34.270 --> 00:04:40.470 align:middle line:90% 00:04:40.470 --> 00:04:41.970 align:middle line:84% Well, amorphous silicon, people know 00:04:41.970 --> 00:04:44.230 align:middle line:84% that amorphous silicon exists for decades, 00:04:44.230 --> 00:04:46.860 align:middle line:90% for a very long time, 00:04:46.860 --> 00:04:48.690 align:middle line:84% For quite a while, people consider it 00:04:48.690 --> 00:04:52.190 align:middle line:84% as a useless material for any kind of electronics, 00:04:52.190 --> 00:04:53.690 align:middle line:90% exactly because of this-- 00:04:53.690 --> 00:04:56.130 align:middle line:84% this is known as a Shockley-Read-Hall 00:04:56.130 --> 00:04:59.230 align:middle line:84% recombination, SRH recombination mechanism. 00:04:59.230 --> 00:05:02.096 align:middle line:90% 00:05:02.096 --> 00:05:04.065 align:middle line:84% So the change comes in when people 00:05:04.065 --> 00:05:05.690 align:middle line:84% start to realize that they can actually 00:05:05.690 --> 00:05:08.990 align:middle line:84% use introducing hydrogen to passivate these defects. 00:05:08.990 --> 00:05:12.330 align:middle line:84% So before, the way people used to actually prepare 00:05:12.330 --> 00:05:15.250 align:middle line:84% this amorphous silicon, is to do things like evaporation, 00:05:15.250 --> 00:05:16.090 align:middle line:90% for example. 00:05:16.090 --> 00:05:17.990 align:middle line:84% So you have essentially a piece of silicon. 00:05:17.990 --> 00:05:20.210 align:middle line:84% You heat it up to well above its melting point. 00:05:20.210 --> 00:05:21.770 align:middle line:84% And it actually essentially vaporizes 00:05:21.770 --> 00:05:23.395 align:middle line:84% and then deployed into a cold substrate 00:05:23.395 --> 00:05:24.510 align:middle line:90% to form amorphous film. 00:05:24.510 --> 00:05:27.530 align:middle line:84% In the process, because these atoms is coming into contact 00:05:27.530 --> 00:05:29.690 align:middle line:84% with this very cold substrate, so effectively, 00:05:29.690 --> 00:05:31.570 align:middle line:90% it gets quenched quickly. 00:05:31.570 --> 00:05:34.810 align:middle line:84% So it cannot essentially form this crystalline structure. 00:05:34.810 --> 00:05:38.210 align:middle line:84% But instead, atoms essentially randomly pack to form 00:05:38.210 --> 00:05:39.250 align:middle line:90% amorphous structure. 00:05:39.250 --> 00:05:41.330 align:middle line:84% But the problem with that amorphous silicon 00:05:41.330 --> 00:05:43.530 align:middle line:84% is that it's pure amorphous silicon. 00:05:43.530 --> 00:05:45.090 align:middle line:90% There's nothing else. 00:05:45.090 --> 00:05:49.810 align:middle line:84% This is one of the cases where being pure is actually not good. 00:05:49.810 --> 00:05:53.280 align:middle line:84% If you go to a chemical vapor deposition process, 00:05:53.280 --> 00:05:55.500 align:middle line:84% for example, the key trick here is 00:05:55.500 --> 00:05:58.720 align:middle line:84% that he's introducing a hydrogen, lots of hydrogen. 00:05:58.720 --> 00:06:00.620 align:middle line:84% So if you think about a chemical reaction 00:06:00.620 --> 00:06:02.540 align:middle line:84% here in a chemical vapor deposition, 00:06:02.540 --> 00:06:06.100 align:middle line:84% you start it out with silane, which is basically SiH4. 00:06:06.100 --> 00:06:09.080 align:middle line:84% You also use a hydrogen actually as a carrier gas. 00:06:09.080 --> 00:06:11.940 align:middle line:84% So there's lots of hydrogen around. 00:06:11.940 --> 00:06:13.440 align:middle line:90% You then go to a plasma. 00:06:13.440 --> 00:06:17.020 align:middle line:84% This plasma then helps you to break down this SIH4 00:06:17.020 --> 00:06:18.900 align:middle line:84% into different kinds of radicals. 00:06:18.900 --> 00:06:22.100 align:middle line:84% So radicals essentially means that you have this excited state 00:06:22.100 --> 00:06:25.460 align:middle line:84% molecules where the SIH4, SIH2, SIH, 00:06:25.460 --> 00:06:28.780 align:middle line:90% also like mobile hydrogen ions. 00:06:28.780 --> 00:06:33.220 align:middle line:84% Then those then cluster onto the substrate surface and then 00:06:33.220 --> 00:06:35.220 align:middle line:84% eventually form the [INAUDIBLE] film, 00:06:35.220 --> 00:06:37.300 align:middle line:84% when they actually are coalesced together. 00:06:37.300 --> 00:06:40.740 align:middle line:84% So now you notice that because the structural unit 00:06:40.740 --> 00:06:43.820 align:middle line:84% we use to form the thin film are these radicals. 00:06:43.820 --> 00:06:47.140 align:middle line:84% And these radicals contain lots of hydrogen. 00:06:47.140 --> 00:06:49.540 align:middle line:84% So the resulting film also incorporate 00:06:49.540 --> 00:06:51.700 align:middle line:90% lots of hydrogen atoms. 00:06:51.700 --> 00:06:54.140 align:middle line:84% So the customary way to label this kind of chemical 00:06:54.140 --> 00:06:56.640 align:middle line:84% composition is like what I'm showing you on the board there. 00:06:56.640 --> 00:06:58.260 align:middle line:90% It's amorphous silicon, h. 00:06:58.260 --> 00:07:01.400 align:middle line:84% So this is called hydrogenated amorphous silicon. 00:07:01.400 --> 00:07:05.660 align:middle line:90% 00:07:05.660 --> 00:07:09.260 align:middle line:84% Because hydrogen is such a small atom-- it's very mobile. 00:07:09.260 --> 00:07:12.860 align:middle line:84% It easily moves around in the entire lattice. 00:07:12.860 --> 00:07:15.580 align:middle line:84% And hydrogen also has one excess electron. 00:07:15.580 --> 00:07:17.660 align:middle line:84% So that electron, it can then combine 00:07:17.660 --> 00:07:20.820 align:middle line:84% with these dangling bonds and form these SIH bonds. 00:07:20.820 --> 00:07:25.380 align:middle line:84% In the process, it helps to annihilate this mid-gap defect 00:07:25.380 --> 00:07:26.000 align:middle line:90% state. 00:07:26.000 --> 00:07:29.980 align:middle line:90% 00:07:29.980 --> 00:07:32.820 align:middle line:84% And that's what then made amorphous silicon becoming 00:07:32.820 --> 00:07:34.760 align:middle line:90% useful electronic material. 00:07:34.760 --> 00:07:37.440 align:middle line:90% 00:07:37.440 --> 00:07:43.460 align:middle line:84% So nowadays, amorphous silicon processing is used quite widely 00:07:43.460 --> 00:07:46.060 align:middle line:84% in a lot of electronic devices, in particular when 00:07:46.060 --> 00:07:50.695 align:middle line:84% you're dealing with so-called macro electronic devices. 00:07:50.695 --> 00:07:52.820 align:middle line:84% So you're all familiar with microelectronic devices 00:07:52.820 --> 00:07:53.800 align:middle line:90% like computer chips. 00:07:53.800 --> 00:07:56.460 align:middle line:84% But there are also another class of devices 00:07:56.460 --> 00:07:59.500 align:middle line:84% where the figure of merit is not about trying 00:07:59.500 --> 00:08:01.740 align:middle line:84% to make very small line width or very high speed. 00:08:01.740 --> 00:08:03.740 align:middle line:84% But rather you would need to make, essentially, 00:08:03.740 --> 00:08:07.820 align:middle line:84% a large area devices, such as a display or solar cell. 00:08:07.820 --> 00:08:10.760 align:middle line:84% So for those kind of microelectronic devices, 00:08:10.760 --> 00:08:14.780 align:middle line:84% the figure of merit is basically a cost per area. 00:08:14.780 --> 00:08:17.700 align:middle line:84% So amorphous silicon is actually particularly good for that 00:08:17.700 --> 00:08:20.180 align:middle line:84% because, number one, unlike crystalline silicon, 00:08:20.180 --> 00:08:21.860 align:middle line:84% if you want to grow crystalline silicon, 00:08:21.860 --> 00:08:23.777 align:middle line:84% you need to go to a single crystalline furnace 00:08:23.777 --> 00:08:25.540 align:middle line:84% and then actually pull the crystals. 00:08:25.540 --> 00:08:27.420 align:middle line:84% So the size of the area you can get 00:08:27.420 --> 00:08:30.940 align:middle line:84% is actually constrained by the wafer size, wafer diameter. 00:08:30.940 --> 00:08:33.438 align:middle line:84% Versus amorphous silicon, later on, we all 00:08:33.438 --> 00:08:35.980 align:middle line:84% have one lecture dedicated to talking about amorphous silicon 00:08:35.980 --> 00:08:36.580 align:middle line:90% layer. 00:08:36.580 --> 00:08:39.020 align:middle line:84% You can actually deposit them on huge glass sheets, 00:08:39.020 --> 00:08:40.520 align:middle line:90% like meters in width. 00:08:40.520 --> 00:08:42.780 align:middle line:84% So each glass sheet can be easily the size 00:08:42.780 --> 00:08:45.800 align:middle line:84% of this entire classroom right in one single deposition. 00:08:45.800 --> 00:08:49.340 align:middle line:84% So it can be very efficient and very high throughput. 00:08:49.340 --> 00:08:51.040 align:middle line:84% So that's what gives you a low cost. 00:08:51.040 --> 00:08:53.190 align:middle line:84% Also, unlike crystalline silicon, 00:08:53.190 --> 00:08:54.940 align:middle line:84% if you want to grow single crystal silicon 00:08:54.940 --> 00:08:55.960 align:middle line:90% you need to do epitaxy. 00:08:55.960 --> 00:08:57.960 align:middle line:84% You need to start with single crystal substrate. 00:08:57.960 --> 00:08:58.918 align:middle line:90% You then grow the film. 00:08:58.918 --> 00:09:01.900 align:middle line:84% So they inherit the single crystal nature of the substrate. 00:09:01.900 --> 00:09:04.740 align:middle line:84% Amorphous film does not have that constraint. 00:09:04.740 --> 00:09:08.523 align:middle line:84% You can deposit it on any substrate, 00:09:08.523 --> 00:09:09.940 align:middle line:84% including glass, which is what you 00:09:09.940 --> 00:09:12.660 align:middle line:84% use for displaying solar cells, those kind of things. 00:09:12.660 --> 00:09:16.180 align:middle line:84% OK, so there's processing benefits 00:09:16.180 --> 00:09:19.180 align:middle line:84% is what lead to essentially this widespread adoption 00:09:19.180 --> 00:09:22.300 align:middle line:84% of amorphous silicon in the microelectronics industry. 00:09:22.300 --> 00:09:24.288 align:middle line:84% Any kind of large-area electronic devices, 00:09:24.288 --> 00:09:26.580 align:middle line:84% you tend to see a lot of amorphous semiconductor coming 00:09:26.580 --> 00:09:27.940 align:middle line:90% in. 00:09:27.940 --> 00:09:28.755 align:middle line:90% Yes. 00:09:28.755 --> 00:09:32.100 align:middle line:84% AUDIENCE: So with the effect through 00:09:32.100 --> 00:09:35.100 align:middle line:84% hydrogenation, does it function very comparably 00:09:35.100 --> 00:09:37.630 align:middle line:84% to a standard crystalline semiconductor? 00:09:37.630 --> 00:09:39.380 align:middle line:84% PROFESSOR: Yeah, so the question is about, 00:09:39.380 --> 00:09:40.860 align:middle line:84% if you eliminate mid-gap state, then how 00:09:40.860 --> 00:09:42.485 align:middle line:84% does the electronic property look like? 00:09:42.485 --> 00:09:44.580 align:middle line:84% So it will behave somewhat similar 00:09:44.580 --> 00:09:45.945 align:middle line:90% to crystalline semiconductors. 00:09:45.945 --> 00:09:48.570 align:middle line:84% You can, essentially, you have conduction band or valence band. 00:09:48.570 --> 00:09:49.370 align:middle line:90% You would dope it. 00:09:49.370 --> 00:09:50.610 align:middle line:84% You can change it to p and n type. 00:09:50.610 --> 00:09:51.770 align:middle line:90% You can form p injunctions. 00:09:51.770 --> 00:09:53.030 align:middle line:84% So in that regard, it becomes very 00:09:53.030 --> 00:09:54.710 align:middle line:84% similar to crystalline semiconductors. 00:09:54.710 --> 00:09:56.750 align:middle line:84% Still it has some unique electronic properties 00:09:56.750 --> 00:09:59.030 align:middle line:84% that crystalline does not possess. 00:09:59.030 --> 00:10:01.498 align:middle line:84% We are going to talk about it later. 00:10:01.498 --> 00:10:03.290 align:middle line:84% Let me just delegate to the future lecture. 00:10:03.290 --> 00:10:07.890 align:middle line:84% We have one lecture dedicated to essentially amorphous silicon. 00:10:07.890 --> 00:10:09.437 align:middle line:84% For now, just keep in mind that you 00:10:09.437 --> 00:10:11.270 align:middle line:84% need to understand that hydrogen is actually 00:10:11.270 --> 00:10:16.350 align:middle line:84% really important in passivating these amorphous silicon. 00:10:16.350 --> 00:10:17.070 align:middle line:90% All right. 00:10:17.070 --> 00:10:20.190 align:middle line:84% So now next one, I've been talking about metallic glass 00:10:20.190 --> 00:10:21.230 align:middle line:90% for a while. 00:10:21.230 --> 00:10:23.310 align:middle line:84% I will just give you one slight heads up about 00:10:23.310 --> 00:10:25.950 align:middle line:84% what's going to come up for metallic glasses or amorphous 00:10:25.950 --> 00:10:26.670 align:middle line:90% metal. 00:10:26.670 --> 00:10:32.190 align:middle line:84% So metal is quite different from the network glass 00:10:32.190 --> 00:10:34.250 align:middle line:84% we were talking about in terms of bonding nature. 00:10:34.250 --> 00:10:37.687 align:middle line:84% We said that network glass like Oxides or Chalcogenides, 00:10:37.687 --> 00:10:39.270 align:middle line:84% they can form amorphous network easily 00:10:39.270 --> 00:10:41.708 align:middle line:84% because the directionality of the covalent bond, which 00:10:41.708 --> 00:10:43.750 align:middle line:84% gives you a lot of space between the atoms, which 00:10:43.750 --> 00:10:46.333 align:middle line:84% allow you to distort the network and accommodate the structure 00:10:46.333 --> 00:10:47.390 align:middle line:90% disorder. 00:10:47.390 --> 00:10:50.150 align:middle line:84% Metal, on the other hand, you have metallic mode. 00:10:50.150 --> 00:10:51.830 align:middle line:84% Metallic bond come from interaction 00:10:51.830 --> 00:10:55.990 align:middle line:84% between outer shell electrons and the atomic nuclei. 00:10:55.990 --> 00:10:59.850 align:middle line:84% So for metallic bonds, if you want to lower energy, 00:10:59.850 --> 00:11:03.390 align:middle line:84% you want to increase the packing density. 00:11:03.390 --> 00:11:05.330 align:middle line:84% That's why lots of metals, if you look at it, 00:11:05.330 --> 00:11:08.190 align:middle line:84% they all have fairly close or close-packed structures 00:11:08.190 --> 00:11:09.750 align:middle line:84% or close to close-packed structures, 00:11:09.750 --> 00:11:13.150 align:middle line:90% near close-packed structures. 00:11:13.150 --> 00:11:15.950 align:middle line:84% Now, if you think about elemental metal, 00:11:15.950 --> 00:11:19.070 align:middle line:84% for elemental metal, all the atoms have the same size. 00:11:19.070 --> 00:11:21.750 align:middle line:84% If you are managing, you have a lot of hard spheres 00:11:21.750 --> 00:11:23.230 align:middle line:84% that has exactly the same diameter. 00:11:23.230 --> 00:11:25.692 align:middle line:84% If you shake it a little bit, and then if you look at it, 00:11:25.692 --> 00:11:27.150 align:middle line:84% locally, you're likely going to see 00:11:27.150 --> 00:11:30.070 align:middle line:90% this kind of periodic packing. 00:11:30.070 --> 00:11:34.350 align:middle line:84% So same idea if you're looking for elemental metal. 00:11:34.350 --> 00:11:38.610 align:middle line:84% Turns out it crystallizes so readily that for a long time, 00:11:38.610 --> 00:11:40.710 align:middle line:84% people do not believe that you can make metal 00:11:40.710 --> 00:11:43.990 align:middle line:90% in amorphous form. 00:11:43.990 --> 00:11:47.630 align:middle line:84% So it's only till like 1960s when people actually developed 00:11:47.630 --> 00:11:50.965 align:middle line:84% ways to essentially do a very rapid quench of a metal belt. 00:11:50.965 --> 00:11:53.590 align:middle line:84% Then people start to essentially prepare this kind of amorphous 00:11:53.590 --> 00:11:54.350 align:middle line:90% metal. 00:11:54.350 --> 00:11:59.410 align:middle line:84% And then later, this group in [INAUDIBLE] is from Japan. 00:11:59.410 --> 00:12:02.470 align:middle line:84% So this scientist, he essentially 00:12:02.470 --> 00:12:06.550 align:middle line:84% developed what's known as bulk metallic glass. 00:12:06.550 --> 00:12:09.770 align:middle line:84% So it's no longer like early days of this metallic glass. 00:12:09.770 --> 00:12:13.250 align:middle line:84% They are all in the form of thin foil which limit, of course, 00:12:13.250 --> 00:12:14.370 align:middle line:90% limit the application. 00:12:14.370 --> 00:12:16.750 align:middle line:84% But it was first developed for metallic glasses 00:12:16.750 --> 00:12:19.790 align:middle line:84% so that you can have millimeter thick or even centimeter thick 00:12:19.790 --> 00:12:22.330 align:middle line:90% of metallic glass components. 00:12:22.330 --> 00:12:26.010 align:middle line:84% So in order to develop this kind of bulk metallic glass, 00:12:26.010 --> 00:12:28.990 align:middle line:84% you need to enhance the glass-forming ability. 00:12:28.990 --> 00:12:35.910 align:middle line:84% That's called the glass-forming ability. 00:12:35.910 --> 00:12:41.510 align:middle line:84% It essentially gauges the ability for the glass 00:12:41.510 --> 00:12:44.350 align:middle line:84% composition to resist crystallization and form 00:12:44.350 --> 00:12:47.030 align:middle line:90% amorphous structure. 00:12:47.030 --> 00:12:49.130 align:middle line:84% Now to maximize glass forming ability, 00:12:49.130 --> 00:12:53.030 align:middle line:84% he proposes three empirical rules. 00:12:53.030 --> 00:12:55.030 align:middle line:84% So the first one, it says that it 00:12:55.030 --> 00:12:57.070 align:middle line:84% has to be a multi component system consisting 00:12:57.070 --> 00:12:58.750 align:middle line:90% of three or more elements. 00:12:58.750 --> 00:13:01.250 align:middle line:84% And the second one actually closely related to that, 00:13:01.250 --> 00:13:03.350 align:middle line:84% saying that there must be a significant size 00:13:03.350 --> 00:13:05.850 align:middle line:84% difference between the three constituent atoms. 00:13:05.850 --> 00:13:08.830 align:middle line:90% 00:13:08.830 --> 00:13:11.190 align:middle line:84% Now, the first two rules, they are actually 00:13:11.190 --> 00:13:13.570 align:middle line:90% both topological in nature. 00:13:13.570 --> 00:13:16.110 align:middle line:84% It does not talk about the chemical nature, electron 00:13:16.110 --> 00:13:18.070 align:middle line:84% affinity, chemical reactivity, whatever, 00:13:18.070 --> 00:13:19.330 align:middle line:90% of the constituent atoms. 00:13:19.330 --> 00:13:21.150 align:middle line:90% It only talk about size. 00:13:21.150 --> 00:13:22.430 align:middle line:90% OK, why? 00:13:22.430 --> 00:13:25.250 align:middle line:84% Because as I said, in metal, in order to low energy, 00:13:25.250 --> 00:13:28.350 align:middle line:84% you need to maximize the packing density. 00:13:28.350 --> 00:13:30.350 align:middle line:84% Now in order to avoid going to this kind 00:13:30.350 --> 00:13:32.830 align:middle line:84% of close-packed periodic structure, what you want 00:13:32.830 --> 00:13:35.190 align:middle line:84% to have is this kind of hierarchical structure 00:13:35.190 --> 00:13:37.070 align:middle line:90% like what I'm showing here. 00:13:37.070 --> 00:13:39.960 align:middle line:84% Suppose you have some large atoms. 00:13:39.960 --> 00:13:43.100 align:middle line:84% You can explode it with smaller atoms. 00:13:43.100 --> 00:13:44.900 align:middle line:84% And if you get the right size ratio, 00:13:44.900 --> 00:13:47.320 align:middle line:84% you can imagine that these small atoms can exactly 00:13:47.320 --> 00:13:49.200 align:middle line:84% surround these large atoms without leaving 00:13:49.200 --> 00:13:51.880 align:middle line:90% a gap in between them. 00:13:51.880 --> 00:13:55.780 align:middle line:84% Now between these larger spheres, 00:13:55.780 --> 00:13:58.560 align:middle line:84% you can also have smaller interstitials, 00:13:58.560 --> 00:14:00.713 align:middle line:84% tetrahedral, octahedral interstitials, 00:14:00.713 --> 00:14:02.380 align:middle line:84% if you want to maximize packing density, 00:14:02.380 --> 00:14:04.640 align:middle line:84% you then also want to find some other atoms that 00:14:04.640 --> 00:14:06.680 align:middle line:84% can exactly fit in those interstitials 00:14:06.680 --> 00:14:09.760 align:middle line:90% without leaving any gaps. 00:14:09.760 --> 00:14:12.300 align:middle line:84% So by having atoms with different sizes, 00:14:12.300 --> 00:14:14.840 align:middle line:84% you can satisfy that geometric constraint. 00:14:14.840 --> 00:14:17.360 align:middle line:84% So you can get a close-packed structure 00:14:17.360 --> 00:14:22.440 align:middle line:84% without introducing a conventional structure order. 00:14:22.440 --> 00:14:26.840 align:middle line:84% So later on we are going to talk about a topological theory that 00:14:26.840 --> 00:14:29.280 align:middle line:84% specifically discuss about the stability of metallic glass 00:14:29.280 --> 00:14:30.020 align:middle line:90% formation. 00:14:30.020 --> 00:14:30.740 align:middle line:90% And we'll see. 00:14:30.740 --> 00:14:33.080 align:middle line:84% It all boils down to essentially how sphere packing. 00:14:33.080 --> 00:14:35.040 align:middle line:90% It becomes geometric problem. 00:14:35.040 --> 00:14:38.260 align:middle line:84% You can determine the radius ratio of different atoms, 00:14:38.260 --> 00:14:40.200 align:middle line:84% as well as the atomical fraction that 00:14:40.200 --> 00:14:43.880 align:middle line:84% maximizes packing density, which also give rise to the best glass 00:14:43.880 --> 00:14:46.640 align:middle line:90% stability. 00:14:46.640 --> 00:14:47.140 align:middle line:90% All right. 00:14:47.140 --> 00:14:48.620 align:middle line:84% So that's the first two conditions there. 00:14:48.620 --> 00:14:50.480 align:middle line:84% Now the last condition, it says that you 00:14:50.480 --> 00:14:52.712 align:middle line:84% need to have a negative enthalpy of mixing. 00:14:52.712 --> 00:14:54.420 align:middle line:84% That's actually quite easy to understand. 00:14:54.420 --> 00:14:57.490 align:middle line:84% This is coming from thermo dynamic perspective. 00:14:57.490 --> 00:14:59.240 align:middle line:84% If you have a negative enthalpy of mixing, 00:14:59.240 --> 00:15:01.448 align:middle line:84% it means it's going to stay together rather than stay 00:15:01.448 --> 00:15:02.220 align:middle line:90% segregated. 00:15:02.220 --> 00:15:05.160 align:middle line:90% So that's it, simple. 00:15:05.160 --> 00:15:09.400 align:middle line:84% So as I said, we're going to discuss about a more 00:15:09.400 --> 00:15:12.760 align:middle line:84% quantitative theory that elaborates 00:15:12.760 --> 00:15:17.560 align:middle line:84% on this close-packing condition for metallic glasses later. 00:15:17.560 --> 00:15:18.060 align:middle line:90% All right. 00:15:18.060 --> 00:15:22.520 align:middle line:84% Now in terms of properties, the most important difference 00:15:22.520 --> 00:15:24.800 align:middle line:84% between amorphous metal and crystalline metal 00:15:24.800 --> 00:15:27.160 align:middle line:84% comes in the fact that amorphous metal does not 00:15:27.160 --> 00:15:30.320 align:middle line:84% have a lot of defects like dislocations or grain 00:15:30.320 --> 00:15:33.600 align:middle line:84% boundaries, because it doesn't have a lattice structure. 00:15:33.600 --> 00:15:35.372 align:middle line:84% We know that these kind of lattice defects 00:15:35.372 --> 00:15:37.080 align:middle line:84% play a very significant role in dictating 00:15:37.080 --> 00:15:40.360 align:middle line:84% the property of a conventional polycrystalline glasses. 00:15:40.360 --> 00:15:42.543 align:middle line:84% So, for example, if grain boundaries, 00:15:42.543 --> 00:15:43.960 align:middle line:84% grain boundaries are where you get 00:15:43.960 --> 00:15:45.620 align:middle line:90% a lot more structural disorder. 00:15:45.620 --> 00:15:47.760 align:middle line:84% So the atoms inevitably are slightly higher 00:15:47.760 --> 00:15:50.920 align:middle line:84% Gibbs-free energy compared to inside the crystalline grain. 00:15:50.920 --> 00:15:52.980 align:middle line:84% So if you dip a metal, a polycrystalline metal, 00:15:52.980 --> 00:15:54.720 align:middle line:84% for example, into a chemical agent, 00:15:54.720 --> 00:15:56.720 align:middle line:84% usually it's the grain boundary that's 00:15:56.720 --> 00:15:58.020 align:middle line:90% getting selectively attacked. 00:15:58.020 --> 00:16:00.160 align:middle line:90% That's the weak link. 00:16:00.160 --> 00:16:02.657 align:middle line:84% So amorphous metal does not have that problem. 00:16:02.657 --> 00:16:04.240 align:middle line:84% So it's actually a lot more chemically 00:16:04.240 --> 00:16:07.540 align:middle line:84% resistant compared to its polycrystalline counterpart. 00:16:07.540 --> 00:16:11.800 align:middle line:84% So that's one reason why they are of interest. 00:16:11.800 --> 00:16:14.635 align:middle line:84% Second reason is for mechanical properties. 00:16:14.635 --> 00:16:16.760 align:middle line:84% When you're trying to introduce plastic deformation 00:16:16.760 --> 00:16:18.360 align:middle line:84% in conventional metal, what happened 00:16:18.360 --> 00:16:21.360 align:middle line:84% there is that dislocation essentially moves. 00:16:21.360 --> 00:16:24.460 align:middle line:84% You have [INAUDIBLE] to solutions slide. 00:16:24.460 --> 00:16:25.680 align:middle line:90% That's actually what happens. 00:16:25.680 --> 00:16:28.260 align:middle line:84% Again, in amorphous metal, you get no dislocations. 00:16:28.260 --> 00:16:30.280 align:middle line:84% So that kind of plastic deformation mechanism 00:16:30.280 --> 00:16:34.210 align:middle line:84% is completely absent in amorphous metal. 00:16:34.210 --> 00:16:37.330 align:middle line:84% So as a result, amorphous metal tend 00:16:37.330 --> 00:16:40.370 align:middle line:84% to have a much higher elastic limit compared 00:16:40.370 --> 00:16:43.768 align:middle line:84% to traditional polycrystalline metal. 00:16:43.768 --> 00:16:45.810 align:middle line:84% So it means that it will stay essentially elastic 00:16:45.810 --> 00:16:48.410 align:middle line:84% without introducing any plastic deformation up 00:16:48.410 --> 00:16:49.590 align:middle line:90% to much higher stress. 00:16:49.590 --> 00:16:52.570 align:middle line:90% 00:16:52.570 --> 00:16:54.950 align:middle line:84% You have taken your mechanics class, 00:16:54.950 --> 00:16:57.290 align:middle line:84% so you know that essentially relates to your strength 00:16:57.290 --> 00:16:58.010 align:middle line:90% of the material. 00:16:58.010 --> 00:17:01.650 align:middle line:84% Your strength essentially represents a material's ability 00:17:01.650 --> 00:17:04.430 align:middle line:90% to resist plastic deformation. 00:17:04.430 --> 00:17:08.859 align:middle line:84% So amorphous metal tend to have much higher yield strength, 00:17:08.859 --> 00:17:10.609 align:middle line:84% like an order of magnitude higher compared 00:17:10.609 --> 00:17:13.050 align:middle line:90% to crystalline counterpart. 00:17:13.050 --> 00:17:15.970 align:middle line:84% And that's also the reason why, for example, Apple has always 00:17:15.970 --> 00:17:18.062 align:middle line:84% been thinking about you may be able to use 00:17:18.062 --> 00:17:20.770 align:middle line:84% amorphous metal to actually make some components where we require 00:17:20.770 --> 00:17:23.410 align:middle line:84% high mechanical strength in that case. 00:17:23.410 --> 00:17:25.990 align:middle line:90% OK, question? 00:17:25.990 --> 00:17:29.530 align:middle line:90% 00:17:29.530 --> 00:17:32.090 align:middle line:84% AUDIENCE: So does it just not exhibit 00:17:32.090 --> 00:17:34.810 align:middle line:84% classic behavior pretty much at all? 00:17:34.810 --> 00:17:36.050 align:middle line:90% PROFESSOR: It does. 00:17:36.050 --> 00:17:38.250 align:middle line:84% If you give it enough stress, eventually it 00:17:38.250 --> 00:17:41.450 align:middle line:84% will yield, by yielding a very different way compared 00:17:41.450 --> 00:17:42.510 align:middle line:90% to conventional metal. 00:17:42.510 --> 00:17:46.210 align:middle line:84% It actually yields catastrophically. 00:17:46.210 --> 00:17:48.650 align:middle line:84% AUDIENCE: So like brittle fracture? 00:17:48.650 --> 00:17:50.630 align:middle line:84% PROFESSOR: No, it's called strain localization. 00:17:50.630 --> 00:17:52.405 align:middle line:90% We going to talk about it. 00:17:52.405 --> 00:17:54.030 align:middle line:84% If it doesn't yield, then it's perfect. 00:17:54.030 --> 00:17:55.490 align:middle line:84% But if it starts to yield, it tends 00:17:55.490 --> 00:17:56.850 align:middle line:84% to have essentially all the strain localized 00:17:56.850 --> 00:17:58.870 align:middle line:84% in a very small region, so, essentially, 00:17:58.870 --> 00:18:01.365 align:middle line:90% this fracture in one region. 00:18:01.365 --> 00:18:02.990 align:middle line:84% OK, we're going to talk about it later. 00:18:02.990 --> 00:18:05.282 align:middle line:84% For now just keep in mind that the big difference there 00:18:05.282 --> 00:18:07.170 align:middle line:84% is that you need to have the absence 00:18:07.170 --> 00:18:09.310 align:middle line:90% of this crystalline defense. 00:18:09.310 --> 00:18:12.370 align:middle line:84% So that's why their property is quite different. 00:18:12.370 --> 00:18:13.290 align:middle line:90% All right. 00:18:13.290 --> 00:18:15.650 align:middle line:84% I also want to mention that I have only really scratched 00:18:15.650 --> 00:18:19.930 align:middle line:84% the surface about different classes of amorphous materials 00:18:19.930 --> 00:18:21.250 align:middle line:90% you can see around the world. 00:18:21.250 --> 00:18:24.410 align:middle line:84% You can have other kind of oxide glasses like phosphate glasses, 00:18:24.410 --> 00:18:27.570 align:middle line:84% where phosphorus is the glass-forming element. 00:18:27.570 --> 00:18:30.010 align:middle line:84% They are actually quite useful in bioactive glasses. 00:18:30.010 --> 00:18:32.530 align:middle line:84% They tend to dissolve in body fluids. 00:18:32.530 --> 00:18:33.750 align:middle line:90% They are also biocompatible. 00:18:33.750 --> 00:18:35.530 align:middle line:84% So it's quite important glass ingredient 00:18:35.530 --> 00:18:37.130 align:middle line:90% for that kind of application. 00:18:37.130 --> 00:18:40.090 align:middle line:90% You have heavy metal oxides. 00:18:40.090 --> 00:18:43.010 align:middle line:84% These are essentially compounds of oxygen 00:18:43.010 --> 00:18:47.210 align:middle line:84% with essential elements like tellurium, 00:18:47.210 --> 00:18:49.650 align:middle line:84% or other kind of transition metal elements. 00:18:49.650 --> 00:18:53.930 align:middle line:84% So some of them, heavy metal oxides, they can form glasses. 00:18:53.930 --> 00:18:57.450 align:middle line:84% Some others, for example like titanium dioxide 00:18:57.450 --> 00:19:00.452 align:middle line:84% that you can easily form amorphous titanium dioxide film. 00:19:00.452 --> 00:19:02.410 align:middle line:84% But they are usually not considered as a glass, 00:19:02.410 --> 00:19:03.950 align:middle line:84% as well, because when you heat them up, 00:19:03.950 --> 00:19:05.492 align:middle line:84% they tend to crystallize when it goes 00:19:05.492 --> 00:19:07.755 align:middle line:84% to glass transition, so similar to amorphous silicon. 00:19:07.755 --> 00:19:09.130 align:middle line:84% So some of these transition metal 00:19:09.130 --> 00:19:12.410 align:middle line:84% oxides, they are amorphous and are not usually called glass. 00:19:12.410 --> 00:19:14.130 align:middle line:84% You can have headlight glasses and alloys 00:19:14.130 --> 00:19:16.170 align:middle line:84% similar to chalcohalide and oxides. 00:19:16.170 --> 00:19:18.810 align:middle line:84% Now instead of using oxygen or sulfur or selenium, 00:19:18.810 --> 00:19:24.370 align:middle line:84% you actually have halides as the other elements. 00:19:24.370 --> 00:19:26.050 align:middle line:84% They are also quite often used for 00:19:26.050 --> 00:19:27.850 align:middle line:90% infrared transmitting fibers. 00:19:27.850 --> 00:19:29.310 align:middle line:90% One example I'm showing here. 00:19:29.310 --> 00:19:32.210 align:middle line:84% ZBLAN, this is a commercially available halide glass 00:19:32.210 --> 00:19:35.710 align:middle line:90% composition for infrared fibers. 00:19:35.710 --> 00:19:36.210 align:middle line:90% you. 00:19:36.210 --> 00:19:37.585 align:middle line:84% Also have other kind of amorphous 00:19:37.585 --> 00:19:39.210 align:middle line:90% minerals I'm showing here. 00:19:39.210 --> 00:19:40.810 align:middle line:90% Opal is one good example. 00:19:40.810 --> 00:19:42.430 align:middle line:90% You have also biominerals. 00:19:42.430 --> 00:19:45.650 align:middle line:84% In fact, if you read that paper I'm quoting there, 00:19:45.650 --> 00:19:50.810 align:middle line:84% it gives you one example about, essentially, a lobster shell. 00:19:50.810 --> 00:19:52.850 align:middle line:90% You have all eaten lobster. 00:19:52.850 --> 00:19:55.570 align:middle line:84% So lobster shell is actually very flexible. 00:19:55.570 --> 00:19:59.210 align:middle line:84% And one of the main ingredients in lobster shell 00:19:59.210 --> 00:20:02.570 align:middle line:84% is actually a calcium carbonate-- 00:20:02.570 --> 00:20:06.670 align:middle line:84% limestone, which is rigid and stiff. 00:20:06.670 --> 00:20:10.010 align:middle line:84% So that's actually a very interesting paper about how they 00:20:10.010 --> 00:20:13.030 align:middle line:84% can actually, essentially, lobster, 00:20:13.030 --> 00:20:14.890 align:middle line:84% they engineer the micro structure 00:20:14.890 --> 00:20:17.170 align:middle line:84% of calcium carbonate with amorphous network 00:20:17.170 --> 00:20:20.610 align:middle line:84% and some hierarchical structure to make it not just 00:20:20.610 --> 00:20:22.490 align:middle line:90% flexible, but also strong. 00:20:22.490 --> 00:20:24.210 align:middle line:90% OK, quite interesting paper. 00:20:24.210 --> 00:20:28.020 align:middle line:84% If you're interested, I'll refer you to that. 00:20:28.020 --> 00:20:30.482 align:middle line:84% All right, so before I wrap up this class, 00:20:30.482 --> 00:20:31.940 align:middle line:84% I just also want to quickly mention 00:20:31.940 --> 00:20:33.820 align:middle line:84% about what's the convention people 00:20:33.820 --> 00:20:36.520 align:middle line:84% use to represent the competition in different classes? 00:20:36.520 --> 00:20:39.240 align:middle line:90% So it's quite straightforward. 00:20:39.240 --> 00:20:41.100 align:middle line:84% In oxide glasses, the convention is just 00:20:41.100 --> 00:20:46.260 align:middle line:84% to list the network modifiers in increasing valence order. 00:20:46.260 --> 00:20:49.740 align:middle line:84% And with the glass network formula, putting it last. 00:20:49.740 --> 00:20:53.420 align:middle line:84% So, for example, think about this glass. 00:20:53.420 --> 00:20:56.480 align:middle line:84% This is basically alkaline, alkaline Earth oxide. 00:20:56.480 --> 00:21:02.180 align:middle line:84% So you have two glass modifiers, calcium and potassium--sorry, 00:21:02.180 --> 00:21:03.640 align:middle line:90% potassium and calcium. 00:21:03.640 --> 00:21:05.940 align:middle line:84% So you start with a lower valence element, which 00:21:05.940 --> 00:21:08.040 align:middle line:90% is potassium and then calcium. 00:21:08.040 --> 00:21:12.220 align:middle line:84% And then with the glass formula, which is SiO2. 00:21:12.220 --> 00:21:14.860 align:middle line:84% You can then write it in terms of either molar fraction 00:21:14.860 --> 00:21:18.220 align:middle line:90% or by weight. 00:21:18.220 --> 00:21:19.935 align:middle line:84% Just don't confuse one with the other. 00:21:19.935 --> 00:21:22.060 align:middle line:84% Make sure that you know what the author is actually 00:21:22.060 --> 00:21:25.540 align:middle line:84% referring to when they're using this kind of representation. 00:21:25.540 --> 00:21:27.860 align:middle line:84% In metallic glasses, on the other hand, 00:21:27.860 --> 00:21:30.420 align:middle line:84% because you don't have glass network formers or network 00:21:30.420 --> 00:21:33.780 align:middle line:84% modifiers, you usually just list the elements 00:21:33.780 --> 00:21:38.180 align:middle line:84% in the order of decreasing amount. 00:21:38.180 --> 00:21:39.600 align:middle line:90% So this is one example here. 00:21:39.600 --> 00:21:40.880 align:middle line:90% This is known as vitreloy. 00:21:40.880 --> 00:21:44.620 align:middle line:84% This is one of the most popular, or most widely used 00:21:44.620 --> 00:21:47.820 align:middle line:90% metallic glass compositions. 00:21:47.820 --> 00:21:50.060 align:middle line:84% Now, I also want to mention that there are always 00:21:50.060 --> 00:21:51.380 align:middle line:90% exceptions to the rule. 00:21:51.380 --> 00:21:54.640 align:middle line:84% These are just the conventions that people customarily adopt. 00:21:54.640 --> 00:21:59.940 align:middle line:84% But if you do see exceptions, that happen all the time. 00:21:59.940 --> 00:22:00.780 align:middle line:90% All right. 00:22:00.780 --> 00:22:03.722 align:middle line:84% So just quickly summarize what we've talked about here. 00:22:03.722 --> 00:22:05.180 align:middle line:84% For this lecture, and the key thing 00:22:05.180 --> 00:22:07.975 align:middle line:84% you want to understand there is that for these oxide glasses, 00:22:07.975 --> 00:22:10.100 align:middle line:84% we talk about the concept of glass formers, network 00:22:10.100 --> 00:22:11.308 align:middle line:90% modifiers. 00:22:11.308 --> 00:22:13.100 align:middle line:84% You need to know how to essentially perform 00:22:13.100 --> 00:22:15.060 align:middle line:84% this kind of simple structure analysis. 00:22:15.060 --> 00:22:18.540 align:middle line:84% I give you one example, how to determine the structure 00:22:18.540 --> 00:22:21.700 align:middle line:84% in an alkaline silicate glass going from essentially a network 00:22:21.700 --> 00:22:25.365 align:middle line:84% glass to inverted glass by looking at chemical composition. 00:22:25.365 --> 00:22:26.740 align:middle line:84% So you need to be able to perform 00:22:26.740 --> 00:22:28.180 align:middle line:84% that kind of simple structure analysis 00:22:28.180 --> 00:22:29.980 align:middle line:84% and determine different structural moieties. 00:22:29.980 --> 00:22:31.780 align:middle line:84% The other very important thing that we are also 00:22:31.780 --> 00:22:33.380 align:middle line:84% going to revisit later in the semester 00:22:33.380 --> 00:22:35.565 align:middle line:90% is actually this boron anomaly. 00:22:35.565 --> 00:22:37.940 align:middle line:84% If you are [? borrowing ?] a glass network by introducing 00:22:37.940 --> 00:22:40.980 align:middle line:84% alkaline atoms, you can either introduce a non-bridging oxygen 00:22:40.980 --> 00:22:43.760 align:middle line:84% or introduce this kind of P3 to P4 conversion. 00:22:43.760 --> 00:22:47.120 align:middle line:84% Aluminum has similar kind of peculiarities there. 00:22:47.120 --> 00:22:48.380 align:middle line:90% Just keep that in mind. 00:22:48.380 --> 00:22:50.300 align:middle line:84% Later on you will see people actually use 00:22:50.300 --> 00:22:54.740 align:middle line:90% that for useful applications. 00:22:54.740 --> 00:22:57.220 align:middle line:84% And then I'm not going to go through a table here. 00:22:57.220 --> 00:22:58.740 align:middle line:84% But this summarizes, essentially, 00:22:58.740 --> 00:23:01.817 align:middle line:84% the key properties of different kind of oxide-based glasses 00:23:01.817 --> 00:23:03.900 align:middle line:84% and how they change with different kind of network 00:23:03.900 --> 00:23:06.220 align:middle line:90% modifiers. 00:23:06.220 --> 00:23:06.860 align:middle line:90% All right. 00:23:06.860 --> 00:23:09.220 align:middle line:84% So any more questions about this section 00:23:09.220 --> 00:23:11.840 align:middle line:84% here before we move on to talk about, as I said, 00:23:11.840 --> 00:23:16.460 align:middle line:84% my favorite section of the entire class? 00:23:16.460 --> 00:23:17.560 align:middle line:90% I like topology. 00:23:17.560 --> 00:23:18.860 align:middle line:90% That's why. 00:23:18.860 --> 00:23:20.978 align:middle line:84% And as you'll see, glass stability 00:23:20.978 --> 00:23:23.020 align:middle line:84% is all about topology, whether it's network glass 00:23:23.020 --> 00:23:25.360 align:middle line:90% or it's metallic glass. 00:23:25.360 --> 00:23:27.860 align:middle line:84% So in this lecture, we're going to talk about glass forming, 00:23:27.860 --> 00:23:31.340 align:middle line:90% how you actually form glasses. 00:23:31.340 --> 00:23:33.000 align:middle line:84% Normally I will skip this slides. 00:23:33.000 --> 00:23:35.780 align:middle line:84% But for this particular one, I have to highlight one thing. 00:23:35.780 --> 00:23:39.460 align:middle line:84% If you are using the Fundamental Organic Glasses, the 1994 00:23:39.460 --> 00:23:43.580 align:middle line:84% version, you need to skip this section entirely. 00:23:43.580 --> 00:23:45.540 align:middle line:90% That section is incorrect. 00:23:45.540 --> 00:23:46.060 align:middle line:90% Simple. 00:23:46.060 --> 00:23:46.560 align:middle line:90% All right. 00:23:46.560 --> 00:23:48.480 align:middle line:84% They actually fix it in the more recent version. 00:23:48.480 --> 00:23:49.820 align:middle line:84% They take out the entire section. 00:23:49.820 --> 00:23:50.945 align:middle line:90% But just keep that in mind. 00:23:50.945 --> 00:23:53.080 align:middle line:84% If you use the 1994 version, don't look at it. 00:23:53.080 --> 00:23:54.315 align:middle line:90% AUDIENCE: Rip it up. 00:23:54.315 --> 00:23:54.940 align:middle line:90% PROFESSOR: Yes. 00:23:54.940 --> 00:23:55.625 align:middle line:90% Oh, well. 00:23:55.625 --> 00:23:57.000 align:middle line:84% Don't do that for a library book. 00:23:57.000 --> 00:24:03.100 align:middle line:90% 00:24:03.100 --> 00:24:03.600 align:middle line:90% All right. 00:24:03.600 --> 00:24:07.500 align:middle line:84% So now let's take a look at, essentially, the glass formation 00:24:07.500 --> 00:24:08.000 align:middle line:90% process. 00:24:08.000 --> 00:24:09.958 align:middle line:84% This is something we have already talked about. 00:24:09.958 --> 00:24:12.340 align:middle line:84% So to form glass, you typically start 00:24:12.340 --> 00:24:14.000 align:middle line:90% from melt. You quench down. 00:24:14.000 --> 00:24:15.403 align:middle line:90% So you bypass crystallization. 00:24:15.403 --> 00:24:17.320 align:middle line:84% You then go through a glass transition regime. 00:24:17.320 --> 00:24:20.990 align:middle line:90% You end up with solid glass. 00:24:20.990 --> 00:24:23.810 align:middle line:84% Well, this is a process that seems quite simple. 00:24:23.810 --> 00:24:26.990 align:middle line:84% There's still a few questions we want to address in this section 00:24:26.990 --> 00:24:28.830 align:middle line:90% here, three questions. 00:24:28.830 --> 00:24:32.790 align:middle line:84% The first one we are keeping talking about you 00:24:32.790 --> 00:24:36.910 align:middle line:84% need to quench this glass melt fast enough in order 00:24:36.910 --> 00:24:38.710 align:middle line:90% to avoid crystallization. 00:24:38.710 --> 00:24:40.973 align:middle line:90% So how fast is fast enough? 00:24:40.973 --> 00:24:42.390 align:middle line:84% What are the quantitative measures 00:24:42.390 --> 00:24:44.310 align:middle line:84% we use to calculate this process there? 00:24:44.310 --> 00:24:46.812 align:middle line:84% So that's the first question we're going to address. 00:24:46.812 --> 00:24:48.270 align:middle line:84% We are going to talk about it using 00:24:48.270 --> 00:24:51.150 align:middle line:84% the so-called kinetic theory of glass formation. 00:24:51.150 --> 00:24:55.290 align:middle line:84% Next one is this glass transition here. 00:24:55.290 --> 00:24:57.848 align:middle line:90% 00:24:57.848 --> 00:24:59.390 align:middle line:84% So we know that this glass transition 00:24:59.390 --> 00:25:01.710 align:middle line:90% has a lot of peculiarities. 00:25:01.710 --> 00:25:03.568 align:middle line:90% It's thermal history dependent. 00:25:03.568 --> 00:25:05.110 align:middle line:84% If you cool down with different rate, 00:25:05.110 --> 00:25:07.110 align:middle line:84% you end up with different glassy state. 00:25:07.110 --> 00:25:09.810 align:middle line:84% Also, despite it being a smooth transition, 00:25:09.810 --> 00:25:11.910 align:middle line:84% it connects two very different-- fundamentally 00:25:11.910 --> 00:25:15.190 align:middle line:84% different-- states of matter. supercooled liquid and glass. 00:25:15.190 --> 00:25:17.090 align:middle line:84% And as I said, these two states of matter, 00:25:17.090 --> 00:25:19.070 align:middle line:84% they are different because they have different thermal expansion 00:25:19.070 --> 00:25:19.830 align:middle line:90% coefficient. 00:25:19.830 --> 00:25:21.517 align:middle line:84% They have different heat capacity. 00:25:21.517 --> 00:25:23.350 align:middle line:84% So they have different atomic configuration. 00:25:23.350 --> 00:25:28.190 align:middle line:84% So what's going on there, during last transition process? 00:25:28.190 --> 00:25:30.230 align:middle line:84% That's a pretty profound question 00:25:30.230 --> 00:25:32.550 align:middle line:84% that people have not fully elucidated yet. 00:25:32.550 --> 00:25:34.390 align:middle line:84% But what I will do is, I will give you 00:25:34.390 --> 00:25:37.190 align:middle line:84% a list of what we call the laboratory definition of a glass 00:25:37.190 --> 00:25:40.070 align:middle line:84% transition that highlights some of the key features that allows 00:25:40.070 --> 00:25:42.737 align:middle line:84% you to essentially explain some of the key features during glass 00:25:42.737 --> 00:25:44.510 align:middle line:90% transition process. 00:25:44.510 --> 00:25:47.670 align:middle line:84% Now the last one is what I've been alluding to many times 00:25:47.670 --> 00:25:48.870 align:middle line:90% already-- 00:25:48.870 --> 00:25:50.430 align:middle line:90% stability. 00:25:50.430 --> 00:25:53.310 align:middle line:84% We know there are glasses that are truly stable like silica. 00:25:53.310 --> 00:25:55.990 align:middle line:84% You can essentially slowly cool it down for a year 00:25:55.990 --> 00:25:57.670 align:middle line:84% without introducing crystallization 00:25:57.670 --> 00:26:00.990 align:middle line:84% versus some other glass competition like-- 00:26:00.990 --> 00:26:01.750 align:middle line:90% whatever. 00:26:01.750 --> 00:26:03.708 align:middle line:84% There, are a lot of unstable glass compositions 00:26:03.708 --> 00:26:06.270 align:middle line:84% which easily crystallize under any kind of perturbation. 00:26:06.270 --> 00:26:09.350 align:middle line:84% So what's the structural origin that 00:26:09.350 --> 00:26:12.470 align:middle line:84% lead to this vastly different glass-forming ability? 00:26:12.470 --> 00:26:15.310 align:middle line:84% It's that glass-forming ability is one of the few properties 00:26:15.310 --> 00:26:18.830 align:middle line:84% where it can expand many, many order of magnitude, 00:26:18.830 --> 00:26:20.810 align:middle line:84% over 10 to the 15th order of magnitude, 00:26:20.810 --> 00:26:22.390 align:middle line:90% which is quite remarkable there. 00:26:22.390 --> 00:26:24.210 align:middle line:84% What's the structural origin behind it? 00:26:24.210 --> 00:26:26.750 align:middle line:90% 00:26:26.750 --> 00:26:28.770 align:middle line:84% So these are the topics of this section here. 00:26:28.770 --> 00:26:31.470 align:middle line:84% As I said, we're going to talk about the kinetic theory. 00:26:31.470 --> 00:26:33.710 align:middle line:84% The kinetic theory pretty much is a revisit 00:26:33.710 --> 00:26:35.950 align:middle line:84% of the crystallization kinetics that you 00:26:35.950 --> 00:26:37.783 align:middle line:90% have learned in kinetics class. 00:26:37.783 --> 00:26:39.450 align:middle line:84% But we're trying to do exactly opposite. 00:26:39.450 --> 00:26:41.250 align:middle line:84% Instead of trying to get crystallization, 00:26:41.250 --> 00:26:43.693 align:middle line:84% we try to avoid crystallization at all costs. 00:26:43.693 --> 00:26:45.110 align:middle line:84% Crystallization is like the valley 00:26:45.110 --> 00:26:46.490 align:middle line:90% of death for glass scientists. 00:26:46.490 --> 00:26:49.030 align:middle line:90% 00:26:49.030 --> 00:26:51.030 align:middle line:84% We're not going to talk about laboratory glass 00:26:51.030 --> 00:26:53.135 align:middle line:84% transition and then the structural theories, 00:26:53.135 --> 00:26:55.010 align:middle line:84% especially the topological constraint theory, 00:26:55.010 --> 00:26:57.710 align:middle line:84% to explain why some glasses are much more stable compared 00:26:57.710 --> 00:26:59.630 align:middle line:90% to others. 00:26:59.630 --> 00:27:00.430 align:middle line:90% All right. 00:27:00.430 --> 00:27:06.630 align:middle line:84% So kinetic theory, as I said, crystallization 00:27:06.630 --> 00:27:08.490 align:middle line:84% is the valley of death for glass scientists. 00:27:08.490 --> 00:27:11.670 align:middle line:84% This is just one example showing you actual crystallized glass. 00:27:11.670 --> 00:27:14.390 align:middle line:84% So this is a rod of transparent glass. 00:27:14.390 --> 00:27:15.370 align:middle line:90% This side is amorphous. 00:27:15.370 --> 00:27:16.620 align:middle line:90% This side is like crystallize. 00:27:16.620 --> 00:27:18.680 align:middle line:84% You can immediately see the difference 00:27:18.680 --> 00:27:21.620 align:middle line:84% because you have crystalline precipitates out of lattice. 00:27:21.620 --> 00:27:23.120 align:middle line:84% And then those crystals can actually 00:27:23.120 --> 00:27:25.320 align:middle line:84% scatter light, which leads to this kind 00:27:25.320 --> 00:27:29.000 align:middle line:84% of a translucent appearance there. 00:27:29.000 --> 00:27:33.240 align:middle line:84% So how do we avoid this kind of crystallization? 00:27:33.240 --> 00:27:36.200 align:middle line:84% What is the kinetics in the process? 00:27:36.200 --> 00:27:39.080 align:middle line:84% So quick review here, in order to form crystallization 00:27:39.080 --> 00:27:41.520 align:middle line:84% from a supercooled liquid you need essentially nucleation 00:27:41.520 --> 00:27:43.200 align:middle line:90% and growth right. 00:27:43.200 --> 00:27:47.040 align:middle line:84% So for nucleation, this is basically 00:27:47.040 --> 00:27:49.840 align:middle line:84% a quick revisit of the thermodynamics of nucleation. 00:27:49.840 --> 00:27:51.952 align:middle line:84% What I'm plotting here is the free energy 00:27:51.952 --> 00:27:53.160 align:middle line:90% as a function of temperature. 00:27:53.160 --> 00:27:55.440 align:middle line:90% Have you all taken kinetics? 00:27:55.440 --> 00:27:57.500 align:middle line:84% Then it should be pretty straightforward. 00:27:57.500 --> 00:28:00.880 align:middle line:84% I will just quickly go through the concepts here. 00:28:00.880 --> 00:28:03.200 align:middle line:84% We know that liquid and crystal, they 00:28:03.200 --> 00:28:05.820 align:middle line:90% have different entropy right. 00:28:05.820 --> 00:28:07.500 align:middle line:84% Liquid has more structure to this order. 00:28:07.500 --> 00:28:08.880 align:middle line:90% That's why it has more entropy. 00:28:08.880 --> 00:28:12.040 align:middle line:84% The slope of this line here, partial derivative 00:28:12.040 --> 00:28:14.480 align:middle line:84% of g with respect to t, give you entropy. 00:28:14.480 --> 00:28:18.140 align:middle line:84% So that's why liquid has a larger slope. 00:28:18.140 --> 00:28:19.300 align:middle line:90% So it has a smaller slope. 00:28:19.300 --> 00:28:21.520 align:middle line:84% That's why they must cross over at some point, which 00:28:21.520 --> 00:28:23.880 align:middle line:90% defines the melting point. 00:28:23.880 --> 00:28:30.000 align:middle line:84% So now for glass foaming, we are always talking about temperature 00:28:30.000 --> 00:28:31.560 align:middle line:90% below melting point. 00:28:31.560 --> 00:28:34.280 align:middle line:84% Crystalline lies below the liquid line. 00:28:34.280 --> 00:28:36.640 align:middle line:84% So supercooled liquid always has the tendency 00:28:36.640 --> 00:28:40.540 align:middle line:84% to relax to crystalline state which is crystallization. 00:28:40.540 --> 00:28:42.920 align:middle line:84% The thermodynamic driving force is then 00:28:42.920 --> 00:28:46.040 align:middle line:84% this delta G. This is the free energy difference 00:28:46.040 --> 00:28:47.300 align:middle line:90% between these two states. 00:28:47.300 --> 00:28:50.933 align:middle line:84% So from a thermal dynamics or kinetics class, 00:28:50.933 --> 00:28:55.360 align:middle line:84% you know that this delta G will scale linearly 00:28:55.360 --> 00:28:57.400 align:middle line:90% with the degree of supercooling. 00:28:57.400 --> 00:29:00.840 align:middle line:84% So degree of supercooling is basically the melting point 00:29:00.840 --> 00:29:04.440 align:middle line:84% minus the temperature at which the crystallization takes place. 00:29:04.440 --> 00:29:06.720 align:middle line:84% So it all boils down to this equation 00:29:06.720 --> 00:29:11.360 align:middle line:84% here, where the Gibbs free energy scales 00:29:11.360 --> 00:29:17.000 align:middle line:84% with the degree of supercooling and also volume of glass. 00:29:17.000 --> 00:29:20.840 align:middle line:84% So this delta S here is the entropy difference 00:29:20.840 --> 00:29:24.400 align:middle line:84% between the solid and liquid state per unit volume. 00:29:24.400 --> 00:29:27.280 align:middle line:90% And that's why I have a V here. 00:29:27.280 --> 00:29:29.900 align:middle line:84% So this is obviously what we call a volumetric term. 00:29:29.900 --> 00:29:31.480 align:middle line:84% If you have more glass transition-- 00:29:31.480 --> 00:29:34.400 align:middle line:84% sorry-- if you have more liquid transition into crystalline then 00:29:34.400 --> 00:29:37.340 align:middle line:84% you have more change of the free energy. 00:29:37.340 --> 00:29:41.360 align:middle line:84% Makes sense if your scale is more [INAUDIBLE]. 00:29:41.360 --> 00:29:44.040 align:middle line:84% Now we also have a barrier energy barrier 00:29:44.040 --> 00:29:46.440 align:middle line:90% for nucleation here. 00:29:46.440 --> 00:29:48.400 align:middle line:84% In order to form this nucleus, you 00:29:48.400 --> 00:29:50.313 align:middle line:84% are trying to precipitate out some atoms 00:29:50.313 --> 00:29:52.480 align:middle line:84% with different structure compared to the surrounding 00:29:52.480 --> 00:29:55.920 align:middle line:90% supercooled liquid matrix. 00:29:55.920 --> 00:29:57.040 align:middle line:90% Excuse me. 00:29:57.040 --> 00:29:58.880 align:middle line:84% So this inevitably creates essentially 00:29:58.880 --> 00:30:02.000 align:middle line:84% interface between the solid nucleus and the surrounding 00:30:02.000 --> 00:30:03.200 align:middle line:90% supercooled liquid. 00:30:03.200 --> 00:30:05.000 align:middle line:84% So this interface has an interface energy 00:30:05.000 --> 00:30:08.640 align:middle line:84% associated with it that we represent as the surface energy 00:30:08.640 --> 00:30:09.140 align:middle line:90% here. 00:30:09.140 --> 00:30:12.640 align:middle line:84% It's basically area of the nucleus times 00:30:12.640 --> 00:30:17.000 align:middle line:84% gamma, which is the surface energy. 00:30:17.000 --> 00:30:19.140 align:middle line:84% So if you plot these two terms here, 00:30:19.140 --> 00:30:22.080 align:middle line:84% you have a surface term, which represents the record. 00:30:22.080 --> 00:30:24.480 align:middle line:84% You have the volumetric term that I talked about 00:30:24.480 --> 00:30:26.520 align:middle line:84% in the last slide in this green curve 00:30:26.520 --> 00:30:31.840 align:middle line:84% here, volumetric term scales with volume, so radius cubed, 00:30:31.840 --> 00:30:35.560 align:middle line:84% if you think about spherical nucleus. 00:30:35.560 --> 00:30:39.360 align:middle line:84% And then the surface term scales with radius squared. 00:30:39.360 --> 00:30:42.720 align:middle line:84% So it means that when the nucleus is small, 00:30:42.720 --> 00:30:44.680 align:middle line:90% surface term always dominates. 00:30:44.680 --> 00:30:48.200 align:middle line:84% But eventually the volumetric term is going to take over. 00:30:48.200 --> 00:30:51.120 align:middle line:84% So this gives rise to essentially a barrier 00:30:51.120 --> 00:30:54.480 align:middle line:84% towards nucleation that you have to overcome in order for nuclei 00:30:54.480 --> 00:30:55.400 align:middle line:90% to form. 00:30:55.400 --> 00:30:58.680 align:middle line:84% So at this very high-- also depends 00:30:58.680 --> 00:31:00.540 align:middle line:84% on what kind of nucleation you have there. 00:31:00.540 --> 00:31:03.345 align:middle line:84% Homogeneous nucleation always has a higher barrier 00:31:03.345 --> 00:31:04.720 align:middle line:84% because you have a larger surface 00:31:04.720 --> 00:31:07.000 align:middle line:84% area, a larger volume for nucleus 00:31:07.000 --> 00:31:08.800 align:middle line:90% versus heterogeneous nucleation. 00:31:08.800 --> 00:31:11.510 align:middle line:84% By essentially forming the nucleus on some surfaces, 00:31:11.510 --> 00:31:14.530 align:middle line:84% you can effectively lower this energy barrier. 00:31:14.530 --> 00:31:15.370 align:middle line:90% All right. 00:31:15.370 --> 00:31:17.570 align:middle line:90% So that's nucleation. 00:31:17.570 --> 00:31:20.370 align:middle line:84% So then, when you talk about kinetics of nucleation, 00:31:20.370 --> 00:31:22.730 align:middle line:84% then I won't go through a theory there because you 00:31:22.730 --> 00:31:23.790 align:middle line:90% are taking kinetics. 00:31:23.790 --> 00:31:26.530 align:middle line:84% But the whole idea is that we're looking at the rate. 00:31:26.530 --> 00:31:30.870 align:middle line:84% How fast can the system overcome this energy barrier 00:31:30.870 --> 00:31:32.290 align:middle line:84% so that it can essentially go down 00:31:32.290 --> 00:31:35.290 align:middle line:84% this slope on the other side, so that the nucleus can then 00:31:35.290 --> 00:31:41.050 align:middle line:84% spontaneously grow rather than dissolve back into liquid phase? 00:31:41.050 --> 00:31:45.530 align:middle line:84% The final formalism, there are basically two factors here. 00:31:45.530 --> 00:31:48.690 align:middle line:90% So one is the kinetic factor. 00:31:48.690 --> 00:31:50.490 align:middle line:84% If you go to higher and higher temperature, 00:31:50.490 --> 00:31:52.630 align:middle line:84% the atoms essentially have a higher mobility. 00:31:52.630 --> 00:31:55.010 align:middle line:90% They become more mobile. 00:31:55.010 --> 00:31:58.210 align:middle line:84% So as a result, the kinetic process is accelerated. 00:31:58.210 --> 00:32:02.450 align:middle line:84% So the kinetic factor would grow monotonically with temperature. 00:32:02.450 --> 00:32:04.610 align:middle line:84% The higher the temperature, the faster it's going. 00:32:04.610 --> 00:32:08.970 align:middle line:84% But you also have the thermodynamic factor there, 00:32:08.970 --> 00:32:12.130 align:middle line:84% where the barrier height essentially depends 00:32:12.130 --> 00:32:14.690 align:middle line:90% on the degree of supercooling. 00:32:14.690 --> 00:32:16.910 align:middle line:84% The higher the degree of supercooling, 00:32:16.910 --> 00:32:18.250 align:middle line:90% the lower the barrier height. 00:32:18.250 --> 00:32:21.730 align:middle line:84% So then there essentially is this kind-- 00:32:21.730 --> 00:32:23.903 align:middle line:84% that you have to strike a balance there. 00:32:23.903 --> 00:32:26.070 align:middle line:84% You want to have enough thermodynamic driving force. 00:32:26.070 --> 00:32:27.390 align:middle line:84% So you need to have enough supercooling. 00:32:27.390 --> 00:32:28.770 align:middle line:84% So temperature cannot be too high. 00:32:28.770 --> 00:32:30.250 align:middle line:84% But you also don't want temperature 00:32:30.250 --> 00:32:32.930 align:middle line:84% to get too low where the atoms become so sluggish they 00:32:32.930 --> 00:32:34.290 align:middle line:90% don't move at all. 00:32:34.290 --> 00:32:39.110 align:middle line:84% So long story short, if you revisit your kinetics class, 00:32:39.110 --> 00:32:41.090 align:middle line:84% it basically says that for nucleation, there's 00:32:41.090 --> 00:32:43.570 align:middle line:90% always an optimal temperature. 00:32:43.570 --> 00:32:45.450 align:middle line:84% And that optimal temperature, it gives rise 00:32:45.450 --> 00:32:49.290 align:middle line:90% to highest nucleation rate. 00:32:49.290 --> 00:32:50.930 align:middle line:84% Above that temperature, essentially you 00:32:50.930 --> 00:32:52.792 align:middle line:84% get thermodynamic driving force limited. 00:32:52.792 --> 00:32:54.250 align:middle line:84% You don't have enough supercooling. 00:32:54.250 --> 00:32:56.510 align:middle line:84% Below that temperature, it's kinetically limited. 00:32:56.510 --> 00:33:00.320 align:middle line:84% You don't have enough atomic mobility. 00:33:00.320 --> 00:33:02.150 align:middle line:84% Same idea, once you have a nucleus, 00:33:02.150 --> 00:33:05.170 align:middle line:90% then you have this grow. 00:33:05.170 --> 00:33:08.730 align:middle line:84% The growth process is actually quite similar. 00:33:08.730 --> 00:33:11.130 align:middle line:84% You essentially need to allow this atom to hop 00:33:11.130 --> 00:33:13.640 align:middle line:84% over the surface energy barrier from liquid state 00:33:13.640 --> 00:33:15.890 align:middle line:84% to the crystalline state, so that this crystallization 00:33:15.890 --> 00:33:16.910 align:middle line:90% process can proceed. 00:33:16.910 --> 00:33:19.490 align:middle line:84% And it's the same dependence there. 00:33:19.490 --> 00:33:23.610 align:middle line:84% You also have, similarly, a thermodynamic factor 00:33:23.610 --> 00:33:25.050 align:middle line:90% and kinetic factor. 00:33:25.050 --> 00:33:29.330 align:middle line:84% And this gives rise to an optimal temperature where you 00:33:29.330 --> 00:33:32.370 align:middle line:90% have the highest growth rate. 00:33:32.370 --> 00:33:35.330 align:middle line:84% So because both nucleation and growth, 00:33:35.330 --> 00:33:37.508 align:middle line:84% they exhibit similar dependence on temperature. 00:33:37.508 --> 00:33:39.050 align:middle line:84% There's always an optimal temperature 00:33:39.050 --> 00:33:41.710 align:middle line:84% where you get the maximum nucleation or growth rate. 00:33:41.710 --> 00:33:44.890 align:middle line:84% So it means that if you look at the overall crystallization 00:33:44.890 --> 00:33:48.370 align:middle line:84% process, there's also an optimal temperature where you have 00:33:48.370 --> 00:33:51.890 align:middle line:90% the fastest crystallization. 00:33:51.890 --> 00:33:56.170 align:middle line:84% So if you are [INAUDIBLE] scientist, 00:33:56.170 --> 00:33:58.670 align:middle line:84% well, this is the overall crystallization rate. 00:33:58.670 --> 00:34:02.667 align:middle line:84% Then the crystallization rate would peak somewhere in between. 00:34:02.667 --> 00:34:04.250 align:middle line:84% So if you are a [INAUDIBLE] scientist, 00:34:04.250 --> 00:34:07.190 align:middle line:84% you then want to avoid that temperature, 00:34:07.190 --> 00:34:09.969 align:middle line:84% because that's where you are going to essentially vitrify 00:34:09.969 --> 00:34:12.330 align:middle line:90% your glass. 00:34:12.330 --> 00:34:16.010 align:middle line:84% Now quantitatively, how do you actually calculate that? 00:34:16.010 --> 00:34:19.170 align:middle line:84% We use the TTD diagram, time, temperature, transformation 00:34:19.170 --> 00:34:20.929 align:middle line:90% diagram. 00:34:20.929 --> 00:34:22.413 align:middle line:84% By the way, speaking of TV diagram, 00:34:22.413 --> 00:34:24.330 align:middle line:84% this is actually a very important core concept 00:34:24.330 --> 00:34:25.427 align:middle line:90% in material science. 00:34:25.427 --> 00:34:26.969 align:middle line:84% In fact, at one point, our department 00:34:26.969 --> 00:34:30.010 align:middle line:84% was trying to do some revision to the graduate curriculum. 00:34:30.010 --> 00:34:31.770 align:middle line:84% We polled all the professors, essentially, 00:34:31.770 --> 00:34:32.850 align:middle line:84% which topic they think they should 00:34:32.850 --> 00:34:35.225 align:middle line:84% include in the graduate core that all the students should 00:34:35.225 --> 00:34:35.889 align:middle line:90% learn. 00:34:35.889 --> 00:34:38.909 align:middle line:84% So we talk about all kinds of topics, thermodynamics, 00:34:38.909 --> 00:34:41.290 align:middle line:84% kinetics, quantum mechanics, everything. 00:34:41.290 --> 00:34:43.210 align:middle line:84% And then the single topic that gets 00:34:43.210 --> 00:34:49.330 align:middle line:84% the most votes, which surprise, surprise, TTD diagram. 00:34:49.330 --> 00:34:52.370 align:middle line:84% So everyone agrees this is a very core concept of material 00:34:52.370 --> 00:34:55.810 align:middle line:84% science that all of you should know and be proficient with. 00:34:55.810 --> 00:34:59.730 align:middle line:84% Now simply put, T diagram is essentially characterize it, 00:34:59.730 --> 00:35:03.820 align:middle line:84% have this curve here, this is like this red curve. 00:35:03.820 --> 00:35:05.660 align:middle line:84% Under isothermal conditions, how long 00:35:05.660 --> 00:35:07.740 align:middle line:84% does it take for crystallization to take place? 00:35:07.740 --> 00:35:10.820 align:middle line:84% So, for example, if you look at 800 Kelvin, 00:35:10.820 --> 00:35:13.020 align:middle line:84% you draw a horizontal line here, intersect this line 00:35:13.020 --> 00:35:13.920 align:middle line:90% at this point. 00:35:13.920 --> 00:35:15.980 align:middle line:84% Then you read out the horizontal axis. 00:35:15.980 --> 00:35:19.900 align:middle line:84% It means that at this 800k, this particular glass composition 00:35:19.900 --> 00:35:22.420 align:middle line:84% to crystallize with about something like, maybe, 00:35:22.420 --> 00:35:23.560 align:middle line:90% 200 seconds. 00:35:23.560 --> 00:35:27.270 align:middle line:90% 00:35:27.270 --> 00:35:29.060 align:middle line:84% Now the basic feature of this kind 00:35:29.060 --> 00:35:32.060 align:middle line:84% of TTD diagram for glass crystallization 00:35:32.060 --> 00:35:34.980 align:middle line:84% is that you always get a crystallization region 00:35:34.980 --> 00:35:36.620 align:middle line:90% like what I'm showing here. 00:35:36.620 --> 00:35:40.300 align:middle line:84% It has this nose because it looks like nose sticking out 00:35:40.300 --> 00:35:41.980 align:middle line:84% here, that essentially correspond 00:35:41.980 --> 00:35:45.380 align:middle line:84% to a specific temperature where you have the fastest 00:35:45.380 --> 00:35:48.020 align:middle line:84% crystallization process, so shortest time 00:35:48.020 --> 00:35:49.220 align:middle line:90% to crystallization. 00:35:49.220 --> 00:35:51.780 align:middle line:90% 00:35:51.780 --> 00:35:54.740 align:middle line:84% So then, obviously, above that this 00:35:54.740 --> 00:35:56.080 align:middle line:90% is the driving force limited. 00:35:56.080 --> 00:35:59.220 align:middle line:84% Below that it becomes a diffusion or atomic mobility 00:35:59.220 --> 00:36:00.620 align:middle line:90% limited. 00:36:00.620 --> 00:36:03.860 align:middle line:84% So now if you want to form a class, 00:36:03.860 --> 00:36:07.540 align:middle line:84% you need to make sure that your quenching process completely 00:36:07.540 --> 00:36:11.660 align:middle line:84% bypass this crystalline region here. 00:36:11.660 --> 00:36:14.680 align:middle line:84% So the way to do it is typically, on a TD diagram, 00:36:14.680 --> 00:36:18.220 align:middle line:84% you draw a line that's exactly tangential 00:36:18.220 --> 00:36:22.100 align:middle line:90% to this crystallization region. 00:36:22.100 --> 00:36:25.020 align:middle line:84% So if you do that, then you can barely 00:36:25.020 --> 00:36:26.940 align:middle line:84% bypass the crystallization and end up 00:36:26.940 --> 00:36:28.980 align:middle line:90% with a fully amorphous state. 00:36:28.980 --> 00:36:34.860 align:middle line:84% Now this line is what we call the critical cooling line. 00:36:34.860 --> 00:36:37.060 align:middle line:84% The slope of this curve-- let me give you 00:36:37.060 --> 00:36:40.260 align:middle line:84% this so-called critical cooling rate. 00:36:40.260 --> 00:36:42.740 align:middle line:84% It's the lowest cooling rate that you 00:36:42.740 --> 00:36:46.440 align:middle line:84% can use to quench your melt, to still avoid crystallization. 00:36:46.440 --> 00:36:49.060 align:middle line:84% This is a very important concept in class size. 00:36:49.060 --> 00:36:51.580 align:middle line:84% So it's a measure of the glass-forming ability. 00:36:51.580 --> 00:36:53.620 align:middle line:84% If a material has a very small glass cooling 00:36:53.620 --> 00:36:55.100 align:middle line:84% rate, a critical cooling rate, it 00:36:55.100 --> 00:36:59.620 align:middle line:84% means that it's a very stable glass and vice versa. 00:36:59.620 --> 00:37:02.700 align:middle line:84% Now, one caveat, for this particular diagram 00:37:02.700 --> 00:37:05.620 align:middle line:84% here, the horizontal axis is in logarithmic time scale. 00:37:05.620 --> 00:37:08.880 align:middle line:84% So if it's a linear cooling with a constant cooling rate, 00:37:08.880 --> 00:37:11.420 align:middle line:84% it's not supposed to be a linear line there. 00:37:11.420 --> 00:37:15.320 align:middle line:84% But if it's a linear scale, then that should be a straight line. 00:37:15.320 --> 00:37:16.820 align:middle line:84% So if when you're actually measuring 00:37:16.820 --> 00:37:18.695 align:middle line:84% this kind of critical cooling rate, make sure 00:37:18.695 --> 00:37:23.060 align:middle line:84% the horizontal axis is actually linear. 00:37:23.060 --> 00:37:27.580 align:middle line:84% So now what I'm doing this next slide here, 00:37:27.580 --> 00:37:30.500 align:middle line:84% I'm essentially summarizing the critical cooling rate 00:37:30.500 --> 00:37:34.620 align:middle line:84% for some of the common glass-forming components. 00:37:34.620 --> 00:37:38.100 align:middle line:84% So you see, for example, like silica, the critical cooling 00:37:38.100 --> 00:37:41.860 align:middle line:84% rate is like 10 to the minus 5 Kelvin per second. 00:37:41.860 --> 00:37:44.340 align:middle line:84% So that's why you can essentially cool off silica 00:37:44.340 --> 00:37:47.320 align:middle line:84% pretty much in any way without worrying about crystallization. 00:37:47.320 --> 00:37:48.760 align:middle line:90% It's very, very, very stable. 00:37:48.760 --> 00:37:53.860 align:middle line:84% You also have metal, like steel or other elemental metal. 00:37:53.860 --> 00:37:57.340 align:middle line:84% The critical cooling rate is like a billion 00:37:57.340 --> 00:37:59.860 align:middle line:90% Kelvin per second. 00:37:59.860 --> 00:38:01.380 align:middle line:84% And that's why people used to think 00:38:01.380 --> 00:38:04.660 align:middle line:84% it's impossible to make amorphous metal. 00:38:04.660 --> 00:38:08.100 align:middle line:84% Now look at this one, vitreloy bulk metallic glass. 00:38:08.100 --> 00:38:10.580 align:middle line:84% It has a critical cooling rate of about 1 Kelvin 00:38:10.580 --> 00:38:14.420 align:middle line:84% per second, much, much lower crystallization tendency 00:38:14.420 --> 00:38:16.500 align:middle line:84% compared to typical elemental metal. 00:38:16.500 --> 00:38:20.080 align:middle line:84% And that's why-- by the way, people can make it into a bulk. 00:38:20.080 --> 00:38:22.320 align:middle line:84% So quantitatively, let me talk about it. 00:38:22.320 --> 00:38:24.780 align:middle line:84% So this critical cooling rate actually 00:38:24.780 --> 00:38:27.460 align:middle line:84% dictates the size or thickness of the sample you can 00:38:27.460 --> 00:38:29.240 align:middle line:90% prepare during amorphous state. 00:38:29.240 --> 00:38:31.460 align:middle line:90% The equation is listed here. 00:38:31.460 --> 00:38:36.040 align:middle line:84% So dmax, this is the maximum thickness of the sample. 00:38:36.040 --> 00:38:38.700 align:middle line:84% You can still maintain being amorphous. 00:38:38.700 --> 00:38:40.340 align:middle line:90% Alpha is thermal diffusivity. 00:38:40.340 --> 00:38:46.100 align:middle line:84% RC is our critical cooling rate and delta T is this guy, 00:38:46.100 --> 00:38:49.900 align:middle line:84% is the temperature difference between the melting point, 00:38:49.900 --> 00:38:55.700 align:middle line:84% or liquidus point, and the lowest temperature. 00:38:55.700 --> 00:39:01.630 align:middle line:84% So the reason you have a maximum sample thickness 00:39:01.630 --> 00:39:04.070 align:middle line:84% is that if you have a material, they 00:39:04.070 --> 00:39:06.050 align:middle line:90% tend to crystallize quickly. 00:39:06.050 --> 00:39:09.590 align:middle line:84% So if you start to quench a bulk piece of sample, 00:39:09.590 --> 00:39:12.310 align:middle line:84% the surface will get quenched very quickly. 00:39:12.310 --> 00:39:15.350 align:middle line:84% But it takes time for heat to get 00:39:15.350 --> 00:39:18.250 align:middle line:84% dissipated in the interior of the material. 00:39:18.250 --> 00:39:21.190 align:middle line:84% It takes time for the heat to escape from inside the material 00:39:21.190 --> 00:39:23.030 align:middle line:90% to the surface. 00:39:23.030 --> 00:39:25.630 align:middle line:84% So, essentially, that means the larger 00:39:25.630 --> 00:39:28.350 align:middle line:84% the thickness of the sample, the slower 00:39:28.350 --> 00:39:31.330 align:middle line:84% the effective cooling rate you can get inside center. 00:39:31.330 --> 00:39:34.230 align:middle line:90% 00:39:34.230 --> 00:39:37.710 align:middle line:84% So if you have a material that's poor glass stability 00:39:37.710 --> 00:39:39.550 align:middle line:84% and you have a large sample thickness, 00:39:39.550 --> 00:39:43.450 align:middle line:84% then the inside may never be able to amortize. 00:39:43.450 --> 00:39:46.390 align:middle line:84% It will always crystallize because it cannot have heat 00:39:46.390 --> 00:39:50.550 align:middle line:84% dissipated fast enough to bypass crystallization. 00:39:50.550 --> 00:39:53.590 align:middle line:84% So that's why now you understand why 00:39:53.590 --> 00:39:56.645 align:middle line:84% people call it bulk metallic glass, because in early days, 00:39:56.645 --> 00:39:58.270 align:middle line:84% we were dealing with this kind of metal 00:39:58.270 --> 00:39:59.520 align:middle line:90% with such a high cooling rate. 00:39:59.520 --> 00:40:01.190 align:middle line:84% If you plug it into the equation, 00:40:01.190 --> 00:40:03.490 align:middle line:84% the thickness you come up is actually very small. 00:40:03.490 --> 00:40:06.430 align:middle line:84% You can only get very thin foil to ensure 00:40:06.430 --> 00:40:09.422 align:middle line:84% you have fast quenching throughout the entire piece. 00:40:09.422 --> 00:40:11.630 align:middle line:84% Bulk metallic glass, because it's much lower critical 00:40:11.630 --> 00:40:14.790 align:middle line:84% cooling rate, you now can afford a maximum thickness 00:40:14.790 --> 00:40:17.050 align:middle line:84% of the order of millimeters or centimeters even. 00:40:17.050 --> 00:40:22.430 align:middle line:90% 00:40:22.430 --> 00:40:22.970 align:middle line:90% All right. 00:40:22.970 --> 00:40:25.190 align:middle line:84% So now, what I have also summarized 00:40:25.190 --> 00:40:28.728 align:middle line:84% on the table on the right-hand side is the critical cooling 00:40:28.728 --> 00:40:30.270 align:middle line:84% rate or, sorry, it's the cooling rate 00:40:30.270 --> 00:40:32.550 align:middle line:84% you can attain using different kind 00:40:32.550 --> 00:40:35.230 align:middle line:90% of glass-preparation techniques. 00:40:35.230 --> 00:40:37.870 align:middle line:84% So you see air quench, just means 00:40:37.870 --> 00:40:40.480 align:middle line:84% that you have a bulk piece of sample leaving on the table that 00:40:40.480 --> 00:40:42.110 align:middle line:90% is slowly cooling air. 00:40:42.110 --> 00:40:44.110 align:middle line:84% It has a relatively slow cooling rate. 00:40:44.110 --> 00:40:46.110 align:middle line:90% Liquid quench is faster. 00:40:46.110 --> 00:40:49.132 align:middle line:84% You can have things like droplet spray or melt spinning. 00:40:49.132 --> 00:40:50.590 align:middle line:84% These are actually processes people 00:40:50.590 --> 00:40:53.470 align:middle line:84% used to use to make metallic glasses. 00:40:53.470 --> 00:40:56.830 align:middle line:84% So, for example, if you are spinning, 00:40:56.830 --> 00:41:00.590 align:middle line:90% basically you have a big drum-- 00:41:00.590 --> 00:41:02.590 align:middle line:84% big drum kept at room temperature. 00:41:02.590 --> 00:41:04.830 align:middle line:84% You then have a little feeder here 00:41:04.830 --> 00:41:09.270 align:middle line:84% that then feeds in essentially droplets of metal. 00:41:09.270 --> 00:41:12.790 align:middle line:84% So the droplet metal will come up into contact with this drum. 00:41:12.790 --> 00:41:14.248 align:middle line:84% And then it will quickly cool down. 00:41:14.248 --> 00:41:15.623 align:middle line:84% And essentially-- oh, by the way, 00:41:15.623 --> 00:41:18.430 align:middle line:84% this drum is incrase spinning, OK, spinning at very high speed. 00:41:18.430 --> 00:41:20.750 align:middle line:84% So then, due to the centrifugal force, 00:41:20.750 --> 00:41:23.950 align:middle line:84% it's then going to essentially spread and form a little foil. 00:41:23.950 --> 00:41:26.270 align:middle line:90% And then essentially spin out. 00:41:26.270 --> 00:41:28.150 align:middle line:84% So what you end up getting here, you 00:41:28.150 --> 00:41:30.190 align:middle line:84% can actually do a continuous production 00:41:30.190 --> 00:41:35.510 align:middle line:84% of thin folio of glass of a metallic glass in this case, 00:41:35.510 --> 00:41:37.773 align:middle line:84% and with a high cooling rate, much higher 00:41:37.773 --> 00:41:39.690 align:middle line:84% cooling rate compared to conventional methods. 00:41:39.690 --> 00:41:43.430 align:middle line:84% So, so you can attain a much higher cooling rate here 00:41:43.430 --> 00:41:45.430 align:middle line:90% in this kind of techniques. 00:41:45.430 --> 00:41:49.490 align:middle line:84% Now if you go to thin films vapor deposition, 00:41:49.490 --> 00:41:52.800 align:middle line:84% you see that vapor deposition gives you a much higher cooling 00:41:52.800 --> 00:41:56.080 align:middle line:84% rate compared to bulk material, synthetic techniques. 00:41:56.080 --> 00:41:59.580 align:middle line:84% And that's because when you're doing thin film deposition, 00:41:59.580 --> 00:42:02.560 align:middle line:84% you essentially have these atoms in atomic state coming 00:42:02.560 --> 00:42:05.400 align:middle line:84% into contact in the molecular atomic state, 00:42:05.400 --> 00:42:07.520 align:middle line:84% come into contact with the substrate. 00:42:07.520 --> 00:42:09.800 align:middle line:84% The substrate has a much larger thermal mass 00:42:09.800 --> 00:42:12.080 align:middle line:84% compared to the individual molecular units. 00:42:12.080 --> 00:42:13.720 align:middle line:84% So that's why the effective cooling 00:42:13.720 --> 00:42:15.720 align:middle line:90% rate can be very, very high. 00:42:15.720 --> 00:42:20.360 align:middle line:84% And that's why, for a lot of the amorphous materials, 00:42:20.360 --> 00:42:23.380 align:middle line:84% you can normally only prepare them in a thin film form, 00:42:23.380 --> 00:42:24.640 align:middle line:90% not in a bulk form. 00:42:24.640 --> 00:42:28.560 align:middle line:84% Examples would be things like amorphous silicon or amorphous 00:42:28.560 --> 00:42:30.260 align:middle line:90% TiO2, amorphous zinc oxide. 00:42:30.260 --> 00:42:32.660 align:middle line:84% You can very easily get amorphous materials, thin film. 00:42:32.660 --> 00:42:34.880 align:middle line:84% But you typically don't get it in bulk state 00:42:34.880 --> 00:42:36.520 align:middle line:90% exactly because of that reason. 00:42:36.520 --> 00:42:41.480 align:middle line:84% So now if you have these two tables in hand, 00:42:41.480 --> 00:42:43.240 align:middle line:84% you can then immediately determine 00:42:43.240 --> 00:42:46.160 align:middle line:84% for each of these materials, what is the technique you 00:42:46.160 --> 00:42:47.860 align:middle line:90% would need to prepare them? 00:42:47.860 --> 00:42:50.220 align:middle line:84% What state is still avoid crystallization? 00:42:50.220 --> 00:42:52.180 align:middle line:84% So, for example, if you look at silver, 00:42:52.180 --> 00:42:55.280 align:middle line:84% you figure that you have to go to vapor deposition in order 00:42:55.280 --> 00:42:56.640 align:middle line:90% to ensure it's amorphous. 00:42:56.640 --> 00:43:00.560 align:middle line:84% Whereas [INAUDIBLE] you can even afford to just simply do 00:43:00.560 --> 00:43:02.800 align:middle line:90% air quench. 00:43:02.800 --> 00:43:06.960 align:middle line:84% We're still getting amorphous structures. 00:43:06.960 --> 00:43:07.500 align:middle line:90% All right. 00:43:07.500 --> 00:43:10.040 align:middle line:84% So key takeaway message here is to be aware 00:43:10.040 --> 00:43:13.400 align:middle line:84% that there is actually a maximum sample thickness where 00:43:13.400 --> 00:43:16.360 align:middle line:84% you can actually maintain amorphous structure if you 00:43:16.360 --> 00:43:18.620 align:middle line:90% have a limited glass stability. 00:43:18.620 --> 00:43:23.000 align:middle line:90% 00:43:23.000 --> 00:43:27.400 align:middle line:84% We're going to revisit that very quickly in the next lecture. 00:43:27.400 --> 00:43:27.900 align:middle line:90% All right. 00:43:27.900 --> 00:43:29.733 align:middle line:84% So that's about basically the kinetic theory 00:43:29.733 --> 00:43:31.160 align:middle line:90% of glass formation. 00:43:31.160 --> 00:43:32.640 align:middle line:84% What we're going to do next is then 00:43:32.640 --> 00:43:35.440 align:middle line:84% I will give you a bit more of a mechanistic explanation 00:43:35.440 --> 00:43:38.340 align:middle line:84% about what's actually going on in that glass-forming process. 00:43:38.340 --> 00:43:41.220 align:middle line:84% So in order to formulate such a theory, 00:43:41.220 --> 00:43:43.520 align:middle line:84% you need to be able to explain the few key features 00:43:43.520 --> 00:43:45.020 align:middle line:90% in the glass transition process. 00:43:45.020 --> 00:43:48.840 align:middle line:84% So first key feature is that glasses, its property 00:43:48.840 --> 00:43:50.832 align:middle line:84% is always thermal history dependent. 00:43:50.832 --> 00:43:53.540 align:middle line:84% If you cool it down at different rates, you get different volume, 00:43:53.540 --> 00:43:55.160 align:middle line:90% you get different enthalpy. 00:43:55.160 --> 00:43:57.920 align:middle line:84% So your theory need to be able to capture that. 00:43:57.920 --> 00:44:00.520 align:middle line:84% Different cooling rate give rise to different structures. 00:44:00.520 --> 00:44:04.937 align:middle line:90% 00:44:04.937 --> 00:44:06.520 align:middle line:84% I have another bullet point here which 00:44:06.520 --> 00:44:08.228 align:middle line:84% says that we can definitely slow cooling. 00:44:08.228 --> 00:44:09.540 align:middle line:90% You have ideal gas state. 00:44:09.540 --> 00:44:11.440 align:middle line:84% It's idealization, basically saying 00:44:11.440 --> 00:44:16.640 align:middle line:84% that if you have an infinitely slow cooling while still 00:44:16.640 --> 00:44:20.440 align:middle line:84% avoid crystallization, then you can imagine that you can-- 00:44:20.440 --> 00:44:25.260 align:middle line:84% line is going to continuously trace, super cool liquid line. 00:44:25.260 --> 00:44:26.500 align:middle line:90% So it's going to extrapolate. 00:44:26.500 --> 00:44:28.360 align:middle line:84% You can go along this dotted line here. 00:44:28.360 --> 00:44:31.640 align:middle line:84% And eventually, it's going to intersect with the solid line. 00:44:31.640 --> 00:44:37.840 align:middle line:84% Now the glass line cannot go below the crystalline line 00:44:37.840 --> 00:44:40.305 align:middle line:84% because glass need to have a higher enthalpy compared 00:44:40.305 --> 00:44:41.180 align:middle line:90% to crystalline solid. 00:44:41.180 --> 00:44:43.960 align:middle line:84% Otherwise, it will become thermodynamically stable phase. 00:44:43.960 --> 00:44:45.100 align:middle line:90% That's just not right. 00:44:45.100 --> 00:44:49.160 align:middle line:84% So it means that for this kind of a ideal glass, 00:44:49.160 --> 00:44:54.120 align:middle line:84% it's going to be forced to turn around to inflate and go 00:44:54.120 --> 00:44:55.200 align:middle line:90% along this line here. 00:44:55.200 --> 00:44:58.560 align:middle line:84% So the glass line will pretty much 00:44:58.560 --> 00:45:01.680 align:middle line:84% overlap with the crystalline line. 00:45:01.680 --> 00:45:03.560 align:middle line:84% So that's actually called ideal glass. 00:45:03.560 --> 00:45:07.400 align:middle line:84% It applies when this glass has basically almost 00:45:07.400 --> 00:45:11.000 align:middle line:84% the same foaming energy as its crystalline counterpart. 00:45:11.000 --> 00:45:16.670 align:middle line:84% It's an idealization of practical glasses. 00:45:16.670 --> 00:45:21.600 align:middle line:84% Anyway, that's not quite relevant here. 00:45:21.600 --> 00:45:25.320 align:middle line:84% So in order to explain this kind of thermal history dependence 00:45:25.320 --> 00:45:27.600 align:middle line:84% of glass structure and properties, 00:45:27.600 --> 00:45:29.420 align:middle line:90% let's revisit this concept here. 00:45:29.420 --> 00:45:32.200 align:middle line:84% When we're talking about stable glass state, 00:45:32.200 --> 00:45:34.360 align:middle line:84% I mentioned that glass structure essentially 00:45:34.360 --> 00:45:37.400 align:middle line:84% sits in some kind of metal stable basin, local minimum 00:45:37.400 --> 00:45:39.880 align:middle line:84% while crystalline is a global minimum. 00:45:39.880 --> 00:45:42.280 align:middle line:84% So we want to give a more quantitative picture 00:45:42.280 --> 00:45:43.680 align:middle line:90% of what we have here. 00:45:43.680 --> 00:45:45.360 align:middle line:84% So we want to introduce in this function 00:45:45.360 --> 00:45:49.050 align:middle line:84% of so-called potential energy landscape. 00:45:49.050 --> 00:45:51.170 align:middle line:84% So in potential energy landscape, 00:45:51.170 --> 00:45:55.010 align:middle line:84% the horizontal axis is still the glass structure. 00:45:55.010 --> 00:45:58.450 align:middle line:84% But in order to quantitatively represent glass structure, 00:45:58.450 --> 00:46:04.690 align:middle line:84% we need to know the position of all the atoms. 00:46:04.690 --> 00:46:10.650 align:middle line:84% Let's say your glass network has a total of n number of atoms. 00:46:10.650 --> 00:46:12.850 align:middle line:84% The position of each atom can be represented 00:46:12.850 --> 00:46:14.870 align:middle line:90% by a xy d coordinate. 00:46:14.870 --> 00:46:19.130 align:middle line:84% So if this know this 3n coordinates, 00:46:19.130 --> 00:46:23.570 align:middle line:84% you can then uniquely determine the structure of the glass. 00:46:23.570 --> 00:46:25.310 align:middle line:84% If you know the structure of the glass, 00:46:25.310 --> 00:46:27.610 align:middle line:84% you also know the interaction potential 00:46:27.610 --> 00:46:29.410 align:middle line:90% between the constituent atoms. 00:46:29.410 --> 00:46:32.450 align:middle line:84% You then know the interaction potential energy 00:46:32.450 --> 00:46:35.370 align:middle line:84% of all the atoms combined together. 00:46:35.370 --> 00:46:38.650 align:middle line:84% OK, so this interaction, this collective, interaction 00:46:38.650 --> 00:46:41.890 align:middle line:84% potential energy, is what we call the potential energy here. 00:46:41.890 --> 00:46:44.170 align:middle line:90% We label the vertical axis. 00:46:44.170 --> 00:46:47.810 align:middle line:84% So what we see here is a well-defined function spanning 00:46:47.810 --> 00:46:52.048 align:middle line:90% across these 3n axis. 00:46:52.048 --> 00:46:54.090 align:middle line:84% Now if you look at what this function looks like, 00:46:54.090 --> 00:46:55.570 align:middle line:84% this is a schematic representation 00:46:55.570 --> 00:46:56.590 align:middle line:90% of what it looks like. 00:46:56.590 --> 00:47:00.210 align:middle line:84% You must have a global minimum that corresponds 00:47:00.210 --> 00:47:02.930 align:middle line:90% to the crystalline state. 00:47:02.930 --> 00:47:07.090 align:middle line:84% You also get many, many, many, many local minima there. 00:47:07.090 --> 00:47:10.630 align:middle line:84% Each of these local minima is what we call the laboratory 00:47:10.630 --> 00:47:12.892 align:middle line:90% glass state. 00:47:12.892 --> 00:47:14.850 align:middle line:84% Essentially means that when you're cooling down 00:47:14.850 --> 00:47:17.850 align:middle line:84% from supercooled liquid, the system 00:47:17.850 --> 00:47:20.690 align:middle line:84% may relax one of these local minima there. 00:47:20.690 --> 00:47:24.130 align:middle line:84% So because each of the minima correspond to one possible state 00:47:24.130 --> 00:47:27.250 align:middle line:84% where you may obtain in your laboratory, 00:47:27.250 --> 00:47:30.450 align:middle line:84% that's why it's called laboratory glass state. 00:47:30.450 --> 00:47:32.530 align:middle line:84% Then ideal glass, as I mentioned, 00:47:32.530 --> 00:47:35.670 align:middle line:84% this is some idealization of the laboratory gassy state. 00:47:35.670 --> 00:47:38.250 align:middle line:84% And it should have almost the same enthalpy 00:47:38.250 --> 00:47:40.810 align:middle line:90% or energy as the crystal. 00:47:40.810 --> 00:47:43.290 align:middle line:84% So that's why ideal glass is almost equally 00:47:43.290 --> 00:47:46.570 align:middle line:90% at height as crystal layer. 00:47:46.570 --> 00:47:52.330 align:middle line:84% So now what's the difference between glass and supercooled 00:47:52.330 --> 00:47:54.290 align:middle line:90% liquid? 00:47:54.290 --> 00:47:56.530 align:middle line:84% So the laboratory definition of glass transition 00:47:56.530 --> 00:47:59.910 align:middle line:84% is coming from a statistical mechanics perspective. 00:47:59.910 --> 00:48:04.090 align:middle line:84% It basically says that liquid is ergodic 00:48:04.090 --> 00:48:06.370 align:middle line:90% and glass is non ergodic. 00:48:06.370 --> 00:48:11.010 align:middle line:84% So glass transition is basically a ergodicity breakdown. 00:48:11.010 --> 00:48:12.750 align:middle line:90% Now let me explain what that is. 00:48:12.750 --> 00:48:14.530 align:middle line:84% So ergodicity, or ergodic, essentially 00:48:14.530 --> 00:48:17.770 align:middle line:84% means that given enough time, a system 00:48:17.770 --> 00:48:21.110 align:middle line:84% can transition through all the possible microscopic states. 00:48:21.110 --> 00:48:25.730 align:middle line:84% That's called ergodic-- versus if a system is confined only 00:48:25.730 --> 00:48:30.650 align:middle line:84% to a small subgroup of states then this is called non ergodic. 00:48:30.650 --> 00:48:35.210 align:middle line:84% We argue that liquid is ergodic because in liquid state, 00:48:35.210 --> 00:48:36.430 align:middle line:90% it's high temperature. 00:48:36.430 --> 00:48:38.590 align:middle line:84% All the atoms have enough thermal energy. 00:48:38.590 --> 00:48:39.990 align:middle line:90% They can easily move around. 00:48:39.990 --> 00:48:41.890 align:middle line:84% It doesn't have a well-defined geometry. 00:48:41.890 --> 00:48:44.490 align:middle line:84% So it means that if it's a liquid, 00:48:44.490 --> 00:48:47.170 align:middle line:84% the system can essentially explore 00:48:47.170 --> 00:48:51.490 align:middle line:84% all of these possible combinations of the laboratory 00:48:51.490 --> 00:48:52.270 align:middle line:90% glass states. 00:48:52.270 --> 00:48:54.810 align:middle line:90% 00:48:54.810 --> 00:48:57.570 align:middle line:90% So liquid is ergodic. 00:48:57.570 --> 00:49:00.890 align:middle line:84% Now if you start to cool down, if you go to gassy state 00:49:00.890 --> 00:49:03.610 align:middle line:84% because it's a low temperature, now the system 00:49:03.610 --> 00:49:05.370 align:middle line:84% does not have enough energy to move around 00:49:05.370 --> 00:49:07.210 align:middle line:84% between these different local minima there. 00:49:07.210 --> 00:49:10.170 align:middle line:84% Basically, you get trapped in one, 00:49:10.170 --> 00:49:13.490 align:middle line:84% or maybe just a few, neighboring local minima. 00:49:13.490 --> 00:49:15.810 align:middle line:90% That's when you have a glass. 00:49:15.810 --> 00:49:17.830 align:middle line:90% So glass is non-ergodic. 00:49:17.830 --> 00:49:20.450 align:middle line:90% 00:49:20.450 --> 00:49:22.490 align:middle line:84% So what happens during glass transition 00:49:22.490 --> 00:49:25.850 align:middle line:84% is that you are transitioning from this ergodic system 00:49:25.850 --> 00:49:27.490 align:middle line:90% into a non ergodic system. 00:49:27.490 --> 00:49:29.310 align:middle line:90% So it's a ergodicity breakdown. 00:49:29.310 --> 00:49:32.050 align:middle line:90% 00:49:32.050 --> 00:49:32.630 align:middle line:90% All right. 00:49:32.630 --> 00:49:35.410 align:middle line:84% So I mentioned that this theory needs 00:49:35.410 --> 00:49:38.050 align:middle line:84% to be able to explain the property difference, 00:49:38.050 --> 00:49:42.420 align:middle line:84% how the property of glasses depend on its thermal history. 00:49:42.420 --> 00:49:44.040 align:middle line:90% So we can take a look at it. 00:49:44.040 --> 00:49:47.780 align:middle line:84% So what happens if you do slow cooling versus fast cooling? 00:49:47.780 --> 00:49:51.220 align:middle line:84% If you do slow cooling, then liquid, 00:49:51.220 --> 00:49:53.860 align:middle line:84% or the molecules or the atoms, still 00:49:53.860 --> 00:49:56.540 align:middle line:84% has time to move around a little bit. 00:49:56.540 --> 00:50:01.180 align:middle line:84% And you will try to settle at one of the deeper local minima 00:50:01.180 --> 00:50:04.220 align:middle line:84% just to minimize the system energy. 00:50:04.220 --> 00:50:06.220 align:middle line:84% So the resulting glass will then have 00:50:06.220 --> 00:50:10.380 align:middle line:84% a lower potential energy and therefore lower enthalpy, 00:50:10.380 --> 00:50:13.420 align:middle line:84% versus if you do a very rapid cooling. 00:50:13.420 --> 00:50:15.740 align:middle line:84% If you do a fast cooling, then the system 00:50:15.740 --> 00:50:18.300 align:middle line:84% does not really have the time to essentially explore 00:50:18.300 --> 00:50:20.220 align:middle line:90% many of the possible states. 00:50:20.220 --> 00:50:24.140 align:middle line:84% It quickly get trapped in one of the accessible states, which 00:50:24.140 --> 00:50:27.140 align:middle line:84% may not be giving you the low energy. 00:50:27.140 --> 00:50:30.620 align:middle line:84% So as a result, your system will be more likely 00:50:30.620 --> 00:50:32.500 align:middle line:84% ending up in a state that actually 00:50:32.500 --> 00:50:38.860 align:middle line:84% has a higher enthalpy compared to the slow, cool glass. 00:50:38.860 --> 00:50:40.500 align:middle line:84% So that's how you actually explain 00:50:40.500 --> 00:50:43.100 align:middle line:84% why you have this cooling rate difference in terms 00:50:43.100 --> 00:50:43.960 align:middle line:90% of glass properties. 00:50:43.960 --> 00:50:46.500 align:middle line:84% Basically, the range of microstates you can access 00:50:46.500 --> 00:50:47.240 align:middle line:90% is different. 00:50:47.240 --> 00:50:50.940 align:middle line:90% It depends on the cooling rate. 00:50:50.940 --> 00:50:58.460 align:middle line:84% More quantitatively, the transition 00:50:58.460 --> 00:51:00.220 align:middle line:84% between these different microstates 00:51:00.220 --> 00:51:02.540 align:middle line:84% is characterized by this time scale here called 00:51:02.540 --> 00:51:04.100 align:middle line:90% intervalley transition time. 00:51:04.100 --> 00:51:08.260 align:middle line:84% So if you look at the definition of intervalley transition time, 00:51:08.260 --> 00:51:11.340 align:middle line:84% [INAUDIBLE] this is basically the attempt frequency, 00:51:11.340 --> 00:51:13.660 align:middle line:84% or the vibration frequency of the structure 00:51:13.660 --> 00:51:14.800 align:middle line:90% between different minima. 00:51:14.800 --> 00:51:18.860 align:middle line:84% B gives you the average barrier height 00:51:18.860 --> 00:51:22.580 align:middle line:84% between the neighboring local minima there. 00:51:22.580 --> 00:51:24.900 align:middle line:84% And this exponential dependence essentially 00:51:24.900 --> 00:51:27.360 align:middle line:84% says that this process is thermally activated. 00:51:27.360 --> 00:51:28.680 align:middle line:90% It follows Arrhenius law. 00:51:28.680 --> 00:51:32.240 align:middle line:84% The higher the temperature, the more vigorous the atomic motion, 00:51:32.240 --> 00:51:33.790 align:middle line:84% the more likely the system is going 00:51:33.790 --> 00:51:36.040 align:middle line:84% to transition from one state to the neighboring state, 00:51:36.040 --> 00:51:37.740 align:middle line:90% and so on and so forth. 00:51:37.740 --> 00:51:44.300 align:middle line:84% So now with the introduction of this intervallic transition time 00:51:44.300 --> 00:51:47.700 align:middle line:84% tau, we can now define a criteria 00:51:47.700 --> 00:51:52.340 align:middle line:84% to determine whether you have a glass or liquid 00:51:52.340 --> 00:51:53.560 align:middle line:90% for your particular system. 00:51:53.560 --> 00:52:00.180 align:middle line:84% So the criteria is this one, t observation is less than tau. 00:52:00.180 --> 00:52:02.660 align:middle line:84% So t observation, this is basically 00:52:02.660 --> 00:52:05.980 align:middle line:84% a time of your experiment, the duration of your experiment 00:52:05.980 --> 00:52:09.460 align:middle line:84% or what we should observe in the sample. 00:52:09.460 --> 00:52:13.860 align:middle line:84% So if your duration of experiment is less than tau, 00:52:13.860 --> 00:52:16.180 align:middle line:84% it means that during your experiment, 00:52:16.180 --> 00:52:18.540 align:middle line:84% your system will likely get trapped 00:52:18.540 --> 00:52:21.580 align:middle line:90% in one of those local minima. 00:52:21.580 --> 00:52:24.620 align:middle line:84% So then you have a non-ergodic system. 00:52:24.620 --> 00:52:28.140 align:middle line:84% And then we then define the system you're examining there 00:52:28.140 --> 00:52:32.780 align:middle line:84% in your experiment as being a glass, versus if you have 00:52:32.780 --> 00:52:34.860 align:middle line:84% opticase, then the system can have enough time 00:52:34.860 --> 00:52:36.580 align:middle line:84% during the experiment to hop between 00:52:36.580 --> 00:52:37.900 align:middle line:90% different microstructures. 00:52:37.900 --> 00:52:42.300 align:middle line:84% Then we consider it as a supercooled liquid. 00:52:42.300 --> 00:52:45.540 align:middle line:84% OK, this is the working definition 00:52:45.540 --> 00:52:50.640 align:middle line:84% of glass transition, this one, T observation less than tau. 00:52:50.640 --> 00:52:53.220 align:middle line:90% 00:52:53.220 --> 00:52:53.900 align:middle line:90% Questions? 00:52:53.900 --> 00:52:59.760 align:middle line:90% 00:52:59.760 --> 00:53:02.140 align:middle line:84% one interesting aspect of this definition 00:53:02.140 --> 00:53:05.900 align:middle line:84% is that whether or not you have a glass 00:53:05.900 --> 00:53:08.140 align:middle line:90% depends on your T observation. 00:53:08.140 --> 00:53:11.900 align:middle line:84% Or in other words, depends on the experiment duration. 00:53:11.900 --> 00:53:14.515 align:middle line:84% So you can be doing different experiments at lots 00:53:14.515 --> 00:53:15.140 align:middle line:90% different time. 00:53:15.140 --> 00:53:16.260 align:middle line:84% For example, if you are doing, say 00:53:16.260 --> 00:53:18.220 align:middle line:84% that you are trying to measure the mechanical property 00:53:18.220 --> 00:53:19.180 align:middle line:90% of [INAUDIBLE] glass. 00:53:19.180 --> 00:53:21.140 align:middle line:84% You are doing some tensile experiments, which 00:53:21.140 --> 00:53:22.740 align:middle line:90% may take you a few minutes. 00:53:22.740 --> 00:53:25.940 align:middle line:84% So provided that within that few minutes, 00:53:25.940 --> 00:53:28.580 align:middle line:84% your structure sits in one valley. 00:53:28.580 --> 00:53:29.240 align:middle line:90% You are OK. 00:53:29.240 --> 00:53:30.860 align:middle line:90% You have glass. 00:53:30.860 --> 00:53:32.580 align:middle line:84% You could also be doing some experiments 00:53:32.580 --> 00:53:35.350 align:middle line:84% that you are looking at long-term relaxation 00:53:35.350 --> 00:53:38.750 align:middle line:84% of your sample, which may take years. 00:53:38.750 --> 00:53:43.030 align:middle line:84% So in that case, the criteria for being glass 00:53:43.030 --> 00:53:44.850 align:middle line:90% becomes a lot more stringent. 00:53:44.850 --> 00:53:47.730 align:middle line:84% You need to make sure that over the time span of few years, 00:53:47.730 --> 00:53:49.930 align:middle line:84% your system is localized in one of the minimum. 00:53:49.930 --> 00:53:52.470 align:middle line:90% 00:53:52.470 --> 00:53:54.550 align:middle line:84% So what you see here is whether you get glass 00:53:54.550 --> 00:53:59.230 align:middle line:84% or you get supercooled liquid, it depends on your experiment, 00:53:59.230 --> 00:54:02.110 align:middle line:84% depends on what you're trying to observe there. 00:54:02.110 --> 00:54:03.510 align:middle line:90% That's why I call it. 00:54:03.510 --> 00:54:06.378 align:middle line:84% This is a working definition of a glass transition. 00:54:06.378 --> 00:54:08.170 align:middle line:84% This is called laboratory glass transition. 00:54:08.170 --> 00:54:13.910 align:middle line:84% It comes from this very practical perspective. 00:54:13.910 --> 00:54:15.993 align:middle line:84% If the condition is satisfied, you can essentially 00:54:15.993 --> 00:54:18.035 align:middle line:84% worry about this kind of structure transformation 00:54:18.035 --> 00:54:19.850 align:middle line:84% inside the glass during your experiment. 00:54:19.850 --> 00:54:21.210 align:middle line:90% Then you can see as a glass. 00:54:21.210 --> 00:54:25.430 align:middle line:90% 00:54:25.430 --> 00:54:29.270 align:middle line:84% So in the end, whether or not you call coil system 00:54:29.270 --> 00:54:32.630 align:middle line:84% a glass depends on your experimental condition 00:54:32.630 --> 00:54:33.410 align:middle line:90% in this case. 00:54:33.410 --> 00:54:37.110 align:middle line:90% 00:54:37.110 --> 00:54:38.090 align:middle line:90% Does that make sense? 00:54:38.090 --> 00:54:44.230 align:middle line:90% 00:54:44.230 --> 00:54:45.830 align:middle line:90% Yes. 00:54:45.830 --> 00:54:47.350 align:middle line:90% I expect you have questions. 00:54:47.350 --> 00:54:47.910 align:middle line:90% Yeah. 00:54:47.910 --> 00:54:49.110 align:middle line:90% AUDIENCE: Sorry. 00:54:49.110 --> 00:54:50.770 align:middle line:84% So is it also a consequence of this 00:54:50.770 --> 00:54:56.870 align:middle line:84% that glass cooled at a given cooling rate 00:54:56.870 --> 00:55:00.810 align:middle line:84% might have different properties, depending on which-- 00:55:00.810 --> 00:55:03.910 align:middle line:90% 00:55:03.910 --> 00:55:07.590 align:middle line:84% PROFESSOR: Yes, basically that means 00:55:07.590 --> 00:55:10.470 align:middle line:84% the glass structure is always stochastic in nature, 00:55:10.470 --> 00:55:11.630 align:middle line:90% always stochastical. 00:55:11.630 --> 00:55:14.150 align:middle line:84% So you have exactly the same glass composition. 00:55:14.150 --> 00:55:17.010 align:middle line:84% You try to cool it down at exactly the same temperature, 00:55:17.010 --> 00:55:18.415 align:middle line:90% same cooling rate. 00:55:18.415 --> 00:55:19.790 align:middle line:84% The structure you're going to get 00:55:19.790 --> 00:55:23.277 align:middle line:84% is not going to be microscopically identical, 00:55:23.277 --> 00:55:25.110 align:middle line:84% because it's basically a stochastic process, 00:55:25.110 --> 00:55:27.130 align:middle line:84% the system trying to explore different local minima. 00:55:27.130 --> 00:55:28.547 align:middle line:84% And you have two different systems 00:55:28.547 --> 00:55:30.640 align:middle line:84% obviously are going to see different structures. 00:55:30.640 --> 00:55:31.890 align:middle line:90% So it's going to be different. 00:55:31.890 --> 00:55:37.750 align:middle line:84% AUDIENCE: But macroscopically, we still observe like the same. 00:55:37.750 --> 00:55:39.430 align:middle line:84% PROFESSOR: Macroscopic, they still 00:55:39.430 --> 00:55:41.470 align:middle line:84% have similar properties, very similar, usually. 00:55:41.470 --> 00:55:43.470 align:middle line:84% AUDIENCE: And then compared to this [INAUDIBLE], 00:55:43.470 --> 00:55:49.590 align:middle line:84% just correspond to different local minima at the same-- 00:55:49.590 --> 00:55:51.390 align:middle line:84% PROFESSOR: Similar energy levels because 00:55:51.390 --> 00:55:53.110 align:middle line:90% of the same cooling kinetics. 00:55:53.110 --> 00:55:54.875 align:middle line:90% And that's why. 00:55:54.875 --> 00:55:56.250 align:middle line:84% Later, we're going to talk about, 00:55:56.250 --> 00:55:58.030 align:middle line:84% for example, how you can potentially-- using this one 00:55:58.030 --> 00:55:59.830 align:middle line:84% single parameter, the fictive temperature, 00:55:59.830 --> 00:56:02.950 align:middle line:84% to label the glass structure, which is essentially 00:56:02.950 --> 00:56:04.210 align:middle line:90% this simplification. 00:56:04.210 --> 00:56:06.750 align:middle line:84% If you can label it just with a cooling rate, and from that, 00:56:06.750 --> 00:56:08.830 align:middle line:84% you can determine the glass structure 00:56:08.830 --> 00:56:10.882 align:middle line:90% like a single variable function. 00:56:10.882 --> 00:56:12.590 align:middle line:84% It's an approximation because later we're 00:56:12.590 --> 00:56:15.910 align:middle line:84% going to show you that that's a vast simplification. 00:56:15.910 --> 00:56:17.177 align:middle line:90% There are cases where you-- 00:56:17.177 --> 00:56:19.010 align:middle line:84% glasses have the same effective temperature. 00:56:19.010 --> 00:56:20.760 align:middle line:84% But you actually get different properties. 00:56:20.760 --> 00:56:23.930 align:middle line:84% But to the first order, I mean, that's what it is. 00:56:23.930 --> 00:56:28.380 align:middle line:84% And that's also what give rise to this inhomogeneity of glass, 00:56:28.380 --> 00:56:30.660 align:middle line:84% even for the one glass sample, the bulk glass sample. 00:56:30.660 --> 00:56:32.180 align:middle line:84% If you look at different locations, 00:56:32.180 --> 00:56:34.555 align:middle line:84% you still get this kind of a little bit slight dispersion 00:56:34.555 --> 00:56:35.562 align:middle line:90% of the properties. 00:56:35.562 --> 00:56:37.020 align:middle line:84% And that's exactly because of that. 00:56:37.020 --> 00:56:39.728 align:middle line:84% The kinetic process, even though it goes through the same cooling 00:56:39.728 --> 00:56:42.600 align:middle line:84% rate, statistically, there's always some variation there 00:56:42.600 --> 00:56:44.020 align:middle line:90% in the glass local structure. 00:56:44.020 --> 00:56:47.000 align:middle line:90% 00:56:47.000 --> 00:56:47.720 align:middle line:90% All right. 00:56:47.720 --> 00:56:50.940 align:middle line:84% Now let's come to the part-- as I said, my favorite part. 00:56:50.940 --> 00:56:53.520 align:middle line:84% Now let's discuss a little bit about now what 00:56:53.520 --> 00:56:57.840 align:middle line:84% is the structure that give rise to the highest glass 00:56:57.840 --> 00:57:00.420 align:middle line:84% network stability to resist crystallization? 00:57:00.420 --> 00:57:02.980 align:middle line:84% We have already shown you this kind of diagram here. 00:57:02.980 --> 00:57:04.640 align:middle line:84% This is when we're talking about, 00:57:04.640 --> 00:57:07.240 align:middle line:84% glass network formers and modifiers. 00:57:07.240 --> 00:57:09.260 align:middle line:84% We see that the network formers and modifiers, 00:57:09.260 --> 00:57:12.320 align:middle line:84% they are all clustered on this periodic table. 00:57:12.320 --> 00:57:14.920 align:middle line:84% For glass formers, they tend to be this kind of non metal 00:57:14.920 --> 00:57:17.440 align:middle line:90% element forming covalent bonds. 00:57:17.440 --> 00:57:20.480 align:middle line:84% And the basic idea behind it is that you 00:57:20.480 --> 00:57:23.622 align:middle line:84% want to have, essentially, like open-network structure 00:57:23.622 --> 00:57:26.080 align:middle line:84% so that you can accommodate a lot of structure deformation. 00:57:26.080 --> 00:57:29.680 align:middle line:84% OK, so this kind of observation is 00:57:29.680 --> 00:57:32.280 align:middle line:84% what lead to so-called absence rules. 00:57:32.280 --> 00:57:34.800 align:middle line:84% So Zachariasen is a scientist that actually proposed 00:57:34.800 --> 00:57:37.480 align:middle line:84% this random network theory, the structure of the glass 00:57:37.480 --> 00:57:38.160 align:middle line:90% materials. 00:57:38.160 --> 00:57:40.600 align:middle line:84% We mentioned that in the first lecture. 00:57:40.600 --> 00:57:44.880 align:middle line:84% On top of that, he also gave rise a few empirical rules 00:57:44.880 --> 00:57:48.400 align:middle line:84% that specifies what kind of compounds 00:57:48.400 --> 00:57:52.520 align:middle line:84% will be glass former versus being a glass modifier, network 00:57:52.520 --> 00:57:53.180 align:middle line:90% modifier. 00:57:53.180 --> 00:57:56.247 align:middle line:90% 00:57:56.247 --> 00:57:58.080 align:middle line:84% For this Zachariasen's rules, a few things I 00:57:58.080 --> 00:57:59.380 align:middle line:84% want to mention before I go into that. 00:57:59.380 --> 00:58:01.240 align:middle line:84% One is that this empirical rule, it means 00:58:01.240 --> 00:58:02.940 align:middle line:90% that there are two exceptions. 00:58:02.940 --> 00:58:06.480 align:middle line:84% It applies to most compounds, but not all of them. 00:58:06.480 --> 00:58:09.858 align:middle line:84% Also it's only applicable to oxide glasses. 00:58:09.858 --> 00:58:11.400 align:middle line:84% So we will be talking about some kind 00:58:11.400 --> 00:58:15.680 align:middle line:84% of oxides with the stoichiometry given by Amon. 00:58:15.680 --> 00:58:17.840 align:middle line:90% So this will be just an oxide. 00:58:17.840 --> 00:58:20.080 align:middle line:84% And the topic of the discussion will 00:58:20.080 --> 00:58:23.080 align:middle line:84% be this element A. Is the glass former 00:58:23.080 --> 00:58:25.120 align:middle line:90% or is it a network modifier? 00:58:25.120 --> 00:58:26.840 align:middle line:90% That's what Zachariah tells you. 00:58:26.840 --> 00:58:29.960 align:middle line:90% 00:58:29.960 --> 00:58:32.600 align:middle line:84% So now let's look at the four rules here. 00:58:32.600 --> 00:58:35.560 align:middle line:84% The first one, it says that an oxygen atom 00:58:35.560 --> 00:58:38.540 align:middle line:84% is linked to no more than two atoms of eight. 00:58:38.540 --> 00:58:42.480 align:middle line:90% 00:58:42.480 --> 00:58:44.680 align:middle line:84% So it means that the coordination number of oxygen 00:58:44.680 --> 00:58:47.480 align:middle line:84% should be 2, which sounds like trivial. 00:58:47.480 --> 00:58:50.640 align:middle line:84% But if you think about close packed structures 00:58:50.640 --> 00:58:53.080 align:middle line:84% like ionic solids, that's often violated. 00:58:53.080 --> 00:58:56.800 align:middle line:84% That's one reason why solids tend to be poor performance. 00:58:56.800 --> 00:59:01.287 align:middle line:84% Now second one, the oxygen coordination around eight. 00:59:01.287 --> 00:59:02.620 align:middle line:90% So we talk about the first rule. 00:59:02.620 --> 00:59:04.527 align:middle line:84% We'll talk about coordination number, oxygen. 00:59:04.527 --> 00:59:06.360 align:middle line:84% The second rule is about coordination number 00:59:06.360 --> 00:59:07.240 align:middle line:90% of this element. 00:59:07.240 --> 00:59:11.160 align:middle line:84% It should be small, say three or four. 00:59:11.160 --> 00:59:14.080 align:middle line:84% So if you combine the first two rules here-- 00:59:14.080 --> 00:59:17.640 align:middle line:84% or is this that you need to have a small coordination 00:59:17.640 --> 00:59:21.400 align:middle line:84% number around both oxygen and the [INAUDIBLE]. 00:59:21.400 --> 00:59:24.400 align:middle line:84% A small coordination number is the typical feature 00:59:24.400 --> 00:59:27.640 align:middle line:90% of a covalent solid. 00:59:27.640 --> 00:59:32.600 align:middle line:84% If you think about ionic solids or think about metallic solids, 00:59:32.600 --> 00:59:34.880 align:middle line:84% the chemical bond is non-directional. 00:59:34.880 --> 00:59:37.880 align:middle line:84% It's either electrostatic interaction or metallic bonds. 00:59:37.880 --> 00:59:40.060 align:middle line:84% So to minimize energy, you want to close packed. 00:59:40.060 --> 00:59:42.680 align:middle line:84% You want to have as high a number of coordination as 00:59:42.680 --> 00:59:45.000 align:middle line:90% possible around each atom there. 00:59:45.000 --> 00:59:48.680 align:middle line:84% As a result, you don't give rise to the open structure that 00:59:48.680 --> 00:59:50.480 align:middle line:84% allow you to actually distort the network 00:59:50.480 --> 00:59:52.840 align:middle line:84% and accommodate this kind of structure disorder there. 00:59:52.840 --> 00:59:55.360 align:middle line:84% So that's why it's not preferred for glass formation. 00:59:55.360 --> 00:59:58.462 align:middle line:84% So as I said, you won't have open structure. 00:59:58.462 --> 00:59:59.920 align:middle line:84% So they give rise to a small energy 00:59:59.920 --> 01:00:02.087 align:middle line:84% difference between the glassy and crystalline state. 01:00:02.087 --> 01:00:04.520 align:middle line:84% If you distort the network, it doesn't cause a huge energy 01:00:04.520 --> 01:00:05.100 align:middle line:90% penalty. 01:00:05.100 --> 01:00:08.480 align:middle line:84% It doesn't build a lot of stress into a network. 01:00:08.480 --> 01:00:08.980 align:middle line:90% All right. 01:00:08.980 --> 01:00:12.120 align:middle line:84% Now next one, the cation polyhedra 01:00:12.120 --> 01:00:14.677 align:middle line:84% shares corners, not edges, not faces. 01:00:14.677 --> 01:00:16.260 align:middle line:84% Let's take a look at one example here. 01:00:16.260 --> 01:00:17.680 align:middle line:90% What's a cation polyhedra? 01:00:17.680 --> 01:00:20.320 align:middle line:84% So if you think about silicon glass, 01:00:20.320 --> 01:00:24.650 align:middle line:84% the basic structural unit is this kind of SI 04 tetrahedra. 01:00:24.650 --> 01:00:31.530 align:middle line:84% So if you look at the tetrahedra with the center as silicon 01:00:31.530 --> 01:00:33.970 align:middle line:84% and with surrounded by oxygen atoms, 01:00:33.970 --> 01:00:36.075 align:middle line:84% this is what we call the cat-eyed polyhedra. 01:00:36.075 --> 01:00:37.950 align:middle line:84% In this case, this is actually a tetrahedron. 01:00:37.950 --> 01:00:41.450 align:middle line:84% If you get boron silicate glass, for example, you get PO3. 01:00:41.450 --> 01:00:44.230 align:middle line:84% In that case, you essentially get a triangle, bo3 triangle. 01:00:44.230 --> 01:00:47.490 align:middle line:84% That's basically a polyhedron in the BO3, class. 01:00:47.490 --> 01:00:50.450 align:middle line:84% Now if you look at two neighboring structure 01:00:50.450 --> 01:00:55.530 align:middle line:84% units, what I'm showing you on this plot here, on this one 01:00:55.530 --> 01:00:58.150 align:middle line:84% here, this is basically sharing a corner. 01:00:58.150 --> 01:01:00.530 align:middle line:84% You have one non-bridging oxygen that connects 01:01:00.530 --> 01:01:03.890 align:middle line:90% to 2, this tetrahedral here. 01:01:03.890 --> 01:01:07.750 align:middle line:84% And then you are only sharing-- the two neighboring tetrahedra 01:01:07.750 --> 01:01:12.650 align:middle line:84% only shares one bridging oxygen. This is called a corner sharing. 01:01:12.650 --> 01:01:14.450 align:middle line:90% Now what about edge sharing? 01:01:14.450 --> 01:01:18.690 align:middle line:84% Edge sharing is when you have two neighboring tetrahedra 01:01:18.690 --> 01:01:23.770 align:middle line:84% shares two bridging oxygen. This is edge sharing. 01:01:23.770 --> 01:01:28.650 align:middle line:90% You can also have face sharing. 01:01:28.650 --> 01:01:34.690 align:middle line:84% If it's face sharing, now I need to really bend it. 01:01:34.690 --> 01:01:36.690 align:middle line:90% This is face sharing. 01:01:36.690 --> 01:01:39.850 align:middle line:84% So you can see that when we're going from corner sharing 01:01:39.850 --> 01:01:41.770 align:middle line:84% to edge sharing and face sharing, 01:01:41.770 --> 01:01:44.570 align:middle line:84% the flexibility of the network essentially monotonically 01:01:44.570 --> 01:01:45.650 align:middle line:90% decreases. 01:01:45.650 --> 01:01:47.130 align:middle line:84% If you think about this structure, 01:01:47.130 --> 01:01:48.390 align:middle line:90% it's actually very rigid. 01:01:48.390 --> 01:01:50.270 align:middle line:84% There's no way I can really distort it. 01:01:50.270 --> 01:01:55.810 align:middle line:84% Versus if you go to a corner shearing structure, 01:01:55.810 --> 01:01:59.597 align:middle line:84% then it gives rise to a lot of potential rooms 01:01:59.597 --> 01:02:01.930 align:middle line:84% to distort the network structure by simply just rotating 01:02:01.930 --> 01:02:03.010 align:middle line:90% this chemical bonds. 01:02:03.010 --> 01:02:07.170 align:middle line:84% Rotation of these chemical bonds give you a much smaller energy 01:02:07.170 --> 01:02:12.210 align:middle line:84% penalty compared to like in the case of a edge or corner face 01:02:12.210 --> 01:02:13.570 align:middle line:90% sharing. 01:02:13.570 --> 01:02:15.790 align:middle line:90% So that's what it means. 01:02:15.790 --> 01:02:18.470 align:middle line:84% If you only have this polyhedron, only shares corners, 01:02:18.470 --> 01:02:20.970 align:middle line:84% then you can actually maximize the structural flexibility 01:02:20.970 --> 01:02:24.290 align:middle line:90% to accommodate this order. 01:02:24.290 --> 01:02:27.850 align:middle line:84% Now finally, last one, at least three corners 01:02:27.850 --> 01:02:30.090 align:middle line:84% has to be shared for all the tetrahedra, 01:02:30.090 --> 01:02:32.730 align:middle line:84% for all the polyhedra, for silica glass. 01:02:32.730 --> 01:02:34.730 align:middle line:84% All four corners are always shared. 01:02:34.730 --> 01:02:38.470 align:middle line:84% In silica glass, all the oxygen is bridging oxygen. 01:02:38.470 --> 01:02:42.130 align:middle line:84% So essentially means that all the corners are shared. 01:02:42.130 --> 01:02:43.610 align:middle line:90% So let's satisfy this rule. 01:02:43.610 --> 01:02:46.210 align:middle line:84% And the reason you have this kind of rule here is because you 01:02:46.210 --> 01:02:48.730 align:middle line:90% want to form a 3D network. 01:02:48.730 --> 01:02:49.310 align:middle line:90% Yes. 01:02:49.310 --> 01:02:52.130 align:middle line:84% AUDIENCE: Does this apply all the way to the edge? 01:02:52.130 --> 01:02:53.130 align:middle line:90% PROFESSOR: To a surface? 01:02:53.130 --> 01:02:54.850 align:middle line:90% AUDIENCE: Yes. 01:02:54.850 --> 01:02:56.970 align:middle line:84% PROFESSOR: No, we don't worry about surface here. 01:02:56.970 --> 01:02:58.690 align:middle line:84% In the summer, you get things like reconstruction 01:02:58.690 --> 01:02:59.310 align:middle line:90% and all that stuff. 01:02:59.310 --> 01:03:00.590 align:middle line:84% So it's always a little bit different. 01:03:00.590 --> 01:03:02.090 align:middle line:84% You get dangling bonds and things. 01:03:02.090 --> 01:03:05.210 align:middle line:84% But this is only talking about the bulk. 01:03:05.210 --> 01:03:08.430 align:middle line:84% Yeah, but basically, if you think about bulk, 01:03:08.430 --> 01:03:11.570 align:middle line:84% in order to form a 3D network, each of the polyhedra need 01:03:11.570 --> 01:03:14.570 align:middle line:90% to share at least three. 01:03:14.570 --> 01:03:17.170 align:middle line:84% If you only share two corners, then the best you can get 01:03:17.170 --> 01:03:19.045 align:middle line:84% is something like a long linear trade. 01:03:19.045 --> 01:03:21.670 align:middle line:84% In order to form a 3D network, you need to share three corners. 01:03:21.670 --> 01:03:23.370 align:middle line:84% So that's what the last rule means. 01:03:23.370 --> 01:03:29.090 align:middle line:84% So now before I go to some specific examples 01:03:29.090 --> 01:03:32.010 align:middle line:84% of Zachariasen's rules, we notice one thing here. 01:03:32.010 --> 01:03:35.010 align:middle line:84% It's that all of these four rules, 01:03:35.010 --> 01:03:39.150 align:middle line:84% it does not talk about the chemical nature of the element. 01:03:39.150 --> 01:03:40.750 align:middle line:84% It doesn't talk about reactivity. 01:03:40.750 --> 01:03:43.710 align:middle line:84% It doesn't talk about electron affinity or electronegativity. 01:03:43.710 --> 01:03:46.330 align:middle line:90% There's nothing like that. 01:03:46.330 --> 01:03:48.410 align:middle line:84% The only thing that really goes in there 01:03:48.410 --> 01:03:51.330 align:middle line:84% is the valent state, which gives you the number of chemical 01:03:51.330 --> 01:03:53.370 align:middle line:84% bonds, one atom forms, as well as 01:03:53.370 --> 01:03:57.090 align:middle line:84% the connectivity between the polyhedra. 01:03:57.090 --> 01:04:00.050 align:middle line:84% These are all topological features 01:04:00.050 --> 01:04:03.770 align:middle line:90% associated with a glass network 01:04:03.770 --> 01:04:06.810 align:middle line:84% So that's why it's exactly because of this nature 01:04:06.810 --> 01:04:09.570 align:middle line:84% that people realize the importance of network topology 01:04:09.570 --> 01:04:10.990 align:middle line:90% in glass forming. 01:04:10.990 --> 01:04:13.725 align:middle line:84% And that's where the topological constraint theory comes in, 01:04:13.725 --> 01:04:16.100 align:middle line:84% predicting glass stability, which I'm going to talk about 01:04:16.100 --> 01:04:17.420 align:middle line:90% in next few slides. 01:04:17.420 --> 01:04:22.180 align:middle line:84% Now, before you go to that, I do want to do a quick practice. 01:04:22.180 --> 01:04:30.280 align:middle line:84% Let's see one example of a glass network. 01:04:30.280 --> 01:04:39.220 align:middle line:84% And let's then practice to see whether or not the declaration 01:04:39.220 --> 01:04:41.420 align:middle line:90% rule is applied, so OK. 01:04:41.420 --> 01:04:44.020 align:middle line:84% Let's look at this simple one here. 01:04:44.020 --> 01:04:46.180 align:middle line:90% Let's consider just zinc oxide. 01:04:46.180 --> 01:04:48.780 align:middle line:90% 01:04:48.780 --> 01:04:51.280 align:middle line:84% This is a crystalline structure for zinc oxide. 01:04:51.280 --> 01:04:52.920 align:middle line:84% It has two kind of structural variants. 01:04:52.920 --> 01:04:54.080 align:middle line:90% You get zinc blend. 01:04:54.080 --> 01:04:58.240 align:middle line:84% You get this kind of a hexagonal structure. 01:04:58.240 --> 01:05:00.710 align:middle line:84% But either way, it turns out the conclusion 01:05:00.710 --> 01:05:02.960 align:middle line:84% is the same, because the local connection is the same. 01:05:02.960 --> 01:05:04.940 align:middle line:84% It's just stacking of different polyhedra. 01:05:04.940 --> 01:05:08.260 align:middle line:84% So now let's try to look at it and see if we satisfy 01:05:08.260 --> 01:05:09.480 align:middle line:90% the Zachariasen's rules. 01:05:09.480 --> 01:05:13.900 align:middle line:84% So first rule here, so this one this would be zinc. 01:05:13.900 --> 01:05:17.340 align:middle line:84% This will be oxygen. So the first rule 01:05:17.340 --> 01:05:21.340 align:middle line:84% says that oxygen needs to be two-fold coordinated. 01:05:21.340 --> 01:05:22.440 align:middle line:90% It is satisfied. 01:05:22.440 --> 01:05:25.140 align:middle line:90% 01:05:25.140 --> 01:05:26.900 align:middle line:84% You can fairly quickly see, what's 01:05:26.900 --> 01:05:28.580 align:middle line:90% the coordination on the oxygen? 01:05:28.580 --> 01:05:30.820 align:middle line:84% For that, you only look at the nearest neighbors. 01:05:30.820 --> 01:05:33.700 align:middle line:84% You look at oxygen linking to zinc. 01:05:33.700 --> 01:05:35.100 align:middle line:90% This is the nearest neighbors. 01:05:35.100 --> 01:05:40.740 align:middle line:84% Each oxygen links to 4 zinc, so actually violate the first rule, 01:05:40.740 --> 01:05:42.500 align:middle line:90% first Zachariasen's rule. 01:05:42.500 --> 01:05:43.660 align:middle line:90% What about the second rule? 01:05:43.660 --> 01:05:45.500 align:middle line:84% Second rule says that the zinc coordination 01:05:45.500 --> 01:05:48.260 align:middle line:90% number has to be three or four. 01:05:48.260 --> 01:05:49.220 align:middle line:90% It's actually four. 01:05:49.220 --> 01:05:51.500 align:middle line:84% So actually four-- actually obeys the second rule 01:05:51.500 --> 01:05:53.820 align:middle line:90% of Zachariasen. 01:05:53.820 --> 01:05:56.820 align:middle line:84% Third rule, neighboring polyhedra 01:05:56.820 --> 01:05:58.940 align:middle line:90% need to be sharing corners. 01:05:58.940 --> 01:06:00.620 align:middle line:84% So what are the neighboring tetrahedra? 01:06:00.620 --> 01:06:02.308 align:middle line:84% So to look at neighboring tetrahedra, 01:06:02.308 --> 01:06:04.100 align:middle line:84% you start by looking at the cat-eye, right? 01:06:04.100 --> 01:06:05.720 align:middle line:84% So in this case, cat-eye was zinc. 01:06:05.720 --> 01:06:06.827 align:middle line:90% So look at this one. 01:06:06.827 --> 01:06:08.660 align:middle line:84% You look at the nearest neighbor zinc, which 01:06:08.660 --> 01:06:10.500 align:middle line:90% would be this one, for example. 01:06:10.500 --> 01:06:13.360 align:middle line:84% So if you look at these two, in this case, 01:06:13.360 --> 01:06:17.780 align:middle line:84% the polyhedra is actually a tetrahedra. 01:06:17.780 --> 01:06:21.740 align:middle line:84% So the neighboring tetrahedra, what do they share? 01:06:21.740 --> 01:06:23.840 align:middle line:90% They do share the corner. 01:06:23.840 --> 01:06:28.300 align:middle line:84% So if a base, this third rule, or the third [INAUDIBLE] rule. 01:06:28.300 --> 01:06:31.260 align:middle line:84% Now, however, if you look a bit more closely, 01:06:31.260 --> 01:06:34.940 align:middle line:84% it's still pretty rigid network because the two neighboring 01:06:34.940 --> 01:06:36.820 align:middle line:84% ones, they share one corner there. 01:06:36.820 --> 01:06:38.700 align:middle line:84% But then they are interlinked through 01:06:38.700 --> 01:06:40.260 align:middle line:90% the next nearest neighbor. 01:06:40.260 --> 01:06:42.340 align:middle line:84% So it's actually still pretty rigid network. 01:06:42.340 --> 01:06:45.620 align:middle line:84% But anyway, that's beyond the simple [INAUDIBLE] rule there. 01:06:45.620 --> 01:06:51.740 align:middle line:84% Finally, each polyhedra should share at least three corners. 01:06:51.740 --> 01:06:53.980 align:middle line:90% It is satisfied? 01:06:53.980 --> 01:06:56.800 align:middle line:84% If you look at polyhedra here, how many corners are shared? 01:06:56.800 --> 01:07:00.295 align:middle line:90% 01:07:00.295 --> 01:07:01.420 align:middle line:90% AUDIENCE: All four of them? 01:07:01.420 --> 01:07:03.280 align:middle line:90% PROFESSOR: All four of them. 01:07:03.280 --> 01:07:03.800 align:middle line:90% So, yeah. 01:07:03.800 --> 01:07:05.860 align:middle line:84% That's why they form a 3D network. 01:07:05.860 --> 01:07:08.180 align:middle line:84% However, [INAUDIBLE] still is a poor glass form 01:07:08.180 --> 01:07:10.360 align:middle line:84% because it doesn't satisfy all these [INAUDIBLE] 01:07:10.360 --> 01:07:13.250 align:middle line:84% rules, which is consistent with experiment. 01:07:13.250 --> 01:07:17.170 align:middle line:84% As I mentioned, you can form a thin film, amorphous zinc oxide. 01:07:17.170 --> 01:07:19.390 align:middle line:84% But it's quite difficult to prepare zinc oxide 01:07:19.390 --> 01:07:21.430 align:middle line:90% in bulk state. 01:07:21.430 --> 01:07:25.530 align:middle line:84% So by the way, when we talk about these Zachariasen's rules, 01:07:25.530 --> 01:07:28.390 align:middle line:84% you are typically talking about glass formation for bulk oxide 01:07:28.390 --> 01:07:29.830 align:middle line:90% glasses. 01:07:29.830 --> 01:07:32.090 align:middle line:84% For thin films, because of the higher quench rate, 01:07:32.090 --> 01:07:34.830 align:middle line:84% you can potentially prepare some amorphous state materials 01:07:34.830 --> 01:07:38.470 align:middle line:84% that conventionally you would not be able to prepare. 01:07:38.470 --> 01:07:39.070 align:middle line:90% All right. 01:07:39.070 --> 01:07:42.110 align:middle line:84% So let's see the early days when people 01:07:42.110 --> 01:07:43.910 align:middle line:84% are looking at this only applies to oxide 01:07:43.910 --> 01:07:45.990 align:middle line:90% glasses, the empirical rules. 01:07:45.990 --> 01:07:51.350 align:middle line:84% Now these Zachariasen's rules definitely heralds 01:07:51.350 --> 01:07:54.330 align:middle line:84% the topological constraint theory, 01:07:54.330 --> 01:07:58.510 align:middle line:84% which is the more recent theory, or most recent attempt people 01:07:58.510 --> 01:08:00.610 align:middle line:84% make trying to explain the glass stability. 01:08:00.610 --> 01:08:06.790 align:middle line:84% So the whole concept of this topological constraint theory 01:08:06.790 --> 01:08:10.550 align:middle line:84% essentially borrows the concept of a network constraints 01:08:10.550 --> 01:08:13.150 align:middle line:90% from basically mechanics. 01:08:13.150 --> 01:08:19.149 align:middle line:84% It classifies the glass network into three kind of topologies. 01:08:19.149 --> 01:08:23.790 align:middle line:84% You can have a flexible or floppy or under constrained 01:08:23.790 --> 01:08:25.029 align:middle line:90% network. 01:08:25.029 --> 01:08:27.890 align:middle line:84% You can have over constrained or what we call 01:08:27.890 --> 01:08:29.189 align:middle line:90% stressed rigid network. 01:08:29.189 --> 01:08:31.950 align:middle line:84% And what's in between is what people call isostatic 01:08:31.950 --> 01:08:34.390 align:middle line:84% or critically constrained network. 01:08:34.390 --> 01:08:39.229 align:middle line:84% Now as I said, the concept comes from mechanics. 01:08:39.229 --> 01:08:42.029 align:middle line:84% So if you think about a simple ball and stick model, 01:08:42.029 --> 01:08:44.029 align:middle line:84% you simplify the atom and chemical bonds as ball 01:08:44.029 --> 01:08:44.810 align:middle line:90% and sticks. 01:08:44.810 --> 01:08:46.189 align:middle line:84% You try to put them together, you essentially 01:08:46.189 --> 01:08:47.272 align:middle line:90% form mechanical structure. 01:08:47.272 --> 01:08:51.430 align:middle line:84% So this network, it can be floppy or flexible. 01:08:51.430 --> 01:08:53.990 align:middle line:84% If it's constrained, the number of constraint 01:08:53.990 --> 01:08:57.430 align:middle line:84% is less than the number of degrees of freedom. 01:08:57.430 --> 01:09:00.010 align:middle line:84% A simple example of a floppy network. 01:09:00.010 --> 01:09:02.710 align:middle line:84% Let's look at specifically this model I'm holding in my hand 01:09:02.710 --> 01:09:03.350 align:middle line:90% here. 01:09:03.350 --> 01:09:05.970 align:middle line:84% The constraints we are talking about here, 01:09:05.970 --> 01:09:08.029 align:middle line:84% there are two kinds of constraints. 01:09:08.029 --> 01:09:13.229 align:middle line:84% you have the bond length and you have the bond angle. 01:09:13.229 --> 01:09:19.350 align:middle line:84% The bond length is what we call the bond angle. 01:09:19.350 --> 01:09:21.350 align:middle line:84% Sorry, the bond length is what we call 01:09:21.350 --> 01:09:23.810 align:middle line:90% the bond-stretching constraint. 01:09:23.810 --> 01:09:27.510 align:middle line:90% 01:09:27.510 --> 01:09:29.850 align:middle line:90% Bond stretching. 01:09:29.850 --> 01:09:34.229 align:middle line:90% 01:09:34.229 --> 01:09:37.170 align:middle line:84% So because we have a well-defined chemical bond 01:09:37.170 --> 01:09:40.229 align:middle line:84% length, essentially says that the spacing between these two 01:09:40.229 --> 01:09:43.430 align:middle line:84% atoms has to equal to the bond length. 01:09:43.430 --> 01:09:46.590 align:middle line:84% So that defines essentially one relation 01:09:46.590 --> 01:09:49.630 align:middle line:84% between the spatial coordinates of the neighboring atoms. 01:09:49.630 --> 01:09:52.430 align:middle line:84% So that's one thing we consider as a constraint there. 01:09:52.430 --> 01:09:54.670 align:middle line:84% That's called bond-stretching constraints. 01:09:54.670 --> 01:09:59.330 align:middle line:84% Now bond angle, this is called bond-bending constraint. 01:09:59.330 --> 01:10:04.990 align:middle line:90% 01:10:04.990 --> 01:10:10.350 align:middle line:84% Well, this one is basically a bond stretching, bond bending. 01:10:10.350 --> 01:10:11.840 align:middle line:84% So if you look at the bond angle, 01:10:11.840 --> 01:10:13.090 align:middle line:90% for example, look at this one. 01:10:13.090 --> 01:10:15.890 align:middle line:84% This is oxygen, silicon, oxygen [INAUDIBLE] tetrahedra. 01:10:15.890 --> 01:10:19.550 align:middle line:84% If it's a rigid chemical bond, it means that I cannot bend this 01:10:19.550 --> 01:10:20.710 align:middle line:90% chemical bond here. 01:10:20.710 --> 01:10:23.950 align:middle line:84% Then it specifies again the relative spatial location 01:10:23.950 --> 01:10:25.750 align:middle line:84% between the two oxygen atoms with respect 01:10:25.750 --> 01:10:27.310 align:middle line:90% to central silicon atom. 01:10:27.310 --> 01:10:30.950 align:middle line:84% So if it's rigid, then this is another geometric constraint 01:10:30.950 --> 01:10:34.710 align:middle line:84% that this network has to satisfy. 01:10:34.710 --> 01:10:37.590 align:middle line:84% So the total number of those constraints summed up together 01:10:37.590 --> 01:10:39.830 align:middle line:84% will give you the number of constraints. 01:10:39.830 --> 01:10:42.810 align:middle line:84% The number of degrees of freedom. 01:10:42.810 --> 01:10:46.910 align:middle line:84% If you have a total of n atoms, each atom 01:10:46.910 --> 01:10:49.430 align:middle line:84% you can characterize spatial position with three spatial 01:10:49.430 --> 01:10:50.845 align:middle line:90% coordinates. 01:10:50.845 --> 01:10:53.470 align:middle line:84% So the total number of geometric degree of freedom is basically 01:10:53.470 --> 01:10:54.470 align:middle line:90% given by 3n. 01:10:54.470 --> 01:10:58.030 align:middle line:90% 01:10:58.030 --> 01:11:01.573 align:middle line:84% So bottom line, if the constraint number 01:11:01.573 --> 01:11:04.240 align:middle line:84% is less than degree of freedom, we call this a flexible network. 01:11:04.240 --> 01:11:06.490 align:middle line:84% And as I'm showing, this is indeed a flexible network. 01:11:06.490 --> 01:11:08.360 align:middle line:84% I can easily twist and turn to go 01:11:08.360 --> 01:11:10.200 align:middle line:84% to different geometric configurations 01:11:10.200 --> 01:11:14.160 align:middle line:84% without violating any of the constraints I mentioned. 01:11:14.160 --> 01:11:15.960 align:middle line:90% So this is a flexible network. 01:11:15.960 --> 01:11:20.680 align:middle line:84% Now on the other hand, what about a stressed, rigid network? 01:11:20.680 --> 01:11:25.300 align:middle line:84% I can give you a very simple example here, our phase sharing. 01:11:25.300 --> 01:11:30.280 align:middle line:90% 01:11:30.280 --> 01:11:40.997 align:middle line:84% If you think about this phase-sharing tetrahedra here, 01:11:40.997 --> 01:11:42.580 align:middle line:84% there's no degree of freedom building. 01:11:42.580 --> 01:11:43.913 align:middle line:90% This is a totally rigid network. 01:11:43.913 --> 01:11:45.560 align:middle line:90% I cannot deform it at all. 01:11:45.560 --> 01:11:47.420 align:middle line:90% In fact, I even have to bend. 01:11:47.420 --> 01:11:49.800 align:middle line:84% I have to violate some constraint here 01:11:49.800 --> 01:11:53.500 align:middle line:84% in order to fit in here, this kind of network there. 01:11:53.500 --> 01:11:56.840 align:middle line:84% This is one case where the number constraint actually 01:11:56.840 --> 01:11:58.823 align:middle line:84% exceeds the number of degrees of freedom. 01:11:58.823 --> 01:12:00.240 align:middle line:84% So you have to actually compromise 01:12:00.240 --> 01:12:03.520 align:middle line:84% some of the constraints in order to fit in this network structure 01:12:03.520 --> 01:12:04.320 align:middle line:90% there. 01:12:04.320 --> 01:12:07.380 align:middle line:84% In order to compromise the constraint, what I'm doing here, 01:12:07.380 --> 01:12:10.140 align:middle line:84% I'm basically bending the chemical bands. 01:12:10.140 --> 01:12:12.480 align:middle line:90% I'm changing the bond angles. 01:12:12.480 --> 01:12:14.840 align:middle line:84% Now, changing the bond angles inevitably 01:12:14.840 --> 01:12:20.200 align:middle line:84% increases the Gibb-free energy of the overall system. 01:12:20.200 --> 01:12:23.300 align:middle line:84% So as a result, this is what we call the stressed rigid network. 01:12:23.300 --> 01:12:26.320 align:middle line:84% It's stressed because actually building stress 01:12:26.320 --> 01:12:27.800 align:middle line:84% due to this excess energy we have 01:12:27.800 --> 01:12:31.340 align:middle line:84% to apply in order to conform to the structure there. 01:12:31.340 --> 01:12:35.880 align:middle line:90% 01:12:35.880 --> 01:12:37.880 align:middle line:90% Oh, all right. 01:12:37.880 --> 01:12:39.180 align:middle line:90% Now I break a chemical bond. 01:12:39.180 --> 01:12:44.920 align:middle line:84% Actually now I violate a constraint-- literally-- anyway. 01:12:44.920 --> 01:12:46.440 align:middle line:90% All right. 01:12:46.440 --> 01:12:47.200 align:middle line:90% OK. 01:12:47.200 --> 01:12:50.040 align:middle line:84% So now what I want to argue here is 01:12:50.040 --> 01:12:54.080 align:middle line:84% that either the floppy network or stress rigid network, 01:12:54.080 --> 01:12:56.780 align:middle line:84% they are both bad for glass stability. 01:12:56.780 --> 01:12:57.860 align:middle line:90% So let me explain why. 01:12:57.860 --> 01:13:00.740 align:middle line:84% If you think about this flexible network, 01:13:00.740 --> 01:13:02.200 align:middle line:84% the key visual there is this system 01:13:02.200 --> 01:13:04.160 align:middle line:84% can very easily transition from one microscopic state 01:13:04.160 --> 01:13:06.640 align:middle line:84% to another microscopic state, because it's all flexible. 01:13:06.640 --> 01:13:09.800 align:middle line:84% So if you look at this potential energy landscape, 01:13:09.800 --> 01:13:12.520 align:middle line:84% this is schematically what it's going to look like. 01:13:12.520 --> 01:13:15.480 align:middle line:84% The different minimums, the energy barrier 01:13:15.480 --> 01:13:17.240 align:middle line:84% separating these different minima 01:13:17.240 --> 01:13:20.180 align:middle line:90% is pretty shallow, pretty low. 01:13:20.180 --> 01:13:21.590 align:middle line:84% Because this network is flexible, 01:13:21.590 --> 01:13:23.840 align:middle line:84% it can easily transition between different microscopic 01:13:23.840 --> 01:13:25.640 align:middle line:90% configurations. 01:13:25.640 --> 01:13:27.280 align:middle line:84% So then what that means is that if you 01:13:27.280 --> 01:13:29.760 align:middle line:84% have a global minima, which is our crystalline state, 01:13:29.760 --> 01:13:33.680 align:middle line:84% because the energy barrier separating this minima 01:13:33.680 --> 01:13:39.600 align:middle line:84% is pretty small, kinetically, this system can very easily 01:13:39.600 --> 01:13:41.880 align:middle line:84% relax towards the global minimum, which 01:13:41.880 --> 01:13:45.080 align:middle line:90% is crystallization. 01:13:45.080 --> 01:13:48.640 align:middle line:84% So simply put, a floppy network is kinetically 01:13:48.640 --> 01:13:50.880 align:middle line:90% two expedient in relaxing. 01:13:50.880 --> 01:13:54.980 align:middle line:90% And it can easily crystallize. 01:13:54.980 --> 01:13:59.680 align:middle line:84% Now what about our stressed rigid network? 01:13:59.680 --> 01:14:01.423 align:middle line:84% So first thing I want to mention here, 01:14:01.423 --> 01:14:03.840 align:middle line:84% as I'm showing you on the plot, the stressed ridge network 01:14:03.840 --> 01:14:06.600 align:middle line:84% is characterized usually by a very deep global minimum 01:14:06.600 --> 01:14:08.840 align:middle line:90% of quasi state. 01:14:08.840 --> 01:14:11.440 align:middle line:84% The reason it becomes a very deep global minimum is 01:14:11.440 --> 01:14:14.600 align:middle line:84% because any kind of deviation from this ideal crystal 01:14:14.600 --> 01:14:17.600 align:middle line:84% structure, inevitably, you have to cause lots of distortion 01:14:17.600 --> 01:14:19.680 align:middle line:84% because it's already a stressed network. 01:14:19.680 --> 01:14:23.800 align:middle line:84% So that distortion is then going to cause a pretty large rise 01:14:23.800 --> 01:14:24.900 align:middle line:90% of the Gibbs free energy. 01:14:24.900 --> 01:14:27.580 align:middle line:84% And that's why it's a very deep global minima. 01:14:27.580 --> 01:14:31.200 align:middle line:90% 01:14:31.200 --> 01:14:33.280 align:middle line:84% Now what does this deep global minima mean? 01:14:33.280 --> 01:14:35.080 align:middle line:84% A deep global minima means there's 01:14:35.080 --> 01:14:37.640 align:middle line:84% a very large thermodynamic driving 01:14:37.640 --> 01:14:41.320 align:middle line:90% force towards crystallization. 01:14:41.320 --> 01:14:45.720 align:middle line:84% So if you think about a macroscopically large glass 01:14:45.720 --> 01:14:50.080 align:middle line:84% sample, in such a macroscopic large glass sample, 01:14:50.080 --> 01:14:51.800 align:middle line:84% because of the statistical fluctuation 01:14:51.800 --> 01:14:53.660 align:middle line:84% of the inherent structure in glasses, 01:14:53.660 --> 01:14:55.660 align:middle line:84% if you look at one location versus the other, 01:14:55.660 --> 01:14:58.250 align:middle line:84% the structure is always a little bit different. 01:14:58.250 --> 01:15:02.170 align:middle line:84% So that means, because it's macroscopic large, almost 01:15:02.170 --> 01:15:04.950 align:middle line:84% inevitably at some corner of the glass sample, 01:15:04.950 --> 01:15:07.690 align:middle line:84% you're going to see some structure that closely resembles 01:15:07.690 --> 01:15:10.530 align:middle line:90% its crystalline state. 01:15:10.530 --> 01:15:14.410 align:middle line:84% So in those regions they can then easily 01:15:14.410 --> 01:15:19.090 align:middle line:84% act as the nucleus for subsequent growth. 01:15:19.090 --> 01:15:21.130 align:middle line:84% And the problem with the stressed region network 01:15:21.130 --> 01:15:23.850 align:middle line:84% is because of this very deep global minima, 01:15:23.850 --> 01:15:26.530 align:middle line:84% as long as the structure resembles crystalline, even 01:15:26.530 --> 01:15:30.050 align:middle line:84% in a very small location, it can be very easily stabilized. 01:15:30.050 --> 01:15:32.428 align:middle line:84% The energy barrier towards nucleation 01:15:32.428 --> 01:15:33.970 align:middle line:84% essentially is very, very low because 01:15:33.970 --> 01:15:36.370 align:middle line:84% of this huge thermodynamic driving force. 01:15:36.370 --> 01:15:39.530 align:middle line:84% So then, as soon as you have that local cluster that 01:15:39.530 --> 01:15:41.390 align:middle line:84% resembles the crystalline structure, 01:15:41.390 --> 01:15:43.850 align:middle line:84% it's then quickly going to propagate and introduce 01:15:43.850 --> 01:15:48.370 align:middle line:84% the crystallization across the entire sample. 01:15:48.370 --> 01:15:51.810 align:middle line:84% So simply put, a stress region network 01:15:51.810 --> 01:15:55.690 align:middle line:84% has a poor amorphous stability because 01:15:55.690 --> 01:15:58.610 align:middle line:84% of the large thermodynamic driving force. 01:15:58.610 --> 01:16:03.270 align:middle line:84% So what we want to do is the right in between. 01:16:03.270 --> 01:16:06.370 align:middle line:84% We need to strike a balance between the kinetic factor 01:16:06.370 --> 01:16:07.950 align:middle line:90% and the thermodynamic factor. 01:16:07.950 --> 01:16:11.930 align:middle line:84% You want to have a sufficiently high barrier 01:16:11.930 --> 01:16:14.082 align:middle line:90% to prevent the crystallization. 01:16:14.082 --> 01:16:16.290 align:middle line:84% You also want to make sure that thermodynamic driving 01:16:16.290 --> 01:16:19.250 align:middle line:84% force towards crystallization is not too large. 01:16:19.250 --> 01:16:22.070 align:middle line:84% So that's why we argue that what's in between here, 01:16:22.070 --> 01:16:25.050 align:middle line:84% the isostatic network, where the number of constraints 01:16:25.050 --> 01:16:28.610 align:middle line:84% are exactly equal to the number of the degree of freedom 01:16:28.610 --> 01:16:32.030 align:middle line:84% will now give rise to the optimal glass stability. 01:16:32.030 --> 01:16:34.810 align:middle line:90% 01:16:34.810 --> 01:16:37.330 align:middle line:84% So that's the whole assumption of the topological constraint 01:16:37.330 --> 01:16:41.370 align:middle line:84% theory, that you want to find a glass structure that gives you 01:16:41.370 --> 01:16:44.470 align:middle line:90% the isostatic network topology. 01:16:44.470 --> 01:16:50.930 align:middle line:90% 01:16:50.930 --> 01:16:51.530 align:middle line:90% Yes. 01:16:51.530 --> 01:16:55.690 align:middle line:84% AUDIENCE: With the same chemical like network, 01:16:55.690 --> 01:16:58.210 align:middle line:84% the same format like formers, as well, 01:16:58.210 --> 01:17:01.250 align:middle line:84% if you change the cooling rate, does that 01:17:01.250 --> 01:17:04.050 align:middle line:90% change the constraints? 01:17:04.050 --> 01:17:06.750 align:middle line:90% The changing, like, the process. 01:17:06.750 --> 01:17:08.750 align:middle line:84% PROFESSOR: OK, that's actually a great question. 01:17:08.750 --> 01:17:10.050 align:middle line:90% I have two answers to that. 01:17:10.050 --> 01:17:11.610 align:middle line:90% To the first order, it does not. 01:17:11.610 --> 01:17:13.318 align:middle line:84% Because if you think about the-- later on 01:17:13.318 --> 01:17:15.777 align:middle line:84% we're going to talk about how you actually count the number 01:17:15.777 --> 01:17:18.190 align:middle line:84% constraint, how to count the number of basic constraints. 01:17:18.190 --> 01:17:20.690 align:middle line:84% The number constraint actually relates to the, essentially, 01:17:20.690 --> 01:17:21.770 align:middle line:90% a valent state. 01:17:21.770 --> 01:17:25.038 align:middle line:84% So because, again, the number of bonds, the number of angles, 01:17:25.038 --> 01:17:27.330 align:middle line:84% they all relate to a number of chemical bonds it forms, 01:17:27.330 --> 01:17:28.230 align:middle line:90% so valent state. 01:17:28.230 --> 01:17:30.770 align:middle line:84% So if you have the same chemical constituent regardless 01:17:30.770 --> 01:17:32.350 align:middle line:84% of cooling rate to the first order, 01:17:32.350 --> 01:17:34.183 align:middle line:84% it doesn't change the number of constraints. 01:17:34.183 --> 01:17:36.850 align:middle line:84% And therefore, it doesn't change the topological architecture 01:17:36.850 --> 01:17:37.890 align:middle line:90% to the first order. 01:17:37.890 --> 01:17:42.090 align:middle line:84% Now the second order we are also going to talk about it 01:17:42.090 --> 01:17:44.970 align:middle line:84% is that some of the constraints can actually get relaxed 01:17:44.970 --> 01:17:46.730 align:middle line:90% at different temperatures. 01:17:46.730 --> 01:17:50.090 align:middle line:84% So if you have a very drastic change 01:17:50.090 --> 01:17:54.170 align:middle line:84% in terms of glass forming, then you may actually have-- 01:17:54.170 --> 01:17:56.530 align:middle line:84% some of the constraints may get a little bit 01:17:56.530 --> 01:17:58.290 align:middle line:90% relaxed compared to the others. 01:17:58.290 --> 01:18:02.410 align:middle line:84% So it does can modify this number constraint a little bit. 01:18:02.410 --> 01:18:05.190 align:middle line:84% But usually that's not a significant factor. 01:18:05.190 --> 01:18:09.690 align:middle line:84% So that's why, when we predict the stability of the network 01:18:09.690 --> 01:18:13.450 align:middle line:84% we give it essentially as a chemical composition. 01:18:13.450 --> 01:18:16.770 align:middle line:84% And the cooling rate is basically a high-order term 01:18:16.770 --> 01:18:17.770 align:middle line:90% that we usually neglect. 01:18:17.770 --> 01:18:19.520 align:middle line:84% We just say that this chemical composition 01:18:19.520 --> 01:18:21.670 align:middle line:84% is more stable against the other one, for example. 01:18:21.670 --> 01:18:24.978 align:middle line:84% That's what this theory will tell you, 01:18:24.978 --> 01:18:26.270 align:middle line:90% Does that answer your question? 01:18:26.270 --> 01:18:28.433 align:middle line:90% AUDIENCE: Yes. 01:18:28.433 --> 01:18:30.350 align:middle line:84% PROFESSOR: I mean, we are running out of time. 01:18:30.350 --> 01:18:31.933 align:middle line:84% So what we will do in the next lecture 01:18:31.933 --> 01:18:33.890 align:middle line:84% is to actually go into deriving what 01:18:33.890 --> 01:18:36.570 align:middle line:84% are the number of constraints and what is the condition 01:18:36.570 --> 01:18:41.870 align:middle line:84% to achieve this isostatic network to maximize stability? 01:18:41.870 --> 01:18:44.090 align:middle line:90% Any last minute questions? 01:18:44.090 --> 01:18:44.690 align:middle line:90% Yes. 01:18:44.690 --> 01:18:47.230 align:middle line:84% AUDIENCE: I suppose like after processing, 01:18:47.230 --> 01:18:52.660 align:middle line:84% is it possible to go make crystalline glass [INAUDIBLE]? 01:18:52.660 --> 01:18:56.348 align:middle line:84% PROFESSOR: You don't say a crystalline glass, right? 01:18:56.348 --> 01:18:57.780 align:middle line:90% AUDIENCE: [INAUDIBLE] glass. 01:18:57.780 --> 01:18:59.360 align:middle line:90% PROFESSOR: Sure, I mean yeah. 01:18:59.360 --> 01:19:00.320 align:middle line:90% You could dope it. 01:19:00.320 --> 01:19:04.140 align:middle line:84% But, I mean, we're actually going 01:19:04.140 --> 01:19:07.380 align:middle line:84% to see it because the number of constraints 01:19:07.380 --> 01:19:10.460 align:middle line:84% depend on essentially the valent state. 01:19:10.460 --> 01:19:13.300 align:middle line:84% So if you dope it, you actually change the network topology. 01:19:13.300 --> 01:19:16.060 align:middle line:84% So you can either increase or decrease glass stability 01:19:16.060 --> 01:19:17.680 align:middle line:90% just by doping it. 01:19:17.680 --> 01:19:18.180 align:middle line:90% Yeah. 01:19:18.180 --> 01:19:23.187 align:middle line:90% 01:19:23.187 --> 01:19:25.520 align:middle line:84% OK, so we're going to talk about it in the next lecture, 01:19:25.520 --> 01:19:25.900 align:middle line:90% as you'll see. 01:19:25.900 --> 01:19:28.220 align:middle line:84% Later on it becomes-- it's a remarkably simple theory. 01:19:28.220 --> 01:19:32.670 align:middle line:84% But it gives very powerful predictions. 01:19:32.670 --> 01:19:51.000 align:middle line:90%