WEBVTT 00:00:00.000 --> 00:00:01.486 align:middle line:90% [SQUEAKING] 00:00:01.486 --> 00:00:02.965 align:middle line:90% [RUSTLING] 00:00:02.965 --> 00:00:04.444 align:middle line:90% [CLICKING] 00:00:04.444 --> 00:00:17.600 align:middle line:90% 00:00:17.600 --> 00:00:19.280 align:middle line:84% JUEJUN HU: All right, so let's pick up 00:00:19.280 --> 00:00:21.583 align:middle line:84% from where we left in the last lecture. 00:00:21.583 --> 00:00:23.000 align:middle line:84% So in the last lecture, I actually 00:00:23.000 --> 00:00:24.360 align:middle line:90% showed you this plot here. 00:00:24.360 --> 00:00:26.800 align:middle line:84% One key takeaway message I want to mention 00:00:26.800 --> 00:00:28.840 align:middle line:84% is that, for any amorphous material, 00:00:28.840 --> 00:00:32.680 align:middle line:84% its property critically depends on its history, processing 00:00:32.680 --> 00:00:35.580 align:middle line:84% history, in particular, thermal history. 00:00:35.580 --> 00:00:38.520 align:middle line:84% It's pretty clear, you can see from this diagram here, 00:00:38.520 --> 00:00:40.542 align:middle line:84% if you cool down glass from the same melt, even 00:00:40.542 --> 00:00:43.000 align:middle line:84% the same composition, if you cool down at different cooling 00:00:43.000 --> 00:00:45.780 align:middle line:84% rates, you get completely different properties. 00:00:45.780 --> 00:00:48.480 align:middle line:84% So this is a quite universal trait 00:00:48.480 --> 00:00:50.392 align:middle line:84% for different kind of amorphous materials. 00:00:50.392 --> 00:00:52.100 align:middle line:84% So if you go to conferences, for example, 00:00:52.100 --> 00:00:54.058 align:middle line:84% you hear people reporting some great properties 00:00:54.058 --> 00:00:55.220 align:middle line:90% about amorphous material. 00:00:55.220 --> 00:00:56.940 align:middle line:84% You now only want to put down the composition. 00:00:56.940 --> 00:00:58.982 align:middle line:84% You also need to make sure to talk to the author, 00:00:58.982 --> 00:01:01.300 align:middle line:84% get all the details about how this material is getting 00:01:01.300 --> 00:01:04.700 align:middle line:84% processed if you want to really duplicate everything 00:01:04.700 --> 00:01:05.723 align:middle line:90% the author is getting. 00:01:05.723 --> 00:01:07.140 align:middle line:84% So that's one important message we 00:01:07.140 --> 00:01:09.900 align:middle line:84% want to keep in mind, history dependence of the properties 00:01:09.900 --> 00:01:11.940 align:middle line:90% of amorphous materials. 00:01:11.940 --> 00:01:14.910 align:middle line:84% So now, in this slide here, I'm basically 00:01:14.910 --> 00:01:16.660 align:middle line:84% summarizing the different states of matter 00:01:16.660 --> 00:01:18.260 align:middle line:90% that we have talked about here. 00:01:18.260 --> 00:01:19.940 align:middle line:90% We obviously have liquids. 00:01:19.940 --> 00:01:21.938 align:middle line:84% And liquids, because all the atoms 00:01:21.938 --> 00:01:24.480 align:middle line:84% do not have a fixed geometric position, they can move around. 00:01:24.480 --> 00:01:26.320 align:middle line:84% There's no crystalline lattice whatsoever. 00:01:26.320 --> 00:01:29.260 align:middle line:84% So that's why they don't have a well-defined shape. 00:01:29.260 --> 00:01:32.480 align:middle line:84% We also have crystals, where the atoms are arranged in a lattice. 00:01:32.480 --> 00:01:35.340 align:middle line:84% They exhibit both short-range order and long-range order. 00:01:35.340 --> 00:01:38.873 align:middle line:84% Finally, we have glass, which sits somewhere in between. 00:01:38.873 --> 00:01:40.540 align:middle line:84% You get short-range order, but you don't 00:01:40.540 --> 00:01:42.060 align:middle line:90% have the long-range order. 00:01:42.060 --> 00:01:45.060 align:middle line:84% The different lines here essentially 00:01:45.060 --> 00:01:47.380 align:middle line:84% connects these different state of matter together. 00:01:47.380 --> 00:01:49.297 align:middle line:84% Between crystal and liquid, obviously, there's 00:01:49.297 --> 00:01:51.260 align:middle line:84% traditional melting and solidification. 00:01:51.260 --> 00:01:54.060 align:middle line:84% For glass, you can go from liquid to glass 00:01:54.060 --> 00:01:55.485 align:middle line:90% by the melt-quenching process. 00:01:55.485 --> 00:01:56.860 align:middle line:84% So the melt-quenching essentially 00:01:56.860 --> 00:01:59.070 align:middle line:84% describes this process we talk about. 00:01:59.070 --> 00:02:00.850 align:middle line:84% You start from a supercooled liquid. 00:02:00.850 --> 00:02:03.443 align:middle line:84% You quickly cool it down, suppress crystallization, 00:02:03.443 --> 00:02:04.610 align:middle line:90% and you get amorphous state. 00:02:04.610 --> 00:02:06.610 align:middle line:84% That's called the melt-quench process. 00:02:06.610 --> 00:02:09.710 align:middle line:90% You can also start from glass. 00:02:09.710 --> 00:02:12.370 align:middle line:84% You heat it up, and then you go to liquid. 00:02:12.370 --> 00:02:16.310 align:middle line:84% So that process is often called softening. 00:02:16.310 --> 00:02:18.590 align:middle line:84% And the reason it's called softening 00:02:18.590 --> 00:02:20.910 align:middle line:84% is because glass is a rigid metal at room temperature, 00:02:20.910 --> 00:02:21.570 align:middle line:90% typically. 00:02:21.570 --> 00:02:23.070 align:middle line:84% But as you heat it up, it eventually 00:02:23.070 --> 00:02:25.530 align:middle line:84% transformed into this viscous fluid, supercooled liquid. 00:02:25.530 --> 00:02:29.750 align:middle line:84% So, radiologically, it shows itself, essentially, 00:02:29.750 --> 00:02:31.425 align:middle line:84% as the material is actually softening. 00:02:31.425 --> 00:02:33.050 align:middle line:84% That's why it's often called softening. 00:02:33.050 --> 00:02:36.190 align:middle line:84% Now, between the glass and crystal, 00:02:36.190 --> 00:02:38.270 align:middle line:84% you can always go from glass crystal 00:02:38.270 --> 00:02:40.270 align:middle line:90% by essentially just heat it up. 00:02:40.270 --> 00:02:43.150 align:middle line:84% You heat up the material, you get more kinetic energy 00:02:43.150 --> 00:02:44.050 align:middle line:90% to the atoms. 00:02:44.050 --> 00:02:44.950 align:middle line:84% Eventually, they're going to find 00:02:44.950 --> 00:02:46.658 align:middle line:84% the thermodynamically stable state, which 00:02:46.658 --> 00:02:48.510 align:middle line:90% is a crystalline state. 00:02:48.510 --> 00:02:51.230 align:middle line:84% The temperature that we use to crystallize, 00:02:51.230 --> 00:02:53.790 align:middle line:84% this is usually called crystallization temperature. 00:02:53.790 --> 00:02:57.030 align:middle line:84% And it's customary in the glass community. 00:02:57.030 --> 00:02:59.970 align:middle line:90% People label it as Tx. 00:02:59.970 --> 00:03:03.570 align:middle line:84% It gives you the temperature you need to crystallize the glass 00:03:03.570 --> 00:03:08.690 align:middle line:84% material for some fixed duration of time that you will need. 00:03:08.690 --> 00:03:12.250 align:middle line:84% I want to mention that this Tx, unlike Tf, this 00:03:12.250 --> 00:03:14.770 align:middle line:84% is very much an empirical parameter. 00:03:14.770 --> 00:03:17.850 align:middle line:84% It depends on lots of factors, how you process your glass 00:03:17.850 --> 00:03:18.750 align:middle line:90% thermal history. 00:03:18.750 --> 00:03:20.610 align:middle line:84% It depends on how long you actually anneal. 00:03:20.610 --> 00:03:23.290 align:middle line:84% It may also depend on a specific annealing technique as well. 00:03:23.290 --> 00:03:26.413 align:middle line:84% So that's why, even for the same glass composition, 00:03:26.413 --> 00:03:28.330 align:middle line:84% you may see quite different Tx here, depending 00:03:28.330 --> 00:03:29.630 align:middle line:90% on who actually report it. 00:03:29.630 --> 00:03:32.410 align:middle line:84% So just keep in mind, this is just empirical parameter 00:03:32.410 --> 00:03:37.130 align:middle line:84% to gauge how stable the glass is against crystallization. 00:03:37.130 --> 00:03:42.410 align:middle line:84% Now, finally, you can also go from crystal back to glass 00:03:42.410 --> 00:03:45.610 align:middle line:90% directly. 00:03:45.610 --> 00:03:47.130 align:middle line:84% You can always amortize the material 00:03:47.130 --> 00:03:50.350 align:middle line:84% by essentially first melting it and then melt-quench it. 00:03:50.350 --> 00:03:51.790 align:middle line:90% So then you actually get glass. 00:03:51.790 --> 00:03:54.210 align:middle line:84% What you can also do, you can directly 00:03:54.210 --> 00:03:58.190 align:middle line:84% go to an amorphization or so-called vitrification process. 00:03:58.190 --> 00:04:01.870 align:middle line:84% And what you will do there is you typically introduce 00:04:01.870 --> 00:04:05.950 align:middle line:84% some energetic process that distort the lattice structure. 00:04:05.950 --> 00:04:09.030 align:middle line:84% So, for example, you can bombard a crystal 00:04:09.030 --> 00:04:11.270 align:middle line:90% using ionizing radiation. 00:04:11.270 --> 00:04:14.050 align:middle line:84% And in this case, those ionizing radiation has enough energy, 00:04:14.050 --> 00:04:15.470 align:middle line:84% it's going to knock the atoms out 00:04:15.470 --> 00:04:17.303 align:middle line:84% of the original lattice position, which then 00:04:17.303 --> 00:04:18.670 align:middle line:90% create crystalline defects. 00:04:18.670 --> 00:04:20.490 align:middle line:84% If you let that process go on and on, 00:04:20.490 --> 00:04:21.970 align:middle line:90% eventually, the defects pileup. 00:04:21.970 --> 00:04:23.670 align:middle line:84% You can actually transform a crystal 00:04:23.670 --> 00:04:25.790 align:middle line:90% into an amorphous structure. 00:04:25.790 --> 00:04:29.790 align:middle line:84% So that's, essentially, a radiation-induced amorphization. 00:04:29.790 --> 00:04:33.390 align:middle line:84% You can also do a mechanical amorphization. 00:04:33.390 --> 00:04:36.002 align:middle line:84% So you can induce plastic deformation in a material. 00:04:36.002 --> 00:04:38.210 align:middle line:84% And when you do that, based on what you have learned, 00:04:38.210 --> 00:04:40.430 align:middle line:84% if you do plastic deformation, you actually 00:04:40.430 --> 00:04:41.750 align:middle line:90% have dislocated motion. 00:04:41.750 --> 00:04:43.430 align:middle line:84% You generate defects, essentially. 00:04:43.430 --> 00:04:45.030 align:middle line:84% So if you repeat that process-- it 00:04:45.030 --> 00:04:46.572 align:middle line:84% goes through very large deformation-- 00:04:46.572 --> 00:04:48.750 align:middle line:84% you can also transform from a crystalline state 00:04:48.750 --> 00:04:50.950 align:middle line:90% directly to amorphous state. 00:04:50.950 --> 00:04:54.330 align:middle line:84% And you can do that by, for example just doing more milling. 00:04:54.330 --> 00:04:56.663 align:middle line:90% You can do mechanical alloying. 00:04:56.663 --> 00:04:58.330 align:middle line:84% With large deformation, you can actually 00:04:58.330 --> 00:05:00.210 align:middle line:84% create directly amorphous materials that way 00:05:00.210 --> 00:05:03.948 align:middle line:84% without having to go through a melting state. 00:05:03.948 --> 00:05:05.490 align:middle line:84% All right, so for this slide, there's 00:05:05.490 --> 00:05:07.490 align:middle line:84% one last thing I want to mention here. 00:05:07.490 --> 00:05:11.250 align:middle line:84% For liquid, I have listed here that the bonding constraint 00:05:11.250 --> 00:05:14.630 align:middle line:90% relaxes as temperature rises. 00:05:14.630 --> 00:05:15.690 align:middle line:90% So what does that mean? 00:05:15.690 --> 00:05:18.650 align:middle line:84% I need to first explain bonding constraints. 00:05:18.650 --> 00:05:21.250 align:middle line:84% So when we are talking about bonding constraints, 00:05:21.250 --> 00:05:24.370 align:middle line:84% there are two types of bonding constraints here. 00:05:24.370 --> 00:05:26.250 align:middle line:84% If you think about chemical bond, 00:05:26.250 --> 00:05:28.650 align:middle line:84% it essentially defines a specific bond length 00:05:28.650 --> 00:05:30.650 align:middle line:84% that gives you the spacing between the two atoms 00:05:30.650 --> 00:05:31.890 align:middle line:90% that form a chemical bond. 00:05:31.890 --> 00:05:34.343 align:middle line:84% So from a topological perspective, 00:05:34.343 --> 00:05:36.510 align:middle line:84% this gives you, essentially, a geometric constraint. 00:05:36.510 --> 00:05:38.770 align:middle line:84% The atoms cannot randomly populate in space. 00:05:38.770 --> 00:05:42.630 align:middle line:84% They have to satisfy certain spacing between them. 00:05:42.630 --> 00:05:47.290 align:middle line:84% So this is called the bond length constraint, the bond 00:05:47.290 --> 00:05:47.810 align:middle line:90% length. 00:05:47.810 --> 00:05:53.420 align:middle line:90% 00:05:53.420 --> 00:05:57.140 align:middle line:84% This is one type of constraint coming from chemical bonds. 00:05:57.140 --> 00:05:59.440 align:middle line:84% You can also have bond angle constraint. 00:05:59.440 --> 00:06:02.460 align:middle line:90% 00:06:02.460 --> 00:06:06.540 align:middle line:84% And this happens, for example, if you think about silica. 00:06:06.540 --> 00:06:15.660 align:middle line:84% In silica, the basic structural unit is this Si tetrahedra. 00:06:15.660 --> 00:06:17.740 align:middle line:84% And we know that in this structure, 00:06:17.740 --> 00:06:19.580 align:middle line:84% we actually have two bond angles. 00:06:19.580 --> 00:06:25.500 align:middle line:84% You have this oxygen, silicon, oxygen bond angle, which 00:06:25.500 --> 00:06:27.600 align:middle line:90% is, of course, 109 degrees. 00:06:27.600 --> 00:06:29.420 align:middle line:90% This is [INAUDIBLE] tetrahedra. 00:06:29.420 --> 00:06:31.160 align:middle line:84% You also have another bond angle. 00:06:31.160 --> 00:06:34.900 align:middle line:84% This is when one tetrahedra connect to the other. 00:06:34.900 --> 00:06:39.460 align:middle line:84% This bond angle, silicon, oxygen silicon, 00:06:39.460 --> 00:06:46.220 align:middle line:84% for crystalline, SiO2, this bond goes 144 degrees. 00:06:46.220 --> 00:06:49.060 align:middle line:84% Now, this bond angle in a crystalline structure 00:06:49.060 --> 00:06:55.440 align:middle line:84% also specifies relative geometric position of the atoms. 00:06:55.440 --> 00:06:57.320 align:middle line:84% So there's also some topological constraints 00:06:57.320 --> 00:07:00.040 align:middle line:84% you place on the position of the atoms. 00:07:00.040 --> 00:07:02.475 align:middle line:84% Now, what we are trying to argue here 00:07:02.475 --> 00:07:04.100 align:middle line:84% is that, if you go to high temperature, 00:07:04.100 --> 00:07:07.640 align:middle line:84% you go to liquid state, because all the atoms can now 00:07:07.640 --> 00:07:10.460 align:middle line:84% start to move around-- you have a lot more kinetic energy-- 00:07:10.460 --> 00:07:13.960 align:middle line:84% some of these constraints start to get relaxed. 00:07:13.960 --> 00:07:16.880 align:middle line:84% So bond length, you can have small variation 00:07:16.880 --> 00:07:18.120 align:middle line:90% of the bond length. 00:07:18.120 --> 00:07:22.420 align:middle line:84% But predominantly, the bond angle is getting compromised. 00:07:22.420 --> 00:07:26.300 align:middle line:84% You don't have to limit to these very specific bond angle values. 00:07:26.300 --> 00:07:28.640 align:middle line:84% There can be variations or dispersions of the bond 00:07:28.640 --> 00:07:30.680 align:middle line:90% angle in the liquid state. 00:07:30.680 --> 00:07:33.400 align:middle line:84% So just to show you one example in the next slide, what 00:07:33.400 --> 00:07:37.000 align:middle line:84% I'm plotting here is actually the bond angle inside, 00:07:37.000 --> 00:07:41.760 align:middle line:84% essentially, a melt silica specifically for this silicon, 00:07:41.760 --> 00:07:46.320 align:middle line:84% oxygen, silicate molecule, so this one we're looking at here 00:07:46.320 --> 00:07:49.500 align:middle line:84% So this is measured by X-ray diffraction in, essentially, 00:07:49.500 --> 00:07:50.620 align:middle line:90% silica glass. 00:07:50.620 --> 00:07:53.180 align:middle line:84% But the idea here is that, in the liquid state, if you 00:07:53.180 --> 00:07:55.820 align:middle line:84% cool down sufficiently fast, you won't give enough time 00:07:55.820 --> 00:07:57.280 align:middle line:90% for the atoms to move around. 00:07:57.280 --> 00:07:58.820 align:middle line:84% So the resulting amorphous structure 00:07:58.820 --> 00:08:01.280 align:middle line:84% captures a lot of structural features in the liquid state. 00:08:01.280 --> 00:08:03.940 align:middle line:84% And this kind of dispersion of bond angle 00:08:03.940 --> 00:08:06.500 align:middle line:84% is something that you actually inherit, the glass inherit, 00:08:06.500 --> 00:08:07.600 align:middle line:90% from the liquid state. 00:08:07.600 --> 00:08:11.180 align:middle line:84% So, clearly, you can see here that, for this bond angle, 00:08:11.180 --> 00:08:13.860 align:middle line:84% silicon, oxygen, silicon, you now 00:08:13.860 --> 00:08:18.120 align:middle line:84% have a pretty wide distribution here around the average value, 00:08:18.120 --> 00:08:21.700 align:middle line:90% which is 144 degrees. 00:08:21.700 --> 00:08:25.160 align:middle line:84% Now, this applies only to this bond angle here, 00:08:25.160 --> 00:08:26.980 align:middle line:90% silicon, oxygen, silicon. 00:08:26.980 --> 00:08:32.910 align:middle line:84% The other one, you also have oxygen, silicon, oxygen. 00:08:32.910 --> 00:08:35.059 align:middle line:84% So for this one, this is the bond angle 00:08:35.059 --> 00:08:36.419 align:middle line:90% within the tetrahedra. 00:08:36.419 --> 00:08:39.140 align:middle line:84% The tetrahedra itself is actually pretty rigid. 00:08:39.140 --> 00:08:40.980 align:middle line:84% So even if you raise the temperature, 00:08:40.980 --> 00:08:43.659 align:middle line:84% this angle still pretty much stays constant, still 00:08:43.659 --> 00:08:45.080 align:middle line:90% about 109 degrees. 00:08:45.080 --> 00:08:47.560 align:middle line:84% What's changing is the essential interconnection 00:08:47.560 --> 00:08:49.280 align:middle line:84% between the different tetrahedras. 00:08:49.280 --> 00:08:51.320 align:middle line:84% So, essentially, you can imagine tetrahedras, 00:08:51.320 --> 00:08:53.612 align:middle line:84% they can actually sort of bend and distort with respect 00:08:53.612 --> 00:08:54.680 align:middle line:90% to each other. 00:08:54.680 --> 00:08:57.040 align:middle line:84% Now, this is actually something that's 00:08:57.040 --> 00:09:00.200 align:middle line:84% quite important because it means that the topological structure 00:09:00.200 --> 00:09:04.880 align:middle line:84% of the network can be modified by temperature. 00:09:04.880 --> 00:09:07.680 align:middle line:84% Later on, we are going to see that this actually affects 00:09:07.680 --> 00:09:10.980 align:middle line:84% the stability of the glass, how stable this network is, 00:09:10.980 --> 00:09:13.600 align:middle line:84% because we're changing the network topology. 00:09:13.600 --> 00:09:15.840 align:middle line:84% So just keep that in mind for now. 00:09:15.840 --> 00:09:21.160 align:middle line:84% If you go to high temperature, some of the constraints 00:09:21.160 --> 00:09:22.720 align:middle line:90% can actually get relaxed. 00:09:22.720 --> 00:09:26.000 align:middle line:90% 00:09:26.000 --> 00:09:28.275 align:middle line:84% All right, another point I also want to make here 00:09:28.275 --> 00:09:30.400 align:middle line:84% is that we have been talking about glass structure, 00:09:30.400 --> 00:09:32.320 align:middle line:84% essentially, in a very qualitative manner. 00:09:32.320 --> 00:09:34.920 align:middle line:84% We also want to introduce some parameters that 00:09:34.920 --> 00:09:37.995 align:middle line:84% allow us to quantitatively describe the glass structure. 00:09:37.995 --> 00:09:40.120 align:middle line:84% So we will be talking about, essentially, this pair 00:09:40.120 --> 00:09:41.265 align:middle line:90% distribution function here. 00:09:41.265 --> 00:09:42.640 align:middle line:84% Before we go to that, I just want 00:09:42.640 --> 00:09:45.223 align:middle line:84% to make the statement that, any kind of structural description 00:09:45.223 --> 00:09:47.490 align:middle line:84% of amorphous solids or glasses, they are always 00:09:47.490 --> 00:09:49.970 align:middle line:90% statistical in nature. 00:09:49.970 --> 00:09:51.610 align:middle line:84% And that makes sense because, if you 00:09:51.610 --> 00:09:53.568 align:middle line:84% think about amorphous structure, if you zoom in 00:09:53.568 --> 00:09:55.430 align:middle line:84% to one location versus the other, 00:09:55.430 --> 00:09:57.010 align:middle line:84% there's always slight differences 00:09:57.010 --> 00:09:58.530 align:middle line:90% from one location to the other. 00:09:58.530 --> 00:10:00.447 align:middle line:84% So when you're talking about any of these kind 00:10:00.447 --> 00:10:02.870 align:middle line:84% of macroscopic parameters to characterize glass structure, 00:10:02.870 --> 00:10:05.730 align:middle line:84% you are always doing ensemble average across the entire bulk 00:10:05.730 --> 00:10:09.430 align:middle line:84% material, across different locations. 00:10:09.430 --> 00:10:10.930 align:middle line:84% All right, so with that in mind, now 00:10:10.930 --> 00:10:13.410 align:middle line:84% let's look at, basically, this ensembled, 00:10:13.410 --> 00:10:16.690 align:middle line:84% averaged, parameter called pair distribution function. 00:10:16.690 --> 00:10:19.810 align:middle line:84% So pair distribution function, g, 00:10:19.810 --> 00:10:22.450 align:middle line:84% to introduce that, let's first introduce this parameter here, 00:10:22.450 --> 00:10:25.730 align:middle line:84% rho, which basically is the average atomic density 00:10:25.730 --> 00:10:28.450 align:middle line:90% in amorphous solid. 00:10:28.450 --> 00:10:31.410 align:middle line:84% And g, we are essentially characterizing 00:10:31.410 --> 00:10:34.490 align:middle line:90% the number density of atoms. 00:10:34.490 --> 00:10:37.090 align:middle line:84% You first start out by defining an origin. 00:10:37.090 --> 00:10:39.890 align:middle line:84% You have one atom sitting at origin. 00:10:39.890 --> 00:10:42.710 align:middle line:84% And we now start to look at how the number density of atoms 00:10:42.710 --> 00:10:46.650 align:middle line:84% varies as you move away from that center atom. 00:10:46.650 --> 00:10:52.390 align:middle line:84% g is defined, basically, as the number density normalized 00:10:52.390 --> 00:10:56.710 align:middle line:84% by the average density over the entire solid. 00:10:56.710 --> 00:11:00.193 align:middle line:84% So g will now be a function of r, where r gives you 00:11:00.193 --> 00:11:02.110 align:middle line:84% the spacing of the point where you're actually 00:11:02.110 --> 00:11:05.490 align:middle line:84% measuring density with respect to the origin atom. 00:11:05.490 --> 00:11:08.510 align:middle line:90% 00:11:08.510 --> 00:11:11.310 align:middle line:84% So we can start by taking a look at some general trends 00:11:11.310 --> 00:11:13.930 align:middle line:90% for this PDF here. 00:11:13.930 --> 00:11:18.543 align:middle line:84% So if the r reaches 0, approaches 0, 00:11:18.543 --> 00:11:20.710 align:middle line:84% it means that you're looking at the point very, very 00:11:20.710 --> 00:11:24.750 align:middle line:90% close to your center atom. 00:11:24.750 --> 00:11:27.590 align:middle line:84% Now, because these atoms, you cannot place two atoms exactly 00:11:27.590 --> 00:11:31.550 align:middle line:84% at the same location, what that means is that, 00:11:31.550 --> 00:11:34.710 align:middle line:84% when r approach 0, the probability of finding another 00:11:34.710 --> 00:11:38.470 align:middle line:84% atom exactly sitting at the same location is basically 0. 00:11:38.470 --> 00:11:43.550 align:middle line:84% So that's why, when r approach 0, the g should also vanish. 00:11:43.550 --> 00:11:49.530 align:middle line:90% 00:11:49.530 --> 00:11:52.373 align:middle line:84% On the other hand, if r approach infinity, 00:11:52.373 --> 00:11:54.290 align:middle line:84% you are looking at a point very, very far away 00:11:54.290 --> 00:11:56.970 align:middle line:90% from the center atom. 00:11:56.970 --> 00:11:59.730 align:middle line:84% Now, remember, we mentioned that in glass materials, 00:11:59.730 --> 00:12:02.370 align:middle line:84% you don't have this kind of long-range structure order. 00:12:02.370 --> 00:12:04.870 align:middle line:84% So if you move very far away from the center atom, 00:12:04.870 --> 00:12:06.328 align:middle line:84% essentially, what you're looking at 00:12:06.328 --> 00:12:08.070 align:middle line:84% is the average glass network structure. 00:12:08.070 --> 00:12:09.670 align:middle line:84% And you expect that now, in this case, 00:12:09.670 --> 00:12:11.930 align:middle line:84% the number density should approach the average number 00:12:11.930 --> 00:12:14.170 align:middle line:84% density of the entire glass network. 00:12:14.170 --> 00:12:16.890 align:middle line:84% And that's equivalent of saying that g should now 00:12:16.890 --> 00:12:18.890 align:middle line:90% approach unity. 00:12:18.890 --> 00:12:21.610 align:middle line:84% So that's a general trend where this function 00:12:21.610 --> 00:12:23.890 align:middle line:90% has to follow here. 00:12:23.890 --> 00:12:25.490 align:middle line:84% Now, more specifically, I'll just 00:12:25.490 --> 00:12:27.210 align:middle line:84% give you one quick example, trying 00:12:27.210 --> 00:12:31.250 align:middle line:84% to compare this g in a crystalline solid versus 00:12:31.250 --> 00:12:34.720 align:middle line:90% in an amorphous solid. 00:12:34.720 --> 00:12:36.890 align:middle line:84% So in a crystalline solid, if you 00:12:36.890 --> 00:12:39.950 align:middle line:84% assume it's an ideal single crystal without any defects, 00:12:39.950 --> 00:12:42.110 align:middle line:84% and we approximate, essentially, all the atoms 00:12:42.110 --> 00:12:45.270 align:middle line:84% as a half sphere, so you can characterize that location using 00:12:45.270 --> 00:12:46.750 align:middle line:84% essentially one single coordinates, 00:12:46.750 --> 00:12:47.810 align:middle line:90% well-defined coordinate. 00:12:47.810 --> 00:12:50.830 align:middle line:84% Then the g function should basically 00:12:50.830 --> 00:12:55.750 align:middle line:84% be a set of delta functions, where each peak correspond 00:12:55.750 --> 00:13:02.350 align:middle line:84% to, essentially, some neighbors, with respect to the center atom. 00:13:02.350 --> 00:13:04.455 align:middle line:84% So, for example, the first peak, this 00:13:04.455 --> 00:13:05.830 align:middle line:84% would represent that you actually 00:13:05.830 --> 00:13:09.150 align:middle line:84% find some atoms at this distance with respect to center atom. 00:13:09.150 --> 00:13:11.650 align:middle line:84% And this would be the atom that's closest to center atom. 00:13:11.650 --> 00:13:14.350 align:middle line:84% So this would be the nearest neighbors. 00:13:14.350 --> 00:13:16.860 align:middle line:84% This one would then correspond to the atoms. 00:13:16.860 --> 00:13:18.610 align:middle line:84% That would be the second nearest neighbor. 00:13:18.610 --> 00:13:21.950 align:middle line:84% This is the third nearest neighbor and so on and so forth. 00:13:21.950 --> 00:13:24.530 align:middle line:84% So every time you have one shell atom coming up, 00:13:24.530 --> 00:13:26.950 align:middle line:84% you have, essentially, one delta function. 00:13:26.950 --> 00:13:32.270 align:middle line:84% For amorphous structure, the g carries similar characteristics 00:13:32.270 --> 00:13:33.570 align:middle line:90% as the crystalline counterpart. 00:13:33.570 --> 00:13:36.030 align:middle line:84% You also see peaks corresponding to each of the delta function 00:13:36.030 --> 00:13:36.550 align:middle line:90% there. 00:13:36.550 --> 00:13:39.320 align:middle line:84% But first thing is that you see the peak getting broadened 00:13:39.320 --> 00:13:41.080 align:middle line:90% a little bit. 00:13:41.080 --> 00:13:43.160 align:middle line:84% This is basically a slight change 00:13:43.160 --> 00:13:45.800 align:middle line:84% of bond length inside the material, 00:13:45.800 --> 00:13:47.200 align:middle line:90% especially for the first one. 00:13:47.200 --> 00:13:50.360 align:middle line:84% This first peak essentially indicates that the chemical bond 00:13:50.360 --> 00:13:51.980 align:middle line:90% length is varying slightly. 00:13:51.980 --> 00:13:55.086 align:middle line:90% 00:13:55.086 --> 00:13:57.680 align:middle line:84% Now, as you move further and further, 00:13:57.680 --> 00:14:00.800 align:middle line:84% you see the peaks start to broaden even more. 00:14:00.800 --> 00:14:03.360 align:middle line:84% And that's because you are essentially 00:14:03.360 --> 00:14:06.720 align:middle line:84% losing this kind of a long-range order. 00:14:06.720 --> 00:14:08.760 align:middle line:84% As you move further and further away, 00:14:08.760 --> 00:14:13.320 align:middle line:84% the specific location of the atoms becomes less well-defined. 00:14:13.320 --> 00:14:15.540 align:middle line:84% So you expect to see the peak start to broaden. 00:14:15.540 --> 00:14:20.080 align:middle line:90% 00:14:20.080 --> 00:14:22.720 align:middle line:84% And, eventually, this function is then 00:14:22.720 --> 00:14:26.480 align:middle line:84% going to approach unity, where all the peak gets smeared out. 00:14:26.480 --> 00:14:29.225 align:middle line:84% That's when you completely lose any kind of short-range order. 00:14:29.225 --> 00:14:30.600 align:middle line:84% And you essentially-- what you're 00:14:30.600 --> 00:14:33.500 align:middle line:84% seeing there is just an average structure of the network. 00:14:33.500 --> 00:14:40.817 align:middle line:90% 00:14:40.817 --> 00:14:41.400 align:middle line:90% Any questions? 00:14:41.400 --> 00:14:43.375 align:middle line:90% Does that make sense? 00:14:43.375 --> 00:14:45.500 align:middle line:84% So later on, we are going to also talk a little bit 00:14:45.500 --> 00:14:47.125 align:middle line:84% about, quantitatively, how you actually 00:14:47.125 --> 00:14:48.860 align:middle line:84% measure this kind of a PDF function 00:14:48.860 --> 00:14:51.820 align:middle line:84% and correlate it with diffraction data. 00:14:51.820 --> 00:14:53.540 align:middle line:84% All right, this slide, you really 00:14:53.540 --> 00:14:55.780 align:middle line:84% don't need to put down any notes here. 00:14:55.780 --> 00:14:58.167 align:middle line:84% I'm just basically saying that, besides PDF, there 00:14:58.167 --> 00:15:00.500 align:middle line:84% are a bunch of other functions that are variants of PDF, 00:15:00.500 --> 00:15:02.460 align:middle line:84% that people also use in literature to characterize 00:15:02.460 --> 00:15:03.293 align:middle line:90% the glass structure. 00:15:03.293 --> 00:15:07.460 align:middle line:84% But they are all, more or less, trivially connected to a PDF. 00:15:07.460 --> 00:15:13.340 align:middle line:90% 00:15:13.340 --> 00:15:15.340 align:middle line:84% All right, so now let me just quickly summarize, 00:15:15.340 --> 00:15:18.140 align:middle line:84% essentially, this first chapter here about the general amorphous 00:15:18.140 --> 00:15:18.760 align:middle line:90% states. 00:15:18.760 --> 00:15:20.427 align:middle line:84% Some of the key points I want to mention 00:15:20.427 --> 00:15:22.700 align:middle line:84% is you need to understand the definition 00:15:22.700 --> 00:15:24.860 align:middle line:84% of amorphous solid versus glasses. 00:15:24.860 --> 00:15:26.460 align:middle line:84% For amorphous solid, you need to have, 00:15:26.460 --> 00:15:28.100 align:middle line:84% essentially, a metastable structure. 00:15:28.100 --> 00:15:30.620 align:middle line:84% You need to have long-range structure order. 00:15:30.620 --> 00:15:32.960 align:middle line:84% For glasses, there's an additional definition there. 00:15:32.960 --> 00:15:35.800 align:middle line:84% You also need to exhibit this glass transition. 00:15:35.800 --> 00:15:38.860 align:middle line:84% Now, glass transition, we're referring to this smooth curve. 00:15:38.860 --> 00:15:40.640 align:middle line:84% When you cool down a supercooled liquid, 00:15:40.640 --> 00:15:44.080 align:middle line:84% it gradually transforms into this different structure 00:15:44.080 --> 00:15:47.200 align:middle line:90% here that we call glass. 00:15:47.200 --> 00:15:49.480 align:middle line:84% It's important to recognize that, glasses, they 00:15:49.480 --> 00:15:51.740 align:middle line:84% are not a collection of very small crystals. 00:15:51.740 --> 00:15:53.240 align:middle line:84% They are also structurally different 00:15:53.240 --> 00:15:55.420 align:middle line:84% fundamentally from the supercooled liquid. 00:15:55.420 --> 00:16:00.040 align:middle line:84% So we will go into more details about the nature of glassy state 00:16:00.040 --> 00:16:04.420 align:middle line:84% and the nature of the glass transition later. 00:16:04.420 --> 00:16:05.920 align:middle line:84% We also just also want to mention 00:16:05.920 --> 00:16:08.708 align:middle line:84% here is that, unlike crystalline material, where everything 00:16:08.708 --> 00:16:10.500 align:middle line:84% is in equilibrium, if you do things slowly, 00:16:10.500 --> 00:16:12.480 align:middle line:84% you always have a reversible process. 00:16:12.480 --> 00:16:16.140 align:middle line:84% For glasses, cool down and reheating up, 00:16:16.140 --> 00:16:17.860 align:middle line:84% they usually do not retrace each other. 00:16:17.860 --> 00:16:19.443 align:middle line:84% You actually get two different curves. 00:16:19.443 --> 00:16:21.963 align:middle line:84% And they also depend on the specific processing condition. 00:16:21.963 --> 00:16:23.880 align:middle line:84% Different cooling rate, different heating rate 00:16:23.880 --> 00:16:28.080 align:middle line:84% give you, essentially, different process dependence. 00:16:28.080 --> 00:16:31.320 align:middle line:84% All right, so now, before I move on to the next section 00:16:31.320 --> 00:16:33.080 align:middle line:84% about different glass families, I just 00:16:33.080 --> 00:16:34.500 align:middle line:84% want to show you that this concept 00:16:34.500 --> 00:16:37.420 align:middle line:84% of crystalline versus amorphous does not only 00:16:37.420 --> 00:16:39.140 align:middle line:90% exist in solid matter. 00:16:39.140 --> 00:16:41.540 align:middle line:90% It also exist in urban planning. 00:16:41.540 --> 00:16:44.700 align:middle line:84% So this is what I would call a crystalline city. 00:16:44.700 --> 00:16:47.442 align:middle line:84% In fact, if you look very closely, somewhere in the Grand 00:16:47.442 --> 00:16:49.900 align:middle line:84% Central Station, you actually see a little edge dislocation 00:16:49.900 --> 00:16:50.440 align:middle line:90% there. 00:16:50.440 --> 00:16:52.980 align:middle line:84% You can go and define the Burgers vector on the Google Map 00:16:52.980 --> 00:16:53.860 align:middle line:90% if you want. 00:16:53.860 --> 00:16:55.320 align:middle line:84% And then what about amorphous city? 00:16:55.320 --> 00:16:57.980 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:16:57.980 --> 00:17:01.620 align:middle line:84% JUEJUN HU: Yes, as a driver, I can attest to the annoyance, 00:17:01.620 --> 00:17:03.380 align:middle line:84% actually driving in Boston streets. 00:17:03.380 --> 00:17:05.720 align:middle line:90% And this is amorphous. 00:17:05.720 --> 00:17:08.339 align:middle line:90% 00:17:08.339 --> 00:17:11.400 align:middle line:84% So we all live in amorphous city. 00:17:11.400 --> 00:17:15.579 align:middle line:90% 00:17:15.579 --> 00:17:19.339 align:middle line:84% All right, any more questions about the first part there? 00:17:19.339 --> 00:17:20.380 align:middle line:90% All good? 00:17:20.380 --> 00:17:23.339 align:middle line:84% So now, in this second part here, what I will do 00:17:23.339 --> 00:17:25.380 align:middle line:84% is I will give you a little bit overview 00:17:25.380 --> 00:17:28.500 align:middle line:84% about the different classes of amorphous materials 00:17:28.500 --> 00:17:31.080 align:middle line:84% we will be discussing throughout the semester. 00:17:31.080 --> 00:17:33.630 align:middle line:90% 00:17:33.630 --> 00:17:35.470 align:middle line:84% I will start by introducing the concept here 00:17:35.470 --> 00:17:37.665 align:middle line:84% about network performance, modified intermediates. 00:17:37.665 --> 00:17:39.790 align:middle line:84% These are the concepts that relate to, essentially, 00:17:39.790 --> 00:17:41.830 align:middle line:90% inorganic network glasses. 00:17:41.830 --> 00:17:46.348 align:middle line:84% Again, metallic glasses, they are sort of a special family. 00:17:46.348 --> 00:17:48.390 align:middle line:84% They have different ways to actually characterize 00:17:48.390 --> 00:17:49.270 align:middle line:90% structures. 00:17:49.270 --> 00:17:51.490 align:middle line:84% We'll go through that later on in the semester. 00:17:51.490 --> 00:17:54.690 align:middle line:84% But for now this applies to things like oxide glasses, 00:17:54.690 --> 00:17:57.190 align:middle line:84% chalcogenide glasses, halide glasses, 00:17:57.190 --> 00:17:59.830 align:middle line:84% essentially, inorganic glasses bound together 00:17:59.830 --> 00:18:01.070 align:middle line:90% through covalent bonds. 00:18:01.070 --> 00:18:04.070 align:middle line:84% Now, these network formers and modifiers 00:18:04.070 --> 00:18:06.550 align:middle line:84% essentially refers to the constituent atoms 00:18:06.550 --> 00:18:08.230 align:middle line:90% inside the glass. 00:18:08.230 --> 00:18:10.270 align:middle line:84% The network formers are the ones that 00:18:10.270 --> 00:18:14.630 align:middle line:84% actually form the backbone of the glass network. 00:18:14.630 --> 00:18:17.550 align:middle line:84% This would be ones like, for example, silicon. 00:18:17.550 --> 00:18:20.430 align:middle line:84% If you think about silica glass, SiO2, 00:18:20.430 --> 00:18:23.990 align:middle line:84% silicon would then link with, essentially, oxygen atoms. 00:18:23.990 --> 00:18:25.950 align:middle line:84% And, eventually, they will interlink together-- 00:18:25.950 --> 00:18:27.790 align:middle line:84% this tetrahedral interlink together-- 00:18:27.790 --> 00:18:29.550 align:middle line:84% to form a three-dimensional network. 00:18:29.550 --> 00:18:33.890 align:middle line:84% So in this case, silicon is basically a network former 00:18:33.890 --> 00:18:36.130 align:middle line:90% for this silica glass. 00:18:36.130 --> 00:18:39.970 align:middle line:84% Now, what about network modifiers? 00:18:39.970 --> 00:18:42.530 align:middle line:84% Network modifiers are the ones that essentially 00:18:42.530 --> 00:18:44.690 align:middle line:84% enter the glass network and actually disrupt 00:18:44.690 --> 00:18:46.010 align:middle line:90% the glass network. 00:18:46.010 --> 00:18:50.850 align:middle line:84% So they typically are some of these metal ions. 00:18:50.850 --> 00:18:53.790 align:middle line:84% So one example here, let's think about, for example, sodium. 00:18:53.790 --> 00:18:56.410 align:middle line:84% What happens if you're adding sodium oxide into a silica 00:18:56.410 --> 00:18:57.050 align:middle line:90% glass? 00:18:57.050 --> 00:18:59.450 align:middle line:84% So significantly, what I'm plotting here, 00:18:59.450 --> 00:19:05.650 align:middle line:84% this is a flattened version of a two SiO2 tetrahedra interlinked 00:19:05.650 --> 00:19:08.410 align:middle line:84% with each other through this oxygen atom. 00:19:08.410 --> 00:19:11.910 align:middle line:84% So in this case here, these two oxygen tetrahedra, 00:19:11.910 --> 00:19:14.970 align:middle line:90% they basically share one corner. 00:19:14.970 --> 00:19:19.430 align:middle line:84% So this is called corner-sharing tetrahedra, in this case. 00:19:19.430 --> 00:19:21.490 align:middle line:84% If you add the sodium in there, now the sodium 00:19:21.490 --> 00:19:24.370 align:middle line:84% is going to actually break up this silicon oxygen chemical 00:19:24.370 --> 00:19:25.130 align:middle line:90% bond. 00:19:25.130 --> 00:19:27.810 align:middle line:84% Instead, you essentially break this connection 00:19:27.810 --> 00:19:29.730 align:middle line:84% between these two tetrahedra there. 00:19:29.730 --> 00:19:31.910 align:middle line:84% And you form, essentially, an oxygen ion 00:19:31.910 --> 00:19:36.750 align:middle line:84% that's electrostatically attracted to the sodium ion. 00:19:36.750 --> 00:19:37.255 align:middle line:90% Yes? 00:19:37.255 --> 00:19:38.630 align:middle line:84% AUDIENCE: What would you consider 00:19:38.630 --> 00:19:42.330 align:middle line:84% the oxygen as, a former, modifier, or intermediate? 00:19:42.330 --> 00:19:44.810 align:middle line:90% JUEJUN HU: Ah, great question. 00:19:44.810 --> 00:19:47.510 align:middle line:84% So the question is about, how do you classify oxygen? 00:19:47.510 --> 00:19:51.150 align:middle line:84% This theory is really the only classification people derive 00:19:51.150 --> 00:19:52.830 align:middle line:90% from oxide glasses. 00:19:52.830 --> 00:19:56.110 align:middle line:84% So they essentially treat oxygen as just one ingredient 00:19:56.110 --> 00:19:57.930 align:middle line:90% in the oxide glasses. 00:19:57.930 --> 00:20:00.710 align:middle line:84% It's not classified as network former or modifiers. 00:20:00.710 --> 00:20:02.270 align:middle line:90% It's just part of the network. 00:20:02.270 --> 00:20:05.870 align:middle line:84% AUDIENCE: So if you were to do metallic glass, 00:20:05.870 --> 00:20:09.265 align:middle line:84% then since it would be oxygen, then-- 00:20:09.265 --> 00:20:10.890 align:middle line:84% JUEJUN HU: The whole thing breaks down. 00:20:10.890 --> 00:20:11.910 align:middle line:90% AUDIENCE: [LAUGHS] 00:20:11.910 --> 00:20:13.493 align:middle line:84% JUEJUN HU: As I said, this really only 00:20:13.493 --> 00:20:16.510 align:middle line:84% applies for oxide glasses, maybe chalcogenide, 00:20:16.510 --> 00:20:19.630 align:middle line:84% which would replace oxygen with sulfur and selenium. 00:20:19.630 --> 00:20:21.850 align:middle line:84% For metallic glasses, the concept is different. 00:20:21.850 --> 00:20:23.807 align:middle line:84% They are talking about clusters, actually. 00:20:23.807 --> 00:20:26.390 align:middle line:84% It's like how you actually pack the meta atom together tightly 00:20:26.390 --> 00:20:28.030 align:middle line:84% into different kinds of clusters. 00:20:28.030 --> 00:20:28.930 align:middle line:84% And then we are going to talk about, 00:20:28.930 --> 00:20:30.563 align:middle line:84% that you essentially have center atoms 00:20:30.563 --> 00:20:32.730 align:middle line:84% and then the surrounding atoms, and how they fulfill 00:20:32.730 --> 00:20:34.730 align:middle line:84% different topological roles, so you can actually 00:20:34.730 --> 00:20:36.350 align:middle line:90% get tight-packing structures. 00:20:36.350 --> 00:20:38.350 align:middle line:84% So completely different theory, basically. 00:20:38.350 --> 00:20:42.530 align:middle line:84% So this part here is only for inorganic network glasses. 00:20:42.530 --> 00:20:44.810 align:middle line:90% I just want to emphasize that. 00:20:44.810 --> 00:20:46.170 align:middle line:90% Does that answer your question? 00:20:46.170 --> 00:20:47.245 align:middle line:90% AUDIENCE: Yes. 00:20:47.245 --> 00:20:49.370 align:middle line:84% JUEJUN HU: All right, so now, talking about oxygen, 00:20:49.370 --> 00:20:51.770 align:middle line:84% I'm going to talk a bit more about oxygen. 00:20:51.770 --> 00:20:57.490 align:middle line:84% So this kind of oxygen, when oxygen link together two 00:20:57.490 --> 00:21:01.970 align:middle line:84% tetrahedra-- or more generally, two polyhedra-- 00:21:01.970 --> 00:21:06.370 align:middle line:84% this is called bridging oxygen because it's like a bridge that 00:21:06.370 --> 00:21:08.810 align:middle line:90% connects two network formers. 00:21:08.810 --> 00:21:12.650 align:middle line:84% If you have oxygen, like what you have here, 00:21:12.650 --> 00:21:15.583 align:middle line:84% it only links to one of the network formers. 00:21:15.583 --> 00:21:17.750 align:middle line:84% And the other end is actually, essentially, hanging. 00:21:17.750 --> 00:21:20.590 align:middle line:84% This is called non-bridging oxygen, NBO. 00:21:20.590 --> 00:21:23.370 align:middle line:90% 00:21:23.370 --> 00:21:26.460 align:middle line:84% So, basically, if you put in things like sodium, 00:21:26.460 --> 00:21:32.660 align:middle line:84% each sodium ion creates one non-bridging oxygen. 00:21:32.660 --> 00:21:35.300 align:middle line:84% The net effect is, initially, you 00:21:35.300 --> 00:21:37.900 align:middle line:84% have a very tightly connected three-dimensional network 00:21:37.900 --> 00:21:39.060 align:middle line:90% in silica. 00:21:39.060 --> 00:21:41.080 align:middle line:84% But now, once you put sodium in there, 00:21:41.080 --> 00:21:42.980 align:middle line:84% you start to break up these connections. 00:21:42.980 --> 00:21:47.320 align:middle line:84% So you decrease the connectivity of the network. 00:21:47.320 --> 00:21:48.820 align:middle line:84% This is a very important terminology 00:21:48.820 --> 00:21:50.500 align:middle line:84% I'm going to refer to many, many times 00:21:50.500 --> 00:21:53.100 align:middle line:84% in the lecture, connectivity, is how 00:21:53.100 --> 00:21:56.660 align:middle line:84% tightly these different tetrahedra or polyhedra are 00:21:56.660 --> 00:21:59.990 align:middle line:90% linked together with each other. 00:21:59.990 --> 00:22:02.240 align:middle line:84% If you have a lot of these kind of broken connections, 00:22:02.240 --> 00:22:04.615 align:middle line:84% then we say that this is not very well-connected network. 00:22:04.615 --> 00:22:06.780 align:middle line:90% It has a poor connectivity. 00:22:06.780 --> 00:22:09.020 align:middle line:84% And as you'll see, they have very significant impact 00:22:09.020 --> 00:22:11.220 align:middle line:90% on the properties of the glass. 00:22:11.220 --> 00:22:16.820 align:middle line:90% 00:22:16.820 --> 00:22:19.620 align:middle line:84% So simply put, network formers, these 00:22:19.620 --> 00:22:22.180 align:middle line:84% are the atoms that make good friends with other atoms. 00:22:22.180 --> 00:22:25.000 align:middle line:84% They can essentially form the backbone network. 00:22:25.000 --> 00:22:27.040 align:middle line:84% Network modifiers, they are loners. 00:22:27.040 --> 00:22:28.840 align:middle line:84% They get in there, break the connections, 00:22:28.840 --> 00:22:31.400 align:middle line:84% essentially create a much less connected network. 00:22:31.400 --> 00:22:33.300 align:middle line:84% You can also have what's in between. 00:22:33.300 --> 00:22:34.600 align:middle line:90% These are called intermediates. 00:22:34.600 --> 00:22:37.320 align:middle line:84% And intermediates, they can sometimes become network former, 00:22:37.320 --> 00:22:38.840 align:middle line:84% sometimes become a network modifier, 00:22:38.840 --> 00:22:40.300 align:middle line:90% depending on specific chemistry. 00:22:40.300 --> 00:22:43.200 align:middle line:90% 00:22:43.200 --> 00:22:46.180 align:middle line:84% All right, now, if you look at the periodic table, 00:22:46.180 --> 00:22:48.580 align:middle line:84% let's take a look at where this different network formers 00:22:48.580 --> 00:22:51.080 align:middle line:84% and modifiers sits in the periodic table. 00:22:51.080 --> 00:22:53.480 align:middle line:84% You immediately notice here, I use different color code 00:22:53.480 --> 00:22:55.600 align:middle line:84% to actually code different kind of atoms here. 00:22:55.600 --> 00:22:58.480 align:middle line:84% So you notice that these different kind of modifier 00:22:58.480 --> 00:23:01.040 align:middle line:84% and formers, they all cluster in specific regions 00:23:01.040 --> 00:23:02.180 align:middle line:90% in the periodic table. 00:23:02.180 --> 00:23:05.760 align:middle line:84% The network formers, they tend to be 00:23:05.760 --> 00:23:09.680 align:middle line:84% these non-metallic atoms that has a relatively 00:23:09.680 --> 00:23:11.520 align:middle line:90% high-valence state. 00:23:11.520 --> 00:23:15.240 align:middle line:84% Typically, they have a lot of outer shell electrons. 00:23:15.240 --> 00:23:17.360 align:middle line:84% Whereas, the network modifiers, these 00:23:17.360 --> 00:23:21.673 align:middle line:84% tend to have a low-valence state and they tend to be metals. 00:23:21.673 --> 00:23:23.340 align:middle line:84% Now, this actually makes a lot of sense. 00:23:23.340 --> 00:23:25.700 align:middle line:84% If you think about what network formers does, 00:23:25.700 --> 00:23:28.180 align:middle line:84% you need to essentially form a polyhedra of oxygen 00:23:28.180 --> 00:23:29.700 align:middle line:90% around these network formers. 00:23:29.700 --> 00:23:32.420 align:middle line:84% And then they have to be able to link with each other to form 3D 00:23:32.420 --> 00:23:33.460 align:middle line:90% network. 00:23:33.460 --> 00:23:36.020 align:middle line:84% So in order to form a 3D network, 00:23:36.020 --> 00:23:38.900 align:middle line:84% the valence state of these network formers should be 00:23:38.900 --> 00:23:42.060 align:middle line:90% at least two. 00:23:42.060 --> 00:23:45.060 align:middle line:84% If you have a two-fold-coordinated atom, 00:23:45.060 --> 00:23:47.060 align:middle line:84% you start to try to train them together. 00:23:47.060 --> 00:23:51.620 align:middle line:84% The best you can do is typically a long 2D train. 00:23:51.620 --> 00:23:53.980 align:middle line:84% If you own the 3D network, you also want to do some kind 00:23:53.980 --> 00:23:55.660 align:middle line:90% of interconnection between them. 00:23:55.660 --> 00:23:58.620 align:middle line:84% So, usually, you will essentially want something with 00:23:58.620 --> 00:24:02.100 align:middle line:84% a valence state greater than 2, so you can form a 3D network. 00:24:02.100 --> 00:24:08.038 align:middle line:84% And that's what these non-metal atoms does. 00:24:08.038 --> 00:24:10.580 align:middle line:84% Now, the other thing is that this these non-metal atoms, they 00:24:10.580 --> 00:24:17.700 align:middle line:84% tend to form covalent bonds with oxygen. So for inorganic network 00:24:17.700 --> 00:24:20.440 align:middle line:84% glasses, it's really important to have covalent bonds 00:24:20.440 --> 00:24:24.320 align:middle line:84% because, unlike ionic bonds or metallic bonds, 00:24:24.320 --> 00:24:26.960 align:middle line:90% covalent bonds are? 00:24:26.960 --> 00:24:29.020 align:middle line:90% Directional. 00:24:29.020 --> 00:24:30.960 align:middle line:90% They have fixed orientation. 00:24:30.960 --> 00:24:33.480 align:middle line:84% Being directional means that there's actually 00:24:33.480 --> 00:24:37.820 align:middle line:84% a lot of space between the different atoms. 00:24:37.820 --> 00:24:40.320 align:middle line:84% Typically, covalent solids, they're never close packed. 00:24:40.320 --> 00:24:43.800 align:middle line:84% From simple crystallography, you know that. 00:24:43.800 --> 00:24:45.560 align:middle line:84% So if they're not close packed, there's 00:24:45.560 --> 00:24:46.900 align:middle line:90% lots of space in between atoms. 00:24:46.900 --> 00:24:49.200 align:middle line:84% It means that you can easily accommodate 00:24:49.200 --> 00:24:51.840 align:middle line:90% geometric distortion. 00:24:51.840 --> 00:24:53.288 align:middle line:84% All the atoms and chemical bonds, 00:24:53.288 --> 00:24:54.580 align:middle line:90% they have a lot of wiggle room. 00:24:54.580 --> 00:24:55.260 align:middle line:90% They can distort. 00:24:55.260 --> 00:24:57.177 align:middle line:84% They can change the bond angle without causing 00:24:57.177 --> 00:24:59.920 align:middle line:90% a lot of energy penalty. 00:24:59.920 --> 00:25:02.040 align:middle line:84% And that's really important for amorphous network 00:25:02.040 --> 00:25:06.960 align:middle line:84% because we want to introduce a structure disorder. 00:25:06.960 --> 00:25:08.680 align:middle line:84% If you can do that without raising 00:25:08.680 --> 00:25:11.100 align:middle line:84% the overall Gibbs-free energy of the system too much, 00:25:11.100 --> 00:25:13.640 align:middle line:90% then you get a stable glass. 00:25:13.640 --> 00:25:17.440 align:middle line:84% So that's why you want to have these kind of non-metal atoms, 00:25:17.440 --> 00:25:19.070 align:middle line:90% essentially, as network formers. 00:25:19.070 --> 00:25:23.850 align:middle line:90% 00:25:23.850 --> 00:25:25.730 align:middle line:84% Now, network modifiers, obviously, these 00:25:25.730 --> 00:25:28.650 align:middle line:84% are the ones that actually form metallic bonds. 00:25:28.650 --> 00:25:31.130 align:middle line:84% So they will be attracted to the oxygen atoms, 00:25:31.130 --> 00:25:33.010 align:middle line:84% just via electrostatic force, which 00:25:33.010 --> 00:25:37.810 align:middle line:84% is, of course, a lot weaker compared to covalent bonds. 00:25:37.810 --> 00:25:40.380 align:middle line:84% And that's why you also decrease the network connectivity. 00:25:40.380 --> 00:25:42.130 align:middle line:84% Also, because they're a low-valence state, 00:25:42.130 --> 00:25:44.172 align:middle line:84% that essentially decreases topological connection 00:25:44.172 --> 00:25:45.410 align:middle line:90% between different clusters. 00:25:45.410 --> 00:25:47.890 align:middle line:90% So that's what they do. 00:25:47.890 --> 00:25:50.730 align:middle line:90% 00:25:50.730 --> 00:25:53.050 align:middle line:84% All right, so now, let's essentially 00:25:53.050 --> 00:25:57.170 align:middle line:84% take a look at a few examples of the glass systems 00:25:57.170 --> 00:26:00.490 align:middle line:84% that we'll be dealing with later on in the semester, starting 00:26:00.490 --> 00:26:05.370 align:middle line:84% with, I will call almost a model of glass silica, SiO2. 00:26:05.370 --> 00:26:07.970 align:middle line:84% It's the basis for any kind of silicate glasses. 00:26:07.970 --> 00:26:11.530 align:middle line:90% 00:26:11.530 --> 00:26:15.090 align:middle line:84% So for SiO2, if you look at the crystalline structure, 00:26:15.090 --> 00:26:17.750 align:middle line:84% what I'm showing you here is just a pancake 2D version 00:26:17.750 --> 00:26:19.770 align:middle line:84% of the crystalline structure of cristobalite, 00:26:19.770 --> 00:26:22.310 align:middle line:84% which is one of, essentially, the structural variants 00:26:22.310 --> 00:26:24.030 align:middle line:90% of crystalline SiO2. 00:26:24.030 --> 00:26:25.290 align:middle line:90% If you look at it, same thing. 00:26:25.290 --> 00:26:27.550 align:middle line:84% Basic structural unit is you have, essentially, 00:26:27.550 --> 00:26:33.150 align:middle line:84% one silicon for oxygen around it to form this tetrahedra that 00:26:33.150 --> 00:26:37.030 align:middle line:84% interlink together to form 3D network. 00:26:37.030 --> 00:26:38.590 align:middle line:84% One thing I want to highlight here 00:26:38.590 --> 00:26:41.048 align:middle line:84% is that you look at what's called the ring structure. 00:26:41.048 --> 00:26:42.590 align:middle line:84% You look at, essentially, these rings 00:26:42.590 --> 00:26:45.050 align:middle line:84% here, closed loop atomic structures. 00:26:45.050 --> 00:26:46.470 align:middle line:90% These are called rings. 00:26:46.470 --> 00:26:49.230 align:middle line:84% In a crystalline silica, all the rings 00:26:49.230 --> 00:26:51.110 align:middle line:84% are so-called six-membered rings. 00:26:51.110 --> 00:26:54.030 align:middle line:84% It means, if you start to count the number of silicon atoms 00:26:54.030 --> 00:26:58.590 align:middle line:84% on the ring, it's always six in each of the ring structures. 00:26:58.590 --> 00:27:01.933 align:middle line:84% If you go to amorphous silica, on the other hand, 00:27:01.933 --> 00:27:03.350 align:middle line:84% you start to find out that you can 00:27:03.350 --> 00:27:05.130 align:middle line:90% get other kind of ring sizes. 00:27:05.130 --> 00:27:06.870 align:middle line:84% You may get seven-membered rings. 00:27:06.870 --> 00:27:09.830 align:middle line:84% You can get five-membered rings, even three-membered rings. 00:27:09.830 --> 00:27:12.390 align:middle line:84% These ring statistics is quite important structure aspect 00:27:12.390 --> 00:27:14.230 align:middle line:90% of amorphous materials. 00:27:14.230 --> 00:27:15.730 align:middle line:84% People can actually use it as a way 00:27:15.730 --> 00:27:21.230 align:middle line:84% to probe the structure of this network there. 00:27:21.230 --> 00:27:23.170 align:middle line:84% You can accommodate this different kind 00:27:23.170 --> 00:27:26.010 align:middle line:84% of a local structure variance here by varying 00:27:26.010 --> 00:27:29.527 align:middle line:84% the bond angle of, essentially, this SiO Si bond. 00:27:29.527 --> 00:27:31.610 align:middle line:84% This is the bond angle that changes to accommodate 00:27:31.610 --> 00:27:32.890 align:middle line:90% structural variations there. 00:27:32.890 --> 00:27:35.490 align:middle line:90% 00:27:35.490 --> 00:27:39.270 align:middle line:84% Despite this kind of structure distortion, in a silica glass, 00:27:39.270 --> 00:27:43.450 align:middle line:84% you still have a fairly tightly connected 3D network. 00:27:43.450 --> 00:27:46.890 align:middle line:84% All of the oxygen in a silica glass 00:27:46.890 --> 00:27:50.330 align:middle line:84% is bridging oxygen. All oxygen atoms always 00:27:50.330 --> 00:27:52.490 align:middle line:84% connect to two silica, so they are always 00:27:52.490 --> 00:27:55.250 align:middle line:84% bridging oxygen. There's no non-bridging oxygens in silica 00:27:55.250 --> 00:27:57.250 align:middle line:90% glass. 00:27:57.250 --> 00:27:59.770 align:middle line:84% So this very high-network connectivity 00:27:59.770 --> 00:28:02.890 align:middle line:84% means that you have a very rigid and very strong 00:28:02.890 --> 00:28:07.210 align:middle line:84% network that does not easily default. 00:28:07.210 --> 00:28:10.410 align:middle line:84% So this dictates many important properties of silica glass. 00:28:10.410 --> 00:28:13.650 align:middle line:84% They have a very high-softening point. 00:28:13.650 --> 00:28:16.140 align:middle line:84% Atoms doesn't really move until very high temperature. 00:28:16.140 --> 00:28:18.140 align:middle line:84% They have low-diffusion coefficient because it's 00:28:18.140 --> 00:28:19.200 align:middle line:90% quite tightly packed. 00:28:19.200 --> 00:28:21.020 align:middle line:84% You don't have lots of room for small atoms 00:28:21.020 --> 00:28:22.940 align:middle line:90% to come squeeze through. 00:28:22.940 --> 00:28:24.960 align:middle line:84% You have small coefficient of thermal expansion. 00:28:24.960 --> 00:28:26.540 align:middle line:84% Let me talk about that a little bit. 00:28:26.540 --> 00:28:31.020 align:middle line:84% So for coefficient of thermal expansion, 00:28:31.020 --> 00:28:37.200 align:middle line:84% in your solid state physics class, you probably talk about, 00:28:37.200 --> 00:28:39.925 align:middle line:84% discuss-- well, did you know about origin 00:28:39.925 --> 00:28:40.800 align:middle line:90% of thermal expansion? 00:28:40.800 --> 00:28:44.420 align:middle line:84% You talk about it in solid state physics class? 00:28:44.420 --> 00:28:46.060 align:middle line:90% I can quickly cover it. 00:28:46.060 --> 00:28:47.300 align:middle line:90% No worries. 00:28:47.300 --> 00:28:49.420 align:middle line:84% So if you think about interatomic interaction 00:28:49.420 --> 00:28:53.140 align:middle line:84% potential, so this would be-- for example, this is energy, u. 00:28:53.140 --> 00:28:57.140 align:middle line:84% And then this is basically the spacing between atoms, this-- 00:28:57.140 --> 00:28:58.140 align:middle line:90% what letter do you like? 00:28:58.140 --> 00:28:59.642 align:middle line:90% AUDIENCE: y. 00:28:59.642 --> 00:29:00.600 align:middle line:90% JUEJUN HU: Ah, OK good. 00:29:00.600 --> 00:29:01.100 align:middle line:90% Great. 00:29:01.100 --> 00:29:02.060 align:middle line:90% [CHUCKLING] 00:29:02.060 --> 00:29:04.660 align:middle line:84% So then you would, essentially, have 00:29:04.660 --> 00:29:07.740 align:middle line:84% this kind of function there, for example, 00:29:07.740 --> 00:29:10.700 align:middle line:84% where the minimum indicates this is the optimum spacing 00:29:10.700 --> 00:29:12.120 align:middle line:90% between the two atoms. 00:29:12.120 --> 00:29:14.440 align:middle line:84% Or this will give you equilibrium position. 00:29:14.440 --> 00:29:20.465 align:middle line:84% You will have a-- if you are at, say, 0 Kelvin, then the atom 00:29:20.465 --> 00:29:22.840 align:middle line:84% will sit right at the bottom of the potential well there. 00:29:22.840 --> 00:29:25.060 align:middle line:84% You have a well-defined structure there. 00:29:25.060 --> 00:29:28.160 align:middle line:84% As you start rising temperature, essentially, your network 00:29:28.160 --> 00:29:29.680 align:middle line:90% starts to get more energy. 00:29:29.680 --> 00:29:33.760 align:middle line:84% It means that you actually can now access higher energy levels 00:29:33.760 --> 00:29:35.720 align:middle line:90% in this potential well. 00:29:35.720 --> 00:29:37.888 align:middle line:84% So if you have an-- in an idealized scenario, 00:29:37.888 --> 00:29:39.680 align:middle line:84% this potential well, you can approximate it 00:29:39.680 --> 00:29:41.380 align:middle line:90% as like a parabola. 00:29:41.380 --> 00:29:43.060 align:middle line:90% So it's symmetric. 00:29:43.060 --> 00:29:46.320 align:middle line:84% If it's symmetric, even if you access these high-energy levels, 00:29:46.320 --> 00:29:48.880 align:middle line:84% the statistical average of the spacing 00:29:48.880 --> 00:29:51.780 align:middle line:84% will still be right in the center. 00:29:51.780 --> 00:29:53.960 align:middle line:90% So there's no thermal expansion. 00:29:53.960 --> 00:29:56.640 align:middle line:84% However, this kind of energy curve 00:29:56.640 --> 00:29:58.640 align:middle line:90% typically is not symmetric. 00:29:58.640 --> 00:30:00.800 align:middle line:84% There's a little bit of so-called anharmonicity 00:30:00.800 --> 00:30:02.440 align:middle line:84% that's always getting introduced. 00:30:02.440 --> 00:30:10.157 align:middle line:84% In fact, usually, the curve will look more like this because you 00:30:10.157 --> 00:30:12.740 align:middle line:84% just simply cannot squeeze two atoms very close to each other. 00:30:12.740 --> 00:30:14.845 align:middle line:84% There's always a very strong repulsion force. 00:30:14.845 --> 00:30:16.220 align:middle line:84% But if you try to pull them away, 00:30:16.220 --> 00:30:18.137 align:middle line:84% the interaction actually weakens a little bit. 00:30:18.137 --> 00:30:21.180 align:middle line:84% So that's why it's a bit softer along this arm. 00:30:21.180 --> 00:30:23.180 align:middle line:84% So now, if you heat it up, you start 00:30:23.180 --> 00:30:25.140 align:middle line:84% to access the higher energy levels. 00:30:25.140 --> 00:30:29.540 align:middle line:84% You find that the average position of your spacing 00:30:29.540 --> 00:30:32.200 align:middle line:84% will now get shifted to the right side. 00:30:32.200 --> 00:30:35.508 align:middle line:84% So what you are actually getting here is essentially like this. 00:30:35.508 --> 00:30:37.300 align:middle line:84% So as you go to higher, higher temperature, 00:30:37.300 --> 00:30:40.300 align:middle line:84% essentially, you start to get longer average spacing 00:30:40.300 --> 00:30:41.580 align:middle line:90% between the atoms. 00:30:41.580 --> 00:30:43.940 align:middle line:84% And that's why you have thermal expansion. 00:30:43.940 --> 00:30:46.420 align:middle line:90% Does that make sense? 00:30:46.420 --> 00:30:48.260 align:middle line:84% Now, what happens if you have a silica, 00:30:48.260 --> 00:30:50.385 align:middle line:84% for example, which have very strong chemical bonds? 00:30:50.385 --> 00:30:53.420 align:middle line:84% What does strong chemical bond do? 00:30:53.420 --> 00:30:55.210 align:middle line:90% You will have a-- 00:30:55.210 --> 00:30:57.760 align:middle line:84% AUDIENCE: It makes the walls really steep. 00:30:57.760 --> 00:31:00.857 align:middle line:84% JUEJUN HU: You have like this, like that. 00:31:00.857 --> 00:31:02.940 align:middle line:84% So if it's really steep, it means that, of course, 00:31:02.940 --> 00:31:04.782 align:middle line:84% this variation is going to be pretty small. 00:31:04.782 --> 00:31:06.740 align:middle line:84% You don't get lots of thermal expansion versus, 00:31:06.740 --> 00:31:10.100 align:middle line:84% if you have some other glasses with softer bonds, you open up, 00:31:10.100 --> 00:31:12.080 align:middle line:84% then you have a large thermal expansion. 00:31:12.080 --> 00:31:15.020 align:middle line:84% So that's why, typically, if you have strong chemical bones, 00:31:15.020 --> 00:31:19.040 align:middle line:84% you tend to have a low coefficient of thermal expansion 00:31:19.040 --> 00:31:20.487 align:middle line:90% in a covalent solid. 00:31:20.487 --> 00:31:21.820 align:middle line:90% Polymers are a different animal. 00:31:21.820 --> 00:31:26.680 align:middle line:90% 00:31:26.680 --> 00:31:30.357 align:middle line:84% And that's why silica, silica as a coefficient 00:31:30.357 --> 00:31:32.440 align:middle line:84% of thermal expansion is actually remarkably small. 00:31:32.440 --> 00:31:36.000 align:middle line:90% It's like 0.5 PPM per Kelvin. 00:31:36.000 --> 00:31:39.720 align:middle line:84% So it means that it expands 10 to the minus 7 00:31:39.720 --> 00:31:43.800 align:middle line:84% in length per degree Celsius, which is really, really small. 00:31:43.800 --> 00:31:47.360 align:middle line:84% Now, to give you a comparison, if you think about window pane 00:31:47.360 --> 00:31:49.007 align:middle line:84% glasses-- these are soda lime glasses-- 00:31:49.007 --> 00:31:50.840 align:middle line:84% the typical coefficient of thermal expansion 00:31:50.840 --> 00:31:51.980 align:middle line:90% is like 10 PPM. 00:31:51.980 --> 00:31:55.820 align:middle line:84% So it's 20 times higher than silica. 00:31:55.820 --> 00:31:57.142 align:middle line:90% Why is that important? 00:31:57.142 --> 00:31:59.600 align:middle line:84% Silica can be very good, for example, if you want something 00:31:59.600 --> 00:32:02.000 align:middle line:84% with very good thermal shock resistance, 00:32:02.000 --> 00:32:06.560 align:middle line:84% like if you have-- just say you have kitchenware. 00:32:06.560 --> 00:32:09.050 align:middle line:84% You want to remove it from the stove, 00:32:09.050 --> 00:32:10.810 align:middle line:84% immediately put it on a cold surface. 00:32:10.810 --> 00:32:12.570 align:middle line:84% Then you get a large temperature gradient. 00:32:12.570 --> 00:32:13.850 align:middle line:84% If you have a high-thermal coefficient 00:32:13.850 --> 00:32:15.650 align:middle line:84% of thermal expansion, it means that different regions 00:32:15.650 --> 00:32:18.150 align:middle line:84% of different temperature have different volume, essentially. 00:32:18.150 --> 00:32:20.890 align:middle line:84% So they build up very high stress, eventually cracks. 00:32:20.890 --> 00:32:24.547 align:middle line:84% If you have a container made out of silica, 00:32:24.547 --> 00:32:25.630 align:middle line:90% nothing's going to happen. 00:32:25.630 --> 00:32:26.890 align:middle line:84% We're actually going to do a little demo, 00:32:26.890 --> 00:32:29.410 align:middle line:84% show you that silica is very, very, very resistant 00:32:29.410 --> 00:32:32.890 align:middle line:90% to any kind of thermal shock. 00:32:32.890 --> 00:32:37.690 align:middle line:84% Downside, why you are not using kitchenware made out of silica? 00:32:37.690 --> 00:32:40.788 align:middle line:84% Silica has a very high softening point. 00:32:40.788 --> 00:32:42.330 align:middle line:84% It means it's actually very difficult 00:32:42.330 --> 00:32:46.290 align:middle line:84% to process silica compared to other soda lime glasses. 00:32:46.290 --> 00:32:51.330 align:middle line:84% You need a furnaces that can go up to 2,000 degrees Celsius, 00:32:51.330 --> 00:32:53.975 align:middle line:84% which is why people are not using it. 00:32:53.975 --> 00:32:54.850 align:middle line:90% So what do people do? 00:32:54.850 --> 00:32:58.315 align:middle line:84% If you want something that's a lot more easy to process, 00:32:58.315 --> 00:33:00.690 align:middle line:84% you have to add some network modifiers, which we're going 00:33:00.690 --> 00:33:01.773 align:middle line:90% to talk about in a second. 00:33:01.773 --> 00:33:03.650 align:middle line:84% Now, before I go to that, I just also want 00:33:03.650 --> 00:33:06.650 align:middle line:84% to mention one very peculiar thing about silica glasses. 00:33:06.650 --> 00:33:07.920 align:middle line:90% It's called volume anomaly. 00:33:07.920 --> 00:33:09.170 align:middle line:90% So for now, look at this plot. 00:33:09.170 --> 00:33:10.890 align:middle line:84% This is basically volume as a function of temperature, 00:33:10.890 --> 00:33:12.330 align:middle line:84% similar to what I showed you in the previous lecture. 00:33:12.330 --> 00:33:14.510 align:middle line:84% Forget about everything on the left-hand side. 00:33:14.510 --> 00:33:16.390 align:middle line:90% Only focus on this one here. 00:33:16.390 --> 00:33:18.250 align:middle line:84% So if you look at only this part here, 00:33:18.250 --> 00:33:19.890 align:middle line:90% it looks actually quite normal. 00:33:19.890 --> 00:33:21.870 align:middle line:84% It's basically supercooled liquid. 00:33:21.870 --> 00:33:24.610 align:middle line:84% And if we're cooling it down, then at some point, 00:33:24.610 --> 00:33:27.230 align:middle line:84% you're going to go deviate from the supercooled liquid 00:33:27.230 --> 00:33:28.790 align:middle line:90% and then go to the glass line. 00:33:28.790 --> 00:33:30.390 align:middle line:90% That makes sense. 00:33:30.390 --> 00:33:33.350 align:middle line:84% What's weird about silica is that if you-- 00:33:33.350 --> 00:33:36.350 align:middle line:84% at some temperature range, its thermal expansion coefficient 00:33:36.350 --> 00:33:38.270 align:middle line:90% is actually negative. 00:33:38.270 --> 00:33:41.150 align:middle line:84% So as you cool it down, it expands. 00:33:41.150 --> 00:33:44.950 align:middle line:84% That's why you see the curve actually goes back up. 00:33:44.950 --> 00:33:48.830 align:middle line:84% So if it goes back up, the glass line 00:33:48.830 --> 00:33:50.750 align:middle line:84% also will deviate from this curve there. 00:33:50.750 --> 00:33:53.550 align:middle line:84% Same thing, if you cool down faster, 00:33:53.550 --> 00:33:56.230 align:middle line:84% you will deviate from the supercooled liquid line earlier. 00:33:56.230 --> 00:33:58.365 align:middle line:84% If you cool down slower, then it actually 00:33:58.365 --> 00:34:00.990 align:middle line:84% traces this supercooled liquid line for a longer period of time 00:34:00.990 --> 00:34:03.190 align:middle line:90% until it go to the glass line. 00:34:03.190 --> 00:34:06.490 align:middle line:84% But the consequence of that is that, in some region-- 00:34:06.490 --> 00:34:10.210 align:middle line:84% in some temperature regime, slow-cooled silica 00:34:10.210 --> 00:34:13.510 align:middle line:84% actually has a volume larger than fast-cooled silica. 00:34:13.510 --> 00:34:17.210 align:middle line:84% This is opposite to most glasses. 00:34:17.210 --> 00:34:17.790 align:middle line:90% Yes? 00:34:17.790 --> 00:34:19.607 align:middle line:90% AUDIENCE: Do you know why? 00:34:19.607 --> 00:34:20.690 align:middle line:90% JUEJUN HU: Great question. 00:34:20.690 --> 00:34:23.873 align:middle line:84% To be honest, I don't have an immediate answer here. 00:34:23.873 --> 00:34:26.290 align:middle line:84% People actually have done lots of, essentially, simulation 00:34:26.290 --> 00:34:26.710 align:middle line:90% studies. 00:34:26.710 --> 00:34:28.969 align:middle line:84% You can look into how to explore the glass structure, silica 00:34:28.969 --> 00:34:30.130 align:middle line:84% glass structure, and why it has this kind 00:34:30.130 --> 00:34:32.010 align:middle line:84% of negative coefficient of expansion. 00:34:32.010 --> 00:34:34.113 align:middle line:84% That's actually beyond my immediate knowledge. 00:34:34.113 --> 00:34:35.530 align:middle line:84% But I can refer you to some papers 00:34:35.530 --> 00:34:37.010 align:middle line:84% if you're interested about why they 00:34:37.010 --> 00:34:38.889 align:middle line:84% have this kind of weird behavior, yeah. 00:34:38.889 --> 00:34:44.250 align:middle line:84% AUDIENCE: So is the main curve your supercooling? 00:34:44.250 --> 00:34:45.770 align:middle line:84% JUEJUN HU: This curve, this line, 00:34:45.770 --> 00:34:48.489 align:middle line:84% is basically how the volume of the supercooled liquid 00:34:48.489 --> 00:34:50.110 align:middle line:84% changes as a function of temperature. 00:34:50.110 --> 00:34:51.170 align:middle line:90% AUDIENCE: So that's the liquid. 00:34:51.170 --> 00:34:53.420 align:middle line:84% JUEJUN HU: So this is a supercooled liquid, this line. 00:34:53.420 --> 00:34:57.910 align:middle line:84% Now, each of this little branch is the glass line 00:34:57.910 --> 00:35:00.410 align:middle line:84% that eventually deviates from supercooled liquid line, where 00:35:00.410 --> 00:35:04.030 align:middle line:84% you have different cooling rates. 00:35:04.030 --> 00:35:07.550 align:middle line:84% Yeah, so this is a fast cooling, slower, even slower, 00:35:07.550 --> 00:35:08.910 align:middle line:90% even slower. 00:35:08.910 --> 00:35:09.990 align:middle line:90% Yeah? 00:35:09.990 --> 00:35:13.510 align:middle line:84% AUDIENCE: So, essentially, if you want to minimize the volume, 00:35:13.510 --> 00:35:16.250 align:middle line:90% you have to-- 00:35:16.250 --> 00:35:17.830 align:middle line:90% yeah, [INAUDIBLE]. 00:35:17.830 --> 00:35:21.037 align:middle line:84% JUEJUN HU: Yeah, you can do that with silicon. 00:35:21.037 --> 00:35:21.870 align:middle line:90% Yeah, so that's why. 00:35:21.870 --> 00:35:24.328 align:middle line:84% In the last lecture, I was saying that the pro I showed you 00:35:24.328 --> 00:35:27.790 align:middle line:84% in the previous class, that's universal, which is enthalpy. 00:35:27.790 --> 00:35:29.930 align:middle line:84% Slow cooling always gives you a low enthalpy. 00:35:29.930 --> 00:35:33.310 align:middle line:90% But volume, not always. 00:35:33.310 --> 00:35:35.350 align:middle line:84% Usually, slow cooling gives you smaller volume, 00:35:35.350 --> 00:35:38.590 align:middle line:84% but not always because of silica. 00:35:38.590 --> 00:35:41.670 align:middle line:84% AUDIENCE: So, presumably, it's like-- 00:35:41.670 --> 00:35:43.630 align:middle line:84% I guess, how do you prevent solidification 00:35:43.630 --> 00:35:47.470 align:middle line:84% at the higher temperatures if you, for some reason, 00:35:47.470 --> 00:35:48.675 align:middle line:90% wanted to explore? 00:35:48.675 --> 00:35:49.550 align:middle line:90% JUEJUN HU: Like here. 00:35:49.550 --> 00:35:50.190 align:middle line:90% AUDIENCE: Yeah, cooling. 00:35:50.190 --> 00:35:51.230 align:middle line:90% JUEJUN HU: Cooling rate. 00:35:51.230 --> 00:35:53.430 align:middle line:90% Let's make it a knob you turn. 00:35:53.430 --> 00:35:57.228 align:middle line:90% The faster you cool, the-- 00:35:57.228 --> 00:35:58.770 align:middle line:84% essentially, if you cool down faster, 00:35:58.770 --> 00:36:00.550 align:middle line:84% you don't allow nearly as much time for the atoms 00:36:00.550 --> 00:36:03.060 align:middle line:84% to rearrange themselves and find a more stable structure. 00:36:03.060 --> 00:36:07.280 align:middle line:84% The supercooled liquid is the more stable structure 00:36:07.280 --> 00:36:09.680 align:middle line:84% that the glass is trying to relax to. 00:36:09.680 --> 00:36:11.707 align:middle line:84% So if you do cool down faster, you 00:36:11.707 --> 00:36:14.040 align:middle line:84% don't get the opportunity to actually relax to this line 00:36:14.040 --> 00:36:14.720 align:middle line:90% here. 00:36:14.720 --> 00:36:18.520 align:middle line:84% It has to deviate and go to the glass line. 00:36:18.520 --> 00:36:21.560 align:middle line:84% AUDIENCE: So it has to be fast enough cooling 00:36:21.560 --> 00:36:25.318 align:middle line:84% not to crystallize, but slow enough cooling to cool it. 00:36:25.318 --> 00:36:26.360 align:middle line:90% JUEJUN HU: Exactly, yeah. 00:36:26.360 --> 00:36:30.560 align:middle line:84% But for silica, practically, it will never crystallize it. 00:36:30.560 --> 00:36:33.980 align:middle line:84% It's like, the cooling rate you need to actually crystallize it, 00:36:33.980 --> 00:36:38.760 align:middle line:84% it's like 10 to the minus 10 degrees Celsius per second. 00:36:38.760 --> 00:36:39.320 align:middle line:90% Impossible. 00:36:39.320 --> 00:36:40.820 align:middle line:84% In fact, later on, I'm going to show 00:36:40.820 --> 00:36:43.540 align:middle line:84% you one example in large telescope mirrors. 00:36:43.540 --> 00:36:46.160 align:middle line:84% People take years to cool on, just 00:36:46.160 --> 00:36:48.720 align:middle line:84% so you don't develop any stress uniformly in the kind 00:36:48.720 --> 00:36:49.980 align:middle line:90% of large optical mirrors. 00:36:49.980 --> 00:36:52.160 align:middle line:90% Again, they don't crystallize. 00:36:52.160 --> 00:36:54.260 align:middle line:84% So there are some glasses that are really very, 00:36:54.260 --> 00:36:56.520 align:middle line:90% very, very, very stable, yeah. 00:36:56.520 --> 00:36:59.840 align:middle line:90% 00:36:59.840 --> 00:37:02.660 align:middle line:90% Any more questions about this? 00:37:02.660 --> 00:37:04.500 align:middle line:84% All right, now, let's take a look 00:37:04.500 --> 00:37:06.820 align:middle line:84% at how we make glass more processable 00:37:06.820 --> 00:37:08.600 align:middle line:84% by lowering the softening temperature. 00:37:08.600 --> 00:37:11.440 align:middle line:84% So the way you do it, adding network modifiers. 00:37:11.440 --> 00:37:15.102 align:middle line:84% Simple one, one example is to do alkaline atoms, like sodium. 00:37:15.102 --> 00:37:17.060 align:middle line:84% As we have already mentioned, every time you're 00:37:17.060 --> 00:37:18.643 align:middle line:84% adding one alkaline ion, you basically 00:37:18.643 --> 00:37:20.860 align:middle line:84% create one non-bridging oxygen. You 00:37:20.860 --> 00:37:23.520 align:middle line:84% break up the network, decrease the network connectivity, 00:37:23.520 --> 00:37:26.020 align:middle line:84% which means that you now start to exhibit properties exactly 00:37:26.020 --> 00:37:27.740 align:middle line:84% opposite to what you have in silica. 00:37:27.740 --> 00:37:30.430 align:middle line:84% You have a low viscosity because atoms is a lot easier 00:37:30.430 --> 00:37:32.180 align:middle line:84% to move past each other now you don't have 00:37:32.180 --> 00:37:33.762 align:middle line:90% a tightly connected network. 00:37:33.762 --> 00:37:36.220 align:middle line:84% You have a much higher diffusion coefficient because you're 00:37:36.220 --> 00:37:38.300 align:middle line:90% creating lots of spaces now. 00:37:38.300 --> 00:37:41.140 align:middle line:84% In between the clusters, you can essentially have smaller atoms 00:37:41.140 --> 00:37:42.220 align:middle line:90% to squeeze through. 00:37:42.220 --> 00:37:44.200 align:middle line:84% So you have a higher diffusion coefficient. 00:37:44.200 --> 00:37:46.340 align:middle line:84% You also have a higher coefficient 00:37:46.340 --> 00:37:49.600 align:middle line:84% of thermal expansion because of the weaker chemical bonds. 00:37:49.600 --> 00:37:53.330 align:middle line:90% 00:37:53.330 --> 00:37:55.900 align:middle line:84% Now, the downside, though, if you 00:37:55.900 --> 00:37:57.800 align:middle line:84% go to alkaline silicate glass, the problem 00:37:57.800 --> 00:37:59.900 align:middle line:90% is the chemical durability. 00:37:59.900 --> 00:38:04.360 align:middle line:90% 00:38:04.360 --> 00:38:07.800 align:middle line:84% So, for example, let's suppose you have sodium. 00:38:07.800 --> 00:38:10.440 align:middle line:84% Let's just look at this simple silicon. 00:38:10.440 --> 00:38:12.720 align:middle line:90% You have oxygen, sodium. 00:38:12.720 --> 00:38:15.360 align:middle line:84% This is what happens if you put sodium into a silicate glass. 00:38:15.360 --> 00:38:16.820 align:middle line:90% Now, you put water in there. 00:38:16.820 --> 00:38:19.840 align:middle line:90% 00:38:19.840 --> 00:38:22.840 align:middle line:84% What's going to happen is that water is going 00:38:22.840 --> 00:38:25.720 align:middle line:84% to break this very weak connection between sodium 00:38:25.720 --> 00:38:32.360 align:middle line:84% and oxygen. What you end up getting is SiOH plus NaOH. 00:38:32.360 --> 00:38:37.020 align:middle line:90% 00:38:37.020 --> 00:38:42.800 align:middle line:84% Now, to make things worse, producing an NaOH essentially 00:38:42.800 --> 00:38:45.080 align:middle line:84% means that you now have a basic solution. 00:38:45.080 --> 00:38:49.180 align:middle line:84% Glasses typically dissolves in a basic solution. 00:38:49.180 --> 00:38:54.480 align:middle line:84% NaOH can actually react with SiO2. 00:38:54.480 --> 00:38:56.140 align:middle line:84% What you end up getting would be, 00:38:56.140 --> 00:39:01.120 align:middle line:84% essentially, a sodium silicate plus water. 00:39:01.120 --> 00:39:03.440 align:middle line:84% And sodium silicate is soluble in water, by the way. 00:39:03.440 --> 00:39:07.020 align:middle line:90% 00:39:07.020 --> 00:39:10.460 align:middle line:84% So what you're seeing here is that, if you put water 00:39:10.460 --> 00:39:12.460 align:middle line:84% into an alkaline silicate glass, you 00:39:12.460 --> 00:39:15.020 align:middle line:84% get preferential leaching of the sodium atoms 00:39:15.020 --> 00:39:18.580 align:middle line:84% into the solution, which turns it basic, which then 00:39:18.580 --> 00:39:21.100 align:middle line:84% allows you to actually attack the backbone of the glass 00:39:21.100 --> 00:39:24.060 align:middle line:90% network. 00:39:24.060 --> 00:39:29.660 align:middle line:84% So that's why actual alkali silica glasses, 00:39:29.660 --> 00:39:31.760 align:middle line:84% people simply don't use it because of this reason. 00:39:31.760 --> 00:39:34.586 align:middle line:90% 00:39:34.586 --> 00:39:37.300 align:middle line:84% There are a few ways to improve the chemical resistance 00:39:37.300 --> 00:39:38.660 align:middle line:90% of these glass materials. 00:39:38.660 --> 00:39:42.220 align:middle line:84% One common strategy is called a fire polishing or flame 00:39:42.220 --> 00:39:42.908 align:middle line:90% polishing. 00:39:42.908 --> 00:39:44.700 align:middle line:84% What you would do is you have, essentially, 00:39:44.700 --> 00:39:47.100 align:middle line:90% your glass products. 00:39:47.100 --> 00:39:49.057 align:middle line:84% After you make it, you then use fire 00:39:49.057 --> 00:39:51.140 align:middle line:84% to essentially do a heat treatment on the surface. 00:39:51.140 --> 00:39:52.700 align:middle line:84% This allows you to essentially have 00:39:52.700 --> 00:39:56.870 align:middle line:84% this sodium ion, too essentially volatile, and leave the network. 00:39:56.870 --> 00:39:58.830 align:middle line:84% So on the surface, you get the layer of glass 00:39:58.830 --> 00:40:01.550 align:middle line:84% that's actually depleted of the sodium ions. 00:40:01.550 --> 00:40:04.190 align:middle line:84% So that way, you can essentially prevent this kind of phenomena 00:40:04.190 --> 00:40:06.830 align:middle line:84% from happening and, therefore, improve the chemical longevity 00:40:06.830 --> 00:40:08.707 align:middle line:90% of the glass material. 00:40:08.707 --> 00:40:11.290 align:middle line:84% We're going to talk a bit more about these kind of strategies, 00:40:11.290 --> 00:40:13.165 align:middle line:84% how to improve the chemical durability later. 00:40:13.165 --> 00:40:16.350 align:middle line:90% 00:40:16.350 --> 00:40:20.070 align:middle line:84% All right, but another very interesting thing I also want 00:40:20.070 --> 00:40:23.830 align:middle line:84% to mention here is that, when you add these sodium atoms 00:40:23.830 --> 00:40:25.410 align:middle line:84% into the glass network, as I said, 00:40:25.410 --> 00:40:28.390 align:middle line:84% every sodium atom creates one non-bridging oxygen. 00:40:28.390 --> 00:40:30.950 align:middle line:84% If you keep on adding sodium atoms, 00:40:30.950 --> 00:40:33.470 align:middle line:84% you create more and more non-bridging oxygen. 00:40:33.470 --> 00:40:37.750 align:middle line:84% At some point, you have so many long-bridging oxygen there, 00:40:37.750 --> 00:40:40.730 align:middle line:84% you can no longer sustain a 3D glass network. 00:40:40.730 --> 00:40:42.910 align:middle line:84% You simply don't have enough connectivity to bring 00:40:42.910 --> 00:40:45.670 align:middle line:90% all the atoms together. 00:40:45.670 --> 00:40:49.030 align:middle line:84% Then what happens is you go to this new regime called 00:40:49.030 --> 00:40:52.590 align:middle line:90% the invert glass. 00:40:52.590 --> 00:40:55.050 align:middle line:84% So what I'm schematically representing here, 00:40:55.050 --> 00:40:59.730 align:middle line:84% each of this little triangle is basically one SIO4 tetrahedra. 00:40:59.730 --> 00:41:03.710 align:middle line:84% Now, because you have broken so many chemical bonds, 00:41:03.710 --> 00:41:05.210 align:middle line:84% you can no longer link them together 00:41:05.210 --> 00:41:06.590 align:middle line:90% to form a continuous network. 00:41:06.590 --> 00:41:10.050 align:middle line:84% Instead, what you get is small fragments 00:41:10.050 --> 00:41:13.130 align:middle line:84% of this tetrahedra linked together. 00:41:13.130 --> 00:41:16.210 align:middle line:84% These fragments are actually attracted to each other 00:41:16.210 --> 00:41:17.930 align:middle line:84% through electrostatic interaction 00:41:17.930 --> 00:41:19.388 align:middle line:90% with the sodium ion in between. 00:41:19.388 --> 00:41:20.930 align:middle line:84% And then, eventually, the whole thing 00:41:20.930 --> 00:41:22.555 align:middle line:84% is bound together through, essentially, 00:41:22.555 --> 00:41:25.210 align:middle line:90% van der Waals force. 00:41:25.210 --> 00:41:31.132 align:middle line:84% So this is also amorphous solid, but sort of the main bonding 00:41:31.132 --> 00:41:33.090 align:middle line:84% mechanism is actually quite different from what 00:41:33.090 --> 00:41:37.490 align:middle line:84% you get here, which is purely covalent bond, more or less. 00:41:37.490 --> 00:41:40.152 align:middle line:84% This invert glass also exhibits a very different trend 00:41:40.152 --> 00:41:42.610 align:middle line:84% in terms of how the property evolves with the concentration 00:41:42.610 --> 00:41:43.850 align:middle line:90% of alkali ion. 00:41:43.850 --> 00:41:46.092 align:middle line:84% So for this regime here, for this initial regime, 00:41:46.092 --> 00:41:48.050 align:middle line:84% you can imagine that, if you put more alkaline, 00:41:48.050 --> 00:41:49.250 align:middle line:90% you get decreased hardness. 00:41:49.250 --> 00:41:50.370 align:middle line:90% It becomes softer. 00:41:50.370 --> 00:41:52.410 align:middle line:84% You have low-glass transition temperature. 00:41:52.410 --> 00:41:55.230 align:middle line:84% You have high-diffusion coefficient and such. 00:41:55.230 --> 00:41:57.070 align:middle line:84% But when you go to the invert glass, 00:41:57.070 --> 00:42:00.895 align:middle line:84% because the force, the chemical force that binds everything 00:42:00.895 --> 00:42:03.270 align:middle line:84% together, is basically the interaction between the sodium 00:42:03.270 --> 00:42:05.950 align:middle line:84% ion and these tetrahedral fragments, 00:42:05.950 --> 00:42:09.190 align:middle line:84% so the more sodium ion we add in there, 00:42:09.190 --> 00:42:12.368 align:middle line:84% the stronger the connection actually becomes. 00:42:12.368 --> 00:42:13.910 align:middle line:84% So you see that the property actually 00:42:13.910 --> 00:42:16.150 align:middle line:84% starts to work, essentially, to change to evolve 00:42:16.150 --> 00:42:17.090 align:middle line:90% in opposite direction. 00:42:17.090 --> 00:42:19.470 align:middle line:84% As you put more sodium in the invert glass, 00:42:19.470 --> 00:42:21.510 align:middle line:90% the hardness actually increases. 00:42:21.510 --> 00:42:24.830 align:middle line:84% The glass transition temperature also starts to rise. 00:42:24.830 --> 00:42:26.530 align:middle line:84% Diffusion coefficient starts to drop. 00:42:26.530 --> 00:42:28.290 align:middle line:90% It's the exactly opposite trend. 00:42:28.290 --> 00:42:37.470 align:middle line:90% 00:42:37.470 --> 00:42:41.590 align:middle line:84% So now, one very interesting exercise is to see, 00:42:41.590 --> 00:42:46.350 align:middle line:84% can we quantitatively predict, at what specific composition 00:42:46.350 --> 00:42:50.010 align:middle line:84% do we have this transition from a non-regular network 00:42:50.010 --> 00:42:53.050 align:middle line:90% glass to an invert glass? 00:42:53.050 --> 00:42:54.730 align:middle line:84% So I will show you one example, how 00:42:54.730 --> 00:42:56.980 align:middle line:84% to actually do a structured determination in this kind 00:42:56.980 --> 00:42:58.530 align:middle line:90% of alkaline silica glass. 00:42:58.530 --> 00:43:00.930 align:middle line:84% So to do that, let's introduce one parameter here, Y. 00:43:00.930 --> 00:43:03.850 align:middle line:84% Y is what we call the average number of corners 00:43:03.850 --> 00:43:06.370 align:middle line:90% shared per SiO4 tetrahedra. 00:43:06.370 --> 00:43:09.690 align:middle line:84% So normally, in a silica glass without sodium, 00:43:09.690 --> 00:43:11.370 align:middle line:84% this number, Y, should be equal to 4 00:43:11.370 --> 00:43:12.450 align:middle line:84% because all four corners should be 00:43:12.450 --> 00:43:14.492 align:middle line:84% connected to some other neighbor in a tetrahedra. 00:43:14.492 --> 00:43:18.090 align:middle line:84% So now, what if we start to add sodium? 00:43:18.090 --> 00:43:20.290 align:middle line:84% Let's assume we have a glass with this kind of molar 00:43:20.290 --> 00:43:21.850 align:middle line:90% competition here. 00:43:21.850 --> 00:43:26.790 align:middle line:84% So then what we want to determine here is, what is Y? 00:43:26.790 --> 00:43:29.650 align:middle line:84% How does Y changes with x, the amount of sodium you 00:43:29.650 --> 00:43:30.930 align:middle line:90% add in there? 00:43:30.930 --> 00:43:32.490 align:middle line:84% So the way you do it is you start 00:43:32.490 --> 00:43:36.290 align:middle line:84% by looking at the total number of oxygen. Total oxygen 00:43:36.290 --> 00:43:40.570 align:middle line:84% in one mole of glass, how much oxygen do you have? 00:43:40.570 --> 00:43:44.830 align:middle line:84% So you have oxygen coming from the SiO2 layer, 00:43:44.830 --> 00:43:47.090 align:middle line:90% which is 2 minus 2x. 00:43:47.090 --> 00:43:51.700 align:middle line:84% You also have x oxygen coming from sodium oxide, which 00:43:51.700 --> 00:43:54.780 align:middle line:90% gives you 2 minus x. 00:43:54.780 --> 00:43:57.920 align:middle line:84% This is the amount of oxygen in one mole of this glass. 00:43:57.920 --> 00:44:01.700 align:middle line:90% 00:44:01.700 --> 00:44:04.920 align:middle line:84% Next thing, we have two kinds of oxygen here. 00:44:04.920 --> 00:44:06.660 align:middle line:84% We have non-bridging oxygen. We have 00:44:06.660 --> 00:44:09.700 align:middle line:84% bridging oxygen. Let's take a look at the amount 00:44:09.700 --> 00:44:12.260 align:middle line:90% of non-bridging oxygen we have. 00:44:12.260 --> 00:44:15.260 align:middle line:84% So every time you add one sodium atom, 00:44:15.260 --> 00:44:18.450 align:middle line:84% you create one non-bridging oxygen. 00:44:18.450 --> 00:44:20.700 align:middle line:84% So the amount of non-bridging oxygen should just equal 00:44:20.700 --> 00:44:23.120 align:middle line:84% to the amount of sodium, which is the 2x. 00:44:23.120 --> 00:44:27.580 align:middle line:90% 00:44:27.580 --> 00:44:29.067 align:middle line:84% Without bridging oxygen, well, that 00:44:29.067 --> 00:44:30.400 align:middle line:90% would be pretty straightforward. 00:44:30.400 --> 00:44:33.340 align:middle line:84% It's basically a total amount of oxygen minus non-bridging 00:44:33.340 --> 00:44:36.080 align:middle line:90% oxygen. It would be 2 minus 3x. 00:44:36.080 --> 00:44:41.480 align:middle line:90% 00:44:41.480 --> 00:44:44.740 align:middle line:84% We also notice that each bridging oxygen 00:44:44.740 --> 00:44:48.960 align:middle line:84% creates two shared corners of the tetrahedra. 00:44:48.960 --> 00:44:49.560 align:middle line:90% Why? 00:44:49.560 --> 00:44:51.360 align:middle line:84% Because each bridging oxygen is always 00:44:51.360 --> 00:44:53.720 align:middle line:90% shared between two tetrahedra. 00:44:53.720 --> 00:44:56.000 align:middle line:84% So, effectively, each bridging oxygen 00:44:56.000 --> 00:44:57.920 align:middle line:90% creates two shared corners. 00:44:57.920 --> 00:45:01.800 align:middle line:84% So the total number of shared corners, 00:45:01.800 --> 00:45:05.980 align:middle line:84% corners that are shared will be 2 times that of bridging oxygen. 00:45:05.980 --> 00:45:08.900 align:middle line:90% So it's going to be 4 minus 6x. 00:45:08.900 --> 00:45:18.080 align:middle line:90% 00:45:18.080 --> 00:45:22.920 align:middle line:84% Last step, we can now define Y. Y, by our definition, 00:45:22.920 --> 00:45:29.000 align:middle line:84% is the number of corners shared, which is 4 minus 6x, 00:45:29.000 --> 00:45:31.640 align:middle line:84% divided by the number of tetrahedra. 00:45:31.640 --> 00:45:34.920 align:middle line:90% 00:45:34.920 --> 00:45:38.280 align:middle line:84% Each tetrahedra has one silicon sitting in the center. 00:45:38.280 --> 00:45:40.240 align:middle line:84% So the number of tetrahedra is basically 00:45:40.240 --> 00:45:44.180 align:middle line:84% the number of silicon we have, which is basically a 1 minus x. 00:45:44.180 --> 00:45:52.380 align:middle line:90% 00:45:52.380 --> 00:45:54.580 align:middle line:84% All right, so now the next question 00:45:54.580 --> 00:45:59.140 align:middle line:84% is, what is the y value that will correspond 00:45:59.140 --> 00:46:02.420 align:middle line:84% to the onset of the transition from a network glass 00:46:02.420 --> 00:46:03.480 align:middle line:90% to invert glass? 00:46:03.480 --> 00:46:10.020 align:middle line:90% 00:46:10.020 --> 00:46:12.300 align:middle line:84% How many corners need to be shared in order to form 3D 00:46:12.300 --> 00:46:12.880 align:middle line:90% network? 00:46:12.880 --> 00:46:16.140 align:middle line:90% 00:46:16.140 --> 00:46:17.580 align:middle line:90% At least two. 00:46:17.580 --> 00:46:19.080 align:middle line:84% In fact, you have to be above two. 00:46:19.080 --> 00:46:21.580 align:middle line:84% If you only have two corners shared between each tetrahedra, 00:46:21.580 --> 00:46:24.000 align:middle line:84% you can form a non-linear shape, which is not really 3D. 00:46:24.000 --> 00:46:26.340 align:middle line:84% You need a little bit above two in order to have interconnects 00:46:26.340 --> 00:46:28.465 align:middle line:84% or cross-linking between different chains to get 3D 00:46:28.465 --> 00:46:29.060 align:middle line:90% network. 00:46:29.060 --> 00:46:32.180 align:middle line:84% So we argue that Y equals to 2 would 00:46:32.180 --> 00:46:37.220 align:middle line:84% be the threshold going from a network glass to invert glass. 00:46:37.220 --> 00:46:39.540 align:middle line:84% You can solve that pretty straightforwardly. 00:46:39.540 --> 00:46:46.956 align:middle line:84% Basically, it will tell you that x basically equals to 0.5. 00:46:46.956 --> 00:46:48.960 align:middle line:84% And that's something people have actually 00:46:48.960 --> 00:46:50.580 align:middle line:90% verified experimentally. 00:46:50.580 --> 00:46:59.320 align:middle line:90% 00:46:59.320 --> 00:47:01.020 align:middle line:84% So what I'm plotting in this plot here, 00:47:01.020 --> 00:47:02.687 align:middle line:84% this is actually experimentally-measured 00:47:02.687 --> 00:47:04.840 align:middle line:84% viscosity inside these glass materials 00:47:04.840 --> 00:47:06.720 align:middle line:90% at different temperatures. 00:47:06.720 --> 00:47:09.480 align:middle line:84% The horizontal axis is basically Y, as we defined. 00:47:09.480 --> 00:47:12.200 align:middle line:84% Vertical axis is the logarithm of viscosity. 00:47:12.200 --> 00:47:15.260 align:middle line:84% What you see here is that, for all the temperature ranges, 00:47:15.260 --> 00:47:17.040 align:middle line:84% you always see this kind of change 00:47:17.040 --> 00:47:19.180 align:middle line:84% of how the viscosity depends on glass condition. 00:47:19.180 --> 00:47:21.360 align:middle line:84% Y, essentially, is the glass composition. 00:47:21.360 --> 00:47:26.360 align:middle line:84% So you always see that viscosity reach a minimum right at Y 00:47:26.360 --> 00:47:28.613 align:middle line:90% equals 2. 00:47:28.613 --> 00:47:30.280 align:middle line:84% On this side, this is, basically, you're 00:47:30.280 --> 00:47:32.263 align:middle line:90% adding more sodium from a glass. 00:47:32.263 --> 00:47:34.180 align:middle line:84% You essentially decrease network connectivity, 00:47:34.180 --> 00:47:35.520 align:middle line:90% so you have a lower viscosity. 00:47:35.520 --> 00:47:38.388 align:middle line:84% And then above this end, this is when you go to invert glass. 00:47:38.388 --> 00:47:40.180 align:middle line:84% You start to put more and more sodium atom, 00:47:40.180 --> 00:47:42.250 align:middle line:84% you actually link the network more 00:47:42.250 --> 00:47:45.430 align:middle line:84% closer together through this electrostatic interaction. 00:47:45.430 --> 00:47:47.930 align:middle line:84% And that's why you see a decrease of the viscosity there. 00:47:47.930 --> 00:47:50.130 align:middle line:84% So this is one example to show that this 00:47:50.130 --> 00:47:53.090 align:middle line:84% is a very simple geometric determination allows 00:47:53.090 --> 00:47:56.747 align:middle line:84% us to predict quantitatively, the glass property change. 00:47:56.747 --> 00:47:58.330 align:middle line:84% All right, so I have already mentioned 00:47:58.330 --> 00:48:00.872 align:middle line:84% that people don't like alkaline silicate glass because it has 00:48:00.872 --> 00:48:05.050 align:middle line:84% poor chemical durability So one kind of a modification people 00:48:05.050 --> 00:48:07.730 align:middle line:84% have made is to-- besides alkaline, you also 00:48:07.730 --> 00:48:10.288 align:middle line:84% get alkaline earth into a glass network. 00:48:10.288 --> 00:48:12.330 align:middle line:84% So alkaline earth would be something like calcium 00:48:12.330 --> 00:48:14.410 align:middle line:90% plus 2 valence state. 00:48:14.410 --> 00:48:16.390 align:middle line:84% If it's calcium, you put it in the network, 00:48:16.390 --> 00:48:18.330 align:middle line:90% it's still a network modifier. 00:48:18.330 --> 00:48:24.370 align:middle line:84% Each calcium creates, actually, two non-bridging oxygen because 00:48:24.370 --> 00:48:26.070 align:middle line:90% of the plus 2 valence state. 00:48:26.070 --> 00:48:29.690 align:middle line:90% 00:48:29.690 --> 00:48:33.930 align:middle line:84% So similar to alkaline silicate glasses, 00:48:33.930 --> 00:48:37.690 align:middle line:84% alkaline earth silicate glasses can also decrease the network 00:48:37.690 --> 00:48:39.250 align:middle line:90% connectivity. 00:48:39.250 --> 00:48:41.710 align:middle line:84% And you have all the similar kind of a property evolution 00:48:41.710 --> 00:48:45.110 align:middle line:84% [INAUDIBLE], but to a much lesser extent 00:48:45.110 --> 00:48:49.550 align:middle line:84% compared to alkaline silicate glass because calcium 00:48:49.550 --> 00:48:51.010 align:middle line:90% is two-fold coordinated. 00:48:51.010 --> 00:48:53.510 align:middle line:84% So it means that you still have some connection 00:48:53.510 --> 00:48:55.510 align:middle line:84% between these two oxygen atoms through 00:48:55.510 --> 00:48:58.030 align:middle line:90% electrostatic interaction. 00:48:58.030 --> 00:49:00.530 align:middle line:84% So you break up the network, but not fully. 00:49:00.530 --> 00:49:03.790 align:middle line:84% You still maintain some connectivity there. 00:49:03.790 --> 00:49:08.670 align:middle line:84% And that's why this kind of alkaline, alkaline earth 00:49:08.670 --> 00:49:12.030 align:middle line:84% glasses, they tend to have a better chemical 00:49:12.030 --> 00:49:19.950 align:middle line:84% durability compared to just pure alkaline silicate glass. 00:49:19.950 --> 00:49:23.350 align:middle line:84% But it also inherits the same advantage, 00:49:23.350 --> 00:49:25.810 align:middle line:84% that you don't need a very high-process temperature, 00:49:25.810 --> 00:49:28.590 align:middle line:84% such as in the case of pure silica. 00:49:28.590 --> 00:49:35.210 align:middle line:84% And that's why the everyday glasses we use, 00:49:35.210 --> 00:49:38.150 align:middle line:84% they pretty much all fall in this category, alkaline, 00:49:38.150 --> 00:49:40.370 align:middle line:90% alkaline earth silicate glass. 00:49:40.370 --> 00:49:43.170 align:middle line:84% You can strike this balance between chemical durability 00:49:43.170 --> 00:49:45.450 align:middle line:90% and processability. 00:49:45.450 --> 00:49:46.930 align:middle line:90% Yes? 00:49:46.930 --> 00:49:51.090 align:middle line:84% AUDIENCE: Why or what's the benefit of having alkali 00:49:51.090 --> 00:49:54.368 align:middle line:84% as well as alkaline earth versus just alkaline? 00:49:54.368 --> 00:49:56.410 align:middle line:84% JUEJUN HU: Alkaline is more effective in lowering 00:49:56.410 --> 00:49:57.750 align:middle line:90% the processing temperature. 00:49:57.750 --> 00:49:58.610 align:middle line:90% AUDIENCE: Oh. 00:49:58.610 --> 00:50:01.010 align:middle line:84% JUEJUN HU: Yeah, that's the idea. 00:50:01.010 --> 00:50:03.370 align:middle line:84% Yeah, and that's what actually allows people to actually 00:50:03.370 --> 00:50:05.745 align:middle line:84% utilize this glass material back from Ancient Roman times 00:50:05.745 --> 00:50:07.912 align:middle line:84% because, at that time, people were not able to reach 00:50:07.912 --> 00:50:08.890 align:middle line:90% very high temperature. 00:50:08.890 --> 00:50:12.890 align:middle line:84% And, again, the origin of where glass comes from, nobody 00:50:12.890 --> 00:50:14.010 align:middle line:90% really knows. 00:50:14.010 --> 00:50:17.610 align:middle line:84% But accidentally, I think people just mixed some of these oxides 00:50:17.610 --> 00:50:18.950 align:middle line:90% together with sand. 00:50:18.950 --> 00:50:20.950 align:middle line:84% And they found that they can actually melt sand, 00:50:20.950 --> 00:50:22.690 align:middle line:84% which, otherwise, we would not be able to do. 00:50:22.690 --> 00:50:24.810 align:middle line:84% And that transparent substance you get in the end 00:50:24.810 --> 00:50:26.170 align:middle line:90% is actually glass. 00:50:26.170 --> 00:50:31.730 align:middle line:84% AUDIENCE: So does the oxygen-calcium-oxygen bridge 00:50:31.730 --> 00:50:36.100 align:middle line:84% create any of the lower effectivity? 00:50:36.100 --> 00:50:36.800 align:middle line:90% JUEJUN HU: Yeah. 00:50:36.800 --> 00:50:39.620 align:middle line:84% AUDIENCE: Is it just like an alternative 00:50:39.620 --> 00:50:44.620 align:middle line:84% to the unstable regular alkaline? 00:50:44.620 --> 00:50:45.760 align:middle line:90% JUEJUN HU: Basically, yes. 00:50:45.760 --> 00:50:47.580 align:middle line:90% It's sort of like-- 00:50:47.580 --> 00:50:49.100 align:middle line:84% they are still connected together. 00:50:49.100 --> 00:50:49.460 align:middle line:90% AUDIENCE: Yeah. 00:50:49.460 --> 00:50:51.085 align:middle line:84% JUEJUN HU: It's just weaker connection. 00:50:51.085 --> 00:50:53.448 align:middle line:84% It's no longer a very strong SiO covalent bond. 00:50:53.448 --> 00:50:55.240 align:middle line:84% It's this kind of electrostatic attraction. 00:50:55.240 --> 00:50:57.520 align:middle line:84% It's weaker, but it's still connected together. 00:50:57.520 --> 00:51:00.575 align:middle line:84% AUDIENCE: Do you can get crazier angles or something? 00:51:00.575 --> 00:51:02.700 align:middle line:84% JUEJUN HU: Actually, you can because, again the two 00:51:02.700 --> 00:51:04.880 align:middle line:84% tetrahedra are not really connected together. 00:51:04.880 --> 00:51:07.320 align:middle line:84% This ionic interaction is electrostatic. 00:51:07.320 --> 00:51:08.320 align:middle line:90% So it's not directional. 00:51:08.320 --> 00:51:13.900 align:middle line:84% So you can actually twist it at all angles, yeah. 00:51:13.900 --> 00:51:14.520 align:middle line:90% Yes? 00:51:14.520 --> 00:51:16.140 align:middle line:84% AUDIENCE: Well, look at the chemical formula. 00:51:16.140 --> 00:51:16.780 align:middle line:90% JUEJUN HU: Yes. 00:51:16.780 --> 00:51:18.860 align:middle line:84% AUDIENCE: And thinking about the 3D structure, 00:51:18.860 --> 00:51:20.680 align:middle line:84% should we think about, more or less, 00:51:20.680 --> 00:51:23.820 align:middle line:84% it's that ratio in a single area, 00:51:23.820 --> 00:51:25.955 align:middle line:90% or just like it's a ratio or-- 00:51:25.955 --> 00:51:27.080 align:middle line:90% JUEJUN HU: It's an average. 00:51:27.080 --> 00:51:27.300 align:middle line:90% AUDIENCE: Oh. 00:51:27.300 --> 00:51:28.620 align:middle line:84% JUEJUN HU: It's an average, yeah. 00:51:28.620 --> 00:51:30.453 align:middle line:84% If you zoom in to every location, obviously, 00:51:30.453 --> 00:51:32.020 align:middle line:84% you get fluctuations of a structure, 00:51:32.020 --> 00:51:33.895 align:middle line:84% and also a little bit of chemical composition 00:51:33.895 --> 00:51:35.880 align:middle line:90% as well, yeah. 00:51:35.880 --> 00:51:37.780 align:middle line:84% Yeah, I'm going to talk about this one. 00:51:37.780 --> 00:51:39.980 align:middle line:84% So this is the typical glass you will get. 00:51:39.980 --> 00:51:41.300 align:middle line:90% This is called soda lime glass. 00:51:41.300 --> 00:51:42.640 align:middle line:90% This guy is soda. 00:51:42.640 --> 00:51:44.760 align:middle line:90% This is a lime. 00:51:44.760 --> 00:51:46.220 align:middle line:84% So this is called soda lime glass. 00:51:46.220 --> 00:51:47.970 align:middle line:84% Now, what's quite remarkable, you may see, 00:51:47.970 --> 00:51:50.040 align:middle line:84% this is a very weird composition. 00:51:50.040 --> 00:51:52.255 align:middle line:90% It's not any integer numbers. 00:51:52.255 --> 00:51:54.880 align:middle line:84% And what's even more remarkable is, if you go around the world, 00:51:54.880 --> 00:51:56.500 align:middle line:84% you look at glasses of different applications, 00:51:56.500 --> 00:51:59.300 align:middle line:84% whether it's windowpane glasses, whether it's container glasses. 00:51:59.300 --> 00:52:03.240 align:middle line:84% Or you go to Ancient Roman times or you go to Medieval Venetians, 00:52:03.240 --> 00:52:05.480 align:middle line:84% they more or less all converge on this composition, 00:52:05.480 --> 00:52:07.340 align:middle line:84% a few percent around their composition. 00:52:07.340 --> 00:52:09.383 align:middle line:90% 00:52:09.383 --> 00:52:11.800 align:middle line:84% Later on, we're going to show you that this composition is 00:52:11.800 --> 00:52:12.883 align:middle line:90% actually quite remarkable. 00:52:12.883 --> 00:52:16.000 align:middle line:84% It corresponds to the most stable glass composition, 00:52:16.000 --> 00:52:19.040 align:middle line:84% specifically for this ratio I'm showing here. 00:52:19.040 --> 00:52:21.463 align:middle line:84% All right, I'm going to leave it as a little question 00:52:21.463 --> 00:52:23.880 align:middle line:84% that we're going to address later when we talk about glass 00:52:23.880 --> 00:52:26.360 align:middle line:84% stability, why you get these kind of very weird numbers 00:52:26.360 --> 00:52:29.160 align:middle line:90% there. 00:52:29.160 --> 00:52:33.740 align:middle line:84% So now I will actually try to do a little bit of demo here. 00:52:33.740 --> 00:52:37.155 align:middle line:84% I promise you that I'm going to show you that silica glasses-- 00:52:37.155 --> 00:52:38.280 align:middle line:90% AUDIENCE: Excuse me, folks. 00:52:38.280 --> 00:52:38.905 align:middle line:90% JUEJUN HU: Yes? 00:52:38.905 --> 00:52:42.060 align:middle line:90% AUDIENCE: [INAUDIBLE] oh. 00:52:42.060 --> 00:52:43.760 align:middle line:90% Yeah, excuse me. 00:52:43.760 --> 00:52:46.300 align:middle line:90% 00:52:46.300 --> 00:52:48.580 align:middle line:84% JUEJUN HU: I mentioned that silica glasses 00:52:48.580 --> 00:52:50.760 align:middle line:84% has a very low-thermal expansion coefficient. 00:52:50.760 --> 00:52:54.700 align:middle line:84% So it's extremely thermal shock resistant versus other glasses, 00:52:54.700 --> 00:53:00.660 align:middle line:84% like soda lime, because of the lower network connectivity, 00:53:00.660 --> 00:53:03.060 align:middle line:84% you now have a much higher thermal expansion coefficient, 00:53:03.060 --> 00:53:04.160 align:middle line:90% about 20 times higher. 00:53:04.160 --> 00:53:09.620 align:middle line:84% So what I have here, I actually have some silica glass slides. 00:53:09.620 --> 00:53:10.640 align:middle line:90% Let me open it up. 00:53:10.640 --> 00:53:15.980 align:middle line:90% 00:53:15.980 --> 00:53:16.480 align:middle line:90% Oh. 00:53:16.480 --> 00:53:22.700 align:middle line:90% 00:53:22.700 --> 00:53:24.400 align:middle line:84% Any of you have scissors or something? 00:53:24.400 --> 00:53:25.370 align:middle line:90% AUDIENCE: Yeah. 00:53:25.370 --> 00:53:27.720 align:middle line:90% [LAUGHTER] 00:53:27.720 --> 00:53:29.400 align:middle line:90% AUDIENCE: I'll take this one. 00:53:29.400 --> 00:53:30.900 align:middle line:90% AUDIENCE: [LAUGHS] 00:53:30.900 --> 00:53:32.720 align:middle line:90% JUEJUN HU: Just cut it open. 00:53:32.720 --> 00:53:34.512 align:middle line:84% AUDIENCE: It's so easy [INAUDIBLE]. 00:53:34.512 --> 00:53:36.220 align:middle line:84% AUDIENCE: You can also reach for a knife. 00:53:36.220 --> 00:53:39.552 align:middle line:90% [CHUCKLING] 00:53:39.552 --> 00:53:41.920 align:middle line:90% 00:53:41.920 --> 00:53:44.640 align:middle line:90% This is my third one. 00:53:44.640 --> 00:53:45.600 align:middle line:90% JUEJUN HU: There we go. 00:53:45.600 --> 00:53:47.000 align:middle line:90% AUDIENCE: What was it? 00:53:47.000 --> 00:53:48.020 align:middle line:90% The compass? 00:53:48.020 --> 00:53:50.772 align:middle line:90% [LAUGHS] No, the caliper. 00:53:50.772 --> 00:53:51.480 align:middle line:90% This is so much-- 00:53:51.480 --> 00:53:53.200 align:middle line:90% [INTERPOSING VOICES] 00:53:53.200 --> 00:53:54.050 align:middle line:90% 00:53:54.050 --> 00:53:56.800 align:middle line:90% AUDIENCE: Should we-- 00:53:56.800 --> 00:53:58.240 align:middle line:90% AUDIENCE: We have a good class. 00:53:58.240 --> 00:54:00.698 align:middle line:84% And Kurt was like, how was it [INAUDIBLE] caliper. 00:54:00.698 --> 00:54:02.240 align:middle line:84% JUEJUN HU: All right, now we have it. 00:54:02.240 --> 00:54:04.285 align:middle line:84% AUDIENCE: Four people pulled out [INAUDIBLE]. 00:54:04.285 --> 00:54:06.160 align:middle line:84% JUEJUN HU: You don't really see a difference. 00:54:06.160 --> 00:54:07.840 align:middle line:90% They look all the same. 00:54:07.840 --> 00:54:10.028 align:middle line:90% This is silica, soda lime. 00:54:10.028 --> 00:54:11.820 align:middle line:84% Let me see when the temperature gets there. 00:54:11.820 --> 00:54:14.900 align:middle line:90% 00:54:14.900 --> 00:54:19.640 align:middle line:84% So what I do, I set the hot plate to 400 degrees Celsius. 00:54:19.640 --> 00:54:22.520 align:middle line:84% I'm just going to place it here for-- you can even-- 00:54:22.520 --> 00:54:23.860 align:middle line:90% any of you want to time it? 00:54:23.860 --> 00:54:25.300 align:middle line:90% Let's be a bit more consistent. 00:54:25.300 --> 00:54:27.360 align:middle line:84% I'll put it there for 30 seconds, throw it into water, 00:54:27.360 --> 00:54:28.485 align:middle line:90% and let's see what happens. 00:54:28.485 --> 00:54:31.370 align:middle line:90% 00:54:31.370 --> 00:54:32.670 align:middle line:90% I can already smell something. 00:54:32.670 --> 00:54:33.410 align:middle line:90% I don't know what they put here. 00:54:33.410 --> 00:54:35.690 align:middle line:84% AUDIENCE: You can see the surface is smoking. 00:54:35.690 --> 00:54:37.273 align:middle line:84% JUEJUN HU: I just grab it from my lab. 00:54:37.273 --> 00:54:39.482 align:middle line:84% I really don't know what my student is using them for 00:54:39.482 --> 00:54:40.150 align:middle line:90% to heat it up. 00:54:40.150 --> 00:54:44.630 align:middle line:84% So I assume it's not something harmful. 00:54:44.630 --> 00:54:47.010 align:middle line:90% AUDIENCE: [LAUGHS] 00:54:47.010 --> 00:54:49.490 align:middle line:84% JUEJUN HU: Otherwise, EHS is going to come and chase me. 00:54:49.490 --> 00:54:50.870 align:middle line:90% AUDIENCE: Oh, [INAUDIBLE]. 00:54:50.870 --> 00:54:53.490 align:middle line:90% 00:54:53.490 --> 00:54:56.310 align:middle line:84% AUDIENCE: No, you're the most honest woman. 00:54:56.310 --> 00:54:58.930 align:middle line:90% AUDIENCE: [CHUCKLES] 00:54:58.930 --> 00:55:06.450 align:middle line:84% JUEJUN HU: All right, so I think it's coming up, if you want to-- 00:55:06.450 --> 00:55:08.030 align:middle line:84% I think 300, probably, is enough. 00:55:08.030 --> 00:55:09.710 align:middle line:90% Let me try to stabilize it here. 00:55:09.710 --> 00:55:12.810 align:middle line:90% 00:55:12.810 --> 00:55:25.010 align:middle line:90% Just do 350, all right? 00:55:25.010 --> 00:55:26.190 align:middle line:90% All right, 330. 00:55:26.190 --> 00:55:27.050 align:middle line:90% We're right there. 00:55:27.050 --> 00:55:28.990 align:middle line:90% So any of you want to count? 00:55:28.990 --> 00:55:32.610 align:middle line:84% I'll try to put it in the same position, 30 seconds, 1, 2, 3. 00:55:32.610 --> 00:55:35.350 align:middle line:90% 00:55:35.350 --> 00:55:39.190 align:middle line:84% AUDIENCE: And this one is silica or silicate? 00:55:39.190 --> 00:55:40.712 align:middle line:90% JUEJUN HU: Soda lime. 00:55:40.712 --> 00:55:42.170 align:middle line:84% So it's going to be quite dramatic. 00:55:42.170 --> 00:55:47.152 align:middle line:90% 00:55:47.152 --> 00:55:48.390 align:middle line:90% AUDIENCE: [LAUGHS] 00:55:48.390 --> 00:55:49.336 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:55:49.336 --> 00:55:50.230 align:middle line:90% JUEJUN HU: Countdown. 00:55:50.230 --> 00:55:52.510 align:middle line:84% Give me a countdown because I need time to grab it. 00:55:52.510 --> 00:56:03.402 align:middle line:84% AUDIENCE: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. 00:56:03.402 --> 00:56:04.773 align:middle line:90% [PHONE RINGING] 00:56:04.773 --> 00:56:06.190 align:middle line:84% AUDIENCE: Oh, it's so [INAUDIBLE]. 00:56:06.190 --> 00:56:09.137 align:middle line:90% JUEJUN HU: All right. 00:56:09.137 --> 00:56:11.470 align:middle line:84% Maybe I should go to a bit-- oh, you can already see it. 00:56:11.470 --> 00:56:12.012 align:middle line:90% AUDIENCE: Oh. 00:56:12.012 --> 00:56:13.393 align:middle line:90% AUDIENCE: Oh. 00:56:13.393 --> 00:56:14.810 align:middle line:84% JUEJUN HU: You can already see it. 00:56:14.810 --> 00:56:15.730 align:middle line:90% I'm going to pass it around. 00:56:15.730 --> 00:56:18.355 align:middle line:84% I don't know if the camera can see it, but it's full of cracks. 00:56:18.355 --> 00:56:20.590 align:middle line:90% AUDIENCE: Yeah. 00:56:20.590 --> 00:56:23.790 align:middle line:84% JUEJUN HU: I will pass it around, take a look. 00:56:23.790 --> 00:56:25.570 align:middle line:90% Yeah, it hasn't break yet. 00:56:25.570 --> 00:56:29.570 align:middle line:90% AUDIENCE: But industrial thing. 00:56:29.570 --> 00:56:32.090 align:middle line:84% AUDIENCE: I'll be so worried if my thing-- 00:56:32.090 --> 00:56:36.730 align:middle line:84% JUEJUN HU: All right, now, this guy, soda lime. 00:56:36.730 --> 00:56:38.048 align:middle line:90% Go. 00:56:38.048 --> 00:56:38.590 align:middle line:90% AUDIENCE: Oh. 00:56:38.590 --> 00:56:43.590 align:middle line:90% 00:56:43.590 --> 00:56:46.890 align:middle line:84% Burgers space is a great name because I like this department. 00:56:46.890 --> 00:56:50.007 align:middle line:90% We just break things. 00:56:50.007 --> 00:56:52.090 align:middle line:84% JUEJUN HU: We are going to break more things later 00:56:52.090 --> 00:56:53.810 align:middle line:84% on in the semester, so don't worry. 00:56:53.810 --> 00:56:54.710 align:middle line:90% There are more. 00:56:54.710 --> 00:56:55.050 align:middle line:84% AUDIENCE: You'll need a hotplate. 00:56:55.050 --> 00:56:56.758 align:middle line:84% AUDIENCE: [INAUDIBLE] put stuff together. 00:56:56.758 --> 00:56:57.810 align:middle line:90% I just want to-- 00:56:57.810 --> 00:56:59.185 align:middle line:84% JUEJUN HU: Give me the countdown? 00:56:59.185 --> 00:57:06.650 align:middle line:84% AUDIENCE: 8, 7, 6, 5, 4, 3, 2, 1. 00:57:06.650 --> 00:57:07.150 align:middle line:90% Oh. 00:57:07.150 --> 00:57:09.915 align:middle line:90% [PHONE RINGING] 00:57:09.915 --> 00:57:10.790 align:middle line:90% JUEJUN HU: All right. 00:57:10.790 --> 00:57:16.490 align:middle line:90% 00:57:16.490 --> 00:57:18.470 align:middle line:84% AUDIENCE: Can I see it for a sec? 00:57:18.470 --> 00:57:20.010 align:middle line:84% JUEJUN HU: It's perfectly intact. 00:57:20.010 --> 00:57:20.802 align:middle line:90% There's some water. 00:57:20.802 --> 00:57:24.070 align:middle line:84% I probably need to wipe it up a little bit. 00:57:24.070 --> 00:57:26.590 align:middle line:90% 00:57:26.590 --> 00:57:29.070 align:middle line:90% I should come with a-- 00:57:29.070 --> 00:57:31.275 align:middle line:90% AUDIENCE: Looks fine to me. 00:57:31.275 --> 00:57:32.650 align:middle line:84% JUEJUN HU: It's perfectly intact. 00:57:32.650 --> 00:57:33.858 align:middle line:90% AUDIENCE: It looks very safe. 00:57:33.858 --> 00:57:36.390 align:middle line:90% 00:57:36.390 --> 00:57:37.230 align:middle line:90% JUEJUN HU: Nothing. 00:57:37.230 --> 00:57:38.070 align:middle line:90% Absolutely nothing. 00:57:38.070 --> 00:57:39.695 align:middle line:84% AUDIENCE: It smells a little bit burnt. 00:57:39.695 --> 00:57:40.730 align:middle line:90% Other than that. 00:57:40.730 --> 00:57:41.958 align:middle line:90% [LAUGHTER] 00:57:41.958 --> 00:57:42.750 align:middle line:90% There's no reason-- 00:57:42.750 --> 00:57:44.070 align:middle line:84% JUEJUN HU: That's a chemical problem we are not 00:57:44.070 --> 00:57:45.550 align:middle line:90% going to address in the class. 00:57:45.550 --> 00:57:48.207 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:57:48.207 --> 00:57:50.290 align:middle line:84% JUEJUN HU: Yeah, you can clearly see a difference. 00:57:50.290 --> 00:57:50.590 align:middle line:90% I know. 00:57:50.590 --> 00:57:53.090 align:middle line:84% Maybe we can-- later on, we can show it under the camera. 00:57:53.090 --> 00:57:53.870 align:middle line:90% AUDIENCE: Yeah. 00:57:53.870 --> 00:57:56.458 align:middle line:90% JUEJUN HU: Yeah. 00:57:56.458 --> 00:57:58.612 align:middle line:84% AUDIENCE: Can you just put it behind like-- 00:57:58.612 --> 00:58:00.570 align:middle line:84% JUEJUN HU: A sheet of paper or something, yeah. 00:58:00.570 --> 00:58:02.312 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:58:02.312 --> 00:58:04.770 align:middle line:84% JUEJUN HU: It'll probably take a separate quick shot there. 00:58:04.770 --> 00:58:06.630 align:middle line:84% AUDIENCE: Can you hold the first one, please? 00:58:06.630 --> 00:58:07.370 align:middle line:90% JUEJUN HU: First one? 00:58:07.370 --> 00:58:07.710 align:middle line:90% AUDIENCE: Yeah. 00:58:07.710 --> 00:58:08.690 align:middle line:90% JUEJUN HU: This is soda lime. 00:58:08.690 --> 00:58:09.590 align:middle line:90% AUDIENCE: This is [INAUDIBLE]. 00:58:09.590 --> 00:58:10.330 align:middle line:90% JUEJUN HU: Can you see it? 00:58:10.330 --> 00:58:11.810 align:middle line:90% Soda lime has lots of cracks. 00:58:11.810 --> 00:58:14.540 align:middle line:90% 00:58:14.540 --> 00:58:16.350 align:middle line:90% AUDIENCE: Yeah, it does. 00:58:16.350 --> 00:58:17.850 align:middle line:84% JUEJUN HU: You can see a difference? 00:58:17.850 --> 00:58:18.150 align:middle line:90% AUDIENCE: Yes. 00:58:18.150 --> 00:58:19.025 align:middle line:90% JUEJUN HU: OK, great. 00:58:19.025 --> 00:58:20.610 align:middle line:90% AUDIENCE: We should [INAUDIBLE]. 00:58:20.610 --> 00:58:23.920 align:middle line:90% 00:58:23.920 --> 00:58:25.680 align:middle line:84% JUEJUN HU: All right, so now you see that. 00:58:25.680 --> 00:58:29.720 align:middle line:84% Well, that's why silica is great for these kind of applications 00:58:29.720 --> 00:58:30.560 align:middle line:90% there. 00:58:30.560 --> 00:58:35.020 align:middle line:84% So now let me switch over from silicate to something else. 00:58:35.020 --> 00:58:37.840 align:middle line:90% Let's talk about borate. 00:58:37.840 --> 00:58:42.540 align:middle line:84% So boron, boron oxide can also form glass in itself. 00:58:42.540 --> 00:58:44.070 align:middle line:90% It's basically B2O3. 00:58:44.070 --> 00:58:45.820 align:middle line:84% The basic structural unit is quite simple. 00:58:45.820 --> 00:58:48.278 align:middle line:84% It's one boron in the center, three oxygens surrounding it. 00:58:48.278 --> 00:58:50.960 align:middle line:84% You form this center, BO3 kind of structure unit, 00:58:50.960 --> 00:58:52.983 align:middle line:84% interlinked to each other to form glass. 00:58:52.983 --> 00:58:55.400 align:middle line:84% Now, one thing I want to mention there is that previously, 00:58:55.400 --> 00:58:57.817 align:middle line:84% in the lecture, I was talking about this fictitious glass, 00:58:57.817 --> 00:59:00.880 align:middle line:84% A2O3, where you form this 2D glass. 00:59:00.880 --> 00:59:05.520 align:middle line:84% I did not mention it as boron because the structure of boron 00:59:05.520 --> 00:59:07.520 align:middle line:90% oxide is actually non-planar. 00:59:07.520 --> 00:59:10.883 align:middle line:84% You still have this kind of BO3 units. 00:59:10.883 --> 00:59:12.300 align:middle line:84% But when they are linked together, 00:59:12.300 --> 00:59:15.440 align:middle line:84% they actually warp out of plane to form this kind of 3D 00:59:15.440 --> 00:59:16.920 align:middle line:90% structure there. 00:59:16.920 --> 00:59:21.140 align:middle line:84% So, basically, that's just boron oxide. 00:59:21.140 --> 00:59:23.300 align:middle line:84% Now, we like to talk about boron oxide 00:59:23.300 --> 00:59:26.240 align:middle line:84% because it has this very unique behavior. 00:59:26.240 --> 00:59:29.780 align:middle line:84% When you start to put alkaline into it, 00:59:29.780 --> 00:59:33.820 align:middle line:84% you can have two kind of structural moieties. 00:59:33.820 --> 00:59:35.700 align:middle line:90% You can have a normal one. 00:59:35.700 --> 00:59:37.960 align:middle line:84% Sodium goes in there, create non-bridging oxygen, 00:59:37.960 --> 00:59:42.040 align:middle line:84% decrease network connectivity, lower processing temperature, 00:59:42.040 --> 00:59:44.500 align:middle line:84% higher diffusion coefficient, all the same. 00:59:44.500 --> 00:59:47.860 align:middle line:84% But you can also have another structural transformation there. 00:59:47.860 --> 00:59:50.540 align:middle line:84% If you think about boron atom, boron have three outer shell 00:59:50.540 --> 00:59:51.780 align:middle line:90% electrons. 00:59:51.780 --> 00:59:54.700 align:middle line:84% You can form three chemical bonds with oxygen, 00:59:54.700 --> 00:59:58.780 align:middle line:84% but this still leaves behind an empty orbit. 00:59:58.780 --> 01:00:00.900 align:middle line:84% Now, sodium is an atom that really 01:00:00.900 --> 01:00:03.620 align:middle line:90% likes to give away electrons. 01:00:03.620 --> 01:00:07.700 align:middle line:84% So the electron can actually be taken up by the boron. 01:00:07.700 --> 01:00:11.420 align:middle line:84% So now boron has one excess electron. 01:00:11.420 --> 01:00:13.900 align:middle line:84% And then this boron, this excess electron 01:00:13.900 --> 01:00:17.300 align:middle line:84% can allow this boron atom to form another chemical bond 01:00:17.300 --> 01:00:21.580 align:middle line:84% with the neighboring oxygen. In this process, 01:00:21.580 --> 01:00:23.763 align:middle line:84% the boron, obviously, becomes negatively charged. 01:00:23.763 --> 01:00:25.680 align:middle line:84% So there's some electrostatic interaction that 01:00:25.680 --> 01:00:29.400 align:middle line:90% then attracts the sodium ion. 01:00:29.400 --> 01:00:33.920 align:middle line:84% But what you end up getting here is that you now 01:00:33.920 --> 01:00:38.040 align:middle line:84% have a four-fold coordinated boron atom because 01:00:38.040 --> 01:00:42.320 align:middle line:90% of the addition of sodium. 01:00:42.320 --> 01:00:47.560 align:middle line:84% And in the process, you increase the network connectivity 01:00:47.560 --> 01:00:48.740 align:middle line:90% instead of decreasing it. 01:00:48.740 --> 01:00:51.900 align:middle line:84% So this is really what's peculiar about boron here. 01:00:51.900 --> 01:00:53.640 align:middle line:84% If you have boron in the network, 01:00:53.640 --> 01:00:56.460 align:middle line:84% sodium can do two things, form NBO. 01:00:56.460 --> 01:01:00.720 align:middle line:84% Or it can induce this, what's called a B3 to B4 conversion. 01:01:00.720 --> 01:01:03.640 align:middle line:84% And they have a completely opposite impact 01:01:03.640 --> 01:01:07.343 align:middle line:90% on the glass property. 01:01:07.343 --> 01:01:08.760 align:middle line:84% One decrease network connectivity. 01:01:08.760 --> 01:01:09.880 align:middle line:84% One increase network connectivity. 01:01:09.880 --> 01:01:10.380 align:middle line:90% Yes? 01:01:10.380 --> 01:01:12.263 align:middle line:84% AUDIENCE: How do you control for [INAUDIBLE]? 01:01:12.263 --> 01:01:13.180 align:middle line:90% JUEJUN HU: Next slide. 01:01:13.180 --> 01:01:15.655 align:middle line:90% [LAUGHTER] 01:01:15.655 --> 01:01:16.780 align:middle line:90% Basically, the composition. 01:01:16.780 --> 01:01:19.180 align:middle line:84% So what I'm showing you here, this is basically just-- 01:01:19.180 --> 01:01:20.860 align:middle line:84% in this case, this is a different kind 01:01:20.860 --> 01:01:22.480 align:middle line:90% of a sodium oxide. 01:01:22.480 --> 01:01:25.060 align:middle line:84% We're all putting them into borate, B2O3. 01:01:25.060 --> 01:01:27.060 align:middle line:84% And what we're seeing here, you follow this kind 01:01:27.060 --> 01:01:28.700 align:middle line:90% of pretty general trend. 01:01:28.700 --> 01:01:31.340 align:middle line:84% Initially, when you start to put sodium in there, 01:01:31.340 --> 01:01:34.460 align:middle line:84% you're introducing B3 to B4 conversion. 01:01:34.460 --> 01:01:36.520 align:middle line:84% So that's why, on the vertical axis, 01:01:36.520 --> 01:01:39.340 align:middle line:84% I'm showing you the fraction of fourfold-coordinated boron. 01:01:39.340 --> 01:01:41.580 align:middle line:84% It monotonically increases initially. 01:01:41.580 --> 01:01:44.180 align:middle line:84% So all the sodium atom you put in there initially, 01:01:44.180 --> 01:01:47.540 align:middle line:84% always introducing this B3 to B4 conversion. 01:01:47.540 --> 01:01:55.180 align:middle line:84% No non-bridging oxygen. Now, beyond a certain point, 01:01:55.180 --> 01:01:58.580 align:middle line:84% then any additional sodium atom in there 01:01:58.580 --> 01:02:01.440 align:middle line:84% or any additional alkaline atom in there, 01:02:01.440 --> 01:02:05.620 align:middle line:84% you're now introducing non-bridging oxygen. 01:02:05.620 --> 01:02:08.620 align:middle line:84% So you can essentially control these two structural moieties 01:02:08.620 --> 01:02:13.460 align:middle line:84% just by changing the composition of the alkaline atom in there. 01:02:13.460 --> 01:02:15.420 align:middle line:90% You first form B3 to B4. 01:02:15.420 --> 01:02:18.390 align:middle line:84% Beyond some point, it becomes NBO. 01:02:18.390 --> 01:02:21.910 align:middle line:84% And that's why now, if you look into all 01:02:21.910 --> 01:02:26.150 align:middle line:84% the different properties of the glass material 01:02:26.150 --> 01:02:29.450 align:middle line:84% as to how it depends on the fraction of your alkaline oxide 01:02:29.450 --> 01:02:30.010 align:middle line:90% in there. 01:02:30.010 --> 01:02:33.470 align:middle line:84% What I'm plotting here, this is a refractive index, density, 01:02:33.470 --> 01:02:35.070 align:middle line:90% glass transition temperature. 01:02:35.070 --> 01:02:37.650 align:middle line:84% This is actually a thermal expansion coefficient. 01:02:37.650 --> 01:02:40.070 align:middle line:84% You notice that they all exhibit some extreme behavior 01:02:40.070 --> 01:02:41.390 align:middle line:90% somewhere in between. 01:02:41.390 --> 01:02:44.550 align:middle line:84% So, for example, if you think about, say, density, 01:02:44.550 --> 01:02:49.290 align:middle line:84% initially, when you start to add in lithium oxide, in this case, 01:02:49.290 --> 01:02:51.113 align:middle line:84% you create this B3 to B4 conversion. 01:02:51.113 --> 01:02:52.530 align:middle line:84% You increase network connectivity. 01:02:52.530 --> 01:02:54.370 align:middle line:84% You have a more tightly bound network. 01:02:54.370 --> 01:02:57.190 align:middle line:84% So you actually increase in density. 01:02:57.190 --> 01:02:59.970 align:middle line:84% At some point, you start to now trigger this NBO formation. 01:02:59.970 --> 01:03:02.512 align:middle line:84% Then you see a decrease in the network connectivity, enhanced 01:03:02.512 --> 01:03:03.110 align:middle line:90% density. 01:03:03.110 --> 01:03:04.730 align:middle line:84% Same thing with refractive index. 01:03:04.730 --> 01:03:07.450 align:middle line:84% Refractive index is actually almost synonymous as density. 01:03:07.450 --> 01:03:09.310 align:middle line:84% It's basically characterized, how 01:03:09.310 --> 01:03:11.910 align:middle line:84% polarizable the electrons are when 01:03:11.910 --> 01:03:14.830 align:middle line:84% they respond to the oscillating electromagnetic field 01:03:14.830 --> 01:03:16.130 align:middle line:90% or incident light. 01:03:16.130 --> 01:03:18.810 align:middle line:84% So if it's more polarizable, you tend to have higher refractive 01:03:18.810 --> 01:03:19.570 align:middle line:90% index. 01:03:19.570 --> 01:03:22.137 align:middle line:84% So if you have a glass network with high density, 01:03:22.137 --> 01:03:24.470 align:middle line:84% in the same volume, you essentially have more electrons, 01:03:24.470 --> 01:03:25.750 align:middle line:90% so it's more polarizable. 01:03:25.750 --> 01:03:27.850 align:middle line:84% Therefore, higher refractive index. 01:03:27.850 --> 01:03:31.370 align:middle line:84% Similarly, for Tg, again, higher network connectivity 01:03:31.370 --> 01:03:34.310 align:middle line:84% gives you a more thermally-stable network. 01:03:34.310 --> 01:03:36.690 align:middle line:90% So you have a higher Tg. 01:03:36.690 --> 01:03:38.810 align:middle line:84% Thermal expansion coefficient, exactly opposite. 01:03:38.810 --> 01:03:41.690 align:middle line:84% More connected network, then you have less room 01:03:41.690 --> 01:03:42.750 align:middle line:90% for thermal expansion. 01:03:42.750 --> 01:03:45.330 align:middle line:84% So you have a lower thermal expansion coefficient. 01:03:45.330 --> 01:03:48.535 align:middle line:90% 01:03:48.535 --> 01:03:50.910 align:middle line:84% Now, if you look into this plot carefully, 01:03:50.910 --> 01:03:54.090 align:middle line:90% you do notice one thing. 01:03:54.090 --> 01:03:56.270 align:middle line:84% The extremum point for these different properties, 01:03:56.270 --> 01:03:57.673 align:middle line:90% they occur at different points. 01:03:57.673 --> 01:03:59.090 align:middle line:84% For thermal expansion coefficient, 01:03:59.090 --> 01:04:01.690 align:middle line:90% for example, the minimum is 20%. 01:04:01.690 --> 01:04:07.290 align:middle line:84% For density, the maximum is somewhere around 40%. 01:04:07.290 --> 01:04:10.410 align:middle line:84% So what this indicates is that the actual structural 01:04:10.410 --> 01:04:12.530 align:middle line:84% transformation is actually a lot more 01:04:12.530 --> 01:04:16.390 align:middle line:84% complicated than the simplified picture I'm giving you here. 01:04:16.390 --> 01:04:20.130 align:middle line:84% Besides this B3 to B4 conversion and then the NBO formation, 01:04:20.130 --> 01:04:23.530 align:middle line:84% thee actually are more than two structural moieties 01:04:23.530 --> 01:04:27.550 align:middle line:84% that's actually introduced when you put alkaline atoms 01:04:27.550 --> 01:04:30.710 align:middle line:90% into a borate network. 01:04:30.710 --> 01:04:33.450 align:middle line:84% The detailed explanation is beyond the scope of this class. 01:04:33.450 --> 01:04:35.270 align:middle line:84% If you're interested, you can read the book 01:04:35.270 --> 01:04:36.910 align:middle line:90% by Shelby, Chapter 5. 01:04:36.910 --> 01:04:38.510 align:middle line:84% He essentially introduces about, there 01:04:38.510 --> 01:04:40.677 align:middle line:84% are multiple structural transformation that actually 01:04:40.677 --> 01:04:42.370 align:middle line:90% takes place in borate glasses. 01:04:42.370 --> 01:04:44.742 align:middle line:84% But for now, for the sake of this class, 01:04:44.742 --> 01:04:46.950 align:middle line:84% what you need to know is that there are, essentially, 01:04:46.950 --> 01:04:48.617 align:middle line:84% these two kinds of structural formations 01:04:48.617 --> 01:04:51.390 align:middle line:84% that give rise to opposite property chains. 01:04:51.390 --> 01:04:54.190 align:middle line:84% Now, one more thing I also want to mention here 01:04:54.190 --> 01:04:57.230 align:middle line:84% is that, if you look at this one, 01:04:57.230 --> 01:05:00.010 align:middle line:84% by tailoring the amount of sodium in there, 01:05:00.010 --> 01:05:01.710 align:middle line:84% you can actually get to some composition 01:05:01.710 --> 01:05:05.070 align:middle line:84% with very low-thermal expansion coefficient compared 01:05:05.070 --> 01:05:07.510 align:middle line:90% to the parent glass. 01:05:07.510 --> 01:05:10.150 align:middle line:84% This is one attractive properties. 01:05:10.150 --> 01:05:12.650 align:middle line:84% That's why people like to add boron 01:05:12.650 --> 01:05:14.150 align:middle line:90% into different kinds of glasses. 01:05:14.150 --> 01:05:17.170 align:middle line:90% 01:05:17.170 --> 01:05:18.810 align:middle line:84% So pure boron glasses, people actually 01:05:18.810 --> 01:05:19.852 align:middle line:90% don't use it quite a lot. 01:05:19.852 --> 01:05:24.302 align:middle line:84% But borosilicate glasses is what people use quite frequently. 01:05:24.302 --> 01:05:26.010 align:middle line:84% So borosilicate glasses, essentially, you 01:05:26.010 --> 01:05:27.210 align:middle line:90% have two glass networm formers. 01:05:27.210 --> 01:05:27.835 align:middle line:90% You have boron. 01:05:27.835 --> 01:05:28.610 align:middle line:90% You have silicon. 01:05:28.610 --> 01:05:30.730 align:middle line:84% Both form the glass network together. 01:05:30.730 --> 01:05:33.090 align:middle line:84% You can then add a little bit alkaline in there. 01:05:33.090 --> 01:05:35.050 align:middle line:84% And what I'm showing in the first bullet point 01:05:35.050 --> 01:05:38.210 align:middle line:84% is how the different chemical compositions affect 01:05:38.210 --> 01:05:39.550 align:middle line:90% the structural transformation. 01:05:39.550 --> 01:05:42.730 align:middle line:84% It's basically controlled by this ratio 01:05:42.730 --> 01:05:47.290 align:middle line:84% here, the ratio between the amount of alkaline oxide 01:05:47.290 --> 01:05:49.250 align:middle line:90% and the boron oxide. 01:05:49.250 --> 01:05:52.250 align:middle line:84% So depending on composition, you may get B3 to B4 01:05:52.250 --> 01:05:53.690 align:middle line:90% or you may get NBO. 01:05:53.690 --> 01:05:54.810 align:middle line:90% Same. 01:05:54.810 --> 01:05:58.130 align:middle line:84% But the idea is that, with some specific combination, 01:05:58.130 --> 01:06:02.530 align:middle line:84% you can introduce a maximum amount of B3 to B4 conversion, 01:06:02.530 --> 01:06:05.050 align:middle line:84% such that you can have a very low-thermal expansion 01:06:05.050 --> 01:06:05.890 align:middle line:90% coefficient. 01:06:05.890 --> 01:06:08.130 align:middle line:84% But at the same time, these glasses 01:06:08.130 --> 01:06:11.760 align:middle line:84% can also be a lot more easier to process compared to silica. 01:06:11.760 --> 01:06:16.180 align:middle line:90% 01:06:16.180 --> 01:06:19.300 align:middle line:84% So that's what made this kind of an alkali borosilicate glass 01:06:19.300 --> 01:06:20.080 align:middle line:90% attractive. 01:06:20.080 --> 01:06:23.588 align:middle line:84% It's like a low-cost replacement of silica 01:06:23.588 --> 01:06:25.380 align:middle line:84% when you have applications, where you don't 01:06:25.380 --> 01:06:28.990 align:middle line:90% want any thermal expansion. 01:06:28.990 --> 01:06:31.980 align:middle line:84% It also provided improved chemical resistance. 01:06:31.980 --> 01:06:34.403 align:middle line:84% Similarly, because of the better network connectivity, 01:06:34.403 --> 01:06:36.320 align:middle line:84% it means that the network is also more stable. 01:06:36.320 --> 01:06:40.460 align:middle line:84% So it's also more resistant to any kind of chemical corrosion. 01:06:40.460 --> 01:06:43.620 align:middle line:84% So one salient example of this kind of a borosilicate glass 01:06:43.620 --> 01:06:45.100 align:middle line:90% is actually Pyrex. 01:06:45.100 --> 01:06:48.060 align:middle line:84% This is a formulation that was developed initially by Corning 01:06:48.060 --> 01:06:49.860 align:middle line:90% about almost a century ago. 01:06:49.860 --> 01:06:53.860 align:middle line:84% And you probably have seen this in labs. 01:06:53.860 --> 01:06:57.100 align:middle line:84% All the lab beakers, you see this one. 01:06:57.100 --> 01:06:58.900 align:middle line:90% I can actually turn around. 01:06:58.900 --> 01:07:01.620 align:middle line:90% You see Pyrex right there. 01:07:01.620 --> 01:07:05.260 align:middle line:84% So these are all made of borosilicate glasses 01:07:05.260 --> 01:07:06.120 align:middle line:90% for obvious reasons. 01:07:06.120 --> 01:07:07.328 align:middle line:90% You need chemical resistance. 01:07:07.328 --> 01:07:09.680 align:middle line:84% You want it to be thermal shock resistant. 01:07:09.680 --> 01:07:13.560 align:middle line:84% People also use it to make high-quality optical elements, 01:07:13.560 --> 01:07:14.300 align:middle line:90% like this one. 01:07:14.300 --> 01:07:16.245 align:middle line:84% This is a large telescope mirror they make out 01:07:16.245 --> 01:07:18.120 align:middle line:84% of borosilicate glass because they don't want 01:07:18.120 --> 01:07:19.240 align:middle line:84% the thermal expansion or temperature 01:07:19.240 --> 01:07:20.865 align:middle line:84% fluctuation to cause any thermal stress 01:07:20.865 --> 01:07:22.408 align:middle line:90% and distort optical properties. 01:07:22.408 --> 01:07:23.700 align:middle line:90% By the way, this is the mirror. 01:07:23.700 --> 01:07:25.760 align:middle line:84% It takes a year to cool down, just 01:07:25.760 --> 01:07:28.600 align:middle line:84% to ensure it's perfectly uniform. 01:07:28.600 --> 01:07:32.000 align:middle line:84% People also use them for space shuttle, the tiles, 01:07:32.000 --> 01:07:33.460 align:middle line:84% to essentially do a thermal shield. 01:07:33.460 --> 01:07:36.060 align:middle line:84% This little black coating on top is actually borosilicate glass. 01:07:36.060 --> 01:07:37.360 align:middle line:84% They mix it with a little bit of carbon 01:07:37.360 --> 01:07:39.280 align:middle line:84% to increase thermal emissivity, so that heat 01:07:39.280 --> 01:07:40.740 align:middle line:90% can escape more efficiently. 01:07:40.740 --> 01:07:41.323 align:middle line:90% But same idea. 01:07:41.323 --> 01:07:43.282 align:middle line:84% You want to minimize any kind of thermal stress 01:07:43.282 --> 01:07:45.400 align:middle line:84% if you don't want to have a-- that's why you want 01:07:45.400 --> 01:07:47.320 align:middle line:90% to eliminate thermal expansion. 01:07:47.320 --> 01:07:50.280 align:middle line:84% Now, speaking of Pyrex, any of you 01:07:50.280 --> 01:07:51.940 align:middle line:90% have this Pyrex ware at home? 01:07:51.940 --> 01:07:54.760 align:middle line:90% 01:07:54.760 --> 01:07:56.220 align:middle line:90% They are not borosilicate. 01:07:56.220 --> 01:07:59.520 align:middle line:90% 01:07:59.520 --> 01:08:02.360 align:middle line:84% Now you have to be careful here when you get Pyrex. 01:08:02.360 --> 01:08:08.500 align:middle line:84% This one, this is all capital or uppercase PYREX, as you can see. 01:08:08.500 --> 01:08:13.540 align:middle line:84% What you have in your kitchen is all lowercase. 01:08:13.540 --> 01:08:15.880 align:middle line:84% Lowercase Pyrex is soda lime glass. 01:08:15.880 --> 01:08:18.580 align:middle line:84% It's just basically tempered soda lime glass. 01:08:18.580 --> 01:08:21.020 align:middle line:84% If you search online, you'll find lots of YouTube videos, 01:08:21.020 --> 01:08:22.120 align:middle line:90% like Pyrex explosion. 01:08:22.120 --> 01:08:23.740 align:middle line:90% That's all lowercase Pyrex. 01:08:23.740 --> 01:08:27.520 align:middle line:84% If you want a real, real borosilicate glass, 01:08:27.520 --> 01:08:32.003 align:middle line:84% you have to be all uppercase PYREX. 01:08:32.003 --> 01:08:33.420 align:middle line:84% Basically, Corning, at some point, 01:08:33.420 --> 01:08:35.000 align:middle line:90% sold a brand to Work Kitchens. 01:08:35.000 --> 01:08:36.960 align:middle line:84% And then they start to make it out of other kinds of glasses. 01:08:36.960 --> 01:08:38.377 align:middle line:84% So I'm not going to get into that. 01:08:38.377 --> 01:08:41.760 align:middle line:84% But bottom line, not all Pyrex is borosilicate. 01:08:41.760 --> 01:08:44.859 align:middle line:84% If you go to Amazon, some vendors 01:08:44.859 --> 01:08:46.859 align:middle line:84% claim they sell borosilicate stuff. 01:08:46.859 --> 01:08:49.100 align:middle line:90% It may not be true. 01:08:49.100 --> 01:08:51.060 align:middle line:84% I actually have left angry comments like, 01:08:51.060 --> 01:08:53.060 align:middle line:90% this is not borosilicate. 01:08:53.060 --> 01:08:55.779 align:middle line:84% That's just me ranting about people 01:08:55.779 --> 01:08:59.460 align:middle line:84% using the term for incorrect competitions. 01:08:59.460 --> 01:09:03.340 align:middle line:84% All right, any more questions about borosilicate? 01:09:03.340 --> 01:09:06.300 align:middle line:84% So then I can also quickly talk about this, 01:09:06.300 --> 01:09:09.560 align:middle line:90% another one, aluminum silicate. 01:09:09.560 --> 01:09:12.825 align:middle line:84% Aluminum silicate is actually quite important for later on, 01:09:12.825 --> 01:09:15.200 align:middle line:84% especially when we talk about applications where you need 01:09:15.200 --> 01:09:16.580 align:middle line:90% good mechanical properties. 01:09:16.580 --> 01:09:19.859 align:middle line:84% All the carbon glasses for smartphones, 01:09:19.859 --> 01:09:22.279 align:middle line:84% for mobile electronic devices, they probably all 01:09:22.279 --> 01:09:24.439 align:middle line:90% contain aluminum. 01:09:24.439 --> 01:09:27.298 align:middle line:84% So aluminum is also three-fold coordinated. 01:09:27.298 --> 01:09:28.840 align:middle line:84% It has similar properties-- although, 01:09:28.840 --> 01:09:32.760 align:middle line:84% similar to a boron there-- in that it can either be a metal. 01:09:32.760 --> 01:09:34.840 align:middle line:84% So introducing each aluminum atom, 01:09:34.840 --> 01:09:38.399 align:middle line:84% actually, introducing three non-bridging oxygen. 01:09:38.399 --> 01:09:42.760 align:middle line:84% But under certain circumstances, aluminum 01:09:42.760 --> 01:09:44.580 align:middle line:90% can also become a glass former. 01:09:44.580 --> 01:09:47.680 align:middle line:90% 01:09:47.680 --> 01:09:50.479 align:middle line:84% You can basically have this kind of a four-fold 01:09:50.479 --> 01:09:56.488 align:middle line:84% coordinate aluminum similar to the B4 structural unit, 01:09:56.488 --> 01:09:58.780 align:middle line:84% so that you actually increase the network connectivity. 01:09:58.780 --> 01:10:00.920 align:middle line:84% And that's, again, entirely controlled 01:10:00.920 --> 01:10:03.385 align:middle line:84% by the stoichiometry of the glass. 01:10:03.385 --> 01:10:05.510 align:middle line:84% So that's why I'm showing this property chain here, 01:10:05.510 --> 01:10:07.970 align:middle line:84% basically, how the activation energy of conductivity 01:10:07.970 --> 01:10:09.930 align:middle line:90% varies as a function of ratio. 01:10:09.930 --> 01:10:12.610 align:middle line:84% You see a minimum there, which corresponds to the transition. 01:10:12.610 --> 01:10:14.277 align:middle line:84% You are going from, essentially, there's 01:10:14.277 --> 01:10:17.710 align:middle line:84% an aluminum foil connection now transitioning into forming NBO. 01:10:17.710 --> 01:10:19.710 align:middle line:84% So that's why there's an inflection point there. 01:10:19.710 --> 01:10:23.650 align:middle line:90% 01:10:23.650 --> 01:10:25.530 align:middle line:90% Good? 01:10:25.530 --> 01:10:27.903 align:middle line:84% All right, so in the next five minutes-- 01:10:27.903 --> 01:10:29.070 align:middle line:90% we still have five minutes-- 01:10:29.070 --> 01:10:30.370 align:middle line:84% I'm going to talk about, start talking about, 01:10:30.370 --> 01:10:31.750 align:middle line:90% now non-oxide glasses. 01:10:31.750 --> 01:10:36.850 align:middle line:84% So whether it's silica, borates, or aluminosilicate, 01:10:36.850 --> 01:10:39.610 align:middle line:84% these all has oxygen in their glass network. 01:10:39.610 --> 01:10:41.890 align:middle line:84% For some applications, you can actually replace oxygen 01:10:41.890 --> 01:10:44.810 align:middle line:90% with other non-metal atoms. 01:10:44.810 --> 01:10:48.490 align:middle line:84% The simple example would be, you do isoelectronic substitution 01:10:48.490 --> 01:10:51.390 align:middle line:84% of oxygen with other group six elements, 01:10:51.390 --> 01:10:53.410 align:middle line:84% so sulfur, selenium, or tellurium. 01:10:53.410 --> 01:10:55.490 align:middle line:84% The resulting glasses is what's called 01:10:55.490 --> 01:10:59.330 align:middle line:84% chalcogenide glasses, or chalcogenide glasses, 01:10:59.330 --> 01:11:02.210 align:middle line:90% depending on who you ask. 01:11:02.210 --> 01:11:05.870 align:middle line:84% The main difference here is that these atoms are a lot bigger 01:11:05.870 --> 01:11:09.670 align:middle line:84% and heavier compared to oxygen. So bigger atoms means 01:11:09.670 --> 01:11:12.590 align:middle line:84% that the interaction between the atomic nuclei 01:11:12.590 --> 01:11:15.550 align:middle line:84% and the outer shell electron is going to be weaker. 01:11:15.550 --> 01:11:19.070 align:middle line:84% So when you form chemical bonds, chemical bonds 01:11:19.070 --> 01:11:21.110 align:middle line:84% formed by these chalcogenide atoms 01:11:21.110 --> 01:11:23.790 align:middle line:84% tend to be a lot weaker compared to the counterpart, where 01:11:23.790 --> 01:11:27.350 align:middle line:84% you contain oxygen. So immediate consequence 01:11:27.350 --> 01:11:32.207 align:middle line:84% is that they tend to have lower mechanical strength. 01:11:32.207 --> 01:11:33.790 align:middle line:84% So if you recall in the first lecture, 01:11:33.790 --> 01:11:35.510 align:middle line:84% I actually sent around a little piece 01:11:35.510 --> 01:11:37.170 align:middle line:90% of infrared transparent glass. 01:11:37.170 --> 01:11:39.590 align:middle line:84% I have told you that, be careful with that one 01:11:39.590 --> 01:11:40.850 align:middle line:90% because it's quite fragile. 01:11:40.850 --> 01:11:44.950 align:middle line:84% That's a chalcogenide glass They also 01:11:44.950 --> 01:11:46.842 align:middle line:84% tend to have a lower softening temperature. 01:11:46.842 --> 01:11:48.550 align:middle line:84% So you can actually process these glasses 01:11:48.550 --> 01:11:51.910 align:middle line:84% at much lower temperature, which can be an advantage. 01:11:51.910 --> 01:11:54.512 align:middle line:84% People use them a lot for molded optics. 01:11:54.512 --> 01:11:56.970 align:middle line:84% You can actually mold it into different kinds of geometries 01:11:56.970 --> 01:11:59.428 align:middle line:84% by, essentially, apply some heat to introduce viscous flow. 01:11:59.428 --> 01:12:01.637 align:middle line:84% And the temperature you need to actually process that 01:12:01.637 --> 01:12:02.750 align:middle line:90% is actually a lot lower. 01:12:02.750 --> 01:12:04.190 align:middle line:84% So the wear and tear, for example, 01:12:04.190 --> 01:12:06.440 align:middle line:84% for the other kind of molds is actually a lot lower as 01:12:06.440 --> 01:12:09.490 align:middle line:84% compared to when you try to mold oxide glasses. 01:12:09.490 --> 01:12:11.610 align:middle line:84% The reason they attract a lot of attention 01:12:11.610 --> 01:12:14.450 align:middle line:84% mostly is for the optical properties. 01:12:14.450 --> 01:12:16.010 align:middle line:84% They have much lower phonon energy 01:12:16.010 --> 01:12:17.450 align:middle line:84% and, therefore, they are transparent to infrared 01:12:17.450 --> 01:12:18.110 align:middle line:90% radiation. 01:12:18.110 --> 01:12:20.510 align:middle line:84% So the reason it's transparent, basically, 01:12:20.510 --> 01:12:23.130 align:middle line:84% if you think about, essentially, atomic network, 01:12:23.130 --> 01:12:24.410 align:middle line:90% you have chemical bonds. 01:12:24.410 --> 01:12:25.350 align:middle line:90% You have atoms. 01:12:25.350 --> 01:12:26.773 align:middle line:84% You can approximate it essentially 01:12:26.773 --> 01:12:29.190 align:middle line:84% as like you have masses attached to the end of the spring. 01:12:29.190 --> 01:12:31.270 align:middle line:84% That's a very simple model of chemical bonds. 01:12:31.270 --> 01:12:34.030 align:middle line:84% So if you imagine it's attached to the end of the spring, 01:12:34.030 --> 01:12:37.370 align:middle line:84% you have a characteristic vibrational frequency. 01:12:37.370 --> 01:12:40.570 align:middle line:84% And if your instant electromagnetic wave 01:12:40.570 --> 01:12:43.930 align:middle line:84% has a frequency that coincides with the characteristic 01:12:43.930 --> 01:12:46.050 align:middle line:84% vibrational frequency of chemical bonds, 01:12:46.050 --> 01:12:48.810 align:middle line:84% then you can actually convert this optical energy 01:12:48.810 --> 01:12:51.730 align:middle line:84% into the vibrational energy of chemical bonds, which 01:12:51.730 --> 01:12:53.530 align:middle line:84% essentially means the absorption. 01:12:53.530 --> 01:12:55.110 align:middle line:84% The vibrational energy is basically thermal energy. 01:12:55.110 --> 01:12:56.985 align:middle line:84% So you convert, essentially, light into heat. 01:12:56.985 --> 01:13:03.590 align:middle line:84% So for trochozonites, because they have a much heavier atom, 01:13:03.590 --> 01:13:05.590 align:middle line:90% so mass increases. 01:13:05.590 --> 01:13:07.450 align:middle line:84% You also have weaker chemical bonds. 01:13:07.450 --> 01:13:09.750 align:middle line:84% So it means that your spring constant is smaller. 01:13:09.750 --> 01:13:12.310 align:middle line:84% So for simple mechanics, you know 01:13:12.310 --> 01:13:14.190 align:middle line:84% that the characteristic vibrational frequency 01:13:14.190 --> 01:13:16.070 align:middle line:84% of this kind of harmonic oscillator 01:13:16.070 --> 01:13:18.230 align:middle line:84% basically scales with square root of mass 01:13:18.230 --> 01:13:20.330 align:middle line:90% divided by spring constant. 01:13:20.330 --> 01:13:23.747 align:middle line:84% So larger mass, smaller spring constant. 01:13:23.747 --> 01:13:25.830 align:middle line:84% Both point to the fact that they have a much lower 01:13:25.830 --> 01:13:28.470 align:middle line:90% vibrational frequency there. 01:13:28.470 --> 01:13:30.758 align:middle line:84% So as a result, for oxide glasses, 01:13:30.758 --> 01:13:32.550 align:middle line:84% you typically have the absorption somewhere 01:13:32.550 --> 01:13:34.910 align:middle line:90% in the mid-infrared regime. 01:13:34.910 --> 01:13:37.190 align:middle line:84% But for these glasses, the absorption 01:13:37.190 --> 01:13:39.570 align:middle line:84% actually can extend to much longer wavelengths. 01:13:39.570 --> 01:13:42.710 align:middle line:84% They are transparent to thermal infrared wavelengths. 01:13:42.710 --> 01:13:46.510 align:middle line:84% So that's why they are actually quite important for, 01:13:46.510 --> 01:13:49.270 align:middle line:84% essentially, infrared imaging applications, like night vision. 01:13:49.270 --> 01:13:52.430 align:middle line:84% You're looking at, essentially, thermal blackbody radiation 01:13:52.430 --> 01:13:54.570 align:middle line:84% from low-temperature bodies, like human body. 01:13:54.570 --> 01:13:57.170 align:middle line:84% Their wavelength is a lot longer compared to visible light. 01:13:57.170 --> 01:13:59.360 align:middle line:84% So that correspond to lower vibrational frequency, 01:13:59.360 --> 01:14:01.580 align:middle line:84% where it will get absorbed in oxide glasses, 01:14:01.580 --> 01:14:03.860 align:middle line:84% but it remains transparent for chalcogenide glasses. 01:14:03.860 --> 01:14:07.230 align:middle line:90% 01:14:07.230 --> 01:14:09.935 align:middle line:84% They also have enhanced optical nonlinearity, which we are not 01:14:09.935 --> 01:14:11.060 align:middle line:90% going to really talk about. 01:14:11.060 --> 01:14:12.160 align:middle line:84% But that also has to do with the fact 01:14:12.160 --> 01:14:14.160 align:middle line:84% that they have a lot more outer shell electrons. 01:14:14.160 --> 01:14:15.827 align:middle line:84% So those outer shell electrons give rise 01:14:15.827 --> 01:14:19.320 align:middle line:84% to much higher probability and nonlinear optical properties 01:14:19.320 --> 01:14:20.120 align:middle line:90% as well. 01:14:20.120 --> 01:14:24.258 align:middle line:84% So I'm actually going to stop here. 01:14:24.258 --> 01:14:25.800 align:middle line:84% And in the next lecture, we are going 01:14:25.800 --> 01:14:29.040 align:middle line:84% to wrap up different classes of amorphous solids 01:14:29.040 --> 01:14:32.950 align:middle line:84% and start to talk about glass forming. 01:14:32.950 --> 01:14:57.000 align:middle line:90%