WEBVTT 00:00:00.000 --> 00:00:01.955 align:middle line:90% [SQUEAKING] 00:00:01.955 --> 00:00:03.410 align:middle line:90% [RUSTLING] 00:00:03.410 --> 00:00:04.865 align:middle line:90% [CLICKING] 00:00:04.865 --> 00:00:16.567 align:middle line:90% 00:00:16.567 --> 00:00:18.900 align:middle line:84% JUEJUN HU: In the last lecture, we discussed about this. 00:00:18.900 --> 00:00:20.317 align:middle line:84% I'll give you a brief introduction 00:00:20.317 --> 00:00:22.120 align:middle line:84% about this topological constraint theory. 00:00:22.120 --> 00:00:24.000 align:middle line:84% The main takeaway message there is 00:00:24.000 --> 00:00:26.880 align:middle line:84% that you want to have essentially 00:00:26.880 --> 00:00:31.360 align:middle line:84% this isostatic network that strikes a balance between having 00:00:31.360 --> 00:00:34.000 align:middle line:84% sufficiently large barrier to prevent 00:00:34.000 --> 00:00:36.860 align:middle line:84% kinetically fast relaxation to the crystalline state. 00:00:36.860 --> 00:00:41.720 align:middle line:84% And also, you don't have a very deep global minimum 00:00:41.720 --> 00:00:44.080 align:middle line:84% such that thermodynamic force doesn't become too large 00:00:44.080 --> 00:00:47.060 align:middle line:84% and induces a very rapid crystallization. 00:00:47.060 --> 00:00:50.080 align:middle line:84% So now the question of identifying 00:00:50.080 --> 00:00:53.400 align:middle line:84% the most stable glass network becomes essentially looking 00:00:53.400 --> 00:00:54.000 align:middle line:90% for-- 00:00:54.000 --> 00:00:55.720 align:middle line:84% essentially counting for the number of constraints 00:00:55.720 --> 00:00:57.720 align:middle line:84% and equating to the number of degrees of freedom 00:00:57.720 --> 00:00:59.160 align:middle line:90% to get isostatic condition. 00:00:59.160 --> 00:01:01.810 align:middle line:84% So now let's take a look at how we can actually do that. 00:01:01.810 --> 00:01:06.150 align:middle line:84% So what we will do next is then let's 00:01:06.150 --> 00:01:10.990 align:middle line:84% consider a kind of atom that has the N-- essentially 00:01:10.990 --> 00:01:13.950 align:middle line:84% forms N chemical bonds or N nearest neighbors. 00:01:13.950 --> 00:01:17.750 align:middle line:84% And what we'll do is let's try to count essentially-- well, 00:01:17.750 --> 00:01:19.470 align:middle line:90% actually, let's use r, sorry. 00:01:19.470 --> 00:01:20.030 align:middle line:90% r. 00:01:20.030 --> 00:01:23.910 align:middle line:84% This will represent the number of chemical bonds one atom forms 00:01:23.910 --> 00:01:25.455 align:middle line:90% with its neighbors. 00:01:25.455 --> 00:01:27.830 align:middle line:84% Now let's start to count what's the number of constraints 00:01:27.830 --> 00:01:30.190 align:middle line:90% we have in the system here. 00:01:30.190 --> 00:01:36.470 align:middle line:84% So let's start with the bond-bending constraints. 00:01:36.470 --> 00:01:38.550 align:middle line:84% Sorry, bond-stretching constraints. 00:01:38.550 --> 00:01:41.950 align:middle line:84% So these are essentially the bond length. 00:01:41.950 --> 00:01:48.030 align:middle line:84% So if you have r number of chemical bonds, what 00:01:48.030 --> 00:01:51.230 align:middle line:84% we want to argue is that for this particular atom, 00:01:51.230 --> 00:01:54.550 align:middle line:84% it contributes r divided by 2 number 00:01:54.550 --> 00:01:56.910 align:middle line:90% of bond-stretching constraints. 00:01:56.910 --> 00:01:59.450 align:middle line:84% Now the reason we include these two vectors there 00:01:59.450 --> 00:02:01.650 align:middle line:84% is because any chemical bond, this is always 00:02:01.650 --> 00:02:03.090 align:middle line:90% formed between two atoms. 00:02:03.090 --> 00:02:05.570 align:middle line:84% So effectively, it's shared between two atoms. 00:02:05.570 --> 00:02:08.370 align:middle line:84% So if you count the number of constraints 00:02:08.370 --> 00:02:12.810 align:middle line:84% contributed by the center atom, this is really r divided by 2. 00:02:12.810 --> 00:02:14.890 align:middle line:90% OK? 00:02:14.890 --> 00:02:15.390 align:middle line:90% All right. 00:02:15.390 --> 00:02:16.598 align:middle line:90% That's a straightforward one. 00:02:16.598 --> 00:02:18.690 align:middle line:84% Now what about bond-bending constraints. 00:02:18.690 --> 00:02:20.950 align:middle line:84% We are talking about, essentially, bond angles. 00:02:20.950 --> 00:02:25.210 align:middle line:84% So for bond-bending constraints, you 00:02:25.210 --> 00:02:27.690 align:middle line:84% need to have at least two chemical bonds in order 00:02:27.690 --> 00:02:30.650 align:middle line:84% to have a bond angle coming from the same atom. 00:02:30.650 --> 00:02:33.350 align:middle line:84% So what we'll do, let's take a look at a few cases here. 00:02:33.350 --> 00:02:37.150 align:middle line:84% Most simple case, suppose you have two chemical bonds. 00:02:37.150 --> 00:02:41.370 align:middle line:84% This is, in this case, r equals to 2. 00:02:41.370 --> 00:02:44.772 align:middle line:84% What will be the bond-bending constraint in this case? 00:02:44.772 --> 00:02:47.230 align:middle line:84% If it's r equal to 2, that's actually very straightforward. 00:02:47.230 --> 00:02:49.090 align:middle line:90% You get one bond angle. 00:02:49.090 --> 00:02:52.310 align:middle line:84% So there's only one bond-bending constraint. 00:02:52.310 --> 00:02:54.370 align:middle line:90% Easy. 00:02:54.370 --> 00:02:57.520 align:middle line:84% Now what if we add another chemical bond? 00:02:57.520 --> 00:03:03.983 align:middle line:90% We have a 3, 4 coordinated atom. 00:03:03.983 --> 00:03:05.900 align:middle line:84% There are a couple of ways of looking at this. 00:03:05.900 --> 00:03:07.960 align:middle line:84% One is just to count the number of, essentially, 00:03:07.960 --> 00:03:08.940 align:middle line:90% bond angles you have. 00:03:08.940 --> 00:03:10.660 align:middle line:84% You can actually have three different pairs. 00:03:10.660 --> 00:03:13.160 align:middle line:84% You can have this bond angle here between these two chemical 00:03:13.160 --> 00:03:13.880 align:middle line:90% bonds. 00:03:13.880 --> 00:03:16.760 align:middle line:84% You have this one between these two chemical bonds. 00:03:16.760 --> 00:03:19.720 align:middle line:84% You also have another one between these two. 00:03:19.720 --> 00:03:22.400 align:middle line:90% 00:03:22.400 --> 00:03:25.440 align:middle line:90% So in this case, r equal 3. 00:03:25.440 --> 00:03:28.422 align:middle line:84% Then the bond-bending constraint would be 3. 00:03:28.422 --> 00:03:29.880 align:middle line:84% Now the other way to think about it 00:03:29.880 --> 00:03:32.540 align:middle line:84% is, starting from this case here, 00:03:32.540 --> 00:03:35.620 align:middle line:90% you have two neighboring atoms. 00:03:35.620 --> 00:03:37.800 align:middle line:90% Then you add the third one. 00:03:37.800 --> 00:03:41.800 align:middle line:84% So anytime you add a new chemical bond, what the bond 00:03:41.800 --> 00:03:43.680 align:middle line:84% angle does is basically specifies 00:03:43.680 --> 00:03:46.680 align:middle line:84% the relative orientation of that chemical bond with respect 00:03:46.680 --> 00:03:49.640 align:middle line:90% to other chemical bonds. 00:03:49.640 --> 00:03:51.400 align:middle line:84% Now, geometrically, let's translate 00:03:51.400 --> 00:03:54.480 align:middle line:84% to a problem of defining the orientation of a vector 00:03:54.480 --> 00:03:57.620 align:middle line:90% in three-dimensional space. 00:03:57.620 --> 00:04:00.260 align:middle line:84% So the orientation of a vector in a three-dimensional space 00:04:00.260 --> 00:04:03.140 align:middle line:84% can be specified fully using two parameters. 00:04:03.140 --> 00:04:07.540 align:middle line:84% If you think about a spherical coordinate system, 00:04:07.540 --> 00:04:09.402 align:middle line:84% or a polar coordinate system, you 00:04:09.402 --> 00:04:10.860 align:middle line:84% can define the orientation by using 00:04:10.860 --> 00:04:12.940 align:middle line:84% essentially one of the polar angle 00:04:12.940 --> 00:04:15.240 align:middle line:84% and then also the azimuthal angle. 00:04:15.240 --> 00:04:18.300 align:middle line:84% So two parameters fully defines the orientation. 00:04:18.300 --> 00:04:21.140 align:middle line:84% So that's why, when you add a third bond, 00:04:21.140 --> 00:04:25.400 align:middle line:84% you actually add two more bond angles effectively 00:04:25.400 --> 00:04:27.700 align:middle line:90% or bond-bending constraints. 00:04:27.700 --> 00:04:28.640 align:middle line:90% So same thing. 00:04:28.640 --> 00:04:35.380 align:middle line:84% Now if you have another one, if you now go to 4 chemical bonds, 00:04:35.380 --> 00:04:39.080 align:middle line:84% it will start from essentially the r equal to 3 case. 00:04:39.080 --> 00:04:40.420 align:middle line:90% This is already 3. 00:04:40.420 --> 00:04:45.350 align:middle line:84% The new one added, you also need two more new parameters in order 00:04:45.350 --> 00:04:47.600 align:middle line:84% to fully specify the orientation of the chemical bond. 00:04:47.600 --> 00:04:52.180 align:middle line:90% So this will be a 5. 00:04:52.180 --> 00:04:55.050 align:middle line:84% And that's where the generic expression comes in. 00:04:55.050 --> 00:05:01.010 align:middle line:84% This will be 2r minus 3 here for any r that's greater or equal 00:05:01.010 --> 00:05:03.410 align:middle line:90% than 2. 00:05:03.410 --> 00:05:06.770 align:middle line:84% This then defines the number of angles 00:05:06.770 --> 00:05:09.410 align:middle line:84% you will need to fully specify the relative orientation 00:05:09.410 --> 00:05:12.990 align:middle line:84% between the different atoms here and the chemical bonds. 00:05:12.990 --> 00:05:15.250 align:middle line:90% Make sense? 00:05:15.250 --> 00:05:15.750 align:middle line:90% All right. 00:05:15.750 --> 00:05:18.530 align:middle line:84% So now, the next part, we have been 00:05:18.530 --> 00:05:23.290 align:middle line:84% talking about one single kind of atom that has a r coordination 00:05:23.290 --> 00:05:24.570 align:middle line:90% number. 00:05:24.570 --> 00:05:26.970 align:middle line:84% So if you're looking at a glass network, 00:05:26.970 --> 00:05:28.772 align:middle line:84% it consists of different kinds of atoms. 00:05:28.772 --> 00:05:30.230 align:middle line:84% To count the number of constraints, 00:05:30.230 --> 00:05:31.605 align:middle line:84% you need to essentially add it up 00:05:31.605 --> 00:05:33.190 align:middle line:90% over all the constituent atoms. 00:05:33.190 --> 00:05:36.970 align:middle line:84% So the total number of constraints-- 00:05:36.970 --> 00:05:40.850 align:middle line:90% total number of constraints-- 00:05:40.850 --> 00:05:45.170 align:middle line:84% this will be essentially you're summing over all the atoms. 00:05:45.170 --> 00:05:51.530 align:middle line:84% So in your network, if you have a total of N number of atoms, 00:05:51.530 --> 00:05:57.910 align:middle line:84% then for each atom you have essentially r divided by 2 plus 00:05:57.910 --> 00:06:02.830 align:middle line:84% 2r minus 3, which gives you pretty straightforwardly this is 00:06:02.830 --> 00:06:08.610 align:middle line:90% just a 2.5r minus 3. 00:06:08.610 --> 00:06:12.390 align:middle line:90% 00:06:12.390 --> 00:06:15.988 align:middle line:84% Just arithmetic sum of all the constraints 00:06:15.988 --> 00:06:18.030 align:middle line:84% where we have assigned the constraint essentially 00:06:18.030 --> 00:06:21.990 align:middle line:84% to associate with each of the atoms there. 00:06:21.990 --> 00:06:22.490 align:middle line:90% All right. 00:06:22.490 --> 00:06:25.850 align:middle line:84% Now next thing, let me introduce one parameter here. 00:06:25.850 --> 00:06:29.550 align:middle line:90% 00:06:29.550 --> 00:06:32.390 align:middle line:84% This is what we call the essentially average coordination 00:06:32.390 --> 00:06:32.930 align:middle line:90% number. 00:06:32.930 --> 00:06:35.310 align:middle line:84% Specifically, it's called mean coordination number. 00:06:35.310 --> 00:06:40.590 align:middle line:90% 00:06:40.590 --> 00:06:43.990 align:middle line:90% Mean Coordination Number, MCN. 00:06:43.990 --> 00:06:46.990 align:middle line:90% 00:06:46.990 --> 00:06:49.590 align:middle line:84% It's basically just the average, weighted average, 00:06:49.590 --> 00:06:52.460 align:middle line:84% of the coordination number weighted by, essentially, 00:06:52.460 --> 00:06:54.160 align:middle line:84% a fraction of the atoms in the solid. 00:06:54.160 --> 00:06:57.380 align:middle line:84% So what we will do for this one, by definition, you 00:06:57.380 --> 00:07:02.140 align:middle line:84% are summing over all the atoms in the solid 00:07:02.140 --> 00:07:05.860 align:middle line:84% and then dividing by N. This is the total number of chemical 00:07:05.860 --> 00:07:15.200 align:middle line:84% bonds, basically, divided by N. So now comes back here. 00:07:15.200 --> 00:07:17.908 align:middle line:90% 00:07:17.908 --> 00:07:19.700 align:middle line:84% We can simplify the expression a little bit 00:07:19.700 --> 00:07:21.020 align:middle line:90% because we are looking at here. 00:07:21.020 --> 00:07:23.960 align:middle line:84% The sum of a sum, you can directly put the N in there 00:07:23.960 --> 00:07:26.460 align:middle line:84% because, for example, you're summing over constant. 00:07:26.460 --> 00:07:28.780 align:middle line:90% So what you have here? 00:07:28.780 --> 00:07:31.600 align:middle line:84% You have a constant factor of 2.5. 00:07:31.600 --> 00:07:33.880 align:middle line:84% You can pull it out of the summation. 00:07:33.880 --> 00:07:37.620 align:middle line:90% It becomes Nr minus. 00:07:37.620 --> 00:07:38.982 align:middle line:90% 3 is just a constant. 00:07:38.982 --> 00:07:40.440 align:middle line:84% So it's the same for all the atoms. 00:07:40.440 --> 00:07:43.540 align:middle line:90% So it's basically 3N. 00:07:43.540 --> 00:07:46.300 align:middle line:84% Now look at this factor here, r summing over 00:07:46.300 --> 00:07:50.450 align:middle line:84% N. You can now apply that expression there. 00:07:50.450 --> 00:07:58.050 align:middle line:84% And now write it as 2.5 mean coordination number times N 00:07:58.050 --> 00:07:59.090 align:middle line:90% minus 3N. 00:07:59.090 --> 00:08:09.450 align:middle line:90% 00:08:09.450 --> 00:08:12.850 align:middle line:84% Now, last part, we need to equate it 00:08:12.850 --> 00:08:16.810 align:middle line:84% to the number of degrees of freedom. 00:08:16.810 --> 00:08:18.570 align:middle line:84% What's the number of degrees of freedom? 00:08:18.570 --> 00:08:19.750 align:middle line:90% You have N atoms. 00:08:19.750 --> 00:08:22.530 align:middle line:84% Each atom, you need to specify its location with xyz 00:08:22.530 --> 00:08:24.250 align:middle line:90% coordinates in 3D space. 00:08:24.250 --> 00:08:28.530 align:middle line:84% So total number of geometric degree of freedom is 3N. 00:08:28.530 --> 00:08:31.050 align:middle line:90% You equate the two together. 00:08:31.050 --> 00:08:35.330 align:middle line:84% You cancel out N. It becomes very straightforward to see 00:08:35.330 --> 00:08:38.929 align:middle line:84% that r, this mean coordination number or average r, 00:08:38.929 --> 00:08:54.870 align:middle line:84% equals to 6 divided by 2.5, which is 2.4. 00:08:54.870 --> 00:08:57.270 align:middle line:84% Now, what we have seen here up to this point 00:08:57.270 --> 00:09:02.390 align:middle line:84% is that the whole problem of glass network stability 00:09:02.390 --> 00:09:05.310 align:middle line:90% reduces to one single number. 00:09:05.310 --> 00:09:07.910 align:middle line:84% The mean coordination number of the glass network 00:09:07.910 --> 00:09:10.910 align:middle line:90% should equal to 2.4. 00:09:10.910 --> 00:09:13.030 align:middle line:84% Topologically, this also makes sense. 00:09:13.030 --> 00:09:14.990 align:middle line:84% Why is mean coordination number important? 00:09:14.990 --> 00:09:22.100 align:middle line:84% It gives you the connectivity between neighboring atoms, 00:09:22.100 --> 00:09:24.350 align:middle line:84% which, of course, relates to the number of constraints 00:09:24.350 --> 00:09:26.670 align:middle line:90% and the isostatic condition. 00:09:26.670 --> 00:09:28.990 align:middle line:84% So we do expect that this has a very important impact 00:09:28.990 --> 00:09:33.590 align:middle line:84% on the topological behavior of the glass network, this number. 00:09:33.590 --> 00:09:39.190 align:middle line:84% So this number, this is also known as the Phillips' 00:09:39.190 --> 00:09:40.990 align:middle line:90% magic coordination number. 00:09:40.990 --> 00:09:42.870 align:middle line:84% JC Phillips is the physicist who first 00:09:42.870 --> 00:09:45.830 align:middle line:84% proposed this whole concept of topological constraint theory. 00:09:45.830 --> 00:09:47.860 align:middle line:84% And it's also a very popular number. 00:09:47.860 --> 00:09:51.700 align:middle line:84% If you go to glass conferences, they 00:09:51.700 --> 00:09:54.960 align:middle line:84% will be talking about this r equals 2.4 all the time. 00:09:54.960 --> 00:09:55.460 align:middle line:90% OK. 00:09:55.460 --> 00:09:59.540 align:middle line:90% 00:09:59.540 --> 00:10:00.280 align:middle line:90% All right. 00:10:00.280 --> 00:10:03.780 align:middle line:84% So if you're happy with that, now what we want to do next? 00:10:03.780 --> 00:10:05.780 align:middle line:84% Let's look at some examples, how we actually 00:10:05.780 --> 00:10:08.940 align:middle line:84% apply this condition to gauge the glass-forming ability 00:10:08.940 --> 00:10:10.440 align:middle line:84% of different composition of glasses. 00:10:10.440 --> 00:10:13.690 align:middle line:90% So let's start with a-- 00:10:13.690 --> 00:10:16.620 align:middle line:90% I'll pick a random glass. 00:10:16.620 --> 00:10:20.820 align:middle line:84% I have on the slides germanium selenide. 00:10:20.820 --> 00:10:22.860 align:middle line:90% Let's see what we can do. 00:10:22.860 --> 00:10:25.980 align:middle line:90% Let's say germanium sulfide. 00:10:25.980 --> 00:10:27.640 align:middle line:90% I'm not being very creative. 00:10:27.640 --> 00:10:32.900 align:middle line:90% 00:10:32.900 --> 00:10:34.180 align:middle line:90% So germanium sulfide. 00:10:34.180 --> 00:10:37.560 align:middle line:84% Let's say it's germanium 1 minus x Sx. 00:10:37.560 --> 00:10:38.060 align:middle line:90% OK. 00:10:38.060 --> 00:10:42.420 align:middle line:90% 00:10:42.420 --> 00:10:42.920 align:middle line:90% All right. 00:10:42.920 --> 00:10:45.580 align:middle line:84% So how do you calculate the mean coordination number? 00:10:45.580 --> 00:10:48.480 align:middle line:84% As I said, this is basically a weighted average 00:10:48.480 --> 00:10:51.480 align:middle line:84% of the coordination number of these constituent atoms weighted 00:10:51.480 --> 00:10:53.120 align:middle line:90% by this atomic fraction. 00:10:53.120 --> 00:10:55.640 align:middle line:84% So in this case, because we already 00:10:55.640 --> 00:10:58.920 align:middle line:84% have the total mole number normalized to unity, 00:10:58.920 --> 00:11:00.900 align:middle line:84% it just becomes r with two atoms. 00:11:00.900 --> 00:11:03.280 align:middle line:84% Germanium is fourfold coordinated. 00:11:03.280 --> 00:11:09.092 align:middle line:84% So it's 4 times its fraction, which is 1 minus x. 00:11:09.092 --> 00:11:10.800 align:middle line:84% It has to be atomic fraction, by the way. 00:11:10.800 --> 00:11:11.940 align:middle line:90% Don't do it with weight. 00:11:11.940 --> 00:11:13.690 align:middle line:84% This has to be atomic fraction when you're 00:11:13.690 --> 00:11:16.400 align:middle line:90% trying to apply this method. 00:11:16.400 --> 00:11:18.260 align:middle line:90% Sulfur is twofold coordinated. 00:11:18.260 --> 00:11:21.120 align:middle line:90% So it's 2 times x. 00:11:21.120 --> 00:11:22.260 align:middle line:90% Let's see what we get. 00:11:22.260 --> 00:11:24.500 align:middle line:90% This becomes 4 minus 4x plus 2x. 00:11:24.500 --> 00:11:31.240 align:middle line:90% This becomes 4 minus 2x. 00:11:31.240 --> 00:11:42.440 align:middle line:84% We then equate to 2.4, which says now x has to be 0.8. 00:11:42.440 --> 00:11:46.550 align:middle line:84% So plugging that here, it means that the most stable glass 00:11:46.550 --> 00:11:51.070 align:middle line:84% composition in the germanium sulfide family should be-- 00:11:51.070 --> 00:11:54.290 align:middle line:90% this one is 0.2, this is 0.8. 00:11:54.290 --> 00:11:54.790 align:middle line:90% Yeah. 00:11:54.790 --> 00:11:57.550 align:middle line:90% 00:11:57.550 --> 00:11:59.710 align:middle line:90% Basically, GeS4. 00:11:59.710 --> 00:12:02.460 align:middle line:84% And in fact, it does agree with the experiment. 00:12:02.460 --> 00:12:04.710 align:middle line:84% This particular stoichiometry gives you the best glass 00:12:04.710 --> 00:12:05.370 align:middle line:90% stability. 00:12:05.370 --> 00:12:10.030 align:middle line:90% 00:12:10.030 --> 00:12:14.230 align:middle line:84% Now, one thing you also probably notice, on the slides, 00:12:14.230 --> 00:12:18.430 align:middle line:84% I have germanium selenide as an example, versus on the board, 00:12:18.430 --> 00:12:20.270 align:middle line:90% I have germanium sulfide. 00:12:20.270 --> 00:12:24.690 align:middle line:84% The result is exactly the same because sulfur and selenium, 00:12:24.690 --> 00:12:27.636 align:middle line:90% they both have two-- 00:12:27.636 --> 00:12:29.630 align:middle line:90% they form two chemical bonds. 00:12:29.630 --> 00:12:32.870 align:middle line:84% This is one feature of this kind of topological theory. 00:12:32.870 --> 00:12:35.990 align:middle line:84% The chemical nature of the atom actually does not matter. 00:12:35.990 --> 00:12:38.630 align:middle line:84% The only thing that really comes into play 00:12:38.630 --> 00:12:40.230 align:middle line:84% is the connectivity or the number 00:12:40.230 --> 00:12:41.450 align:middle line:90% of chemical bonds they form. 00:12:41.450 --> 00:12:45.300 align:middle line:90% 00:12:45.300 --> 00:12:46.600 align:middle line:90% Now one more exercise. 00:12:46.600 --> 00:12:55.500 align:middle line:84% Let's try, let's say, arsenic selenide. 00:12:55.500 --> 00:12:58.540 align:middle line:84% So same thing, 1 minus x, arsenic, x. 00:12:58.540 --> 00:13:01.600 align:middle line:84% So in this case-- this will be pretty straightforward 00:13:01.600 --> 00:13:03.660 align:middle line:90% now-- arsenic is group 5. 00:13:03.660 --> 00:13:05.900 align:middle line:90% So it's threefold coordinated. 00:13:05.900 --> 00:13:09.900 align:middle line:90% It will become 3 1 minus x. 00:13:09.900 --> 00:13:12.780 align:middle line:84% Sulfur, same thing twofold coordinated. 00:13:12.780 --> 00:13:14.540 align:middle line:90% 2x. 00:13:14.540 --> 00:13:21.220 align:middle line:84% It becomes 3 minus x equals to 2.4, which then tells you 00:13:21.220 --> 00:13:25.380 align:middle line:90% that x has to be 0.6. 00:13:25.380 --> 00:13:30.180 align:middle line:84% And 0.6, if you come back here, it's basically 00:13:30.180 --> 00:13:34.980 align:middle line:84% arsenic 0.4, sulfur 0.6, which you can simplify it 00:13:34.980 --> 00:13:42.400 align:middle line:84% as As2S3, which you notice, this happened 00:13:42.400 --> 00:13:47.200 align:middle line:84% to be the stoichiometric compound composition. 00:13:47.200 --> 00:13:51.320 align:middle line:84% This is a coincidence, but arsenic sulfide indeed 00:13:51.320 --> 00:13:52.660 align:middle line:90% is actually a very stable glass. 00:13:52.660 --> 00:13:55.450 align:middle line:84% It's probably one of the most commonly used chalcogenide 00:13:55.450 --> 00:13:56.700 align:middle line:90% glasses for many applications. 00:13:56.700 --> 00:13:57.540 align:middle line:90% It's very stable. 00:13:57.540 --> 00:14:01.400 align:middle line:90% 00:14:01.400 --> 00:14:01.900 align:middle line:90% All right. 00:14:01.900 --> 00:14:03.820 align:middle line:84% Now, a little bit of exercise for you. 00:14:03.820 --> 00:14:06.560 align:middle line:90% What about SiO2? 00:14:06.560 --> 00:14:10.360 align:middle line:84% Not SiO2, I mean S, silicon oxide glass. 00:14:10.360 --> 00:14:14.200 align:middle line:90% Si, 1 minus x. 00:14:14.200 --> 00:14:16.508 align:middle line:90% Oxygen, x. 00:14:16.508 --> 00:14:17.300 align:middle line:90% What would that be? 00:14:17.300 --> 00:14:21.600 align:middle line:90% 00:14:21.600 --> 00:14:23.480 align:middle line:84% You can see the answer, in fact, without even 00:14:23.480 --> 00:14:24.760 align:middle line:90% doing the calculation. 00:14:24.760 --> 00:14:27.120 align:middle line:84% Because you may have noticed, silicon 00:14:27.120 --> 00:14:29.160 align:middle line:90% is the same as germanium. 00:14:29.160 --> 00:14:31.880 align:middle line:90% Oxygen is the same as sulfur. 00:14:31.880 --> 00:14:33.360 align:middle line:90% So what does that mean? 00:14:33.360 --> 00:14:35.280 align:middle line:84% The most stable composition should be SiO4? 00:14:35.280 --> 00:14:46.150 align:middle line:90% 00:14:46.150 --> 00:14:47.850 align:middle line:84% That does not agree with the experiment. 00:14:47.850 --> 00:14:51.310 align:middle line:84% In fact, SiO2 is one of the most stable glass, as I 00:14:51.310 --> 00:14:55.230 align:middle line:90% will talk about repeatedly. 00:14:55.230 --> 00:14:57.090 align:middle line:90% So why is that? 00:14:57.090 --> 00:15:00.653 align:middle line:90% 00:15:00.653 --> 00:15:02.070 align:middle line:84% Well, this has to actually go back 00:15:02.070 --> 00:15:04.110 align:middle line:84% to something we actually discussed 00:15:04.110 --> 00:15:06.930 align:middle line:90% in the previous lecture. 00:15:06.930 --> 00:15:09.790 align:middle line:90% 00:15:09.790 --> 00:15:13.310 align:middle line:84% So in the first section, when we were talking about liquid, 00:15:13.310 --> 00:15:15.310 align:middle line:84% I mention that because liquid usually 00:15:15.310 --> 00:15:17.890 align:middle line:84% resides at high temperature, at high temperature, 00:15:17.890 --> 00:15:19.650 align:middle line:84% the atoms have lots of kinetic energy. 00:15:19.650 --> 00:15:20.870 align:middle line:90% They can move around. 00:15:20.870 --> 00:15:23.110 align:middle line:84% So it means that some of the constraints 00:15:23.110 --> 00:15:25.932 align:middle line:84% can get compromised, can get relaxed. 00:15:25.932 --> 00:15:27.390 align:middle line:84% I specifically give you the example 00:15:27.390 --> 00:15:29.810 align:middle line:84% here where if you look at this plot, 00:15:29.810 --> 00:15:32.790 align:middle line:84% it says that one of the chemical bond angles, specifically 00:15:32.790 --> 00:15:36.430 align:middle line:84% Si-O-Si bond angle, it shows a very large dispersion 00:15:36.430 --> 00:15:37.990 align:middle line:90% in the glass network. 00:15:37.990 --> 00:15:40.270 align:middle line:84% So effectively, at that high temperature, 00:15:40.270 --> 00:15:43.850 align:middle line:84% this bond angle is being relaxed. 00:15:43.850 --> 00:15:47.630 align:middle line:84% So if this bond angle is being relaxed, 00:15:47.630 --> 00:15:51.130 align:middle line:84% the way we count the constraint has to be modified. 00:15:51.130 --> 00:15:54.210 align:middle line:84% This r equals to 2.4 no longer applies. 00:15:54.210 --> 00:15:57.850 align:middle line:84% What we have to do, we have to go back to the fundamentals. 00:15:57.850 --> 00:16:01.390 align:middle line:84% And let's now redo the bond-counting process, 00:16:01.390 --> 00:16:03.890 align:middle line:84% but now specifically distinguishing between the two 00:16:03.890 --> 00:16:07.690 align:middle line:90% types of bond angles. 00:16:07.690 --> 00:16:12.468 align:middle line:84% So if you still think about the SiO glass structure-- 00:16:12.468 --> 00:16:14.010 align:middle line:84% we have already mentioned about that. 00:16:14.010 --> 00:16:17.450 align:middle line:84% This is basically silicon-oxygen tetrahedra. 00:16:17.450 --> 00:16:19.250 align:middle line:90% They share corners. 00:16:19.250 --> 00:16:22.250 align:middle line:84% And that's how you form the silica glass network. 00:16:22.250 --> 00:16:25.130 align:middle line:90% 00:16:25.130 --> 00:16:28.090 align:middle line:84% Now keep in mind, the bond angle that's getting relaxed 00:16:28.090 --> 00:16:29.330 align:middle line:90% is this one. 00:16:29.330 --> 00:16:32.650 align:middle line:84% It's what links between the two neighboring tetrahedrons. 00:16:32.650 --> 00:16:36.930 align:middle line:84% The bond angle, the oxygen-silicon-oxygen bond 00:16:36.930 --> 00:16:40.800 align:middle line:84% angle, this one is not getting relaxed because the tetrahedra 00:16:40.800 --> 00:16:42.240 align:middle line:90% itself is quite rigid. 00:16:42.240 --> 00:16:45.560 align:middle line:84% So it doesn't really deform, even under high temperature. 00:16:45.560 --> 00:16:48.280 align:middle line:84% So what that means is when we are calculating 00:16:48.280 --> 00:16:52.560 align:middle line:84% the bond-bending constraints, any chemical bond coming 00:16:52.560 --> 00:16:59.000 align:middle line:84% from silicon, we still have those constraints intact. 00:16:59.000 --> 00:17:03.880 align:middle line:84% But for chemical bonds that originate from this oxygen atom, 00:17:03.880 --> 00:17:09.200 align:middle line:84% we should not count the bond-bending constraints. 00:17:09.200 --> 00:17:12.599 align:middle line:84% That's how we discount this particular one. 00:17:12.599 --> 00:17:14.240 align:middle line:84% So now let's go back and take a look 00:17:14.240 --> 00:17:15.660 align:middle line:90% at the number of constraints. 00:17:15.660 --> 00:17:21.160 align:middle line:84% First thing, if you look at the bond-stretching constraints, 00:17:21.160 --> 00:17:21.925 align:middle line:90% it's the same. 00:17:21.925 --> 00:17:24.300 align:middle line:84% Chemical bond angle doesn't really get changed that much. 00:17:24.300 --> 00:17:26.920 align:middle line:84% So the bond-stretching constraints, 00:17:26.920 --> 00:17:28.940 align:middle line:90% it will still be 1/2 r. 00:17:28.940 --> 00:17:31.880 align:middle line:90% 00:17:31.880 --> 00:17:35.400 align:middle line:84% So if you follow the convention we have here-- 00:17:35.400 --> 00:17:40.900 align:middle line:84% let's look at the silica glass with Si x, oxygen, 1 minus x. 00:17:40.900 --> 00:17:43.060 align:middle line:84% Let's use this particular stoichiometry here. 00:17:43.060 --> 00:17:45.500 align:middle line:84% Now let's consider a bond-stretching constraints. 00:17:45.500 --> 00:17:49.520 align:middle line:84% For the bond-stretching constraints, we have 1/2 r here, 00:17:49.520 --> 00:17:51.500 align:middle line:90% which for silicon is 4. 00:17:51.500 --> 00:17:55.500 align:middle line:90% 00:17:55.500 --> 00:17:57.740 align:middle line:84% We then have to times the fraction 00:17:57.740 --> 00:17:58.960 align:middle line:90% of silicon in the network. 00:17:58.960 --> 00:18:01.300 align:middle line:90% So silicon is x in this case. 00:18:01.300 --> 00:18:03.980 align:middle line:84% So if you think about essentially, 00:18:03.980 --> 00:18:07.377 align:middle line:84% effectively, one more of this molecule, then 00:18:07.377 --> 00:18:09.460 align:middle line:84% the more number of the bond-stretching constraints 00:18:09.460 --> 00:18:13.220 align:middle line:84% is going to be what I'm writing here. 00:18:13.220 --> 00:18:17.020 align:middle line:84% So then, for oxygen, again, it's r divided by 2. 00:18:17.020 --> 00:18:18.300 align:middle line:90% Oxygen, r is 2. 00:18:18.300 --> 00:18:19.900 align:middle line:90% So this is 2 divided by 2. 00:18:19.900 --> 00:18:22.980 align:middle line:84% And then times, in this case, 1 minus x. 00:18:22.980 --> 00:18:24.900 align:middle line:90% So let's see what we have here. 00:18:24.900 --> 00:18:28.340 align:middle line:90% This is basically 2x. 00:18:28.340 --> 00:18:30.780 align:middle line:90% This is basically 2 minus-- 00:18:30.780 --> 00:18:34.460 align:middle line:90% sorry, 1 minus x. 00:18:34.460 --> 00:18:40.610 align:middle line:90% So it's 1 plus x. 00:18:40.610 --> 00:18:48.330 align:middle line:90% 00:18:48.330 --> 00:18:51.310 align:middle line:84% So now let's look at bond-bending constraints. 00:18:51.310 --> 00:18:56.530 align:middle line:90% 00:18:56.530 --> 00:19:00.210 align:middle line:84% For bond-bending constraints, we have already did the calculation 00:19:00.210 --> 00:19:03.730 align:middle line:84% that it's given by essentially a 2r minus 3. 00:19:03.730 --> 00:19:05.290 align:middle line:84% But in our calculation, this time, 00:19:05.290 --> 00:19:09.450 align:middle line:84% we should only account for the chemical bonds that originate 00:19:09.450 --> 00:19:10.970 align:middle line:90% from the silicon atom. 00:19:10.970 --> 00:19:13.250 align:middle line:84% So when we apply that to r minus 3 equation, 00:19:13.250 --> 00:19:15.650 align:middle line:84% we should apply only to the silicon atoms. 00:19:15.650 --> 00:19:21.970 align:middle line:84% So for silicon, it's 2r, which is 4, minus 3. 00:19:21.970 --> 00:19:26.250 align:middle line:84% But now we should time it with the fraction of silicon 00:19:26.250 --> 00:19:34.600 align:middle line:84% and drop the second term that relates to oxygen. So 00:19:34.600 --> 00:19:36.660 align:middle line:84% what we have here, 2 times 4 minus 3. 00:19:36.660 --> 00:19:37.280 align:middle line:90% This is 5. 00:19:37.280 --> 00:19:39.120 align:middle line:90% 5 times x. 00:19:39.120 --> 00:19:41.640 align:middle line:90% That's what we have. 00:19:41.640 --> 00:19:43.240 align:middle line:90% 5x. 00:19:43.240 --> 00:19:49.680 align:middle line:84% So now, add up together total number of constraints. 00:19:49.680 --> 00:19:53.280 align:middle line:84% This would be a sum of the two, which just trivially gives you 1 00:19:53.280 --> 00:19:54.460 align:middle line:90% plus 6x. 00:19:54.460 --> 00:19:57.360 align:middle line:90% 00:19:57.360 --> 00:20:01.100 align:middle line:84% We similarly equate it to the number of degrees of freedom. 00:20:01.100 --> 00:20:04.920 align:middle line:90% 00:20:04.920 --> 00:20:06.880 align:middle line:84% Now, the way we are doing it here, 00:20:06.880 --> 00:20:08.960 align:middle line:84% the formula I'm using here, I'm basically 00:20:08.960 --> 00:20:12.820 align:middle line:84% assuming that we have one more of these molecules. 00:20:12.820 --> 00:20:15.600 align:middle line:84% And then the number of constraints 00:20:15.600 --> 00:20:18.520 align:middle line:84% we calculated here, the unit of this one is actually more. 00:20:18.520 --> 00:20:21.280 align:middle line:90% This is 1 plus 6x more. 00:20:21.280 --> 00:20:25.560 align:middle line:84% So for one more of this molecule here, 00:20:25.560 --> 00:20:32.320 align:middle line:84% then the number of degrees of freedom should be 3. 00:20:32.320 --> 00:20:33.940 align:middle line:90% Sorry, it should be just 3. 00:20:33.940 --> 00:20:35.933 align:middle line:90% 3 more. 00:20:35.933 --> 00:20:37.600 align:middle line:84% I should say one more atom, to be exact. 00:20:37.600 --> 00:20:39.500 align:middle line:90% That's confusing. 00:20:39.500 --> 00:20:43.660 align:middle line:84% The total number of atoms, silicon plus oxygen, 00:20:43.660 --> 00:20:44.680 align:middle line:90% equal to 1 mole. 00:20:44.680 --> 00:20:46.138 align:middle line:84% That's the way I'm writing it here. 00:20:46.138 --> 00:20:47.780 align:middle line:84% Because x plus 1 minus x equals 1. 00:20:47.780 --> 00:20:51.740 align:middle line:84% So we have three more of degree of freedom. 00:20:51.740 --> 00:20:56.400 align:middle line:84% If you equate the two, then it's straightforward to see 00:20:56.400 --> 00:21:07.044 align:middle line:90% that our x becomes 0.5. 00:21:07.044 --> 00:21:08.020 align:middle line:90% Hmm? 00:21:08.020 --> 00:21:09.380 align:middle line:90% No, no, sorry. 00:21:09.380 --> 00:21:12.220 align:middle line:90% It should be 1/3. 00:21:12.220 --> 00:21:14.340 align:middle line:90% x is 1/3. 00:21:14.340 --> 00:21:21.480 align:middle line:84% So if x is 1/3, then the condition would exactly be SiO2. 00:21:21.480 --> 00:21:26.195 align:middle line:90% 00:21:26.195 --> 00:21:28.500 align:middle line:84% So now we have agreement with experiment. 00:21:28.500 --> 00:21:32.590 align:middle line:84% SiO2 indeed is a very, very, very stable glass. 00:21:32.590 --> 00:21:36.223 align:middle line:90% 00:21:36.223 --> 00:21:36.890 align:middle line:90% AUDIENCE: Sorry. 00:21:36.890 --> 00:21:39.730 align:middle line:84% Can you just explain the origin of why 00:21:39.730 --> 00:21:42.730 align:middle line:90% we're relaxing the oxygen-- 00:21:42.730 --> 00:21:44.967 align:middle line:90% or the oxygen is similar? 00:21:44.967 --> 00:21:46.550 align:middle line:84% JUEJUN HU: This comes from experiment. 00:21:46.550 --> 00:21:48.708 align:middle line:84% It's actually a bit difficult. In the next slide, 00:21:48.708 --> 00:21:50.250 align:middle line:84% I'm going to show you how we actually 00:21:50.250 --> 00:21:52.290 align:middle line:90% do that, in a couple of slides. 00:21:52.290 --> 00:21:55.930 align:middle line:84% But it's a bit difficult for you to predict a priori which 00:21:55.930 --> 00:21:58.890 align:middle line:84% bonding constraint are relaxed, which ones are not. 00:21:58.890 --> 00:22:05.810 align:middle line:84% So the way we can discount this Si-O-Si bond-angle constraint 00:22:05.810 --> 00:22:08.090 align:middle line:84% is because if you go to experiment, when you actually 00:22:08.090 --> 00:22:10.030 align:middle line:84% do the experiment from diffraction, 00:22:10.030 --> 00:22:12.250 align:middle line:84% you actually measure the distribution 00:22:12.250 --> 00:22:15.810 align:middle line:84% of bond angles in the silica glass network. 00:22:15.810 --> 00:22:18.670 align:middle line:84% What you find out is that instead of having a narrow peak, 00:22:18.670 --> 00:22:20.980 align:middle line:84% you get this very, very broad peak. 00:22:20.980 --> 00:22:22.730 align:middle line:84% If you have a very broad peak, essentially 00:22:22.730 --> 00:22:24.830 align:middle line:84% means that, essentially, between the two chemical bonds, 00:22:24.830 --> 00:22:26.390 align:middle line:84% the bond angle is actually not fixed. 00:22:26.390 --> 00:22:27.150 align:middle line:90% It's very floppy. 00:22:27.150 --> 00:22:28.590 align:middle line:90% You can actually bend it. 00:22:28.590 --> 00:22:31.250 align:middle line:84% So if you can bend it over a large range, 00:22:31.250 --> 00:22:33.790 align:middle line:84% that constraint is no longer existent. 00:22:33.790 --> 00:22:36.750 align:middle line:84% It does not place a constraint in, essentially, 00:22:36.750 --> 00:22:38.590 align:middle line:90% the geometric position of atoms. 00:22:38.590 --> 00:22:40.050 align:middle line:90% So that's why we discount it. 00:22:40.050 --> 00:22:43.870 align:middle line:84% Basically, it depends on our experimental evidence. 00:22:43.870 --> 00:22:48.450 align:middle line:84% And this usually happens actually for oxide glasses, 00:22:48.450 --> 00:22:51.110 align:middle line:84% especially for things like silica. 00:22:51.110 --> 00:22:52.950 align:middle line:84% if you add network modifiers, you 00:22:52.950 --> 00:22:54.970 align:middle line:84% decrease the glass transition temperature, 00:22:54.970 --> 00:22:56.210 align:middle line:90% then this phenomena is OK. 00:22:56.210 --> 00:22:57.630 align:middle line:90% It's not that severe. 00:22:57.630 --> 00:23:00.270 align:middle line:84% The problem with silica is that because it has no network 00:23:00.270 --> 00:23:04.790 align:middle line:84% modifiers, its glass transition temperature is very, very high. 00:23:04.790 --> 00:23:07.230 align:middle line:84% So at the glass-forming temperature, 00:23:07.230 --> 00:23:09.150 align:middle line:84% some of the constraints will be relaxed 00:23:09.150 --> 00:23:11.990 align:middle line:84% because of very high kinetic energy of the atoms. 00:23:11.990 --> 00:23:12.870 align:middle line:90% So that's why. 00:23:12.870 --> 00:23:16.330 align:middle line:84% So that's why I put the statement on top there. 00:23:16.330 --> 00:23:20.190 align:middle line:84% "The constraint number should be evaluated at the glass-forming 00:23:20.190 --> 00:23:22.030 align:middle line:90% temperature." 00:23:22.030 --> 00:23:26.070 align:middle line:84% Because the temperature range where the glass 00:23:26.070 --> 00:23:31.980 align:middle line:84% stability matters is when you're actually trying to form glass. 00:23:31.980 --> 00:23:33.440 align:middle line:84% When you're trying to form glass, 00:23:33.440 --> 00:23:35.160 align:middle line:84% you need to bypass the crystallization. 00:23:35.160 --> 00:23:36.380 align:middle line:90% You need to suppress that. 00:23:36.380 --> 00:23:40.380 align:middle line:84% And so that's why the glass stability should also 00:23:40.380 --> 00:23:42.980 align:middle line:84% be assessed at that particular temperature. 00:23:42.980 --> 00:23:47.620 align:middle line:90% 00:23:47.620 --> 00:23:49.820 align:middle line:84% So for something like silica, that actually 00:23:49.820 --> 00:23:50.840 align:middle line:90% makes a difference. 00:23:50.840 --> 00:23:52.487 align:middle line:84% Now if you look at chalcogenides, 00:23:52.487 --> 00:23:54.320 align:middle line:84% if you look at the example, I'm giving here, 00:23:54.320 --> 00:23:56.120 align:middle line:84% I like to use chalcogenides as an example 00:23:56.120 --> 00:23:57.580 align:middle line:84% not because I myself work on chalcogenides. 00:23:57.580 --> 00:23:59.560 align:middle line:84% It's because chalcogenides, as I mentioned, 00:23:59.560 --> 00:24:02.260 align:middle line:84% they usually typically have low glass transition temperature. 00:24:02.260 --> 00:24:04.880 align:middle line:84% Their transition temperature is like 100, 200 degrees Celsius. 00:24:04.880 --> 00:24:08.620 align:middle line:84% So at that much lower temperature, 00:24:08.620 --> 00:24:11.823 align:middle line:84% most of the constraint is perfectly maintained. 00:24:11.823 --> 00:24:13.740 align:middle line:84% So that's why they serve as very good examples 00:24:13.740 --> 00:24:16.300 align:middle line:84% to actually illustrate the, essentially, efficacy 00:24:16.300 --> 00:24:18.340 align:middle line:90% of the theory there. 00:24:18.340 --> 00:24:20.420 align:middle line:90% OK. 00:24:20.420 --> 00:24:21.140 align:middle line:90% Make sense? 00:24:21.140 --> 00:24:21.820 align:middle line:90% AUDIENCE: Yes. 00:24:21.820 --> 00:24:22.540 align:middle line:90% JUEJUN HU: OK. 00:24:22.540 --> 00:24:23.660 align:middle line:90% Now last point here. 00:24:23.660 --> 00:24:25.700 align:middle line:84% I also have a one question there. 00:24:25.700 --> 00:24:28.770 align:middle line:84% Why does oxides and chalcogenides make good glasses? 00:24:28.770 --> 00:24:36.010 align:middle line:84% Now, if you think about this r equals 2.4 number there, oxygen 00:24:36.010 --> 00:24:38.062 align:middle line:84% and sulfur, they have essentially two. 00:24:38.062 --> 00:24:39.270 align:middle line:90% They form two chemical bonds. 00:24:39.270 --> 00:24:42.010 align:middle line:90% So you have two chemical bonds. 00:24:42.010 --> 00:24:43.650 align:middle line:84% If all the atom has two chemical bonds, 00:24:43.650 --> 00:24:45.775 align:middle line:84% then you can imagine that the best thing you can do 00:24:45.775 --> 00:24:47.450 align:middle line:84% is form essentially long linear chains. 00:24:47.450 --> 00:24:50.530 align:middle line:84% If r equals 2.4, you add some other atoms 00:24:50.530 --> 00:24:51.750 align:middle line:90% with higher valence number. 00:24:51.750 --> 00:24:55.250 align:middle line:84% Essentially, those atoms can serve as cross-linking points. 00:24:55.250 --> 00:24:59.290 align:middle line:84% They then cross-link these long chains to form 3D network. 00:24:59.290 --> 00:25:02.210 align:middle line:84% So topologically, that's part of the reason why 00:25:02.210 --> 00:25:04.823 align:middle line:84% oxygen and chalcogenides, oxides or chalcogenides, 00:25:04.823 --> 00:25:06.490 align:middle line:84% they are preferred as glass constituents 00:25:06.490 --> 00:25:08.782 align:middle line:84% because it's very easy to add some additional elements, 00:25:08.782 --> 00:25:11.110 align:middle line:84% nonmetal elements, to actually reach that 2.4 number. 00:25:11.110 --> 00:25:14.490 align:middle line:90% 00:25:14.490 --> 00:25:15.170 align:middle line:90% OK. 00:25:15.170 --> 00:25:20.330 align:middle line:84% So by the way, in the p-set, I'm actually 00:25:20.330 --> 00:25:21.510 align:middle line:90% giving you one more example. 00:25:21.510 --> 00:25:24.130 align:middle line:84% You remember I mentioned about this soda lime glass 00:25:24.130 --> 00:25:31.350 align:middle line:84% composition, something like 16 Na2O, 10 CaO, 74 SiO2. 00:25:31.350 --> 00:25:34.568 align:middle line:84% In the p-set, which I already posted on the Canvas website, 00:25:34.568 --> 00:25:36.110 align:middle line:84% by the way, you can actually go ahead 00:25:36.110 --> 00:25:38.652 align:middle line:84% and do the calculation for that particular glass composition. 00:25:38.652 --> 00:25:42.950 align:middle line:84% What you'll find out is that r exactly equals 2.4 for that one. 00:25:42.950 --> 00:25:45.870 align:middle line:84% So there's a good reason why people converge 00:25:45.870 --> 00:25:48.910 align:middle line:84% to that particular composition-- because it's a glass stability. 00:25:48.910 --> 00:25:51.730 align:middle line:84% Again, people do it previously empirically. 00:25:51.730 --> 00:25:53.630 align:middle line:84% But now, here's some theoretical insight 00:25:53.630 --> 00:25:55.610 align:middle line:84% to see why that actually matters. 00:25:55.610 --> 00:25:59.670 align:middle line:90% 00:25:59.670 --> 00:26:01.910 align:middle line:84% Now, building a bit more on this concept 00:26:01.910 --> 00:26:03.650 align:middle line:84% of temperature-dependent constraints. 00:26:03.650 --> 00:26:07.190 align:middle line:84% So I've already said that as you raise the temperature, 00:26:07.190 --> 00:26:09.070 align:middle line:84% some of the constraints will start to relax. 00:26:09.070 --> 00:26:13.530 align:middle line:84% So you can further elaborate on this concept. 00:26:13.530 --> 00:26:17.390 align:middle line:84% You can assign one onset temperature or one threshold 00:26:17.390 --> 00:26:20.070 align:middle line:84% temperature to each of the constraints. 00:26:20.070 --> 00:26:22.750 align:middle line:84% Above that temperature, you can consider the constraint 00:26:22.750 --> 00:26:26.540 align:middle line:84% as being absent or getting relaxed. 00:26:26.540 --> 00:26:28.042 align:middle line:84% And that temperature will obviously 00:26:28.042 --> 00:26:30.000 align:middle line:84% be different for different kind of constraints. 00:26:30.000 --> 00:26:33.060 align:middle line:84% So for the more soft bond angles, 00:26:33.060 --> 00:26:36.280 align:middle line:84% like Si-O-Sio, this will relax at low temperature. 00:26:36.280 --> 00:26:38.680 align:middle line:84% But for this one, this is a much more rigid structure. 00:26:38.680 --> 00:26:41.220 align:middle line:84% O-Si-O, this one won't get relaxed. 00:26:41.220 --> 00:26:44.040 align:middle line:84% The bond length, the bond-stretching constraints, 00:26:44.040 --> 00:26:46.100 align:middle line:84% usually, those are also only relaxed 00:26:46.100 --> 00:26:48.220 align:middle line:90% at very high temperature. 00:26:48.220 --> 00:26:52.643 align:middle line:84% So then what you can do is that you can actually now derive-- 00:26:52.643 --> 00:26:54.060 align:middle line:84% if you know that onset temperature 00:26:54.060 --> 00:26:55.660 align:middle line:84% for different constraints, you can now 00:26:55.660 --> 00:27:00.420 align:middle line:84% derive the number of constraints as a function of temperature. 00:27:00.420 --> 00:27:00.960 align:middle line:90% OK? 00:27:00.960 --> 00:27:04.980 align:middle line:90% 00:27:04.980 --> 00:27:08.460 align:middle line:84% Now the other peculiarity I also have to mention here 00:27:08.460 --> 00:27:11.140 align:middle line:84% is that the glass structure can also 00:27:11.140 --> 00:27:15.060 align:middle line:84% be a function of composition and temperature as well. 00:27:15.060 --> 00:27:18.460 align:middle line:84% One good example will be think about borate glasses. 00:27:18.460 --> 00:27:21.620 align:middle line:84% So borate glasses, if you put alkaline in there, 00:27:21.620 --> 00:27:23.960 align:middle line:84% you can get this essentially nonbridging oxygen. 00:27:23.960 --> 00:27:25.740 align:middle line:84% You can get [? BO3-to-BO4 ?] conversion. 00:27:25.740 --> 00:27:28.020 align:middle line:84% So if you want to determine the number of constraints, 00:27:28.020 --> 00:27:29.920 align:middle line:84% it's quite important to decide what 00:27:29.920 --> 00:27:35.187 align:middle line:84% is the structural regime you are located at. 00:27:35.187 --> 00:27:37.520 align:middle line:84% So determining constraints may be a bit more complicated 00:27:37.520 --> 00:27:40.477 align:middle line:84% than just simply counting the number of valence states. 00:27:40.477 --> 00:27:42.560 align:middle line:84% You need to know what structural moieties actually 00:27:42.560 --> 00:27:44.680 align:middle line:90% exists in the gas network. 00:27:44.680 --> 00:27:46.620 align:middle line:84% But if you have that information, 00:27:46.620 --> 00:27:49.200 align:middle line:84% then what you can generate is a plot, 00:27:49.200 --> 00:27:50.340 align:middle line:90% like what I'm showing here. 00:27:50.340 --> 00:27:52.665 align:middle line:84% This is quoted from a paper discussing about this. 00:27:52.665 --> 00:27:54.540 align:middle line:84% I have already posted this paper, by the way, 00:27:54.540 --> 00:27:55.457 align:middle line:90% on the Canvas website. 00:27:55.457 --> 00:27:57.200 align:middle line:84% It's a pretty nice summary about how 00:27:57.200 --> 00:28:00.885 align:middle line:84% people use this theory, not just for predicting glass stability. 00:28:00.885 --> 00:28:02.260 align:middle line:84% So if you look at this plot here, 00:28:02.260 --> 00:28:04.520 align:middle line:84% essentially, what they were doing 00:28:04.520 --> 00:28:06.960 align:middle line:84% there is that, using this topological constraint 00:28:06.960 --> 00:28:10.200 align:middle line:84% theory with the known onset temperature 00:28:10.200 --> 00:28:11.840 align:middle line:84% of different constraints, they can now 00:28:11.840 --> 00:28:14.120 align:middle line:84% determine the number of constraints inside this kind 00:28:14.120 --> 00:28:15.540 align:middle line:90% of a ternary system. 00:28:15.540 --> 00:28:18.480 align:middle line:84% This is actually a alkali-alkaline-earth borate 00:28:18.480 --> 00:28:20.880 align:middle line:90% glass. 00:28:20.880 --> 00:28:23.681 align:middle line:90% So now, why is this important? 00:28:23.681 --> 00:28:25.056 align:middle line:84% The key thing here is that if you 00:28:25.056 --> 00:28:28.230 align:middle line:84% know the number of constraints, you can also actually predict 00:28:28.230 --> 00:28:29.930 align:middle line:90% the entropy of the system. 00:28:29.930 --> 00:28:32.157 align:middle line:90% 00:28:32.157 --> 00:28:33.990 align:middle line:84% Now, that actually makes sense because think 00:28:33.990 --> 00:28:34.890 align:middle line:90% about what entropy is. 00:28:34.890 --> 00:28:36.390 align:middle line:84% Entropy is the number of microstates 00:28:36.390 --> 00:28:37.730 align:middle line:90% the system can access. 00:28:37.730 --> 00:28:40.550 align:middle line:84% If you have more constraints, each constraint essentially 00:28:40.550 --> 00:28:42.550 align:middle line:84% restricts the geometric configuration 00:28:42.550 --> 00:28:44.630 align:middle line:84% your network can actually access. 00:28:44.630 --> 00:28:47.350 align:middle line:84% So it's quite natural that you can actually 00:28:47.350 --> 00:28:48.950 align:middle line:84% go from the number of constraints 00:28:48.950 --> 00:28:51.390 align:middle line:84% to essentially the number of microstates, 00:28:51.390 --> 00:28:53.990 align:middle line:90% which gives you entropy. 00:28:53.990 --> 00:28:58.710 align:middle line:84% So if you know entropy, there are a number 00:28:58.710 --> 00:29:01.150 align:middle line:84% of statistical theories that allows you to connect entropy 00:29:01.150 --> 00:29:03.422 align:middle line:84% to other thermodynamic and rheological parameters. 00:29:03.422 --> 00:29:05.130 align:middle line:84% You can calculate, for example, enthalpy. 00:29:05.130 --> 00:29:07.370 align:middle line:84% Then you know the forming energy of different glass compositions, 00:29:07.370 --> 00:29:08.850 align:middle line:90% which one can be more stable. 00:29:08.850 --> 00:29:14.270 align:middle line:90% You can know the viscosity. 00:29:14.270 --> 00:29:15.750 align:middle line:90% Again, it also makes sense. 00:29:15.750 --> 00:29:18.710 align:middle line:84% Viscosity essentially is the ability of glass to flow, 00:29:18.710 --> 00:29:19.410 align:middle line:90% basically. 00:29:19.410 --> 00:29:23.650 align:middle line:84% So if you have a more rigid versus a more floppy network, 00:29:23.650 --> 00:29:26.090 align:middle line:84% they will obviously have an impact on essentially the flow 00:29:26.090 --> 00:29:29.090 align:middle line:84% behavior or rheological behavior of the glass fluid. 00:29:29.090 --> 00:29:32.810 align:middle line:84% So you can actually know lots of very important glass parameters, 00:29:32.810 --> 00:29:35.090 align:middle line:84% just based on counting the number of constraints 00:29:35.090 --> 00:29:36.810 align:middle line:90% available in the system. 00:29:36.810 --> 00:29:41.650 align:middle line:84% And specifically, viscosity is also very important 00:29:41.650 --> 00:29:45.290 align:middle line:84% because, in the glass community, the way 00:29:45.290 --> 00:29:48.490 align:middle line:84% we define Tg, glass transition temperature, 00:29:48.490 --> 00:29:52.090 align:middle line:84% this is defined with respect to viscosity. 00:29:52.090 --> 00:29:58.010 align:middle line:84% So Tg in the glass community is defined as viscosity eta equals 00:29:58.010 --> 00:30:02.010 align:middle line:90% to 10 to the 12 pascal-second. 00:30:02.010 --> 00:30:04.010 align:middle line:84% Later, we are going to elaborate on this concept 00:30:04.010 --> 00:30:06.850 align:middle line:84% a bit more when we talk about viscosity of glasses. 00:30:06.850 --> 00:30:11.770 align:middle line:84% But if you can predict the viscosity 00:30:11.770 --> 00:30:14.770 align:middle line:84% as a function of temperature and glass composition, 00:30:14.770 --> 00:30:18.610 align:middle line:84% you can now actually generate the Tg for all glass composition 00:30:18.610 --> 00:30:19.680 align:middle line:90% groups. 00:30:19.680 --> 00:30:23.200 align:middle line:84% This is of very significant practical importance 00:30:23.200 --> 00:30:26.220 align:middle line:84% because Tg is a very important glass-processing parameter. 00:30:26.220 --> 00:30:29.495 align:middle line:84% It defines the processability of the glass. 00:30:29.495 --> 00:30:31.120 align:middle line:84% So now you already see that this theory 00:30:31.120 --> 00:30:32.920 align:middle line:90% can be actually very powerful. 00:30:32.920 --> 00:30:35.020 align:middle line:84% As I said, if you go and look at this paper, 00:30:35.020 --> 00:30:36.985 align:middle line:84% this is a paper from a group in Corning. 00:30:36.985 --> 00:30:38.360 align:middle line:84% They're actually already applying 00:30:38.360 --> 00:30:40.160 align:middle line:84% this kind of topological constraint theory 00:30:40.160 --> 00:30:42.240 align:middle line:84% to guide the design of some of the latest glasses you see 00:30:42.240 --> 00:30:43.700 align:middle line:90% in consumer electronic devices. 00:30:43.700 --> 00:30:46.680 align:middle line:90% 00:30:46.680 --> 00:30:50.960 align:middle line:84% Any more questions about this part? 00:30:50.960 --> 00:30:51.540 align:middle line:90% All right. 00:30:51.540 --> 00:30:54.040 align:middle line:84% Now before I move on, I also want to quickly just highlight 00:30:54.040 --> 00:30:56.177 align:middle line:84% a few points about how you actually correctly count 00:30:56.177 --> 00:30:57.260 align:middle line:90% the number of constraints. 00:30:57.260 --> 00:30:59.620 align:middle line:90% We already covered some of this. 00:30:59.620 --> 00:31:01.520 align:middle line:84% For bond-stretching constraints, this 00:31:01.520 --> 00:31:03.320 align:middle line:90% is a more straightforward one. 00:31:03.320 --> 00:31:05.280 align:middle line:84% You can basically just apply the 8 minus 00:31:05.280 --> 00:31:10.185 align:middle line:84% N rule for these nonmetal covalent-bonded solids. 00:31:10.185 --> 00:31:11.560 align:middle line:84% If you have group 5, for example, 00:31:11.560 --> 00:31:13.760 align:middle line:90% it's 8 minus 5 equals 3. 00:31:13.760 --> 00:31:15.220 align:middle line:90% You have three chemical bonds. 00:31:15.220 --> 00:31:16.782 align:middle line:90% Group 6, two chemical bonds. 00:31:16.782 --> 00:31:17.740 align:middle line:90% And so on and so forth. 00:31:17.740 --> 00:31:20.030 align:middle line:90% So that's 3 [INAUDIBLE]. 00:31:20.030 --> 00:31:22.830 align:middle line:84% However, there's exceptions here. 00:31:22.830 --> 00:31:26.230 align:middle line:84% The exceptions mostly come in for those heavy elements. 00:31:26.230 --> 00:31:29.350 align:middle line:84% I'm giving you an example there, tellurium. 00:31:29.350 --> 00:31:32.670 align:middle line:84% Tellurium is notorious because they can actually 00:31:32.670 --> 00:31:35.390 align:middle line:84% form any valence-- they form any valence state from minus 2 00:31:35.390 --> 00:31:36.170 align:middle line:90% to plus 6. 00:31:36.170 --> 00:31:38.870 align:middle line:90% Anything in between. 00:31:38.870 --> 00:31:41.550 align:middle line:84% So if you see any glass containing tellurium, 00:31:41.550 --> 00:31:43.190 align:middle line:84% you have to be very careful there. 00:31:43.190 --> 00:31:45.310 align:middle line:84% You actually need to perform either structural 00:31:45.310 --> 00:31:47.470 align:middle line:84% characterization, like some diffraction techniques 00:31:47.470 --> 00:31:50.290 align:middle line:84% to actually ascertain what are the chemical mole numbers, 00:31:50.290 --> 00:31:52.682 align:middle line:84% or you have to perform some first-principle calculations 00:31:52.682 --> 00:31:54.890 align:middle line:84% to actually determine the actual coordination number. 00:31:54.890 --> 00:31:57.590 align:middle line:84% So just be very careful with those heavy elements, 00:31:57.590 --> 00:32:00.290 align:middle line:84% where its valence state is subject to change. 00:32:00.290 --> 00:32:02.790 align:middle line:90% 00:32:02.790 --> 00:32:03.290 align:middle line:90% All right. 00:32:03.290 --> 00:32:08.272 align:middle line:84% For bond-bending constraints, we have covered this. 00:32:08.272 --> 00:32:10.230 align:middle line:84% For glasses with low glass-forming temperature, 00:32:10.230 --> 00:32:12.313 align:middle line:84% like chalcogenides, that's pretty straightforward. 00:32:12.313 --> 00:32:14.610 align:middle line:84% You can safely apply this to r minus 3 equation there. 00:32:14.610 --> 00:32:18.300 align:middle line:84% But for glasses with high glass-forming temperatures, 00:32:18.300 --> 00:32:20.050 align:middle line:84% you have to account for the fact that some 00:32:20.050 --> 00:32:21.508 align:middle line:84% of the bond-bending constraints may 00:32:21.508 --> 00:32:24.370 align:middle line:84% get relaxed because of the high energy of the atoms. 00:32:24.370 --> 00:32:26.930 align:middle line:84% So in that case, you also have to do either experiment, 00:32:26.930 --> 00:32:29.730 align:middle line:84% like diffraction experiments, to look at structure and relaxation 00:32:29.730 --> 00:32:32.850 align:middle line:84% of the configuration, or you do simulations to actually predict 00:32:32.850 --> 00:32:33.770 align:middle line:90% it. 00:32:33.770 --> 00:32:35.530 align:middle line:90% OK? 00:32:35.530 --> 00:32:37.130 align:middle line:90% All right. 00:32:37.130 --> 00:32:41.370 align:middle line:84% So in this slide, I also want to highlight another fact 00:32:41.370 --> 00:32:43.930 align:middle line:84% that this magic number, 2.4, is not 00:32:43.930 --> 00:32:46.790 align:middle line:84% only important for determining the glass network stability, 00:32:46.790 --> 00:32:49.130 align:middle line:84% it also impacts the properties of glasses. 00:32:49.130 --> 00:32:53.210 align:middle line:84% So many glass properties, they will actually 00:32:53.210 --> 00:32:56.130 align:middle line:84% exhibit essentially an extrema that 00:32:56.130 --> 00:32:59.730 align:middle line:84% corresponds to this mean coordination number of 2.4. 00:32:59.730 --> 00:33:01.110 align:middle line:90% So I'm giving two examples here. 00:33:01.110 --> 00:33:03.170 align:middle line:84% So for example, on the left-hand side, 00:33:03.170 --> 00:33:07.610 align:middle line:84% I'm actually showing you how the molar volume varies 00:33:07.610 --> 00:33:09.130 align:middle line:84% as a function of mean coordination 00:33:09.130 --> 00:33:12.050 align:middle line:84% number in these binary and ternary glasses. 00:33:12.050 --> 00:33:17.800 align:middle line:84% In both cases here, you notice that there's a dip right at 2.4. 00:33:17.800 --> 00:33:20.640 align:middle line:84% On the right-hand side, this is the actually heat capacity. 00:33:20.640 --> 00:33:23.188 align:middle line:84% Again, similarly, you see a little dip here at 2.4. 00:33:23.188 --> 00:33:25.480 align:middle line:84% And later, on when we talk about mechanical properties, 00:33:25.480 --> 00:33:27.522 align:middle line:84% you're going to see that all the elastic modulus, 00:33:27.522 --> 00:33:31.440 align:middle line:84% they also usually show a extrema right at 2.4. 00:33:31.440 --> 00:33:33.692 align:middle line:84% So that's why the glass scientists 00:33:33.692 --> 00:33:35.900 align:middle line:84% appreciate the importance of this magic number there. 00:33:35.900 --> 00:33:39.640 align:middle line:90% It's definitely quite important. 00:33:39.640 --> 00:33:40.300 align:middle line:90% All right. 00:33:40.300 --> 00:33:43.120 align:middle line:84% So now, before we wrap up this part about glass-forming theory, 00:33:43.120 --> 00:33:45.760 align:middle line:84% I also want to quickly mention about, practically, 00:33:45.760 --> 00:33:48.720 align:middle line:84% how do you actually measure and essentially gauge 00:33:48.720 --> 00:33:50.040 align:middle line:90% glass-forming ability? 00:33:50.040 --> 00:33:52.800 align:middle line:84% So one of the very common figure of merit 00:33:52.800 --> 00:33:54.800 align:middle line:84% many people use to essentially measure 00:33:54.800 --> 00:33:56.858 align:middle line:84% the glass-forming ability is this delta T. 00:33:56.858 --> 00:33:58.400 align:middle line:84% It's basically the difference between 00:33:58.400 --> 00:34:03.840 align:middle line:84% crystallization temperature and glass transition temperature. 00:34:03.840 --> 00:34:06.640 align:middle line:84% So Tx, as we have mentioned, this 00:34:06.640 --> 00:34:09.400 align:middle line:84% is the temperature at which you start 00:34:09.400 --> 00:34:10.960 align:middle line:84% to see crystallization of a sample 00:34:10.960 --> 00:34:12.900 align:middle line:84% under certain annealing conditions. 00:34:12.900 --> 00:34:16.500 align:middle line:84% So the higher Tx, the most stable a glass is. 00:34:16.500 --> 00:34:19.764 align:middle line:84% And above Tg is where you start to see 00:34:19.764 --> 00:34:21.139 align:middle line:84% significant structural relaxation 00:34:21.139 --> 00:34:22.181 align:middle line:90% and those kind of things. 00:34:22.181 --> 00:34:25.620 align:middle line:84% So the gap in between gives you the ability of the network 00:34:25.620 --> 00:34:27.860 align:middle line:84% to resist this kind of relaxation. 00:34:27.860 --> 00:34:30.980 align:middle line:84% So that's why it makes sense that this actually a figure 00:34:30.980 --> 00:34:33.179 align:middle line:84% of merit to gauge the glass stability. 00:34:33.179 --> 00:34:36.219 align:middle line:84% Now, that said, I do want to mention 00:34:36.219 --> 00:34:40.580 align:middle line:84% that this figure of merit is very much an empirical parameter 00:34:40.580 --> 00:34:44.020 align:middle line:84% because if you think about Tx, I have already 00:34:44.020 --> 00:34:46.239 align:middle line:84% mentioned that Tx itself is an empirical parameter. 00:34:46.239 --> 00:34:47.560 align:middle line:84% It depends on how you actually anneal it, 00:34:47.560 --> 00:34:49.739 align:middle line:84% how you prepare the glass, and how long you actually 00:34:49.739 --> 00:34:50.600 align:middle line:90% anneal it even. 00:34:50.600 --> 00:34:53.580 align:middle line:84% So Tx can be varied quite a bit depending 00:34:53.580 --> 00:34:55.540 align:middle line:84% on specific experimental conditions. 00:34:55.540 --> 00:34:58.540 align:middle line:90% Now, what about Tg? 00:34:58.540 --> 00:35:00.700 align:middle line:84% Tg, depending on who you talk to, 00:35:00.700 --> 00:35:02.420 align:middle line:90% you have different definitions. 00:35:02.420 --> 00:35:03.980 align:middle line:84% If you talk to a glass scientist, 00:35:03.980 --> 00:35:06.480 align:middle line:84% they'll tell you this is the definition. 00:35:06.480 --> 00:35:08.300 align:middle line:84% It's defined with respect to viscosity. 00:35:08.300 --> 00:35:11.340 align:middle line:84% Now if you go to talk with a polymer scientist, 00:35:11.340 --> 00:35:13.330 align:middle line:90% you may get a different answer. 00:35:13.330 --> 00:35:16.170 align:middle line:84% They prefer to actually measure Tg 00:35:16.170 --> 00:35:20.010 align:middle line:84% from thermal measurements, essentially, 00:35:20.010 --> 00:35:21.890 align:middle line:90% or calorimetric measurements. 00:35:21.890 --> 00:35:26.930 align:middle line:84% So for example, you can measure the heat capacity of a glass 00:35:26.930 --> 00:35:29.130 align:middle line:90% or polymer, amorphous polymer. 00:35:29.130 --> 00:35:31.170 align:middle line:84% And we know that if you think about this plot 00:35:31.170 --> 00:35:34.000 align:middle line:84% there where we look at enthalpy as a function of temperature, 00:35:34.000 --> 00:35:36.250 align:middle line:84% there's actually a slope change when you go from glass 00:35:36.250 --> 00:35:38.430 align:middle line:90% to supercooled liquid. 00:35:38.430 --> 00:35:44.210 align:middle line:84% Supercooled liquid tend to have a higher heat capacity 00:35:44.210 --> 00:35:46.970 align:middle line:84% because you have more degrees of freedom to access in the network 00:35:46.970 --> 00:35:47.470 align:middle line:90% there. 00:35:47.470 --> 00:35:49.310 align:middle line:84% So that's why it has higher capacity. 00:35:49.310 --> 00:35:51.190 align:middle line:84% And glass tends to have lower heat capacity. 00:35:51.190 --> 00:35:53.330 align:middle line:84% Now the question is, how do you actually 00:35:53.330 --> 00:35:55.730 align:middle line:90% connect the two in between? 00:35:55.730 --> 00:35:58.570 align:middle line:84% So you may get something like this, which is good. 00:35:58.570 --> 00:36:00.250 align:middle line:90% Nice, smooth curve. 00:36:00.250 --> 00:36:03.490 align:middle line:84% But practically, you may also get-- well, 00:36:03.490 --> 00:36:06.310 align:middle line:84% if it's something like that, that's pretty straightforward. 00:36:06.310 --> 00:36:08.090 align:middle line:84% The way you define Tg is you do extension 00:36:08.090 --> 00:36:09.350 align:middle line:90% between these two lines there. 00:36:09.350 --> 00:36:13.080 align:middle line:84% The crossover point defines you what the Tg is. 00:36:13.080 --> 00:36:16.320 align:middle line:84% Now, you may also get something like that, 00:36:16.320 --> 00:36:18.840 align:middle line:84% or you may get something like this. 00:36:18.840 --> 00:36:24.320 align:middle line:84% It all depends on relaxation behavior in that regime. 00:36:24.320 --> 00:36:25.820 align:middle line:84% I mean, some people still define it. 00:36:25.820 --> 00:36:28.783 align:middle line:84% They can, for example, define, if you extend these two lines, 00:36:28.783 --> 00:36:30.700 align:middle line:84% the crossover point actually gives you the Tg. 00:36:30.700 --> 00:36:34.442 align:middle line:84% But as you can see, this is a bit arbitrary. 00:36:34.442 --> 00:36:36.400 align:middle line:84% And it also depends on how you actually perform 00:36:36.400 --> 00:36:38.440 align:middle line:90% the thermal measurement there. 00:36:38.440 --> 00:36:40.880 align:middle line:90% So that's why. 00:36:40.880 --> 00:36:42.320 align:middle line:90% You have to be careful. 00:36:42.320 --> 00:36:44.780 align:middle line:84% When you're trying to compare this delta T number here, 00:36:44.780 --> 00:36:47.560 align:middle line:84% you have to essentially compare apples to apples. 00:36:47.560 --> 00:36:50.280 align:middle line:84% Make sure you are comparing two sets of experiments that's 00:36:50.280 --> 00:36:52.120 align:middle line:84% performed under similar conditions 00:36:52.120 --> 00:36:54.040 align:middle line:90% and apply similar criteria. 00:36:54.040 --> 00:36:55.640 align:middle line:90% All right. 00:36:55.640 --> 00:36:57.860 align:middle line:90% Now, one quick thing. 00:36:57.860 --> 00:36:59.940 align:middle line:84% There are some alternative figures of merit here. 00:36:59.940 --> 00:37:02.200 align:middle line:84% This one is called Hruby coefficient. 00:37:02.200 --> 00:37:03.140 align:middle line:90% It's very similar. 00:37:03.140 --> 00:37:05.320 align:middle line:84% It's basically just normalizing the two melting points of glass 00:37:05.320 --> 00:37:06.880 align:middle line:84% to account for that different glass compositions have 00:37:06.880 --> 00:37:07.922 align:middle line:90% different melting points. 00:37:07.922 --> 00:37:11.500 align:middle line:90% So it's like normalized delta T. 00:37:11.500 --> 00:37:16.060 align:middle line:84% So we can wrap up this chapter here. 00:37:16.060 --> 00:37:19.020 align:middle line:84% So we have basically covered three main theoretical aspects 00:37:19.020 --> 00:37:19.960 align:middle line:90% of glass transition. 00:37:19.960 --> 00:37:21.220 align:middle line:90% We talk about kinetic theory. 00:37:21.220 --> 00:37:25.320 align:middle line:84% On that, the most important part is T-T-T diagram. 00:37:25.320 --> 00:37:28.260 align:middle line:84% You need to be very proficient about how to read and interpret 00:37:28.260 --> 00:37:30.220 align:middle line:84% the T-T-T diagram and use that to actually make 00:37:30.220 --> 00:37:32.260 align:middle line:84% informed decisions about the glass-processing temperature 00:37:32.260 --> 00:37:33.000 align:middle line:90% conditions. 00:37:33.000 --> 00:37:35.300 align:middle line:90% We talk about glass. 00:37:35.300 --> 00:37:37.160 align:middle line:84% We talk about laboratory glass transition. 00:37:37.160 --> 00:37:39.600 align:middle line:84% Basically, glass transition is ergodicity breakdown. 00:37:39.600 --> 00:37:40.620 align:middle line:90% Liquid is ergodic. 00:37:40.620 --> 00:37:42.080 align:middle line:90% Glass network is nonergodic. 00:37:42.080 --> 00:37:44.660 align:middle line:84% That can also explain why you have this history 00:37:44.660 --> 00:37:46.260 align:middle line:90% dependence of glass properties. 00:37:46.260 --> 00:37:49.500 align:middle line:84% And finally, we have seen one example 00:37:49.500 --> 00:37:53.340 align:middle line:84% where topology can actually predict glass stability 00:37:53.340 --> 00:37:54.637 align:middle line:90% for network glasses. 00:37:54.637 --> 00:37:56.220 align:middle line:84% We are going to see that example again 00:37:56.220 --> 00:37:57.580 align:middle line:90% when we go to metallic glasses. 00:37:57.580 --> 00:38:00.227 align:middle line:84% It's a different kind of topology but same idea. 00:38:00.227 --> 00:38:02.560 align:middle line:84% It's not so much about the chemical nature of the atoms, 00:38:02.560 --> 00:38:04.977 align:middle line:84% but it's just about essentially coordination and geometric 00:38:04.977 --> 00:38:07.260 align:middle line:84% constraint that actually limit the glass stability. 00:38:07.260 --> 00:38:09.490 align:middle line:90% All right 00:38:09.490 --> 00:38:12.450 align:middle line:84% So any more questions about this part 00:38:12.450 --> 00:38:15.730 align:middle line:84% before we move on to the next one? 00:38:15.730 --> 00:38:20.170 align:middle line:84% So now the next lecture, as I mentioned in the first lecture 00:38:20.170 --> 00:38:22.770 align:middle line:84% there, the way we organize this class is 00:38:22.770 --> 00:38:24.490 align:middle line:84% that we will have one section talking 00:38:24.490 --> 00:38:26.090 align:middle line:84% about the fundamental theory, and then 00:38:26.090 --> 00:38:27.730 align:middle line:84% we have one section talking about the practical 00:38:27.730 --> 00:38:29.188 align:middle line:84% applications, how to actually apply 00:38:29.188 --> 00:38:32.750 align:middle line:84% the theories into something with practical significance. 00:38:32.750 --> 00:38:35.295 align:middle line:84% So for glass forming, we are going 00:38:35.295 --> 00:38:37.170 align:middle line:84% to see some applications, how we can actually 00:38:37.170 --> 00:38:40.710 align:middle line:84% use that to guide the design of phase-change materials. 00:38:40.710 --> 00:38:44.290 align:middle line:90% 00:38:44.290 --> 00:38:45.830 align:middle line:84% So what are phase-change materials? 00:38:45.830 --> 00:38:47.752 align:middle line:84% It depends on who you talk to, again. 00:38:47.752 --> 00:38:49.210 align:middle line:84% There are actually two main classes 00:38:49.210 --> 00:38:51.170 align:middle line:90% of phase-change materials. 00:38:51.170 --> 00:38:53.130 align:middle line:84% In the energy storage community, people 00:38:53.130 --> 00:38:55.690 align:middle line:84% use phase-change materials to actually store energy. 00:38:55.690 --> 00:38:57.447 align:middle line:90% Energy relies on latent heat. 00:38:57.447 --> 00:38:59.530 align:middle line:84% The phase-change materials I'm talking about here, 00:38:59.530 --> 00:39:02.110 align:middle line:84% these are more for optoelectronic applications, 00:39:02.110 --> 00:39:03.110 align:middle line:90% electronic applications. 00:39:03.110 --> 00:39:05.150 align:middle line:84% People use them for memory applications. 00:39:05.150 --> 00:39:06.730 align:middle line:90% Electronic memories. 00:39:06.730 --> 00:39:10.030 align:middle line:84% So this particular class of Phase-Change Material, or PCM 00:39:10.030 --> 00:39:12.790 align:middle line:84% as we call it, they can switch between amorphous 00:39:12.790 --> 00:39:13.890 align:middle line:90% and crystalline states. 00:39:13.890 --> 00:39:16.470 align:middle line:90% 00:39:16.470 --> 00:39:19.590 align:middle line:84% What's really unique about this kind of phase-change material 00:39:19.590 --> 00:39:22.650 align:middle line:84% is that while you actually change the atomic arrangement, 00:39:22.650 --> 00:39:25.710 align:middle line:84% you also change the electrical and optical properties 00:39:25.710 --> 00:39:26.730 align:middle line:90% dramatically. 00:39:26.730 --> 00:39:30.394 align:middle line:90% 00:39:30.394 --> 00:39:36.350 align:middle line:84% The amorphous state tends to be more electrically insulating. 00:39:36.350 --> 00:39:39.510 align:middle line:84% It also tends to have a low optical reflectance, which 00:39:39.510 --> 00:39:42.270 align:middle line:84% is basically low refractive index, in this case. 00:39:42.270 --> 00:39:45.090 align:middle line:84% Versus crystalline state, it becomes electrically conductive. 00:39:45.090 --> 00:39:47.190 align:middle line:84% It's actually become a degenerate semiconductor. 00:39:47.190 --> 00:39:49.732 align:middle line:84% And then it also has a very high optical reflectance and much 00:39:49.732 --> 00:39:51.150 align:middle line:90% higher refractive index. 00:39:51.150 --> 00:39:53.130 align:middle line:90% This is quite unique behavior. 00:39:53.130 --> 00:39:55.910 align:middle line:84% Most of the materials, its electrical and optical 00:39:55.910 --> 00:39:59.370 align:middle line:84% properties are largely dictated by the constituent elements. 00:39:59.370 --> 00:40:03.990 align:middle line:84% So if you change the structure from amorphous to crystalline, 00:40:03.990 --> 00:40:06.620 align:middle line:84% it doesn't really cause such a huge perturbation 00:40:06.620 --> 00:40:08.540 align:middle line:84% of electrical optical properties. 00:40:08.540 --> 00:40:11.738 align:middle line:84% So that's why only a handful of materials 00:40:11.738 --> 00:40:13.280 align:middle line:84% can be called phase-change materials, 00:40:13.280 --> 00:40:15.740 align:middle line:84% despite that practically all materials can switch 00:40:15.740 --> 00:40:17.580 align:middle line:84% between amorphous and crystalline state 00:40:17.580 --> 00:40:19.780 align:middle line:84% as long as you quench fast enough. 00:40:19.780 --> 00:40:23.180 align:middle line:84% We are going to talk about the structural origins, why 00:40:23.180 --> 00:40:24.920 align:middle line:84% this material is so peculiar, later on. 00:40:24.920 --> 00:40:27.820 align:middle line:84% But for now, you can actually switch these two states 00:40:27.820 --> 00:40:28.760 align:middle line:90% reversibly. 00:40:28.760 --> 00:40:30.840 align:middle line:84% So you can go from amorphous to crystalline. 00:40:30.840 --> 00:40:32.580 align:middle line:90% This is called step process. 00:40:32.580 --> 00:40:34.340 align:middle line:84% In a step process, what you do is 00:40:34.340 --> 00:40:39.700 align:middle line:84% you try to heat up the material to above its crystallization 00:40:39.700 --> 00:40:43.580 align:middle line:84% temperature, Tx, but below the melting point. 00:40:43.580 --> 00:40:46.940 align:middle line:84% And then, within this temperature range 00:40:46.940 --> 00:40:48.780 align:middle line:84% here, the thermodynamically stable state 00:40:48.780 --> 00:40:51.060 align:middle line:90% is actually crystalline state. 00:40:51.060 --> 00:40:54.000 align:middle line:84% So then, if you hold it there for some time, 00:40:54.000 --> 00:40:57.420 align:middle line:84% allow the atoms to move around and find the thermodynamically 00:40:57.420 --> 00:41:00.800 align:middle line:84% stable position, then you actually induce crystallization. 00:41:00.800 --> 00:41:02.800 align:middle line:84% Now if you want to go in the reverse direction-- 00:41:02.800 --> 00:41:06.050 align:middle line:84% this is called the reset process in the memory community-- 00:41:06.050 --> 00:41:07.300 align:middle line:90% you essentially apply a pulse. 00:41:07.300 --> 00:41:09.280 align:middle line:90% Very short, pulse, but intense. 00:41:09.280 --> 00:41:11.400 align:middle line:84% You melt the material so it becomes liquid. 00:41:11.400 --> 00:41:13.880 align:middle line:84% You very quickly cool down to essentially bypass 00:41:13.880 --> 00:41:14.880 align:middle line:90% crystallization. 00:41:14.880 --> 00:41:17.580 align:middle line:84% You then freeze in this kind of liquid-like amorphous state. 00:41:17.580 --> 00:41:18.640 align:middle line:90% That's what you get. 00:41:18.640 --> 00:41:20.140 align:middle line:84% And you can amorphize the material. 00:41:20.140 --> 00:41:22.680 align:middle line:90% 00:41:22.680 --> 00:41:25.440 align:middle line:84% So because you can do this kind of reversible switching 00:41:25.440 --> 00:41:27.960 align:middle line:84% between the two states here, and these two states 00:41:27.960 --> 00:41:29.558 align:middle line:84% has a very large contrast in terms 00:41:29.558 --> 00:41:31.100 align:middle line:84% of electrical and optical properties, 00:41:31.100 --> 00:41:33.440 align:middle line:84% people are using them as essentially memories. 00:41:33.440 --> 00:41:35.800 align:middle line:84% You can encode digital ones and zeros 00:41:35.800 --> 00:41:37.640 align:middle line:84% in the two states of the material, 00:41:37.640 --> 00:41:39.160 align:middle line:84% and you can read out, essentially, 00:41:39.160 --> 00:41:41.620 align:middle line:84% this kind of information either electrically, 00:41:41.620 --> 00:41:44.440 align:middle line:84% by looking at resistance, or optically, 00:41:44.440 --> 00:41:46.320 align:middle line:84% by essentially shining a laser on that 00:41:46.320 --> 00:41:48.680 align:middle line:90% and looking at reflectance. 00:41:48.680 --> 00:41:53.200 align:middle line:84% So this is a material that has already 00:41:53.200 --> 00:41:57.940 align:middle line:84% been very widely deployed in commercial data storage. 00:41:57.940 --> 00:42:02.380 align:middle line:84% Rewritable CDs, DVDs, they are made of phase-change materials. 00:42:02.380 --> 00:42:06.550 align:middle line:90% 00:42:06.550 --> 00:42:08.870 align:middle line:84% Companies like Intel or Samsung, they 00:42:08.870 --> 00:42:10.870 align:middle line:84% have also developed electronic memories 00:42:10.870 --> 00:42:13.150 align:middle line:84% based on this kind of phase-change materials. 00:42:13.150 --> 00:42:17.470 align:middle line:84% So that's why this is quite important here. 00:42:17.470 --> 00:42:19.683 align:middle line:84% So now, for this next slide, what I want to do, 00:42:19.683 --> 00:42:21.350 align:middle line:84% before I go into more detail description 00:42:21.350 --> 00:42:23.670 align:middle line:84% about the properties, I want to first define 00:42:23.670 --> 00:42:26.470 align:middle line:84% a few key performance metrics and try to link it 00:42:26.470 --> 00:42:27.870 align:middle line:90% to the material properties. 00:42:27.870 --> 00:42:30.590 align:middle line:84% Key performance metrics for memory storage applications. 00:42:30.590 --> 00:42:34.130 align:middle line:84% So for memory, these are the important parameters here. 00:42:34.130 --> 00:42:35.730 align:middle line:90% You want data retention. 00:42:35.730 --> 00:42:37.230 align:middle line:84% Basically, it means that if you have 00:42:37.230 --> 00:42:38.813 align:middle line:84% stored something in your memory there, 00:42:38.813 --> 00:42:40.478 align:middle line:84% you want it to stay for some time. 00:42:40.478 --> 00:42:42.270 align:middle line:84% Like for rewritable CDs, DVDs, you probably 00:42:42.270 --> 00:42:44.290 align:middle line:84% want it to stay for at least a few years 00:42:44.290 --> 00:42:45.990 align:middle line:90% before it gets wiped out. 00:42:45.990 --> 00:42:50.430 align:middle line:84% So now the question-- what is the relevant material property 00:42:50.430 --> 00:42:53.810 align:middle line:90% that dictates data retention? 00:42:53.810 --> 00:42:54.310 align:middle line:90% Yes? 00:42:54.310 --> 00:42:55.650 align:middle line:84% AUDIENCE: That'd be phase stability. 00:42:55.650 --> 00:42:56.275 align:middle line:90% JUEJUN HU: Yes. 00:42:56.275 --> 00:42:57.150 align:middle line:90% Which phase? 00:42:57.150 --> 00:42:58.818 align:middle line:90% AUDIENCE: I'd say amorphous. 00:42:58.818 --> 00:42:59.610 align:middle line:90% JUEJUN HU: Perfect. 00:42:59.610 --> 00:42:59.670 align:middle line:90% Yeah. 00:42:59.670 --> 00:43:01.290 align:middle line:84% Because crystalline is thermodynamically stable. 00:43:01.290 --> 00:43:02.600 align:middle line:90% So it should stay forever. 00:43:02.600 --> 00:43:04.558 align:middle line:84% So really, the problem is just amorphous phase. 00:43:04.558 --> 00:43:05.980 align:middle line:84% You don't want it to crystallize. 00:43:05.980 --> 00:43:09.820 align:middle line:84% So you want some material that has 00:43:09.820 --> 00:43:11.880 align:middle line:84% sufficient glass-forming ability. 00:43:11.880 --> 00:43:15.260 align:middle line:84% So it doesn't really easily crystallize. 00:43:15.260 --> 00:43:16.100 align:middle line:90% Now, next one. 00:43:16.100 --> 00:43:17.482 align:middle line:90% What about programming speed? 00:43:17.482 --> 00:43:18.940 align:middle line:84% Essentially, it means that you need 00:43:18.940 --> 00:43:21.820 align:middle line:84% to be able to write information into the memory quickly. 00:43:21.820 --> 00:43:24.760 align:middle line:84% So there are two processes there. 00:43:24.760 --> 00:43:26.380 align:middle line:90% You have set and reset. 00:43:26.380 --> 00:43:30.320 align:middle line:84% Which one do you think is the faster process, amorphous 00:43:30.320 --> 00:43:32.120 align:middle line:84% to crystalline or crystalline to amorphous? 00:43:32.120 --> 00:43:35.584 align:middle line:90% 00:43:35.584 --> 00:43:38.060 align:middle line:84% AUDIENCE: Crystalline to amorphous? 00:43:38.060 --> 00:43:38.688 align:middle line:90% JUEJUN HU: Yes. 00:43:38.688 --> 00:43:40.980 align:middle line:84% I mean, you can already read it from the problem there, 00:43:40.980 --> 00:43:43.720 align:middle line:84% but the idea is that if you go from amorphous to crystalline, 00:43:43.720 --> 00:43:45.740 align:middle line:84% you need to heat it up and hold it there for some time 00:43:45.740 --> 00:43:47.532 align:middle line:84% because you need to allow the atoms to move 00:43:47.532 --> 00:43:50.040 align:middle line:84% around and actually find the right position, 00:43:50.040 --> 00:43:53.700 align:middle line:84% versus crystalline to amorphous, you actually 00:43:53.700 --> 00:43:55.580 align:middle line:90% want to do it very, very fast. 00:43:55.580 --> 00:43:57.820 align:middle line:84% You just heat it up, quickly quench down. 00:43:57.820 --> 00:44:00.460 align:middle line:84% You don't want the atoms to be allowed to relax. 00:44:00.460 --> 00:44:03.640 align:middle line:84% So inherently, amorphization is always 00:44:03.640 --> 00:44:06.200 align:middle line:90% faster than crystallization. 00:44:06.200 --> 00:44:08.040 align:middle line:84% So what that also means is that when 00:44:08.040 --> 00:44:10.760 align:middle line:84% you're talking about programming speed, 00:44:10.760 --> 00:44:13.917 align:middle line:84% you want the material that can crystallize quickly 00:44:13.917 --> 00:44:15.500 align:middle line:84% because that's the rate-limiting step. 00:44:15.500 --> 00:44:17.960 align:middle line:90% 00:44:17.960 --> 00:44:18.460 align:middle line:90% All right. 00:44:18.460 --> 00:44:21.570 align:middle line:84% So now if you look at the first two conditions there, 00:44:21.570 --> 00:44:24.640 align:middle line:90% there's a trade-off. 00:44:24.640 --> 00:44:26.640 align:middle line:84% You want something that can retain the data that 00:44:26.640 --> 00:44:27.740 align:middle line:90% doesn't want to crystallize. 00:44:27.740 --> 00:44:30.448 align:middle line:84% But you also want something that crystallizes very quickly so you 00:44:30.448 --> 00:44:32.720 align:middle line:90% can program fast. 00:44:32.720 --> 00:44:36.712 align:middle line:84% Can you get something with a balance in between the two? 00:44:36.712 --> 00:44:38.920 align:middle line:84% Now, for that, I do want to highlight one thing, very 00:44:38.920 --> 00:44:39.712 align:middle line:90% important thing. 00:44:39.712 --> 00:44:41.420 align:middle line:84% When you're talking about data retention, 00:44:41.420 --> 00:44:43.160 align:middle line:84% you're typically talking about stability of phase 00:44:43.160 --> 00:44:45.480 align:middle line:84% at near room temperature, near operating condition. 00:44:45.480 --> 00:44:47.040 align:middle line:84% Even for computer memories, you're 00:44:47.040 --> 00:44:49.540 align:middle line:84% probably talking about maybe 100 degree Celsius or something 00:44:49.540 --> 00:44:51.040 align:middle line:90% inside your box, mainframe. 00:44:51.040 --> 00:44:54.120 align:middle line:84% But for crystallization, when you're actually 00:44:54.120 --> 00:44:58.520 align:middle line:84% trying to program it, you do it at much higher temperature. 00:44:58.520 --> 00:45:01.190 align:middle line:84% You want to do it actually at the nose temperature 00:45:01.190 --> 00:45:02.918 align:middle line:84% of a T-T-T curve because that gives you 00:45:02.918 --> 00:45:04.210 align:middle line:90% a shorter crystallization time. 00:45:04.210 --> 00:45:06.390 align:middle line:84% And for these chalcogenides glasses-- 00:45:06.390 --> 00:45:08.302 align:middle line:90% well, for this PCM. 00:45:08.302 --> 00:45:09.510 align:middle line:90% We're going to talk about it. 00:45:09.510 --> 00:45:10.730 align:middle line:90% They are chalcogenides. 00:45:10.730 --> 00:45:12.590 align:middle line:84% For this kind of phase-change materials, 00:45:12.590 --> 00:45:14.310 align:middle line:84% the typical crystallization temperature 00:45:14.310 --> 00:45:16.910 align:middle line:84% is of the order of a few hundred degrees Celsius, 00:45:16.910 --> 00:45:18.770 align:middle line:90% say 200, 300 degrees Celsius. 00:45:18.770 --> 00:45:23.310 align:middle line:84% So that's considerably higher compared to room temperature. 00:45:23.310 --> 00:45:25.030 align:middle line:84% So basically, what we want to do is 00:45:25.030 --> 00:45:28.990 align:middle line:84% we want to maintain good glass stability near room temperature, 00:45:28.990 --> 00:45:32.390 align:middle line:84% but maximize or expedite the kinetic crystallization 00:45:32.390 --> 00:45:34.350 align:middle line:90% at elevated temperature. 00:45:34.350 --> 00:45:36.530 align:middle line:90% So how do you engineer that? 00:45:36.530 --> 00:45:40.430 align:middle line:90% 00:45:40.430 --> 00:45:43.845 align:middle line:84% What is the material parameter that's relevant to that? 00:45:43.845 --> 00:45:45.470 align:middle line:84% I mean, effectively what I'm asking is, 00:45:45.470 --> 00:45:47.470 align:middle line:84% what material parameter dictates the temperature 00:45:47.470 --> 00:45:49.030 align:middle line:90% dependence of kinetics? 00:45:49.030 --> 00:45:51.750 align:middle line:84% Or how do you describe the temperature 00:45:51.750 --> 00:45:53.350 align:middle line:90% dependence of kinetics? 00:45:53.350 --> 00:45:55.725 align:middle line:84% AUDIENCE: That it's a critical component? 00:45:55.725 --> 00:45:56.350 align:middle line:90% JUEJUN HU: Yes. 00:45:56.350 --> 00:45:58.730 align:middle line:84% I mean, that's the parameter you measure eventually, 00:45:58.730 --> 00:45:59.570 align:middle line:90% the performance. 00:45:59.570 --> 00:46:02.153 align:middle line:84% But think about the temperature dependence of critical cooling 00:46:02.153 --> 00:46:02.938 align:middle line:90% rate, for example. 00:46:02.938 --> 00:46:04.730 align:middle line:84% Not exactly, but the temperature dependence 00:46:04.730 --> 00:46:08.425 align:middle line:84% of the crystallization speed, crystallization time, 00:46:08.425 --> 00:46:11.050 align:middle line:84% or temperature dependence of any kinetic process, what equation 00:46:11.050 --> 00:46:12.542 align:middle line:90% we use to describe it. 00:46:12.542 --> 00:46:14.250 align:middle line:84% AUDIENCE: Is it the temperature-dependent 00:46:14.250 --> 00:46:15.992 align:middle line:90% constraints? 00:46:15.992 --> 00:46:17.950 align:middle line:84% JUEJUN HU: There's something simpler than that. 00:46:17.950 --> 00:46:19.270 align:middle line:90% Think about kinetics class. 00:46:19.270 --> 00:46:21.830 align:middle line:84% How do you describe, when you change temperature, 00:46:21.830 --> 00:46:23.830 align:middle line:84% how fast does the process change? 00:46:23.830 --> 00:46:25.678 align:middle line:90% AUDIENCE: Like to activate them? 00:46:25.678 --> 00:46:26.470 align:middle line:90% JUEJUN HU: Exactly. 00:46:26.470 --> 00:46:27.330 align:middle line:90% Arrhenius law. 00:46:27.330 --> 00:46:30.970 align:middle line:84% So yeah, if you think about Arrhenius law, 00:46:30.970 --> 00:46:33.635 align:middle line:84% you go through the math, you can fairly easily 00:46:33.635 --> 00:46:36.010 align:middle line:84% find out that what you want is actually a high activation 00:46:36.010 --> 00:46:38.170 align:middle line:90% energy. 00:46:38.170 --> 00:46:40.570 align:middle line:84% Activation energy basically goes into exponent 00:46:40.570 --> 00:46:41.890 align:middle line:90% in the exponential law. 00:46:41.890 --> 00:46:43.970 align:middle line:84% So if you have a high activation energy, 00:46:43.970 --> 00:46:46.150 align:middle line:84% then you create a very large drastic change. 00:46:46.150 --> 00:46:48.108 align:middle line:84% As you change the temperature, the kinetic rate 00:46:48.108 --> 00:46:50.870 align:middle line:90% changes very, very fast. 00:46:50.870 --> 00:46:53.595 align:middle line:84% So effectively, I mean, most of the actual practical 00:46:53.595 --> 00:46:54.970 align:middle line:84% phase-change materials, they tend 00:46:54.970 --> 00:46:58.920 align:middle line:84% to have a fairly high nominal activation 00:46:58.920 --> 00:47:01.500 align:middle line:90% energy for crystallization. 00:47:01.500 --> 00:47:04.840 align:middle line:84% And that's why, in terms of crystallization 00:47:04.840 --> 00:47:07.760 align:middle line:84% at high temperature, they can crystallize within a matter 00:47:07.760 --> 00:47:09.540 align:middle line:90% of a few tens of nanoseconds. 00:47:09.540 --> 00:47:10.800 align:middle line:90% So very, very fast. 00:47:10.800 --> 00:47:14.680 align:middle line:84% But at room temperature, they can retain data for 10 years. 00:47:14.680 --> 00:47:16.320 align:middle line:84% That's all because of this dependence 00:47:16.320 --> 00:47:18.785 align:middle line:84% of crystallization rate as a function of temperature. 00:47:18.785 --> 00:47:20.660 align:middle line:84% Now that's a somewhat simplified explanation. 00:47:20.660 --> 00:47:23.280 align:middle line:84% I do want to mention that it turns out, 00:47:23.280 --> 00:47:26.600 align:middle line:84% the viscosity, and hence crystallization velocity 00:47:26.600 --> 00:47:29.180 align:middle line:84% of phase-change materials, they do not obey Arrhenius law. 00:47:29.180 --> 00:47:30.900 align:middle line:84% They do not exactly obey Arrhenius law. 00:47:30.900 --> 00:47:32.020 align:middle line:90% But that's a good approximation. 00:47:32.020 --> 00:47:33.280 align:middle line:90% We'll stay for that for now. 00:47:33.280 --> 00:47:34.780 align:middle line:84% We'll talk about it when we actually 00:47:34.780 --> 00:47:36.860 align:middle line:84% talk about the viscosity of glass-forming fluids. 00:47:36.860 --> 00:47:39.640 align:middle line:84% But for now, we want something with high activation energy 00:47:39.640 --> 00:47:40.760 align:middle line:90% barrier. 00:47:40.760 --> 00:47:41.260 align:middle line:90% All right. 00:47:41.260 --> 00:47:43.733 align:middle line:84% Now, next thing, recording density. 00:47:43.733 --> 00:47:46.400 align:middle line:84% Recording density means that you want to put as much information 00:47:46.400 --> 00:47:49.720 align:middle line:84% as possible, as large a number of bits as possible into one 00:47:49.720 --> 00:47:50.460 align:middle line:90% single area. 00:47:50.460 --> 00:47:54.280 align:middle line:84% So that has to do with essentially the scaling 00:47:54.280 --> 00:47:56.320 align:middle line:90% behavior of the material. 00:47:56.320 --> 00:47:58.940 align:middle line:84% If you want to make your memory element very, very small, 00:47:58.940 --> 00:48:01.685 align:middle line:84% each bit, for example, each unit cell in state 00:48:01.685 --> 00:48:03.060 align:middle line:84% of the art phase-change memories, 00:48:03.060 --> 00:48:04.720 align:middle line:90% they are tens of nanometers. 00:48:04.720 --> 00:48:06.340 align:middle line:90% So it's a very, very small cell. 00:48:06.340 --> 00:48:08.060 align:middle line:84% So it's important to identify, do you 00:48:08.060 --> 00:48:10.000 align:middle line:84% have any kind of size dependence or material properties? 00:48:10.000 --> 00:48:11.667 align:middle line:84% Does it change crystallization behavior? 00:48:11.667 --> 00:48:14.318 align:middle line:84% Does surface or interface actually matter at that scale? 00:48:14.318 --> 00:48:15.860 align:middle line:84% So those are the things that actually 00:48:15.860 --> 00:48:19.180 align:middle line:84% come into play when you determine the recording density. 00:48:19.180 --> 00:48:21.220 align:middle line:84% Another factor that also comes in there 00:48:21.220 --> 00:48:22.480 align:middle line:90% is actually the driver size. 00:48:22.480 --> 00:48:24.340 align:middle line:90% This has to do with electronics. 00:48:24.340 --> 00:48:26.680 align:middle line:84% You need to have electronics actually drive the memory. 00:48:26.680 --> 00:48:30.100 align:middle line:84% So the size of that driving electronics also matters there. 00:48:30.100 --> 00:48:33.500 align:middle line:84% And finally, last thing is that you can potentially 00:48:33.500 --> 00:48:35.820 align:middle line:84% increase the recording density in this kind 00:48:35.820 --> 00:48:38.260 align:middle line:84% of phase-change materials there by doing 00:48:38.260 --> 00:48:40.860 align:middle line:90% a so-called multi-bit operation. 00:48:40.860 --> 00:48:43.640 align:middle line:84% So it means that, in one single unit cell, 00:48:43.640 --> 00:48:45.317 align:middle line:84% you now only have two endpoint states. 00:48:45.317 --> 00:48:46.400 align:middle line:90% This is fully crystalline. 00:48:46.400 --> 00:48:47.440 align:middle line:90% This is fully amorphous. 00:48:47.440 --> 00:48:49.620 align:middle line:84% You have lots of states in between that 00:48:49.620 --> 00:48:52.500 align:middle line:84% give you essentially partial crystallization. 00:48:52.500 --> 00:48:54.140 align:middle line:84% And those intermediate states allow 00:48:54.140 --> 00:48:56.690 align:middle line:84% you to essentially store multiple bits 00:48:56.690 --> 00:48:59.050 align:middle line:90% within one single unit cell. 00:48:59.050 --> 00:49:01.870 align:middle line:84% So if you read the literature, people have done 3-bit, 00:49:01.870 --> 00:49:02.828 align:middle line:90% for example, recording. 00:49:02.828 --> 00:49:04.370 align:middle line:84% Essentially, it means that you define 00:49:04.370 --> 00:49:06.910 align:middle line:84% 8 states instead of 2 states within one single unit cell. 00:49:06.910 --> 00:49:09.810 align:middle line:84% 8 different levels of crystallization. 00:49:09.810 --> 00:49:11.792 align:middle line:84% So that's one benefit, actually, for this kind 00:49:11.792 --> 00:49:12.750 align:middle line:90% of phase-change memory. 00:49:12.750 --> 00:49:17.250 align:middle line:84% You can do multi-level operation or multi-bit operation. 00:49:17.250 --> 00:49:17.750 align:middle line:90% All right. 00:49:17.750 --> 00:49:19.490 align:middle line:90% Next one, endurance. 00:49:19.490 --> 00:49:22.210 align:middle line:84% Endurance is a terminology people using a memory community 00:49:22.210 --> 00:49:24.490 align:middle line:84% to describe cycling lifetime-- how many times you 00:49:24.490 --> 00:49:28.088 align:middle line:84% can essentially write and erase your information in the memory 00:49:28.088 --> 00:49:29.130 align:middle line:90% before it starts to fail. 00:49:29.130 --> 00:49:33.050 align:middle line:90% 00:49:33.050 --> 00:49:35.890 align:middle line:84% So to boost endurance, this has to do with-- essentially, 00:49:35.890 --> 00:49:38.472 align:middle line:84% you have to know the failure mechanism. 00:49:38.472 --> 00:49:39.930 align:middle line:84% What causes failure and degradation 00:49:39.930 --> 00:49:42.055 align:middle line:84% in this kind of phase-change material over repeated 00:49:42.055 --> 00:49:46.170 align:middle line:84% amorphization and crystallization cycles? 00:49:46.170 --> 00:49:48.390 align:middle line:84% In general, for electronic memories, 00:49:48.390 --> 00:49:51.470 align:middle line:84% there's two main mechanisms that actually lead to a failure. 00:49:51.470 --> 00:49:55.160 align:middle line:84% One is electromigration because, as I will show you 00:49:55.160 --> 00:49:58.797 align:middle line:84% later on, the way we actually apply this kind of energy pulses 00:49:58.797 --> 00:50:01.380 align:middle line:84% to crystallize it and amorphize it, to essentially heat it up, 00:50:01.380 --> 00:50:03.720 align:middle line:84% is by passing current through it, by joule heating. 00:50:03.720 --> 00:50:05.582 align:middle line:84% But when you pass current through it, 00:50:05.582 --> 00:50:08.040 align:middle line:84% it means that you apply electric field across the material. 00:50:08.040 --> 00:50:09.740 align:middle line:84% If you apply electric field to the material, 00:50:09.740 --> 00:50:11.198 align:middle line:84% you get so-called electromigration. 00:50:11.198 --> 00:50:12.780 align:middle line:84% The atoms can move in electric field. 00:50:12.780 --> 00:50:14.988 align:middle line:84% And eventually, this leads to segregation and failure 00:50:14.988 --> 00:50:16.260 align:middle line:90% of the device. 00:50:16.260 --> 00:50:19.840 align:middle line:84% You can even get voids, nanovoids, at some point 00:50:19.840 --> 00:50:23.600 align:middle line:84% because of the atomic migration, which then lead 00:50:23.600 --> 00:50:25.000 align:middle line:90% to, essentially, open circuits. 00:50:25.000 --> 00:50:27.760 align:middle line:84% So that's one mechanism of failure. 00:50:27.760 --> 00:50:29.920 align:middle line:84% The second one is actually a phase stability. 00:50:29.920 --> 00:50:31.640 align:middle line:84% We will go into a bit more details 00:50:31.640 --> 00:50:35.040 align:middle line:84% later, but some of these phase-change memory 00:50:35.040 --> 00:50:36.980 align:middle line:84% materials, when they actually melt, 00:50:36.980 --> 00:50:38.460 align:middle line:90% they do not melt congruently. 00:50:38.460 --> 00:50:40.620 align:middle line:84% They phase-segregate when they go to liquid phase. 00:50:40.620 --> 00:50:42.440 align:middle line:84% So over time, that can actually accumulate. 00:50:42.440 --> 00:50:44.690 align:middle line:84% Essentially, it means you have essentially composition 00:50:44.690 --> 00:50:48.720 align:middle line:84% segregation, which harm the stability of the material. 00:50:48.720 --> 00:50:49.220 align:middle line:90% All right. 00:50:49.220 --> 00:50:51.000 align:middle line:90% Last part, power consumption. 00:50:51.000 --> 00:50:54.620 align:middle line:84% You want the energy-efficient memories. 00:50:54.620 --> 00:50:56.500 align:middle line:84% So what dictates the power you will need 00:50:56.500 --> 00:51:00.140 align:middle line:90% to crystallize the amorphous? 00:51:00.140 --> 00:51:04.297 align:middle line:84% For amorphization, you need to melt it. 00:51:04.297 --> 00:51:06.380 align:middle line:84% So what that means you need to do is, first thing, 00:51:06.380 --> 00:51:07.860 align:middle line:90% you need to heat it up. 00:51:07.860 --> 00:51:09.540 align:middle line:84% You need to heat it up to melting point. 00:51:09.540 --> 00:51:12.340 align:middle line:84% So this has to do with essentially the volume, as well 00:51:12.340 --> 00:51:14.460 align:middle line:84% as the heat capacity of the material. 00:51:14.460 --> 00:51:17.180 align:middle line:84% Second part is that there's the latent heat. 00:51:17.180 --> 00:51:20.060 align:middle line:84% You need to supply the enthalpy of melting to actually melt it 00:51:20.060 --> 00:51:21.740 align:middle line:90% into liquid. 00:51:21.740 --> 00:51:24.300 align:middle line:84% So for the amorphization process, 00:51:24.300 --> 00:51:26.940 align:middle line:84% the overall power consumption has to do, essentially, 00:51:26.940 --> 00:51:29.240 align:middle line:84% with the heat capacity as well as enthalpy of melting. 00:51:29.240 --> 00:51:31.860 align:middle line:84% it's sort of like, basically, the total heat 00:51:31.860 --> 00:51:36.820 align:middle line:84% you need to essentially melt it is the sum of two terms there. 00:51:36.820 --> 00:51:39.940 align:middle line:84% For crystallization, heat capacity 00:51:39.940 --> 00:51:43.240 align:middle line:84% also matters, obviously, but for crystallization, 00:51:43.240 --> 00:51:45.260 align:middle line:84% what matters more is actually crystallization 00:51:45.260 --> 00:51:48.340 align:middle line:84% speed, because you want to heat it up and hold it there 00:51:48.340 --> 00:51:50.152 align:middle line:84% for some time until it crystallizes. 00:51:50.152 --> 00:51:52.610 align:middle line:84% The longer you hold there at elevated temperature, the more 00:51:52.610 --> 00:51:54.010 align:middle line:90% power you have to consume. 00:51:54.010 --> 00:51:56.530 align:middle line:84% So in that regard, you want a composition 00:51:56.530 --> 00:51:58.090 align:middle line:84% that can crystallize fast so that you 00:51:58.090 --> 00:52:00.930 align:middle line:84% can crystallize it quickly and have a lower power consumption. 00:52:00.930 --> 00:52:03.370 align:middle line:84% Now, another thing that also relates 00:52:03.370 --> 00:52:05.370 align:middle line:84% to power consumption that's not directly related 00:52:05.370 --> 00:52:07.210 align:middle line:84% to a property of phase-change materials 00:52:07.210 --> 00:52:11.250 align:middle line:84% is actually a heat conductivity, thermal conductivity. 00:52:11.250 --> 00:52:13.250 align:middle line:84% So if you are surrounded with materials 00:52:13.250 --> 00:52:15.470 align:middle line:84% with very good thermal insulation properties, 00:52:15.470 --> 00:52:17.210 align:middle line:84% you can confine the heat pretty much 00:52:17.210 --> 00:52:20.090 align:middle line:84% only to your phase-change material 00:52:20.090 --> 00:52:22.730 align:middle line:84% rather than dissipating the heat to a much larger surrounding 00:52:22.730 --> 00:52:23.690 align:middle line:90% medium. 00:52:23.690 --> 00:52:25.250 align:middle line:84% So that helps you essentially limit 00:52:25.250 --> 00:52:27.930 align:middle line:84% the amount of thermal mass, and therefore 00:52:27.930 --> 00:52:30.073 align:middle line:90% make it more energy efficient. 00:52:30.073 --> 00:52:31.990 align:middle line:84% So that's also something to account for there. 00:52:31.990 --> 00:52:32.490 align:middle line:90% All right. 00:52:32.490 --> 00:52:34.450 align:middle line:84% So if we keep that in mind, now let's actually 00:52:34.450 --> 00:52:37.210 align:middle line:84% take a look at a specific example 00:52:37.210 --> 00:52:40.330 align:middle line:90% of phase-change materials. 00:52:40.330 --> 00:52:42.530 align:middle line:84% The most commonly used phase-change material, 00:52:42.530 --> 00:52:44.790 align:middle line:84% they all come from this chalcogenide family. 00:52:44.790 --> 00:52:46.130 align:middle line:90% It's a ternary alloy. 00:52:46.130 --> 00:52:48.650 align:middle line:84% It's germanium antimony tellurium, 00:52:48.650 --> 00:52:51.870 align:middle line:90% or people call it GST. 00:52:51.870 --> 00:52:58.930 align:middle line:84% It was discovered by a few groups in Japan back in 1970s, 00:52:58.930 --> 00:52:59.490 align:middle line:90% 1980s. 00:52:59.490 --> 00:53:01.237 align:middle line:84% They found that this composition allows 00:53:01.237 --> 00:53:03.070 align:middle line:84% you to crystallize very, very quickly, which 00:53:03.070 --> 00:53:05.410 align:middle line:84% satisfies this property for, essentially, fast memories. 00:53:05.410 --> 00:53:08.030 align:middle line:84% Now, specifically, if you look at the composition 00:53:08.030 --> 00:53:11.070 align:middle line:84% there, what I'm showing here is like ternary diagram 00:53:11.070 --> 00:53:14.350 align:middle line:84% of a germanium antimony tellurium system. 00:53:14.350 --> 00:53:17.590 align:middle line:84% Most of the phase-change memory material 00:53:17.590 --> 00:53:20.090 align:middle line:84% come from this pseudobinary system. 00:53:20.090 --> 00:53:24.670 align:middle line:84% It's this tie-line between the germanium tellurium and antimony 00:53:24.670 --> 00:53:25.830 align:middle line:90% telluride. 00:53:25.830 --> 00:53:29.110 align:middle line:84% So one particular composition that's 00:53:29.110 --> 00:53:33.030 align:middle line:84% probably the most prevalent is this one, Ge2, antimony 2, 00:53:33.030 --> 00:53:34.150 align:middle line:90% tellurium 5. 00:53:34.150 --> 00:53:37.190 align:middle line:90% This is called GST 225. 00:53:37.190 --> 00:53:39.390 align:middle line:84% This is the most widely used composition 00:53:39.390 --> 00:53:42.230 align:middle line:84% for this kind of phase-change memory applications. 00:53:42.230 --> 00:53:44.150 align:middle line:84% But then you can, of course, tailor 00:53:44.150 --> 00:53:48.940 align:middle line:84% it to go to other compositions to engineer its properties. 00:53:48.940 --> 00:53:50.718 align:middle line:90% So now, if you think about the-- 00:53:50.718 --> 00:53:53.260 align:middle line:84% apply the glass-forming theory to this particular composition 00:53:53.260 --> 00:53:55.177 align:middle line:84% here, we need to think about the, essentially, 00:53:55.177 --> 00:53:56.180 align:middle line:90% glass stability. 00:53:56.180 --> 00:53:58.900 align:middle line:84% This is one of the cases you actually don't want good glass 00:53:58.900 --> 00:54:00.628 align:middle line:90% stability. 00:54:00.628 --> 00:54:02.420 align:middle line:84% Because good glass stability-- or let's say 00:54:02.420 --> 00:54:03.860 align:middle line:84% you don't want too good glass stability. 00:54:03.860 --> 00:54:05.860 align:middle line:84% Too good glass stability means it takes forever 00:54:05.860 --> 00:54:09.500 align:middle line:84% to crystallize, which is bad if you want a fast memory. 00:54:09.500 --> 00:54:15.040 align:middle line:84% So it turns out, if you look at these kind of compositions here, 00:54:15.040 --> 00:54:17.540 align:middle line:90% they are all stressed rigid. 00:54:17.540 --> 00:54:19.700 align:middle line:84% They have a mean coordination number 00:54:19.700 --> 00:54:22.860 align:middle line:84% that's significantly larger than isostatic condition, which 00:54:22.860 --> 00:54:25.020 align:middle line:84% explains why these compositions, they actually 00:54:25.020 --> 00:54:26.980 align:middle line:90% crystallize so fast. 00:54:26.980 --> 00:54:31.063 align:middle line:84% In fact, being stressed rigid is also beneficial 00:54:31.063 --> 00:54:32.980 align:middle line:84% because, as I said, stressed rigid essentially 00:54:32.980 --> 00:54:36.300 align:middle line:84% means that you form a very deep valley or deep minimum 00:54:36.300 --> 00:54:38.940 align:middle line:84% corresponding to crystalline state. 00:54:38.940 --> 00:54:41.580 align:middle line:84% And in this phase-change materials, 00:54:41.580 --> 00:54:43.580 align:middle line:84% in order to induce crystallization, what happens 00:54:43.580 --> 00:54:49.130 align:middle line:84% is that there are some atomic arrangements that 00:54:49.130 --> 00:54:51.852 align:middle line:84% closely resemble their crystalline configuration. 00:54:51.852 --> 00:54:53.810 align:middle line:84% So when crystallization happens, essentially it 00:54:53.810 --> 00:54:55.650 align:middle line:84% started out from these kind of arrangements 00:54:55.650 --> 00:54:58.050 align:middle line:84% that resemble the crystalline orientation, crystalline 00:54:58.050 --> 00:54:58.950 align:middle line:90% arrangement. 00:54:58.950 --> 00:55:01.210 align:middle line:84% And then the crystallization speed, growth speed, 00:55:01.210 --> 00:55:04.150 align:middle line:84% is actually very, very fast once you have a nuclei. 00:55:04.150 --> 00:55:05.650 align:middle line:84% These represent some of the material 00:55:05.650 --> 00:55:07.930 align:middle line:84% that has the fastest crystal growth 00:55:07.930 --> 00:55:10.270 align:middle line:90% speed in all material systems. 00:55:10.270 --> 00:55:12.130 align:middle line:84% So then, if you have one nuclei, it quickly 00:55:12.130 --> 00:55:13.880 align:middle line:84% can propagate through the entire material. 00:55:13.880 --> 00:55:17.090 align:middle line:84% And that's how you actually get fast crystallization. 00:55:17.090 --> 00:55:20.090 align:middle line:84% So that's why people want to do it specifically 00:55:20.090 --> 00:55:21.650 align:middle line:90% in the stressed rigid network. 00:55:21.650 --> 00:55:23.170 align:middle line:84% Now one caveat I do want to mention 00:55:23.170 --> 00:55:26.810 align:middle line:84% there is that if you look at this material system, 00:55:26.810 --> 00:55:29.810 align:middle line:84% we have two heavy elements that I have specifically 00:55:29.810 --> 00:55:31.400 align:middle line:84% listed in the previous slide deck 00:55:31.400 --> 00:55:33.650 align:middle line:84% that it's very difficult to determine the coordination 00:55:33.650 --> 00:55:34.150 align:middle line:90% number. 00:55:34.150 --> 00:55:38.330 align:middle line:84% So if you look at this particular PRB paper there, 00:55:38.330 --> 00:55:40.850 align:middle line:84% the authors actually did some first-principle calculations 00:55:40.850 --> 00:55:43.330 align:middle line:84% to actually predict what's the real coordination number 00:55:43.330 --> 00:55:44.610 align:middle line:90% for these elements there. 00:55:44.610 --> 00:55:47.510 align:middle line:84% So it's different from you just use 8 minus N rule. 00:55:47.510 --> 00:55:49.430 align:middle line:84% What they have come up is this line here. 00:55:49.430 --> 00:55:51.030 align:middle line:84% If you go along this dotted line, 00:55:51.030 --> 00:55:54.607 align:middle line:84% this corresponds to the extra isostatic composition. 00:55:54.607 --> 00:55:55.690 align:middle line:90% This is, again, different. 00:55:55.690 --> 00:55:57.470 align:middle line:84% If you try to apply that simple 8 minus N rule, 00:55:57.470 --> 00:55:58.970 align:middle line:84% it's going to get different results. 00:55:58.970 --> 00:56:03.588 align:middle line:84% Anything to the right-hand side here, this is stressed rigid. 00:56:03.588 --> 00:56:05.630 align:middle line:84% So if you add more fourfold-coordinated germanium 00:56:05.630 --> 00:56:07.070 align:middle line:84% or threefold-coordinated antimony, 00:56:07.070 --> 00:56:09.030 align:middle line:84% you actually increase the coordination number. 00:56:09.030 --> 00:56:10.950 align:middle line:84% And so what that also means is that if you 00:56:10.950 --> 00:56:13.970 align:middle line:84% go along this direction, you get compositions. 00:56:13.970 --> 00:56:16.470 align:middle line:84% They are becoming less and less stable. 00:56:16.470 --> 00:56:19.750 align:middle line:84% And less stable means faster crystallization. 00:56:19.750 --> 00:56:22.670 align:middle line:84% So that's why I have shown here, these 00:56:22.670 --> 00:56:25.010 align:middle line:84% are some examples of fast switching compositions, 00:56:25.010 --> 00:56:27.790 align:middle line:84% like this one here and this one here. 00:56:27.790 --> 00:56:29.590 align:middle line:84% So these fast switching compositions, 00:56:29.590 --> 00:56:32.510 align:middle line:84% they all lie to the right side, to this side line 00:56:32.510 --> 00:56:35.590 align:middle line:84% there, indicating a reduced glass stability. 00:56:35.590 --> 00:56:38.150 align:middle line:90% 00:56:38.150 --> 00:56:41.310 align:middle line:84% Now the other possible way to tailor the composition 00:56:41.310 --> 00:56:44.620 align:middle line:84% is sometimes you may want to have high thermal stability 00:56:44.620 --> 00:56:45.120 align:middle line:90% alloys. 00:56:45.120 --> 00:56:46.620 align:middle line:84% This will be useful if you're trying 00:56:46.620 --> 00:56:48.340 align:middle line:84% to use your materials or the memories 00:56:48.340 --> 00:56:51.100 align:middle line:84% in high operating temperature environments. 00:56:51.100 --> 00:56:54.900 align:middle line:84% So they typically go along this line here, this red line, 00:56:54.900 --> 00:56:57.320 align:middle line:84% by increasing the germanium concentration. 00:56:57.320 --> 00:57:00.100 align:middle line:84% Now we wonder, if you go along this line, 00:57:00.100 --> 00:57:03.120 align:middle line:84% you also increase the mean coordination number. 00:57:03.120 --> 00:57:06.980 align:middle line:84% So the network actually becomes less stable. 00:57:06.980 --> 00:57:09.580 align:middle line:84% So why you can have a better thermal stability, 00:57:09.580 --> 00:57:12.020 align:middle line:90% or in other words, better Tx? 00:57:12.020 --> 00:57:14.300 align:middle line:84% So this actually has to do with the definition 00:57:14.300 --> 00:57:16.200 align:middle line:90% of glass-forming ability. 00:57:16.200 --> 00:57:18.740 align:middle line:84% So when you're talking about high thermal stability, what 00:57:18.740 --> 00:57:22.200 align:middle line:84% you want is the high Tx, high crystallization temperature. 00:57:22.200 --> 00:57:25.480 align:middle line:84% But when we actually measure the glass-forming ability, 00:57:25.480 --> 00:57:30.540 align:middle line:84% the figure of merit is actually delta T. Tx minus Tg. 00:57:30.540 --> 00:57:32.320 align:middle line:84% So if you go along this axis here, 00:57:32.320 --> 00:57:36.015 align:middle line:84% turns out the Tg also increases because germanium, 00:57:36.015 --> 00:57:38.140 align:middle line:84% as fourfold coordinated, increased the connectivity 00:57:38.140 --> 00:57:38.980 align:middle line:90% of the network. 00:57:38.980 --> 00:57:41.180 align:middle line:90% So you also increase Tg. 00:57:41.180 --> 00:57:44.500 align:middle line:84% So you actually have decreased glass stability, 00:57:44.500 --> 00:57:48.320 align:middle line:90% but the Tx increases as well. 00:57:48.320 --> 00:57:50.720 align:middle line:84% So it just has to do with how you actually 00:57:50.720 --> 00:57:55.840 align:middle line:84% identify the right figure of merit for specific applications. 00:57:55.840 --> 00:57:56.340 align:middle line:90% All right. 00:57:56.340 --> 00:57:58.320 align:middle line:84% So now, last point I also want to make here 00:57:58.320 --> 00:57:59.520 align:middle line:84% is that I have already highlighted 00:57:59.520 --> 00:58:01.145 align:middle line:84% that this kind of phase-change material 00:58:01.145 --> 00:58:03.280 align:middle line:84% is quite unique in that they exhibit 00:58:03.280 --> 00:58:06.160 align:middle line:84% a huge contrast of properties between amorphous 00:58:06.160 --> 00:58:07.440 align:middle line:90% and crystalline states. 00:58:07.440 --> 00:58:10.680 align:middle line:84% This has to do with the chemical bonding nature. 00:58:10.680 --> 00:58:14.280 align:middle line:84% In the amorphous network, you have the conventional covalent 00:58:14.280 --> 00:58:17.320 align:middle line:84% bond, but when you go to crystalline state, 00:58:17.320 --> 00:58:20.480 align:middle line:84% you have the so-called resonant bonding. 00:58:20.480 --> 00:58:23.600 align:middle line:84% So to explain that, let's take a look 00:58:23.600 --> 00:58:27.720 align:middle line:84% at the structure of this kind of GST alloy. 00:58:27.720 --> 00:58:32.340 align:middle line:84% So GST alloy has a quasicubic structure. 00:58:32.340 --> 00:58:34.960 align:middle line:90% It's pretty close to cubic. 00:58:34.960 --> 00:58:38.360 align:middle line:84% It's basically sodium chloride structure. 00:58:38.360 --> 00:58:40.360 align:middle line:84% So if you look at the sodium chloride structure, 00:58:40.360 --> 00:58:43.950 align:middle line:84% you have two penetrating sets of FCC lattices. 00:58:43.950 --> 00:58:48.350 align:middle line:84% And tellurium occupies one set of the lattice sites. 00:58:48.350 --> 00:58:50.630 align:middle line:84% Germanium antimony combined occupy 00:58:50.630 --> 00:58:53.430 align:middle line:90% another set of lattice sites. 00:58:53.430 --> 00:58:56.190 align:middle line:84% But if you look at the stoichiometry, for 225, 00:58:56.190 --> 00:58:58.390 align:middle line:90% germanium plus antimony is 4. 00:58:58.390 --> 00:59:00.110 align:middle line:90% It's less than tellurium. 00:59:00.110 --> 00:59:04.230 align:middle line:84% So it means that this is not a perfect cubic structure. 00:59:04.230 --> 00:59:11.150 align:middle line:84% You get lots of native vacancies that comes in the lattice layer. 00:59:11.150 --> 00:59:13.605 align:middle line:90% All right. 00:59:13.605 --> 00:59:16.230 align:middle line:84% And that's why there's actually distortion through the lattice. 00:59:16.230 --> 00:59:18.250 align:middle line:84% So that's why I say it's quasicubic. 00:59:18.250 --> 00:59:19.150 align:middle line:90% It's close to cubic. 00:59:19.150 --> 00:59:22.470 align:middle line:90% 00:59:22.470 --> 00:59:22.970 align:middle line:90% All right. 00:59:22.970 --> 00:59:25.470 align:middle line:84% So now, if you look at the chemical bond configuration, 00:59:25.470 --> 00:59:27.930 align:middle line:84% let's look at one plane here, one two-dimensional plane. 00:59:27.930 --> 00:59:30.668 align:middle line:84% Let's suppose we're looking at, say, germanium tellurium plane. 00:59:30.668 --> 00:59:32.210 align:middle line:84% It can be germanium antimony as well. 00:59:32.210 --> 00:59:33.710 align:middle line:90% Doesn't matter. 00:59:33.710 --> 00:59:37.390 align:middle line:84% Now, if you think about conventional covalent bonds, 00:59:37.390 --> 00:59:40.490 align:middle line:84% in a covalent bond, the two bonding atoms each 00:59:40.490 --> 00:59:43.050 align:middle line:84% contribute one electron, and these two electrons 00:59:43.050 --> 00:59:46.530 align:middle line:84% are tightly confined between these two atoms there. 00:59:46.530 --> 00:59:49.570 align:middle line:84% This is how you actually form the covalent bond. 00:59:49.570 --> 00:59:52.030 align:middle line:84% For phase-change material, on the other hand, 00:59:52.030 --> 00:59:54.210 align:middle line:84% if you think about this conventional covalent bond 00:59:54.210 --> 00:59:58.090 align:middle line:84% picture, there are two different equivalent ways 00:59:58.090 --> 00:59:59.750 align:middle line:90% to arrange the chemical bonds. 00:59:59.750 --> 01:00:02.050 align:middle line:84% They are actually energetically equivalent if you 01:00:02.050 --> 01:00:05.130 align:middle line:84% look at these two pictures here, this one versus this one. 01:00:05.130 --> 01:00:07.170 align:middle line:84% So this solid line, this thicker line, 01:00:07.170 --> 01:00:09.990 align:middle line:84% essentially represents an actual chemical bond. 01:00:09.990 --> 01:00:12.865 align:middle line:84% So you can essentially generate a chemical bond 01:00:12.865 --> 01:00:14.990 align:middle line:84% like what I'm arranging on the left-hand side here. 01:00:14.990 --> 01:00:17.240 align:middle line:84% These are the atoms that actually have chemical bonds. 01:00:17.240 --> 01:00:20.550 align:middle line:84% Or you can also connect them together in a different manner 01:00:20.550 --> 01:00:21.050 align:middle line:90% there. 01:00:21.050 --> 01:00:24.010 align:middle line:84% Now these two, by symmetry, you can easily 01:00:24.010 --> 01:00:28.530 align:middle line:84% tell that they should be energetically equivalent. 01:00:28.530 --> 01:00:30.330 align:middle line:84% So what actually happens in this process 01:00:30.330 --> 01:00:33.890 align:middle line:84% is that these two states are actually going hybridized. 01:00:33.890 --> 01:00:37.530 align:middle line:84% So instead of getting a well-defined covalent bond, what 01:00:37.530 --> 01:00:39.960 align:middle line:84% you get is this average connection 01:00:39.960 --> 01:00:41.800 align:middle line:84% between all the neighboring atoms. 01:00:41.800 --> 01:00:44.460 align:middle line:84% And the electrons essentially becomes delocalized. 01:00:44.460 --> 01:00:47.540 align:middle line:84% They can now move around between these neighboring atoms here. 01:00:47.540 --> 01:00:52.000 align:middle line:90% 01:00:52.000 --> 01:00:54.160 align:middle line:84% Now, in fact, you might have seen 01:00:54.160 --> 01:00:56.960 align:middle line:84% one example of resonant bonding when 01:00:56.960 --> 01:00:58.840 align:middle line:84% you go to chemistry, if you think 01:00:58.840 --> 01:01:04.200 align:middle line:84% about benzene, benzene molecules. 01:01:04.200 --> 01:01:06.900 align:middle line:84% This is a six-membered carbon ring. 01:01:06.900 --> 01:01:08.380 align:middle line:90% You have some double bonds. 01:01:08.380 --> 01:01:09.732 align:middle line:90% You have some single bonds. 01:01:09.732 --> 01:01:11.440 align:middle line:84% You probably have learned from chemistry, 01:01:11.440 --> 01:01:13.523 align:middle line:84% saying that there are actually two resonant states 01:01:13.523 --> 01:01:14.780 align:middle line:90% for this benzene molecule. 01:01:14.780 --> 01:01:16.503 align:middle line:84% You can go from that configuration 01:01:16.503 --> 01:01:17.420 align:middle line:90% to this configuration. 01:01:17.420 --> 01:01:18.880 align:middle line:84% They are energetically equivalent. 01:01:18.880 --> 01:01:20.440 align:middle line:84% So what we actually end up having is 01:01:20.440 --> 01:01:23.380 align:middle line:84% that the pi electrons essentially become delocalized. 01:01:23.380 --> 01:01:26.880 align:middle line:84% They just move around inside this benzene ring. 01:01:26.880 --> 01:01:29.600 align:middle line:84% So the mechanism that leads to electron delocalization 01:01:29.600 --> 01:01:34.320 align:middle line:84% in phase-change materials is similar to what you have 01:01:34.320 --> 01:01:38.430 align:middle line:90% in the benzene structure there. 01:01:38.430 --> 01:01:42.230 align:middle line:84% Now I do want to highlight that the actual chemical 01:01:42.230 --> 01:01:45.190 align:middle line:84% nature is still quite different compared to benzene. 01:01:45.190 --> 01:01:47.980 align:middle line:84% And that's why some people like to call it a different name. 01:01:47.980 --> 01:01:50.230 align:middle line:84% They actually classify this kind of particular bonding 01:01:50.230 --> 01:01:52.750 align:middle line:84% in phase-change materials as a new type of chemical bonding 01:01:52.750 --> 01:01:54.150 align:middle line:90% called metavalent bonds. 01:01:54.150 --> 01:01:57.150 align:middle line:84% But anyway, that's the terminology people use. 01:01:57.150 --> 01:02:01.390 align:middle line:84% Regardless, what happens if you have 01:02:01.390 --> 01:02:02.830 align:middle line:90% this kind of resonant bonding? 01:02:02.830 --> 01:02:05.910 align:middle line:84% This resonant bonding, it only exists 01:02:05.910 --> 01:02:07.950 align:middle line:90% in the crystalline structure. 01:02:07.950 --> 01:02:08.590 align:middle line:90% Why? 01:02:08.590 --> 01:02:10.215 align:middle line:84% Because if you look at these two states 01:02:10.215 --> 01:02:12.170 align:middle line:84% here, in a crystalline structure, 01:02:12.170 --> 01:02:13.830 align:middle line:84% you get this kind of periodic order. 01:02:13.830 --> 01:02:17.030 align:middle line:84% So these two, they are structurally equivalent. 01:02:17.030 --> 01:02:19.430 align:middle line:84% And that's why they are energetically the same. 01:02:19.430 --> 01:02:20.672 align:middle line:90% That's why they hybridize. 01:02:20.672 --> 01:02:22.630 align:middle line:84% Now, if you break this kind of structure order, 01:02:22.630 --> 01:02:24.250 align:middle line:84% you introduce structure disorder, 01:02:24.250 --> 01:02:26.590 align:middle line:84% then you also break the symmetry between these two 01:02:26.590 --> 01:02:28.470 align:middle line:90% types of states. 01:02:28.470 --> 01:02:31.550 align:middle line:84% And as a result, in amorphous network, 01:02:31.550 --> 01:02:35.170 align:middle line:84% the bonding becomes predominantly covalent. 01:02:35.170 --> 01:02:38.110 align:middle line:90% 01:02:38.110 --> 01:02:42.490 align:middle line:84% So this kind of a hybridization is the consequence 01:02:42.490 --> 01:02:45.330 align:middle line:90% of symmetry and periodicity. 01:02:45.330 --> 01:02:49.450 align:middle line:84% If you break that, then you actually lose that nature. 01:02:49.450 --> 01:02:51.910 align:middle line:84% So now, what's the difference in terms of properties? 01:02:51.910 --> 01:02:53.710 align:middle line:84% If you think about covalent bonds, 01:02:53.710 --> 01:02:55.510 align:middle line:84% the electron is very tightly localized. 01:02:55.510 --> 01:02:58.170 align:middle line:84% So it means that it doesn't really move around very far. 01:02:58.170 --> 01:02:59.710 align:middle line:90% Versus resonant bonding. 01:02:59.710 --> 01:03:01.870 align:middle line:84% Electrons are now allowed to move. 01:03:01.870 --> 01:03:02.910 align:middle line:90% They become mobile. 01:03:02.910 --> 01:03:05.730 align:middle line:84% They can move much longer distances in the solid. 01:03:05.730 --> 01:03:08.490 align:middle line:84% This corresponds to much higher electronic 01:03:08.490 --> 01:03:12.400 align:middle line:90% polarizability and conductivity. 01:03:12.400 --> 01:03:14.150 align:middle line:84% When you want to conduct electric current, 01:03:14.150 --> 01:03:17.030 align:middle line:84% you basically want the electron to move around in a solid. 01:03:17.030 --> 01:03:19.180 align:middle line:84% So that's why, when you go to crystalline state, 01:03:19.180 --> 01:03:20.930 align:middle line:84% these materials typically have much higher 01:03:20.930 --> 01:03:23.330 align:middle line:84% electronic conductivity because of the delocalization 01:03:23.330 --> 01:03:24.190 align:middle line:90% of electrons. 01:03:24.190 --> 01:03:26.770 align:middle line:90% 01:03:26.770 --> 01:03:30.890 align:middle line:84% In terms of optical properties, refractive index of material 01:03:30.890 --> 01:03:34.350 align:middle line:84% actually has to do with the electronic polarizability. 01:03:34.350 --> 01:03:39.400 align:middle line:90% 01:03:39.400 --> 01:03:41.240 align:middle line:84% Light is basically electromagnetic wave. 01:03:41.240 --> 01:03:43.120 align:middle line:84% It's an oscillating electromagnetic field. 01:03:43.120 --> 01:03:46.060 align:middle line:84% So if a material has very high electronic polarizability, 01:03:46.060 --> 01:03:47.920 align:middle line:84% it means electrons can easily keep up 01:03:47.920 --> 01:03:50.480 align:middle line:84% with this oscillating electromagnetic field. 01:03:50.480 --> 01:03:52.720 align:middle line:84% So as a result, you have much higher, much stronger 01:03:52.720 --> 01:03:53.620 align:middle line:90% optical response. 01:03:53.620 --> 01:03:55.920 align:middle line:84% And therefore, you have a higher refractive index. 01:03:55.920 --> 01:03:56.620 align:middle line:90% So same thing. 01:03:56.620 --> 01:03:58.203 align:middle line:84% That's why the crystalline state tends 01:03:58.203 --> 01:04:00.280 align:middle line:84% to have a much higher refractive index compared 01:04:00.280 --> 01:04:01.500 align:middle line:90% to amorphous counterpart. 01:04:01.500 --> 01:04:04.520 align:middle line:90% 01:04:04.520 --> 01:04:06.340 align:middle line:84% And that's why this material is so unique. 01:04:06.340 --> 01:04:08.500 align:middle line:84% You don't see that behavior in typical materials. 01:04:08.500 --> 01:04:10.080 align:middle line:84% You only find it in some materials 01:04:10.080 --> 01:04:12.640 align:middle line:84% that actually form this kind of a resonant or metavalent 01:04:12.640 --> 01:04:13.180 align:middle line:90% bonding. 01:04:13.180 --> 01:04:17.000 align:middle line:90% 01:04:17.000 --> 01:04:18.460 align:middle line:90% All right. 01:04:18.460 --> 01:04:19.960 align:middle line:84% So our next part, now let's actually 01:04:19.960 --> 01:04:22.040 align:middle line:84% take a look at the thermodynamics 01:04:22.040 --> 01:04:25.480 align:middle line:84% and kinetics of the phase transition process. 01:04:25.480 --> 01:04:27.960 align:middle line:84% For thermodynamics, of course, as a material scientist, 01:04:27.960 --> 01:04:29.340 align:middle line:90% we all like phase diagrams. 01:04:29.340 --> 01:04:31.600 align:middle line:84% So this is one of probably the more complicated phase 01:04:31.600 --> 01:04:34.180 align:middle line:84% diagrams you will see in this kind of binary system. 01:04:34.180 --> 01:04:35.920 align:middle line:84% It's actually a pseudobinary system. 01:04:35.920 --> 01:04:37.620 align:middle line:84% This is between the germanium tellurium 01:04:37.620 --> 01:04:39.060 align:middle line:90% and the antimony telluride. 01:04:39.060 --> 01:04:41.920 align:middle line:84% So this gives you all the GST variants along that tie-line 01:04:41.920 --> 01:04:42.420 align:middle line:90% there. 01:04:42.420 --> 01:04:45.540 align:middle line:90% So GST 225 is this guy. 01:04:45.540 --> 01:04:48.380 align:middle line:90% This is our GST 225. 01:04:48.380 --> 01:04:49.620 align:middle line:90% Now notice one thing. 01:04:49.620 --> 01:04:51.140 align:middle line:90% It's a line compound. 01:04:51.140 --> 01:04:54.900 align:middle line:84% But this solid compound, it doesn't go all the way 01:04:54.900 --> 01:04:56.320 align:middle line:90% to the liquid region. 01:04:56.320 --> 01:04:58.500 align:middle line:84% There's a little gap right there. 01:04:58.500 --> 01:05:01.460 align:middle line:84% So what happens if you reach this temperature? 01:05:01.460 --> 01:05:03.140 align:middle line:90% You go into a two-phase region. 01:05:03.140 --> 01:05:05.180 align:middle line:84% It essentially means that this solid 01:05:05.180 --> 01:05:08.460 align:middle line:84% decomposes into a antimony-rich liquid 01:05:08.460 --> 01:05:11.660 align:middle line:90% and a germanium-rich solid. 01:05:11.660 --> 01:05:14.560 align:middle line:84% This is called a noncongruent melting. 01:05:14.560 --> 01:05:17.240 align:middle line:84% It essentially means that this liquid line-- sorry, 01:05:17.240 --> 01:05:19.860 align:middle line:84% this solid line doesn't go all the way to the liquid region 01:05:19.860 --> 01:05:20.980 align:middle line:90% there. 01:05:20.980 --> 01:05:22.580 align:middle line:84% So then this is actually-- this can 01:05:22.580 --> 01:05:24.980 align:middle line:84% be a concern from a reliability perspective 01:05:24.980 --> 01:05:26.820 align:middle line:90% or endurance perspective. 01:05:26.820 --> 01:05:29.020 align:middle line:84% If you are trying to melt this material, 01:05:29.020 --> 01:05:31.810 align:middle line:84% then you always form essentially different compositional regions. 01:05:31.810 --> 01:05:34.530 align:middle line:84% And over repeated cycles, this can eventually 01:05:34.530 --> 01:05:36.530 align:middle line:84% lead to a compositional segregation, which then 01:05:36.530 --> 01:05:38.450 align:middle line:90% eventually leads to failure. 01:05:38.450 --> 01:05:41.250 align:middle line:84% So that's why I'm saying that noncongruent melting and phase 01:05:41.250 --> 01:05:43.830 align:middle line:84% stability is one factor that limits endurance. 01:05:43.830 --> 01:05:49.350 align:middle line:90% 01:05:49.350 --> 01:05:51.850 align:middle line:84% Now, you can find some other compositions where you actually 01:05:51.850 --> 01:05:53.450 align:middle line:90% have congruent melting. 01:05:53.450 --> 01:05:54.930 align:middle line:84% And then people have actually shown 01:05:54.930 --> 01:05:57.810 align:middle line:84% that those compositions can give you a much better endurance. 01:05:57.810 --> 01:06:03.310 align:middle line:90% 01:06:03.310 --> 01:06:09.570 align:middle line:84% Now, despite that, this GST 225 is still very remarkable. 01:06:09.570 --> 01:06:10.810 align:middle line:90% They can be cycled. 01:06:10.810 --> 01:06:12.850 align:middle line:84% If you look at the literature report or even 01:06:12.850 --> 01:06:16.010 align:middle line:84% commercial devices, 10 to the 6 to 10 to 8 cycles 01:06:16.010 --> 01:06:17.962 align:middle line:90% is very normal. 01:06:17.962 --> 01:06:20.170 align:middle line:84% People were able to get some [INAUDIBLE] results, get 01:06:20.170 --> 01:06:24.250 align:middle line:84% 10 to 11, 10 to 12 cycle numbers in laboratory devices. 01:06:24.250 --> 01:06:25.925 align:middle line:84% So it's already quite remarkable. 01:06:25.925 --> 01:06:26.550 align:middle line:90% Think about it. 01:06:26.550 --> 01:06:30.063 align:middle line:84% You to move atoms around, melt it, quench it, melt it, 01:06:30.063 --> 01:06:32.480 align:middle line:84% quench it, and crystallize it, so many cycles, while still 01:06:32.480 --> 01:06:34.460 align:middle line:84% maintaining this kind of stable performance. 01:06:34.460 --> 01:06:37.960 align:middle line:84% So there's a lot of material engineering 01:06:37.960 --> 01:06:41.240 align:middle line:84% that goes into engineering this kind of durable materials. 01:06:41.240 --> 01:06:41.740 align:middle line:90% All right. 01:06:41.740 --> 01:06:43.320 align:middle line:90% That's for the thermodynamics. 01:06:43.320 --> 01:06:44.160 align:middle line:90% Now kinetics. 01:06:44.160 --> 01:06:45.800 align:middle line:90% T-T-T diagram, obviously. 01:06:45.800 --> 01:06:47.040 align:middle line:90% My favorite. 01:06:47.040 --> 01:06:51.800 align:middle line:84% So this is like a schematic T-T-T diagram for GST alloys. 01:06:51.800 --> 01:06:53.880 align:middle line:90% A few things here. 01:06:53.880 --> 01:06:56.600 align:middle line:84% First thing is, let's look at the nose here. 01:06:56.600 --> 01:06:59.320 align:middle line:84% If you look at the nose, there are two regions here. 01:06:59.320 --> 01:07:00.220 align:middle line:90% I have two lines. 01:07:00.220 --> 01:07:01.863 align:middle line:84% One corresponds to 10% crystallization. 01:07:01.863 --> 01:07:03.780 align:middle line:84% The other one corresponds 90% crystallization. 01:07:03.780 --> 01:07:06.800 align:middle line:84% So if you look at near the nose temperature, 01:07:06.800 --> 01:07:09.640 align:middle line:84% the time scale we are talking about here 01:07:09.640 --> 01:07:15.120 align:middle line:84% is of the order of a nanosecond to tens of nanoseconds. 01:07:15.120 --> 01:07:17.980 align:middle line:84% So this is a very, very fast crystallization. 01:07:17.980 --> 01:07:20.240 align:middle line:84% You can essentially program these materials 01:07:20.240 --> 01:07:22.560 align:middle line:84% within a matter of tens of nanoseconds. 01:07:22.560 --> 01:07:27.340 align:middle line:84% Now, this is sort of like a semi-logarithm plot. 01:07:27.340 --> 01:07:29.860 align:middle line:84% So the slope here roughly gives you 01:07:29.860 --> 01:07:38.200 align:middle line:84% the activation energy or the inverse slope, basically. 01:07:38.200 --> 01:07:39.920 align:middle line:84% If you look at now right this point here, 01:07:39.920 --> 01:07:41.200 align:middle line:90% this is near room temperature. 01:07:41.200 --> 01:07:44.020 align:middle line:84% At room temperature, we are already 01:07:44.020 --> 01:07:48.240 align:middle line:84% talking about crystallization time 01:07:48.240 --> 01:07:51.700 align:middle line:90% that's of the order of years. 01:07:51.700 --> 01:07:54.660 align:middle line:84% So that's why this material can be essentially very 01:07:54.660 --> 01:07:56.900 align:middle line:84% fast in programming, but also very stable 01:07:56.900 --> 01:07:58.460 align:middle line:90% over a long period of time. 01:07:58.460 --> 01:08:01.100 align:middle line:84% Now, a few of these lines I'm showing 01:08:01.100 --> 01:08:03.580 align:middle line:84% here, this line, these two solid lines give you 01:08:03.580 --> 01:08:05.020 align:middle line:84% essentially possible routes people 01:08:05.020 --> 01:08:07.680 align:middle line:84% use to essentially do the crystallization process, 01:08:07.680 --> 01:08:11.740 align:middle line:84% whereas this orange line gives you the temperature trace 01:08:11.740 --> 01:08:14.540 align:middle line:90% for amorphization process. 01:08:14.540 --> 01:08:17.979 align:middle line:84% Now, if you look at the cooling rate for this line, 01:08:17.979 --> 01:08:19.520 align:middle line:90% it's actually very, very fast. 01:08:19.520 --> 01:08:28.410 align:middle line:84% It's of the order of 10 to the 10 kelvin per second. 01:08:28.410 --> 01:08:29.295 align:middle line:90% What does this mean? 01:08:29.295 --> 01:08:31.670 align:middle line:84% You need to quench your material at this very high speed. 01:08:31.670 --> 01:08:32.510 align:middle line:90% How do you do that? 01:08:32.510 --> 01:08:33.229 align:middle line:90% Few things. 01:08:33.229 --> 01:08:36.832 align:middle line:84% The material has to be sufficiently small. 01:08:36.832 --> 01:08:38.290 align:middle line:84% If you have a large volume, you can 01:08:38.290 --> 01:08:41.130 align:middle line:84% imagine that it takes time for the heat inside the material 01:08:41.130 --> 01:08:45.830 align:middle line:84% to dissipate to the surface and then essentially to cool down. 01:08:45.830 --> 01:08:48.350 align:middle line:84% So as we have mentioned in the previous lecture, 01:08:48.350 --> 01:08:51.410 align:middle line:84% this imposes essentially a thickness or linear dimension 01:08:51.410 --> 01:08:54.970 align:middle line:84% limit to the unit cell you can have where you can still achieve 01:08:54.970 --> 01:08:57.569 align:middle line:90% this reversible switching. 01:08:57.569 --> 01:09:00.649 align:middle line:84% You can go ahead and do the calculation. 01:09:00.649 --> 01:09:06.450 align:middle line:84% Roughly, for GST 225, the maximum linear dimension 01:09:06.450 --> 01:09:09.130 align:middle line:84% you can still quench down without crystallization 01:09:09.130 --> 01:09:12.770 align:middle line:84% is of the order of about 100 nanometers. 01:09:12.770 --> 01:09:14.510 align:middle line:84% So if you want to reversibly switch it, 01:09:14.510 --> 01:09:17.609 align:middle line:84% you really cannot make the material too large 01:09:17.609 --> 01:09:19.990 align:middle line:84% because it's such a fast crystallization material. 01:09:19.990 --> 01:09:25.743 align:middle line:90% 01:09:25.743 --> 01:09:28.410 align:middle line:84% And it's also quite important to engineer a thermal environment. 01:09:28.410 --> 01:09:30.327 align:middle line:84% That's why there's actually a trade-off there. 01:09:30.327 --> 01:09:33.310 align:middle line:84% I have previously mentioned that if essentially you enhance 01:09:33.310 --> 01:09:36.350 align:middle line:84% thermal conductivity in the surrounding media, 01:09:36.350 --> 01:09:38.170 align:middle line:84% actually decrease the thermal conductivity, 01:09:38.170 --> 01:09:39.712 align:middle line:84% you can have better heat confinement, 01:09:39.712 --> 01:09:41.710 align:middle line:84% and therefore make it more energy efficient. 01:09:41.710 --> 01:09:43.550 align:middle line:84% The trade-off there is that you don't 01:09:43.550 --> 01:09:45.365 align:middle line:84% want to make it too thermally insulating, 01:09:45.365 --> 01:09:47.990 align:middle line:84% otherwise you will not be able to achieve this critical cooling 01:09:47.990 --> 01:09:48.550 align:middle line:90% rate. 01:09:48.550 --> 01:09:50.790 align:middle line:84% So there's a fine balance you have to achieve there. 01:09:50.790 --> 01:09:53.790 align:middle line:84% You have to quench fast enough to amorphize it, but also 01:09:53.790 --> 01:09:56.230 align:middle line:84% be sufficiently insulating to confine 01:09:56.230 --> 01:09:58.910 align:middle line:84% the heat within the volume you want to make it 01:09:58.910 --> 01:10:01.530 align:middle line:90% more energy efficient. 01:10:01.530 --> 01:10:02.030 align:middle line:90% OK. 01:10:02.030 --> 01:10:04.950 align:middle line:90% 01:10:04.950 --> 01:10:05.630 align:middle line:90% Yes? 01:10:05.630 --> 01:10:06.255 align:middle line:90% AUDIENCE: Yeah. 01:10:06.255 --> 01:10:11.070 align:middle line:84% How do you actually quench it that fast at that scale? 01:10:11.070 --> 01:10:13.070 align:middle line:84% Especially I assume you have many 01:10:13.070 --> 01:10:17.290 align:middle line:84% of these bits next to each other. 01:10:17.290 --> 01:10:20.510 align:middle line:84% JUEJUN HU: It depends on the specific device. 01:10:20.510 --> 01:10:22.270 align:middle line:84% So for example, if you are looking 01:10:22.270 --> 01:10:26.820 align:middle line:84% at optical storage, your rewritable CDs and DVDs, 01:10:26.820 --> 01:10:29.100 align:middle line:84% they basically use a focused laser beam 01:10:29.100 --> 01:10:31.620 align:middle line:84% to essentially illuminate a very small spot. 01:10:31.620 --> 01:10:33.660 align:middle line:84% And the surrounding material, it still 01:10:33.660 --> 01:10:36.300 align:middle line:84% remains at pretty much room temperature. 01:10:36.300 --> 01:10:39.340 align:middle line:84% So because the spot is so small, when you actually 01:10:39.340 --> 01:10:41.357 align:middle line:84% remove the heat, it can quickly exchange heat 01:10:41.357 --> 01:10:42.440 align:middle line:90% with all the surroundings. 01:10:42.440 --> 01:10:44.420 align:middle line:84% It has a very large surface-to-volume ratio 01:10:44.420 --> 01:10:45.440 align:middle line:90% because it's so small. 01:10:45.440 --> 01:10:48.340 align:middle line:84% So then that leads to a very fast heat dissipation. 01:10:48.340 --> 01:10:50.340 align:middle line:84% And that's why you can cool down that fast. 01:10:50.340 --> 01:10:52.260 align:middle line:84% For electronic memories, you actually 01:10:52.260 --> 01:10:53.827 align:middle line:90% use a resistive heating. 01:10:53.827 --> 01:10:55.160 align:middle line:90% You actually have a little cell. 01:10:55.160 --> 01:10:56.040 align:middle line:90% You have electrodes. 01:10:56.040 --> 01:10:57.780 align:middle line:84% You actually pass current through it. 01:10:57.780 --> 01:11:00.702 align:middle line:84% So as soon as you turn off the current, then, 01:11:00.702 --> 01:11:02.160 align:middle line:84% again, because a very small volume, 01:11:02.160 --> 01:11:04.380 align:middle line:84% it's actually typically of a little wire, 01:11:04.380 --> 01:11:06.920 align:middle line:84% you can actually also induce this very fast cooling there. 01:11:06.920 --> 01:11:09.700 align:middle line:84% So it all boils down to essentially small volume 01:11:09.700 --> 01:11:13.380 align:middle line:84% and high surface-to-volume ratio to expedite this heat 01:11:13.380 --> 01:11:15.160 align:middle line:90% dissipation. 01:11:15.160 --> 01:11:15.660 align:middle line:90% OK. 01:11:15.660 --> 01:11:18.340 align:middle line:90% 01:11:18.340 --> 01:11:18.840 align:middle line:90% OK. 01:11:18.840 --> 01:11:20.980 align:middle line:84% In fact, we will probably end the lecture 01:11:20.980 --> 01:11:22.417 align:middle line:90% just five minutes earlier. 01:11:22.417 --> 01:11:24.000 align:middle line:84% We'll leave essentially all the device 01:11:24.000 --> 01:11:25.920 align:middle line:90% sections to next lecture here. 01:11:25.920 --> 01:11:28.340 align:middle line:84% Any questions you want to discuss here before we-- 01:11:28.340 --> 01:11:31.680 align:middle line:90% 01:11:31.680 --> 01:11:32.420 align:middle line:90% all good? 01:11:32.420 --> 01:11:33.360 align:middle line:90% OK. 01:11:33.360 --> 01:11:35.818 align:middle line:84% So next lecture, we're going to discuss about, essentially, 01:11:35.818 --> 01:11:37.760 align:middle line:84% the different device implementations 01:11:37.760 --> 01:11:40.170 align:middle line:90% of phase-change materials. 01:11:40.170 --> 01:12:23.000 align:middle line:90%