WEBVTT 00:00:00.000 --> 00:00:01.958 align:middle line:90% [SQUEAKING] 00:00:01.958 --> 00:00:04.388 align:middle line:90% [RUSTLING] 00:00:04.388 --> 00:00:06.818 align:middle line:90% [CLICKING] 00:00:06.818 --> 00:00:16.005 align:middle line:90% 00:00:16.005 --> 00:00:16.880 align:middle line:90% JUEJUN HU: All right. 00:00:16.880 --> 00:00:17.380 align:middle line:90% All right. 00:00:17.380 --> 00:00:21.440 align:middle line:84% So now last lecture, we talked about essentially 00:00:21.440 --> 00:00:25.085 align:middle line:84% the X-ray diffraction theory for amorphous materials. 00:00:25.085 --> 00:00:26.960 align:middle line:84% If you forget about everything I talked about 00:00:26.960 --> 00:00:28.752 align:middle line:84% in the last lecture, there's only one thing 00:00:28.752 --> 00:00:30.280 align:middle line:90% you really need to remember. 00:00:30.280 --> 00:00:32.907 align:middle line:90% It should be this equation here. 00:00:32.907 --> 00:00:34.740 align:middle line:84% Again, you don't need to remember specifics, 00:00:34.740 --> 00:00:37.480 align:middle line:84% but you need to keep in mind that there is such equation 00:00:37.480 --> 00:00:40.480 align:middle line:84% that actually kind of links the X-ray diffraction 00:00:40.480 --> 00:00:42.320 align:middle line:84% spectra, or the structure vector, 00:00:42.320 --> 00:00:46.280 align:middle line:84% directly to the pair distribution function. 00:00:46.280 --> 00:00:51.730 align:middle line:84% So while that may seem very easy, as I have mentioned, 00:00:51.730 --> 00:00:53.480 align:middle line:84% there are actually a number of Corrections 00:00:53.480 --> 00:00:55.640 align:middle line:84% you have to carefully perform in order 00:00:55.640 --> 00:01:00.570 align:middle line:84% to transform experimentally measured data into the pair 00:01:00.570 --> 00:01:01.590 align:middle line:90% distribution function. 00:01:01.590 --> 00:01:03.882 align:middle line:84% So what I'm showing here, this is actually 00:01:03.882 --> 00:01:06.090 align:middle line:84% a few steps we have to go through to actually process 00:01:06.090 --> 00:01:06.970 align:middle line:90% the raw data. 00:01:06.970 --> 00:01:08.570 align:middle line:84% So what I'm showing, this is basically 00:01:08.570 --> 00:01:11.090 align:middle line:90% an example of raw data. 00:01:11.090 --> 00:01:12.850 align:middle line:84% Normally, if you collect a spectrum 00:01:12.850 --> 00:01:15.330 align:middle line:84% from XRD lab, what you will get is essentially 00:01:15.330 --> 00:01:21.570 align:middle line:84% the intensity counts as a function of the theta, which 00:01:21.570 --> 00:01:25.730 align:middle line:84% you can easily convert into the scattering vector 00:01:25.730 --> 00:01:30.050 align:middle line:84% by just following the equation that q equals to 2 k sine theta. 00:01:30.050 --> 00:01:33.790 align:middle line:84% So now the corrections you have to perform, first thing, 00:01:33.790 --> 00:01:36.770 align:middle line:84% there are a few corrections you have 00:01:36.770 --> 00:01:44.130 align:middle line:84% to execute here to eliminate some of the side effects, OK? 00:01:44.130 --> 00:01:47.290 align:middle line:84% So first one is essentially detector dead time. 00:01:47.290 --> 00:01:49.130 align:middle line:84% So what that means is that the detector 00:01:49.130 --> 00:01:50.930 align:middle line:84% you use in the XRD machine, there's 00:01:50.930 --> 00:01:54.050 align:middle line:90% actually a response time. 00:01:54.050 --> 00:01:57.070 align:middle line:84% So if there is a photon comes in, an X-ray photon comes in, 00:01:57.070 --> 00:01:58.530 align:middle line:84% it's going to give you a reading. 00:01:58.530 --> 00:02:00.947 align:middle line:84% But then it takes a short period of time for that detector 00:02:00.947 --> 00:02:03.170 align:middle line:90% to actually recover. 00:02:03.170 --> 00:02:06.010 align:middle line:84% If you have a high flux of photons coming in, such 00:02:06.010 --> 00:02:09.117 align:middle line:84% that two photons may come in at almost the same time, 00:02:09.117 --> 00:02:11.450 align:middle line:84% then the detector basically will only pick up one photon 00:02:11.450 --> 00:02:13.850 align:middle line:84% because it does not have enough time to actually recover 00:02:13.850 --> 00:02:16.130 align:middle line:90% to read the next photon. 00:02:16.130 --> 00:02:19.450 align:middle line:84% So this kind of error becomes essentially more severe 00:02:19.450 --> 00:02:23.310 align:middle line:84% as you go to higher and higher X-ray scattering intensity. 00:02:23.310 --> 00:02:25.490 align:middle line:84% So that's something you have to correct if you want 00:02:25.490 --> 00:02:27.170 align:middle line:90% to get the right line shape. 00:02:27.170 --> 00:02:28.415 align:middle line:90% Second thing is background. 00:02:28.415 --> 00:02:29.790 align:middle line:84% And that's quite straightforward. 00:02:29.790 --> 00:02:33.570 align:middle line:84% That happens especially when you have thin film samples. 00:02:33.570 --> 00:02:35.850 align:middle line:90% The sample itself is in vacuum. 00:02:35.850 --> 00:02:37.730 align:middle line:90% You need some kind of holders. 00:02:37.730 --> 00:02:39.850 align:middle line:84% If it's a thin film, you also have the substrate. 00:02:39.850 --> 00:02:42.690 align:middle line:84% So all of those, that's irrelevant to your actual sample 00:02:42.690 --> 00:02:43.550 align:middle line:90% information. 00:02:43.550 --> 00:02:46.890 align:middle line:84% They should all be removed, so recalibration. 00:02:46.890 --> 00:02:50.690 align:middle line:90% Now, next one, absorption. 00:02:50.690 --> 00:02:53.450 align:middle line:84% This goes back to our assumption where 00:02:53.450 --> 00:02:59.640 align:middle line:84% we said that when we go through our derivation, 00:02:59.640 --> 00:03:01.940 align:middle line:84% we assume that the attenuation of X-ray in the sample 00:03:01.940 --> 00:03:02.992 align:middle line:90% is actually very weak. 00:03:02.992 --> 00:03:04.200 align:middle line:90% That's actually not the case. 00:03:04.200 --> 00:03:06.660 align:middle line:84% There's always a little bit of absorption and scattering 00:03:06.660 --> 00:03:09.287 align:middle line:84% and attenuation due to scattering when you actually 00:03:09.287 --> 00:03:10.120 align:middle line:90% go through a sample. 00:03:10.120 --> 00:03:11.820 align:middle line:84% So you also have to correct for that. 00:03:11.820 --> 00:03:15.300 align:middle line:84% Similarly, for addition, the entire theory 00:03:15.300 --> 00:03:17.880 align:middle line:84% we discussed in last lecture is basically a scalar theory, 00:03:17.880 --> 00:03:19.123 align:middle line:90% scalar scattering theory. 00:03:19.123 --> 00:03:20.540 align:middle line:84% We have not accounted for the fact 00:03:20.540 --> 00:03:22.707 align:middle line:84% that there are actually two orthogonal polarizations 00:03:22.707 --> 00:03:23.700 align:middle line:90% for the incident X-ray. 00:03:23.700 --> 00:03:25.700 align:middle line:84% So that's something we also have to correct for. 00:03:25.700 --> 00:03:27.500 align:middle line:84% Multiple scattering refers to the fact 00:03:27.500 --> 00:03:30.540 align:middle line:84% that the scattered X-ray, by the atoms, 00:03:30.540 --> 00:03:33.820 align:middle line:84% they can actually get scattered again as they propagate 00:03:33.820 --> 00:03:35.460 align:middle line:90% from the outside sample. 00:03:35.460 --> 00:03:38.140 align:middle line:84% So this is what's called multiple scattering. 00:03:38.140 --> 00:03:41.888 align:middle line:84% And finally, inelastic processes mostly 00:03:41.888 --> 00:03:44.180 align:middle line:84% are Compton scattering and sometimes also fluorescence, 00:03:44.180 --> 00:03:44.800 align:middle line:90% as well. 00:03:44.800 --> 00:03:47.320 align:middle line:84% So those are also introducing undesirable background. 00:03:47.320 --> 00:03:48.560 align:middle line:90% You also have to subtract. 00:03:48.560 --> 00:03:52.260 align:middle line:84% So after you have done all the correction there, what you see 00:03:52.260 --> 00:03:55.300 align:middle line:84% is that the curve essentially changes a little bit. 00:03:55.300 --> 00:03:56.880 align:middle line:84% There's a minor correction there. 00:03:56.880 --> 00:03:59.060 align:middle line:90% The actual shape changes. 00:03:59.060 --> 00:04:00.820 align:middle line:84% For crystalline material, a lot of this 00:04:00.820 --> 00:04:02.653 align:middle line:84% actually doesn't really matter, because what 00:04:02.653 --> 00:04:05.380 align:middle line:84% you care about is actually fitting the peaks. 00:04:05.380 --> 00:04:07.280 align:middle line:84% Versus amorphous material, on the other hand, 00:04:07.280 --> 00:04:10.220 align:middle line:84% because you actually have to rely on the shape of the curve 00:04:10.220 --> 00:04:12.840 align:middle line:84% in your transformation to get a pair distribution function. 00:04:12.840 --> 00:04:15.173 align:middle line:84% So this correction actually becomes a lot more important 00:04:15.173 --> 00:04:16.660 align:middle line:84% when it comes to amorphous samples. 00:04:16.660 --> 00:04:18.420 align:middle line:90% OK. 00:04:18.420 --> 00:04:20.899 align:middle line:90% All right, next part. 00:04:20.899 --> 00:04:24.620 align:middle line:84% We then need to basically normalize the spectrum. 00:04:24.620 --> 00:04:27.740 align:middle line:90% 00:04:27.740 --> 00:04:30.820 align:middle line:84% Now, what we want to do, if you go back, 00:04:30.820 --> 00:04:33.340 align:middle line:84% we actually need to calculate this one, the structure factor 00:04:33.340 --> 00:04:33.840 align:middle line:90% here. 00:04:33.840 --> 00:04:36.580 align:middle line:84% So the definition of structure effect 00:04:36.580 --> 00:04:40.220 align:middle line:84% here, it links to the scatter intensity with this vector here, 00:04:40.220 --> 00:04:43.660 align:middle line:84% N times average f sub m squared, where f sub m, as we said, 00:04:43.660 --> 00:04:47.420 align:middle line:84% this is the scattering coefficient. 00:04:47.420 --> 00:04:51.340 align:middle line:84% In principle, if you know your sample's composition 00:04:51.340 --> 00:04:53.848 align:middle line:84% and you perform a very careful calibration 00:04:53.848 --> 00:04:56.390 align:middle line:84% on your experimental setup to know the scattering coefficient 00:04:56.390 --> 00:04:58.910 align:middle line:84% for all the constituent atoms, you 00:04:58.910 --> 00:05:03.030 align:middle line:84% can determine, essentially, this coefficient just experimentally. 00:05:03.030 --> 00:05:06.103 align:middle line:84% In practice, there's actually an easier trick. 00:05:06.103 --> 00:05:07.770 align:middle line:84% You don't really have to do that, right? 00:05:07.770 --> 00:05:10.190 align:middle line:84% Now, keep in mind, this scattering coefficient, 00:05:10.190 --> 00:05:13.030 align:middle line:84% this scattering coefficient, it depends on the specific sample 00:05:13.030 --> 00:05:13.530 align:middle line:90% setup. 00:05:13.530 --> 00:05:15.990 align:middle line:84% Different XRD machines have different X-ray collection 00:05:15.990 --> 00:05:18.570 align:middle line:84% efficiency, different X-ray intensity. 00:05:18.570 --> 00:05:24.870 align:middle line:84% So this vector is actually instrument-dependent. 00:05:24.870 --> 00:05:26.870 align:middle line:84% So if you want to get it a priori, 00:05:26.870 --> 00:05:28.910 align:middle line:84% you have to do very careful calibrations. 00:05:28.910 --> 00:05:30.470 align:middle line:84% Now, what I want to mention here is that you actually 00:05:30.470 --> 00:05:31.553 align:middle line:90% don't have to do that, OK? 00:05:31.553 --> 00:05:33.390 align:middle line:84% You can play one trick, avoid having 00:05:33.390 --> 00:05:35.030 align:middle line:84% to do that calibration yet still being 00:05:35.030 --> 00:05:38.150 align:middle line:84% able to normalize the spectrum converted from intensity 00:05:38.150 --> 00:05:40.070 align:middle line:90% to structure factor. 00:05:40.070 --> 00:05:42.630 align:middle line:84% This is to leverage on a phenomenon 00:05:42.630 --> 00:05:45.870 align:middle line:84% called coherent independent scattering. 00:05:45.870 --> 00:05:47.830 align:middle line:84% So to explain how that works, let's 00:05:47.830 --> 00:05:50.410 align:middle line:84% again-- it goes back to the definition of Q here. 00:05:50.410 --> 00:05:55.090 align:middle line:84% So we have mentioned that Q, if you just look at the magnitude, 00:05:55.090 --> 00:05:59.350 align:middle line:84% forget about direction, it is basically 2 times k sub i times 00:05:59.350 --> 00:06:02.910 align:middle line:90% sine theta. 00:06:02.910 --> 00:06:06.610 align:middle line:84% You can also write k in terms of lambda. 00:06:06.610 --> 00:06:11.830 align:middle line:84% So this would be 4 pi over lambda sine theta. 00:06:11.830 --> 00:06:15.290 align:middle line:84% Now what happens if you look at very large Q? 00:06:15.290 --> 00:06:17.830 align:middle line:90% 00:06:17.830 --> 00:06:20.390 align:middle line:84% If Q is very large, effectively-- 00:06:20.390 --> 00:06:23.030 align:middle line:84% because sine theta maximally is bound by essentially unity, 00:06:23.030 --> 00:06:23.530 align:middle line:90% right? 00:06:23.530 --> 00:06:26.230 align:middle line:84% So very large Q necessarily means 00:06:26.230 --> 00:06:29.750 align:middle line:84% that you're looking at very small wavelength. 00:06:29.750 --> 00:06:33.990 align:middle line:84% And when wavelength becomes much smaller than the lattice, 00:06:33.990 --> 00:06:38.030 align:middle line:84% then what happens is that the optical path length difference 00:06:38.030 --> 00:06:40.350 align:middle line:84% for the X-ray scatter by different atoms 00:06:40.350 --> 00:06:44.390 align:middle line:84% will always be differ by many, many wavelengths. 00:06:44.390 --> 00:06:48.790 align:middle line:84% So now if you try to add up this scattered signal from all 00:06:48.790 --> 00:06:52.800 align:middle line:84% the different atoms, because of the large path length 00:06:52.800 --> 00:06:58.640 align:middle line:84% difference, you essentially lose coherence. 00:06:58.640 --> 00:07:02.440 align:middle line:84% Essentially, interference effect gets averaged out. 00:07:02.440 --> 00:07:05.800 align:middle line:84% So as a result, instead of adding up 00:07:05.800 --> 00:07:09.320 align:middle line:84% the amplitude because of the random phase caused 00:07:09.320 --> 00:07:12.680 align:middle line:84% by the the very large path length difference compared 00:07:12.680 --> 00:07:17.400 align:middle line:84% to wavelengths, you can simply just add up the intensity, as 00:07:17.400 --> 00:07:20.880 align:middle line:90% if interference is nonexistent. 00:07:20.880 --> 00:07:24.160 align:middle line:84% This only applies when Q is very, very large. 00:07:24.160 --> 00:07:27.172 align:middle line:84% When Q is small, wavelength becomes comparable to lambda, 00:07:27.172 --> 00:07:28.880 align:middle line:84% then you cannot apply this approximation. 00:07:28.880 --> 00:07:32.840 align:middle line:84% There's always a definitive phase delay between the X-rays 00:07:32.840 --> 00:07:35.000 align:middle line:90% scattered by different atoms. 00:07:35.000 --> 00:07:35.720 align:middle line:90% OK? 00:07:35.720 --> 00:07:36.300 align:middle line:90% Yes. 00:07:36.300 --> 00:07:40.180 align:middle line:84% STUDENT: So what is lambda in this case? 00:07:40.180 --> 00:07:41.788 align:middle line:90% It's like a particular-- 00:07:41.788 --> 00:07:43.080 align:middle line:90% JUEJUN HU: It's a fixed number. 00:07:43.080 --> 00:07:44.560 align:middle line:90% It's a fixed number. 00:07:44.560 --> 00:07:47.000 align:middle line:90% Well, the X-ray machine, yeah. 00:07:47.000 --> 00:07:50.600 align:middle line:84% But the idea here is that when you actually 00:07:50.600 --> 00:07:53.275 align:middle line:84% need to perform this transformation, 00:07:53.275 --> 00:07:54.900 align:middle line:84% in the transformation, if you remember, 00:07:54.900 --> 00:07:58.177 align:middle line:84% the integration goes from 0 to infinity. 00:07:58.177 --> 00:08:00.260 align:middle line:84% If you go back, we can look at the equation again. 00:08:00.260 --> 00:08:01.355 align:middle line:90% OK? 00:08:01.355 --> 00:08:01.980 align:middle line:90% STUDENT: Right. 00:08:01.980 --> 00:08:02.360 align:middle line:90% Yeah. 00:08:02.360 --> 00:08:03.985 align:middle line:84% JUEJUN HU: And you're integrating over, 00:08:03.985 --> 00:08:06.200 align:middle line:84% Q, which basically means that you're 00:08:06.200 --> 00:08:10.120 align:middle line:84% integrating over essentially sine theta effectively. 00:08:10.120 --> 00:08:10.760 align:middle line:90% STUDENT: Yes. 00:08:10.760 --> 00:08:11.480 align:middle line:90% JUEJUN HU: Right. 00:08:11.480 --> 00:08:14.940 align:middle line:84% So in order I will talk about this point actually in a second. 00:08:14.940 --> 00:08:18.193 align:middle line:84% In order to be able to integrate to a very large number-- again, 00:08:18.193 --> 00:08:20.360 align:middle line:84% in empirical experiment, you cannot really integrate 00:08:20.360 --> 00:08:20.880 align:middle line:90% infinity. 00:08:20.880 --> 00:08:22.840 align:middle line:84% You have to cut off at some point. 00:08:22.840 --> 00:08:25.100 align:middle line:84% But in order to get a good approximation. 00:08:25.100 --> 00:08:28.140 align:middle line:84% So that you collect large enough Q range, 00:08:28.140 --> 00:08:30.640 align:middle line:84% you need to ensure that your lambda is actually small enough 00:08:30.640 --> 00:08:32.559 align:middle line:90% to start with. 00:08:32.559 --> 00:08:33.520 align:middle line:90% STUDENT: OK. 00:08:33.520 --> 00:08:34.200 align:middle line:90% JUEJUN HU: Yeah. 00:08:34.200 --> 00:08:41.120 align:middle line:84% So then when you actually are looking at this large Q range, 00:08:41.120 --> 00:08:43.400 align:middle line:84% effectively you are looking at the range 00:08:43.400 --> 00:08:47.760 align:middle line:84% where the interference becomes very weak. 00:08:47.760 --> 00:08:50.890 align:middle line:84% If the spacing between the atoms is much larger in wavelengths, 00:08:50.890 --> 00:08:52.867 align:middle line:90% let's say 100 lambda, right. 00:08:52.867 --> 00:08:54.450 align:middle line:84% So then you can imagine if you differ, 00:08:54.450 --> 00:08:56.890 align:middle line:84% that atomic spacing differ by a little bit, 00:08:56.890 --> 00:09:00.730 align:middle line:84% you can already change face easily from 0 to 2 pi entirely. 00:09:00.730 --> 00:09:02.670 align:middle line:84% If you average out across the entire solid, 00:09:02.670 --> 00:09:06.090 align:middle line:84% essentially any kind of phase difference becomes very-- 00:09:06.090 --> 00:09:07.930 align:middle line:84% the effect becomes very negligible. 00:09:07.930 --> 00:09:11.970 align:middle line:84% Effectively, you are adding up the scatter X-ray intensity 00:09:11.970 --> 00:09:13.850 align:middle line:90% in a coherent way. 00:09:13.850 --> 00:09:16.350 align:middle line:90% That's what it means. 00:09:16.350 --> 00:09:17.730 align:middle line:90% Does that make sense. 00:09:17.730 --> 00:09:19.710 align:middle line:90% Yeah so. 00:09:19.710 --> 00:09:21.550 align:middle line:84% STUDENT: Do you want Q to be large 00:09:21.550 --> 00:09:23.350 align:middle line:90% so that you get that averaging? 00:09:23.350 --> 00:09:25.290 align:middle line:84% JUEJUN HU: Basically, it's when Q is large, 00:09:25.290 --> 00:09:29.770 align:middle line:84% the diffraction effect gets smeared out. 00:09:29.770 --> 00:09:33.050 align:middle line:84% All the atoms scatter X-ray independently 00:09:33.050 --> 00:09:35.210 align:middle line:90% and you just add some intensity. 00:09:35.210 --> 00:09:37.615 align:middle line:84% Now, without the interference between X-rays scattered 00:09:37.615 --> 00:09:39.490 align:middle line:84% by different atoms, you don't get essentially 00:09:39.490 --> 00:09:41.650 align:middle line:84% like all the peaks and valleys like what you 00:09:41.650 --> 00:09:43.090 align:middle line:90% see in a normal X-ray spectrum. 00:09:43.090 --> 00:09:45.590 align:middle line:84% You just get a featureless background. 00:09:45.590 --> 00:09:47.907 align:middle line:90% 00:09:47.907 --> 00:09:49.990 align:middle line:84% And that's actually what we're trying to use here. 00:09:49.990 --> 00:09:55.650 align:middle line:84% What we are trying to argue is that when the Q gets very large. 00:09:55.650 --> 00:09:59.610 align:middle line:90% S Q has to approach unity. 00:09:59.610 --> 00:10:02.050 align:middle line:84% Essentially, the scatter X-ray intensity 00:10:02.050 --> 00:10:06.250 align:middle line:84% will be the sub, just the simple scalar sum of the scatter 00:10:06.250 --> 00:10:08.870 align:middle line:84% intensity from all the atoms, which basically is Nf squared. 00:10:08.870 --> 00:10:12.635 align:middle line:90% 00:10:12.635 --> 00:10:15.010 align:middle line:84% All of these peaks and valleys, this 00:10:15.010 --> 00:10:18.570 align:middle line:84% is a consequence of interference due to the different phase 00:10:18.570 --> 00:10:22.290 align:middle line:84% of X-ray, we get pitting scatter from different atoms there. 00:10:22.290 --> 00:10:24.790 align:middle line:84% But if you no longer have the interference effect, 00:10:24.790 --> 00:10:26.650 align:middle line:84% then it's just going to be an f squared 00:10:26.650 --> 00:10:30.170 align:middle line:84% scatter intensity, which means that as Q becomes unity. 00:10:30.170 --> 00:10:32.690 align:middle line:90% 00:10:32.690 --> 00:10:35.970 align:middle line:84% So the whole idea is that when Q becomes very large, 00:10:35.970 --> 00:10:38.410 align:middle line:84% SQ approaches unity, you can use that property 00:10:38.410 --> 00:10:42.930 align:middle line:84% to essentially calibrate this curve here to renormalize it. 00:10:42.930 --> 00:10:45.540 align:middle line:84% You just use this section of the curve. 00:10:45.540 --> 00:10:47.260 align:middle line:90% STUDENT: Oh, OK. 00:10:47.260 --> 00:10:47.880 align:middle line:90% I understand. 00:10:47.880 --> 00:10:48.520 align:middle line:90% JUEJUN HU: To normalize it. 00:10:48.520 --> 00:10:50.840 align:middle line:84% So essentially you just divide it by this part of the curve, 00:10:50.840 --> 00:10:52.340 align:middle line:84% divide in high curve by this section 00:10:52.340 --> 00:10:55.540 align:middle line:84% here, and you end up getting normalized curve like this. 00:10:55.540 --> 00:11:02.860 align:middle line:84% So SQ should converge to unity at very large Q numbers. 00:11:02.860 --> 00:11:05.980 align:middle line:84% So this is one way to avoid having to experimentally 00:11:05.980 --> 00:11:09.260 align:middle line:84% determine this Nf squared numbers, which 00:11:09.260 --> 00:11:12.980 align:middle line:84% could be a quite challenging experiment actually. 00:11:12.980 --> 00:11:14.840 align:middle line:84% You need to know exactly the composition. 00:11:14.840 --> 00:11:17.340 align:middle line:84% You need to collect the samples, the atom, the pure atoms 00:11:17.340 --> 00:11:19.600 align:middle line:84% with exactly those kind of constituent atoms. 00:11:19.600 --> 00:11:21.433 align:middle line:84% You need to perform a scattering experiment, 00:11:21.433 --> 00:11:22.740 align:middle line:90% carefully measure intensity. 00:11:22.740 --> 00:11:26.340 align:middle line:84% So you need to do that in order to get to this number here. 00:11:26.340 --> 00:11:28.435 align:middle line:90% STUDENT: OK. 00:11:28.435 --> 00:11:29.060 align:middle line:90% JUEJUN HU: Yes? 00:11:29.060 --> 00:11:31.380 align:middle line:84% STUDENT: Wait, I haven't formed my thought yet. 00:11:31.380 --> 00:11:36.600 align:middle line:84% So basically, the coherent independent scattering, 00:11:36.600 --> 00:11:40.907 align:middle line:84% which is the the N and the fm squared, is not desirable? 00:11:40.907 --> 00:11:43.240 align:middle line:84% JUEJUN HU: If you try to extract structural information, 00:11:43.240 --> 00:11:44.160 align:middle line:90% it's not desirable. 00:11:44.160 --> 00:11:45.040 align:middle line:90% STUDENT: It's not desirable. 00:11:45.040 --> 00:11:45.707 align:middle line:90% JUEJUN HU: Yeah. 00:11:45.707 --> 00:11:49.115 align:middle line:84% STUDENT: So you go to values where Q is very large. 00:11:49.115 --> 00:11:49.740 align:middle line:90% JUEJUN HU: Yes. 00:11:49.740 --> 00:11:54.443 align:middle line:84% STUDENT: And thus your SQ gets overpowered. 00:11:54.443 --> 00:11:56.860 align:middle line:84% JUEJUN HU: Oh, as SQ actually approach unity, essentially, 00:11:56.860 --> 00:11:58.680 align:middle line:84% the interference effect becomes very small. 00:11:58.680 --> 00:12:00.340 align:middle line:90% Yeah. 00:12:00.340 --> 00:12:01.840 align:middle line:90% If you want to say overpower. 00:12:01.840 --> 00:12:02.340 align:middle line:90% Maybe. 00:12:02.340 --> 00:12:05.700 align:middle line:90% 00:12:05.700 --> 00:12:11.820 align:middle line:84% STUDENT: So N fm squared, so you basically just 00:12:11.820 --> 00:12:19.580 align:middle line:84% fit like on this plot from Q into to 16, you fit that line, 00:12:19.580 --> 00:12:20.140 align:middle line:90% or fit that-- 00:12:20.140 --> 00:12:22.260 align:middle line:84% JUEJUN HU: Right, you approach this featureless curve. 00:12:22.260 --> 00:12:22.927 align:middle line:90% STUDENT: Gotcha. 00:12:22.927 --> 00:12:23.580 align:middle line:90% OK. 00:12:23.580 --> 00:12:24.880 align:middle line:84% JUEJUN HU: And then you just divide it by this curve. 00:12:24.880 --> 00:12:27.420 align:middle line:84% Divide the original spectrum by this curve here. 00:12:27.420 --> 00:12:30.420 align:middle line:84% STUDENT: Because SQ is basically unity. 00:12:30.420 --> 00:12:33.243 align:middle line:84% And so therefore i is just your-- 00:12:33.243 --> 00:12:34.160 align:middle line:90% JUEJUN HU: Nf squared. 00:12:34.160 --> 00:12:37.360 align:middle line:84% STUDENT: And then you can apply that to your lower Q values. 00:12:37.360 --> 00:12:39.500 align:middle line:84% JUEJUN HU: Right, because Nf squared is a constant. 00:12:39.500 --> 00:12:40.840 align:middle line:84% STUDENT: Where your structural data really is. 00:12:40.840 --> 00:12:41.500 align:middle line:90% JUEJUN HU: Yes. 00:12:41.500 --> 00:12:42.000 align:middle line:90% Yeah. 00:12:42.000 --> 00:12:43.730 align:middle line:84% Because Nf squared is a constant, right? 00:12:43.730 --> 00:12:45.110 align:middle line:90% It does not depend on Q. 00:12:45.110 --> 00:12:45.610 align:middle line:90% STUDENT: OK. 00:12:45.610 --> 00:12:48.208 align:middle line:90% 00:12:48.208 --> 00:12:49.250 align:middle line:90% STUDENT: It's a constant? 00:12:49.250 --> 00:12:51.690 align:middle line:84% JUEJUN HU: Well, no, I mean there's a dependence. 00:12:51.690 --> 00:12:53.970 align:middle line:84% There's a specific functional form that people know. 00:12:53.970 --> 00:12:55.553 align:middle line:84% Sorry, I should not say it's constant. 00:12:55.553 --> 00:12:56.710 align:middle line:90% Yeah. 00:12:56.710 --> 00:12:58.210 align:middle line:84% Essentially you know this red curve. 00:12:58.210 --> 00:12:59.830 align:middle line:84% You know the shape of the red curve. 00:12:59.830 --> 00:13:02.590 align:middle line:84% You just need to essentially offset it to the right level 00:13:02.590 --> 00:13:06.150 align:middle line:84% because you need to know what is your actual SQ. 00:13:06.150 --> 00:13:15.910 align:middle line:90% 00:13:15.910 --> 00:13:20.230 align:middle line:84% So bottom line is that you can use this feature 00:13:20.230 --> 00:13:22.230 align:middle line:90% to normalize SQ. 00:13:22.230 --> 00:13:25.510 align:middle line:84% And you can see here, most of the useful structured data 00:13:25.510 --> 00:13:27.090 align:middle line:84% actually resides in this region here. 00:13:27.090 --> 00:13:30.450 align:middle line:84% When Q becomes very large, essentially it approaches unity, 00:13:30.450 --> 00:13:34.030 align:middle line:84% then the data becomes not very useful anymore. 00:13:34.030 --> 00:13:35.710 align:middle line:90% OK? 00:13:35.710 --> 00:13:38.210 align:middle line:84% In fact, if you look at the integration equation, 00:13:38.210 --> 00:13:41.670 align:middle line:84% it also makes sense, because what's actually in the integrand 00:13:41.670 --> 00:13:44.870 align:middle line:90% is SQ minus 1. 00:13:44.870 --> 00:13:49.330 align:middle line:84% So when SQ approaches 1, essentially it's 0. 00:13:49.330 --> 00:13:51.732 align:middle line:84% So you no longer contribute to the integration. 00:13:51.732 --> 00:13:54.190 align:middle line:84% So that's why I said what's really useful is the part where 00:13:54.190 --> 00:13:55.570 align:middle line:90% you actually have oscillations. 00:13:55.570 --> 00:13:57.990 align:middle line:84% That's what really contributes to the equation there. 00:13:57.990 --> 00:14:01.230 align:middle line:90% 00:14:01.230 --> 00:14:01.810 align:middle line:90% All right. 00:14:01.810 --> 00:14:08.050 align:middle line:84% So now last thing I also want to mention after you normalize it, 00:14:08.050 --> 00:14:11.870 align:middle line:84% there's still always a truncation error. 00:14:11.870 --> 00:14:13.750 align:middle line:84% Because even though I mentioned that you 00:14:13.750 --> 00:14:16.670 align:middle line:84% have to try to integrate from 0 to infinity according 00:14:16.670 --> 00:14:18.710 align:middle line:84% to the equation, in practice, there's 00:14:18.710 --> 00:14:20.790 align:middle line:84% always a maximum Q you can reach, 00:14:20.790 --> 00:14:22.750 align:middle line:84% which is dictated by when your sine [? theta ?] 00:14:22.750 --> 00:14:23.850 align:middle line:90% is equal to unity. 00:14:23.850 --> 00:14:27.515 align:middle line:90% 00:14:27.515 --> 00:14:28.890 align:middle line:84% When your sine is equal to unity, 00:14:28.890 --> 00:14:32.190 align:middle line:84% your Qmax is given by 4 pi divided by lambda, 00:14:32.190 --> 00:14:34.330 align:middle line:84% and lambda is your X-ray source wavelength. 00:14:34.330 --> 00:14:38.630 align:middle line:90% 00:14:38.630 --> 00:14:42.200 align:middle line:84% So in order for this calculation to be accurate, 00:14:42.200 --> 00:14:47.720 align:middle line:84% you want this Qmax to fall in the range 00:14:47.720 --> 00:14:50.300 align:middle line:84% where this curve has almost become featureless. 00:14:50.300 --> 00:14:52.760 align:middle line:90% You want Q to be somewhere here. 00:14:52.760 --> 00:14:55.820 align:middle line:84% You don't want the Qmax to get truncated somewhere, like here. 00:14:55.820 --> 00:15:05.440 align:middle line:90% 00:15:05.440 --> 00:15:07.200 align:middle line:84% What that means experimentally is 00:15:07.200 --> 00:15:10.640 align:middle line:84% that you want to select an X-ray source with sufficiently 00:15:10.640 --> 00:15:13.720 align:middle line:84% small wavelength, so that this truncation 00:15:13.720 --> 00:15:15.300 align:middle line:90% error can be minimized. 00:15:15.300 --> 00:15:21.000 align:middle line:90% 00:15:21.000 --> 00:15:23.715 align:middle line:90% OK? 00:15:23.715 --> 00:15:26.240 align:middle line:84% Now this actually has some practical limitations 00:15:26.240 --> 00:15:27.800 align:middle line:90% for experiments. 00:15:27.800 --> 00:15:31.780 align:middle line:84% If you want to actually analyze the PDF for amorphous material, 00:15:31.780 --> 00:15:36.800 align:middle line:84% suppose you want to do it here, you go to the XRD facility here. 00:15:36.800 --> 00:15:38.642 align:middle line:84% They use a copper K-alpha source. 00:15:38.642 --> 00:15:40.600 align:middle line:84% Turns out copper K-alpha source, the wavelength 00:15:40.600 --> 00:15:41.808 align:middle line:90% is actually not short enough. 00:15:41.808 --> 00:15:43.480 align:middle line:90% It's 1.54 Angstrom. 00:15:43.480 --> 00:15:45.000 align:middle line:90% OK? 00:15:45.000 --> 00:15:46.920 align:middle line:84% If we were to plot it on the plot, 00:15:46.920 --> 00:15:49.800 align:middle line:84% it will fall in somewhere around here. 00:15:49.800 --> 00:15:52.120 align:middle line:90% OK? 00:15:52.120 --> 00:15:55.120 align:middle line:84% So it will not be able to get a very accurate pair distribution 00:15:55.120 --> 00:15:57.800 align:middle line:84% function by using an X-ray source with a copper 00:15:57.800 --> 00:16:00.320 align:middle line:90% K-alpha source. 00:16:00.320 --> 00:16:03.720 align:middle line:84% You have to find alternative sources, melatonin or silver 00:16:03.720 --> 00:16:06.640 align:middle line:84% sources, that actually offers much shorter wavelengths 00:16:06.640 --> 00:16:09.860 align:middle line:84% in order to get more reliable reconstruction of the PDF. 00:16:09.860 --> 00:16:10.360 align:middle line:90% OK? 00:16:10.360 --> 00:16:16.220 align:middle line:90% 00:16:16.220 --> 00:16:18.640 align:middle line:84% So this slide basically summarizes the sources of error 00:16:18.640 --> 00:16:20.680 align:middle line:84% in this kind of reconstruction process. 00:16:20.680 --> 00:16:24.320 align:middle line:84% I already mentioned about this data truncation error 00:16:24.320 --> 00:16:27.320 align:middle line:84% coming from the fact that in practice, you will never 00:16:27.320 --> 00:16:28.760 align:middle line:90% integrate from 0 to infinity. 00:16:28.760 --> 00:16:31.160 align:middle line:84% You always cut off as a maximum Q value dictated 00:16:31.160 --> 00:16:32.540 align:middle line:90% by the X-ray source wavelength. 00:16:32.540 --> 00:16:35.200 align:middle line:90% 00:16:35.200 --> 00:16:38.490 align:middle line:84% So that's why if you want to minimize this data truncation 00:16:38.490 --> 00:16:43.570 align:middle line:84% error, you either have to use less commonly used X-ray sources 00:16:43.570 --> 00:16:46.008 align:middle line:84% like melatonin sources or silver sources, that 00:16:46.008 --> 00:16:47.050 align:middle line:90% have shorter wavelengths. 00:16:47.050 --> 00:16:52.530 align:middle line:84% Or an even better approach is to go to a synchrotron source. 00:16:52.530 --> 00:16:55.695 align:middle line:84% Synchrotron source offers X-ray with a wide wavelength range. 00:16:55.695 --> 00:16:57.570 align:middle line:84% You can always pick a short wavelength window 00:16:57.570 --> 00:16:59.490 align:middle line:84% to perform your diffraction experiment 00:16:59.490 --> 00:17:01.015 align:middle line:90% and then get your PDF data. 00:17:01.015 --> 00:17:02.890 align:middle line:84% In fact, most of the time, that's what people 00:17:02.890 --> 00:17:04.598 align:middle line:84% actually will do when they try to extract 00:17:04.598 --> 00:17:05.990 align:middle line:90% this kind of PDF data. 00:17:05.990 --> 00:17:08.170 align:middle line:90% They just go to synchrotron. 00:17:08.170 --> 00:17:11.130 align:middle line:84% So that's one source of error, coming from basically 00:17:11.130 --> 00:17:12.190 align:middle line:90% the horizontal axis. 00:17:12.190 --> 00:17:15.170 align:middle line:84% Now, you can also get some source of error coming 00:17:15.170 --> 00:17:17.730 align:middle line:90% from essentially shot noise. 00:17:17.730 --> 00:17:20.210 align:middle line:90% So what shot noise means? 00:17:20.210 --> 00:17:22.730 align:middle line:84% If you think about X-ray, X-ray is really 00:17:22.730 --> 00:17:26.829 align:middle line:84% not a continuous stream of optical intensity, right? 00:17:26.829 --> 00:17:29.770 align:middle line:84% It consists of discrete X-ray photons. 00:17:29.770 --> 00:17:32.450 align:middle line:84% And when the photons actually arrive at our detector, 00:17:32.450 --> 00:17:35.610 align:middle line:84% it's a completely statistical event. 00:17:35.610 --> 00:17:38.890 align:middle line:84% You can integrate over a certain period of time, like one second, 00:17:38.890 --> 00:17:42.035 align:middle line:84% and you intensity of the source is 00:17:42.035 --> 00:17:43.410 align:middle line:84% what it tells you is that there's 00:17:43.410 --> 00:17:44.952 align:middle line:84% an average number of photons is going 00:17:44.952 --> 00:17:48.010 align:middle line:84% to fall in the detector within that one-second time interval. 00:17:48.010 --> 00:17:50.610 align:middle line:84% But it doesn't tell you within that one second, what 00:17:50.610 --> 00:17:53.050 align:middle line:84% are the exact time points when all those photons actually 00:17:53.050 --> 00:17:54.770 align:middle line:90% hit the detector. 00:17:54.770 --> 00:17:55.970 align:middle line:90% OK? 00:17:55.970 --> 00:17:57.490 align:middle line:90% Make sense? 00:17:57.490 --> 00:18:02.110 align:middle line:84% So now, if you are trying to measure the intensity, 00:18:02.110 --> 00:18:04.730 align:middle line:84% you always have a finite integration time. 00:18:04.730 --> 00:18:08.290 align:middle line:84% So this statistical nature of the photons 00:18:08.290 --> 00:18:10.050 align:middle line:84% means that the actual number of photons 00:18:10.050 --> 00:18:12.370 align:middle line:84% you collected within that finite period of time 00:18:12.370 --> 00:18:15.032 align:middle line:90% would also fluctuate. 00:18:15.032 --> 00:18:16.990 align:middle line:84% Sometimes it would be more than average number, 00:18:16.990 --> 00:18:19.610 align:middle line:84% sometimes maybe a bit less than average number. 00:18:19.610 --> 00:18:21.330 align:middle line:90% It's completely statistical. 00:18:21.330 --> 00:18:23.730 align:middle line:84% The shorter the integration time is, 00:18:23.730 --> 00:18:25.630 align:middle line:84% the larger the fluctuation is going to be. 00:18:25.630 --> 00:18:28.730 align:middle line:90% 00:18:28.730 --> 00:18:31.370 align:middle line:90% OK, that's called a shot noise. 00:18:31.370 --> 00:18:34.220 align:middle line:84% It comes from the intrinsic discrete nature 00:18:34.220 --> 00:18:36.660 align:middle line:90% of a photon stream. 00:18:36.660 --> 00:18:39.420 align:middle line:84% So what shot noise will give you essentially 00:18:39.420 --> 00:18:41.940 align:middle line:84% means that your curve, there's actually an error bar 00:18:41.940 --> 00:18:43.480 align:middle line:90% in the vertical axis direction. 00:18:43.480 --> 00:18:46.140 align:middle line:84% The intensity is actually not exactly what you measured. 00:18:46.140 --> 00:18:48.820 align:middle line:84% So this can lead to a reconstruction error. 00:18:48.820 --> 00:18:50.780 align:middle line:84% Now to decrease the actual noise is actually 00:18:50.780 --> 00:18:51.800 align:middle line:90% pretty straightforward. 00:18:51.800 --> 00:18:53.940 align:middle line:84% You just increase the integration time. 00:18:53.940 --> 00:18:56.480 align:middle line:84% The more you integrate, the more you average out the effect. 00:18:56.480 --> 00:18:59.700 align:middle line:84% And then you can actually decrease the noise there OK. 00:18:59.700 --> 00:19:02.112 align:middle line:90% Downside, it takes longer. 00:19:02.112 --> 00:19:03.820 align:middle line:84% You have to book your synchrotron machine 00:19:03.820 --> 00:19:04.720 align:middle line:90% for a longer period of time. 00:19:04.720 --> 00:19:06.700 align:middle line:84% You also make it more accurate practically. 00:19:06.700 --> 00:19:09.940 align:middle line:84% Next one, finite resolution, similarly, you also 00:19:09.940 --> 00:19:13.540 align:middle line:84% want to measure many, many angular values in order 00:19:13.540 --> 00:19:15.500 align:middle line:84% to ensure your structure factor is a precisely 00:19:15.500 --> 00:19:17.420 align:middle line:90% constructed function. 00:19:17.420 --> 00:19:18.920 align:middle line:84% You have to use slow scan basically, 00:19:18.920 --> 00:19:21.295 align:middle line:84% which means that you have to book your source for an even 00:19:21.295 --> 00:19:22.260 align:middle line:90% longer period of time. 00:19:22.260 --> 00:19:23.880 align:middle line:90% So that's what it boils down to. 00:19:23.880 --> 00:19:26.220 align:middle line:84% If you really want to get a good PDF, 00:19:26.220 --> 00:19:28.660 align:middle line:84% you have to really spend your time with your X-ray source 00:19:28.660 --> 00:19:32.540 align:middle line:84% to collect this high-quality data there. 00:19:32.540 --> 00:19:34.620 align:middle line:84% I also just want to highlight that a lot 00:19:34.620 --> 00:19:38.040 align:middle line:84% of these corrections, you don't really have to perform by hand. 00:19:38.040 --> 00:19:41.500 align:middle line:84% People have developed software packages where you can actually 00:19:41.500 --> 00:19:43.620 align:middle line:84% automatically process the accuracy spectra 00:19:43.620 --> 00:19:45.980 align:middle line:84% and give you the PDF data, so, whew, 00:19:45.980 --> 00:19:49.060 align:middle line:84% you don't have to worry about integration yourself. 00:19:49.060 --> 00:19:51.818 align:middle line:84% Yeah, but you still want to understand the physics, 00:19:51.818 --> 00:19:54.360 align:middle line:84% so you can actually properly apply those kind of corrections, 00:19:54.360 --> 00:19:56.740 align:middle line:84% make sure you are actually doing the right thing. 00:19:56.740 --> 00:19:58.280 align:middle line:84% That's why I'm talking all about it. 00:19:58.280 --> 00:20:00.700 align:middle line:90% OK. 00:20:00.700 --> 00:20:03.300 align:middle line:84% So that's about X-ray diffraction. 00:20:03.300 --> 00:20:05.700 align:middle line:84% Now, I also want to discuss about you can also 00:20:05.700 --> 00:20:09.140 align:middle line:84% use other kinds of waves to probe the internal structure 00:20:09.140 --> 00:20:10.403 align:middle line:90% of materials besides X-ray. 00:20:10.403 --> 00:20:11.320 align:middle line:90% You can use electrons. 00:20:11.320 --> 00:20:14.140 align:middle line:90% You can also use neutrons. 00:20:14.140 --> 00:20:17.460 align:middle line:84% Electrons are used because they have the advantage that they 00:20:17.460 --> 00:20:19.660 align:middle line:84% are basically integrated with the electron 00:20:19.660 --> 00:20:23.020 align:middle line:84% microscope, typically transmission electron 00:20:23.020 --> 00:20:23.920 align:middle line:90% microscope. 00:20:23.920 --> 00:20:25.420 align:middle line:84% So it means that you can essentially 00:20:25.420 --> 00:20:27.820 align:middle line:84% look at the structure of the materials 00:20:27.820 --> 00:20:30.328 align:middle line:84% while also examining the morphology in exactly 00:20:30.328 --> 00:20:31.870 align:middle line:84% the same instrument, you can actually 00:20:31.870 --> 00:20:33.710 align:middle line:90% do a one-to-one correlation. 00:20:33.710 --> 00:20:35.990 align:middle line:84% You can look at the structure, look at the morphology, 00:20:35.990 --> 00:20:39.030 align:middle line:84% essentially look at zooming into a specific regime 00:20:39.030 --> 00:20:40.830 align:middle line:90% of a region of interest. 00:20:40.830 --> 00:20:43.070 align:middle line:84% And then perform a local diffraction experiment just 00:20:43.070 --> 00:20:45.590 align:middle line:84% to look at the diffraction spectra from that small region 00:20:45.590 --> 00:20:46.350 align:middle line:90% there. 00:20:46.350 --> 00:20:47.150 align:middle line:90% OK. 00:20:47.150 --> 00:20:49.390 align:middle line:84% This is basically called the Selected Area Electron 00:20:49.390 --> 00:20:53.470 align:middle line:84% Diffraction, or SAED, and it becomes very useful 00:20:53.470 --> 00:20:56.090 align:middle line:84% if you're analyzing a sample that's actually not homogeneous, 00:20:56.090 --> 00:20:56.790 align:middle line:90% right? 00:20:56.790 --> 00:21:00.110 align:middle line:84% You may have, for example, an amorphous matrix with lots 00:21:00.110 --> 00:21:02.830 align:middle line:90% of crystalline precipitates. 00:21:02.830 --> 00:21:05.230 align:middle line:84% And you don't want to perform a macroscopic diffraction 00:21:05.230 --> 00:21:07.692 align:middle line:84% experiment such that your data get contaminated with all 00:21:07.692 --> 00:21:08.650 align:middle line:90% the crystalline phases. 00:21:08.650 --> 00:21:10.990 align:middle line:84% You just want to look at amorphous matrix. 00:21:10.990 --> 00:21:13.230 align:middle line:84% You can easily do that with selected area electron 00:21:13.230 --> 00:21:15.670 align:middle line:84% diffraction by focusing your electron beam only 00:21:15.670 --> 00:21:17.830 align:middle line:90% to the amorphous phase regime. 00:21:17.830 --> 00:21:21.110 align:middle line:84% OK, so that's one reason why electron diffraction 00:21:21.110 --> 00:21:24.760 align:middle line:90% is quite useful there. 00:21:24.760 --> 00:21:27.490 align:middle line:84% The other peculiarity about electron diffraction 00:21:27.490 --> 00:21:30.230 align:middle line:84% I also want to mention here is that the electron waves 00:21:30.230 --> 00:21:34.030 align:middle line:84% has a much smaller wavelength compared to X-rays. 00:21:34.030 --> 00:21:37.870 align:middle line:84% And this goes back to the fact that electrons are like photons. 00:21:37.870 --> 00:21:40.670 align:middle line:90% It has a non-zero static mass. 00:21:40.670 --> 00:21:41.310 align:middle line:90% OK? 00:21:41.310 --> 00:21:42.930 align:middle line:84% So you have a non-zero static mass. 00:21:42.930 --> 00:21:45.430 align:middle line:84% It means that its momentum tends to be a lot larger compared 00:21:45.430 --> 00:21:46.670 align:middle line:90% to X-ray photons. 00:21:46.670 --> 00:21:49.570 align:middle line:84% A larger momentum, according to the de Broglie relation, 00:21:49.570 --> 00:21:52.230 align:middle line:84% corresponds to a small wavelength. 00:21:52.230 --> 00:21:54.470 align:middle line:84% So if you remember for X-rays, we 00:21:54.470 --> 00:21:58.110 align:middle line:84% are talking about wavelengths of angstroms, one angstrom. 00:21:58.110 --> 00:22:01.510 align:middle line:84% Electrons have a wavelength that's two orders of magnitude 00:22:01.510 --> 00:22:04.910 align:middle line:90% smaller, so much, much smaller. 00:22:04.910 --> 00:22:07.430 align:middle line:84% So for electron diffraction, what that means 00:22:07.430 --> 00:22:11.030 align:middle line:84% is that the electron wavelength also becomes much smaller 00:22:11.030 --> 00:22:13.230 align:middle line:84% compared to the lattice constant of the material 00:22:13.230 --> 00:22:14.910 align:middle line:90% or the atomic spacing. 00:22:14.910 --> 00:22:17.647 align:middle line:84% So this is very similar to the demo experiment 00:22:17.647 --> 00:22:18.730 align:middle line:90% I did in the last lecture. 00:22:18.730 --> 00:22:20.938 align:middle line:84% Remember, I used a laser light to actually illuminate 00:22:20.938 --> 00:22:21.893 align:middle line:90% the spring. 00:22:21.893 --> 00:22:23.310 align:middle line:84% In that case, the laser wavelength 00:22:23.310 --> 00:22:25.790 align:middle line:84% is also much smaller compared to the feature 00:22:25.790 --> 00:22:27.510 align:middle line:90% size of the spring there. 00:22:27.510 --> 00:22:30.780 align:middle line:84% And what you have seen there is in that case, 00:22:30.780 --> 00:22:34.840 align:middle line:84% essentially the deflection angle becomes very, very small. 00:22:34.840 --> 00:22:37.320 align:middle line:84% So that's also exactly the case in the case 00:22:37.320 --> 00:22:38.660 align:middle line:90% of electron diffraction there. 00:22:38.660 --> 00:22:40.500 align:middle line:84% If you have electron beam coming down right, 00:22:40.500 --> 00:22:42.280 align:middle line:90% say this is your sample. 00:22:42.280 --> 00:22:45.520 align:middle line:84% Then what happens is that the deflection 00:22:45.520 --> 00:22:49.440 align:middle line:84% angle of the scatter or the diffracted electron beam, 00:22:49.440 --> 00:22:51.960 align:middle line:84% this angle theta is actually very, very small. 00:22:51.960 --> 00:22:54.000 align:middle line:84% Most of the electrons travel pretty much 00:22:54.000 --> 00:22:58.360 align:middle line:84% still in this vertical direction there. 00:22:58.360 --> 00:23:01.533 align:middle line:84% So that's why if you look at electron diffraction spectra, 00:23:01.533 --> 00:23:03.700 align:middle line:84% what it looks like typically is something like this. 00:23:03.700 --> 00:23:05.040 align:middle line:90% You take an image like this. 00:23:05.040 --> 00:23:07.920 align:middle line:84% You see this little black shadow there? 00:23:07.920 --> 00:23:09.880 align:middle line:84% This is actually the beam blocker. 00:23:09.880 --> 00:23:12.240 align:middle line:84% What the beam blocker does is essentially 00:23:12.240 --> 00:23:19.040 align:middle line:84% it blocks this undiffracted or unscattered beam. 00:23:19.040 --> 00:23:20.800 align:middle line:84% You only focus on information coming 00:23:20.800 --> 00:23:23.120 align:middle line:84% from the deflected electron beams there. 00:23:23.120 --> 00:23:23.620 align:middle line:90% OK? 00:23:23.620 --> 00:23:24.560 align:middle line:90% You look at the surroundings. 00:23:24.560 --> 00:23:25.060 align:middle line:90% OK. 00:23:25.060 --> 00:23:27.280 align:middle line:84% So the shadow is basically casted by this little beam 00:23:27.280 --> 00:23:27.940 align:middle line:90% blocker there. 00:23:27.940 --> 00:23:32.960 align:middle line:90% 00:23:32.960 --> 00:23:35.280 align:middle line:84% And if you look at the amorphous sample then 00:23:35.280 --> 00:23:38.480 align:middle line:84% the typical electron diffraction pattern would look something 00:23:38.480 --> 00:23:42.000 align:middle line:84% like this, you have actually a set of diffused rings OK? 00:23:42.000 --> 00:23:46.100 align:middle line:84% Which contains effectively the pair distribution function. 00:23:46.100 --> 00:23:48.200 align:middle line:84% If it's crystalline material, then you 00:23:48.200 --> 00:23:50.240 align:middle line:84% have essentially discrete dots coming 00:23:50.240 --> 00:23:53.880 align:middle line:84% from a coherent scattering by the atoms in a crystalline grid. 00:23:53.880 --> 00:23:56.040 align:middle line:84% So the information contained here 00:23:56.040 --> 00:23:58.180 align:middle line:84% is very, very similar to X-ray diffraction, 00:23:58.180 --> 00:24:00.200 align:middle line:84% except that you can do a selective area 00:24:00.200 --> 00:24:02.240 align:middle line:84% diffraction rather than averaging 00:24:02.240 --> 00:24:04.080 align:middle line:90% over macroscopic sample. 00:24:04.080 --> 00:24:06.960 align:middle line:84% You can also do neutrons besides electrons. 00:24:06.960 --> 00:24:09.680 align:middle line:84% Unlike electrons, electrons mostly 00:24:09.680 --> 00:24:12.280 align:middle line:84% when you use electron beam to actually illuminate a sample, 00:24:12.280 --> 00:24:15.760 align:middle line:84% electrons mostly interact with electrons, 00:24:15.760 --> 00:24:19.800 align:middle line:84% because you have very strong coulombic repulsion. 00:24:19.800 --> 00:24:22.480 align:middle line:84% Neutrons, on the other hand, because it's charged neutral, 00:24:22.480 --> 00:24:26.330 align:middle line:84% they tend to interact with atomic nuclei 00:24:26.330 --> 00:24:27.790 align:middle line:90% instead of with electrons. 00:24:27.790 --> 00:24:30.130 align:middle line:84% It doesn't really interact that much with electrons. 00:24:30.130 --> 00:24:31.610 align:middle line:90% It also has a much higher mass. 00:24:31.610 --> 00:24:33.110 align:middle line:84% So it means that it's very difficult 00:24:33.110 --> 00:24:36.690 align:middle line:84% to actually deflect its trajectory 00:24:36.690 --> 00:24:38.310 align:middle line:90% with light-mass electrons. 00:24:38.310 --> 00:24:43.090 align:middle line:84% So that's why it only gets scattered with atomic nuclei. 00:24:43.090 --> 00:24:45.190 align:middle line:84% Because it interacts with atomic nuclei, 00:24:45.190 --> 00:24:47.450 align:middle line:84% one very interesting feature for neutron diffraction 00:24:47.450 --> 00:24:49.370 align:middle line:84% is that you can easily distinguish 00:24:49.370 --> 00:24:51.310 align:middle line:84% between the neighboring elements, 00:24:51.310 --> 00:24:57.130 align:middle line:84% meaning elements with similar z numbers or even isotopes. 00:24:57.130 --> 00:25:00.610 align:middle line:84% If you're trying to use electron diffraction or X-ray 00:25:00.610 --> 00:25:04.033 align:middle line:84% diffraction to look at solids containing different isotopes, 00:25:04.033 --> 00:25:05.450 align:middle line:84% it will not be able to distinguish 00:25:05.450 --> 00:25:07.325 align:middle line:84% between different isotopes, because they have 00:25:07.325 --> 00:25:10.090 align:middle line:90% the same electronic structure. 00:25:10.090 --> 00:25:12.210 align:middle line:84% But they have a different number of neutrons 00:25:12.210 --> 00:25:14.610 align:middle line:84% in the atomic nuclei, which can be picked out 00:25:14.610 --> 00:25:16.210 align:middle line:90% by neutron diffraction. 00:25:16.210 --> 00:25:18.690 align:middle line:90% So that's quite a unique aspect. 00:25:18.690 --> 00:25:22.370 align:middle line:84% Another consequence is that the neutron diffraction is also 00:25:22.370 --> 00:25:24.302 align:middle line:84% a lot more sensitive to light elements. 00:25:24.302 --> 00:25:26.010 align:middle line:84% So this goes back to the fact that if you 00:25:26.010 --> 00:25:30.170 align:middle line:84% have a light element, say carbon, boron, and lithium, 00:25:30.170 --> 00:25:33.540 align:middle line:84% those, they have very few number of outer shell electrons. 00:25:33.540 --> 00:25:35.290 align:middle line:84% So smaller number of outer shell electrons 00:25:35.290 --> 00:25:36.890 align:middle line:84% means that the diffraction effect 00:25:36.890 --> 00:25:42.610 align:middle line:84% of either X-ray or for electrons becomes a lot smaller. 00:25:42.610 --> 00:25:44.530 align:middle line:84% So that's why electron diffraction 00:25:44.530 --> 00:25:47.058 align:middle line:84% tends to miss out a lot of the light elements, 00:25:47.058 --> 00:25:48.850 align:middle line:84% while neutron diffraction can pick them up. 00:25:48.850 --> 00:25:51.650 align:middle line:90% 00:25:51.650 --> 00:25:53.170 align:middle line:90% OK. 00:25:53.170 --> 00:25:54.990 align:middle line:90% That's about diffraction. 00:25:54.990 --> 00:25:58.930 align:middle line:90% 00:25:58.930 --> 00:26:00.030 align:middle line:90% Any more questions? 00:26:00.030 --> 00:26:02.930 align:middle line:90% Happy with that? 00:26:02.930 --> 00:26:04.130 align:middle line:90% All right. 00:26:04.130 --> 00:26:09.010 align:middle line:84% Now let's go to another technique, Raman spectroscopy. 00:26:09.010 --> 00:26:12.113 align:middle line:84% So Raman spectroscopy, obviously, 00:26:12.113 --> 00:26:14.530 align:middle line:84% rely on Raman scattering, which is a phenomenon discovered 00:26:14.530 --> 00:26:16.730 align:middle line:90% by the Indian physicist, Raman. 00:26:16.730 --> 00:26:20.370 align:middle line:84% And this is just a quote from him 00:26:20.370 --> 00:26:23.900 align:middle line:84% saying that he derived inspiration of Raman scattering 00:26:23.900 --> 00:26:27.900 align:middle line:84% coming from essentially sailing on the Mediterranean Sea, 00:26:27.900 --> 00:26:31.100 align:middle line:84% looking at the wonderful blue opalescence of the Mediterranean 00:26:31.100 --> 00:26:34.540 align:middle line:84% Sea, which is basically light scattering. 00:26:34.540 --> 00:26:36.800 align:middle line:90% 00:26:36.800 --> 00:26:38.040 align:middle line:90% STUDENT: That is inspiring. 00:26:38.040 --> 00:26:42.740 align:middle line:90% 00:26:42.740 --> 00:26:45.340 align:middle line:84% JUEJUN HU: OK, so what is Raman scattering? 00:26:45.340 --> 00:26:47.580 align:middle line:84% Essentially, it's a inelastic interaction 00:26:47.580 --> 00:26:50.040 align:middle line:90% of photons with the atoms. 00:26:50.040 --> 00:26:53.780 align:middle line:84% OK, always the crystalline lattice. 00:26:53.780 --> 00:26:58.420 align:middle line:84% There can be two kinds of Raman scattering processes. 00:26:58.420 --> 00:27:02.780 align:middle line:84% In one case, the phonon can get scattered 00:27:02.780 --> 00:27:05.700 align:middle line:84% and then it transfers energy to the lattice. 00:27:05.700 --> 00:27:08.820 align:middle line:84% Essentially, it loses a phonon or excites 00:27:08.820 --> 00:27:10.860 align:middle line:90% a phonon in the lattice. 00:27:10.860 --> 00:27:13.700 align:middle line:84% In this case, the photon energy will decrease. 00:27:13.700 --> 00:27:16.060 align:middle line:84% This is called a Stokes scattering. 00:27:16.060 --> 00:27:17.820 align:middle line:84% You also have the opposite process 00:27:17.820 --> 00:27:21.300 align:middle line:84% where the photon comes in, the lattice actually 00:27:21.300 --> 00:27:26.500 align:middle line:84% transfers energy to the photon, so that the lattice essentially 00:27:26.500 --> 00:27:27.600 align:middle line:90% excites itself. 00:27:27.600 --> 00:27:29.840 align:middle line:84% It goes from excited state back to the ground state. 00:27:29.840 --> 00:27:33.860 align:middle line:84% And in this case, photon, actually its frequency actually 00:27:33.860 --> 00:27:36.200 align:middle line:90% will shift, go to high energy. 00:27:36.200 --> 00:27:38.620 align:middle line:84% This is called anti-Stokes scattering. 00:27:38.620 --> 00:27:40.100 align:middle line:84% Sometimes people like to represent 00:27:40.100 --> 00:27:43.380 align:middle line:84% this kind of phenomena with this kind of energy diagram here. 00:27:43.380 --> 00:27:45.780 align:middle line:84% The argument is that when this kind of Raman scattering 00:27:45.780 --> 00:27:51.900 align:middle line:84% happens, you excite the solid initially to a virtual state, 00:27:51.900 --> 00:27:53.920 align:middle line:84% and these virtual states are very short lived. 00:27:53.920 --> 00:27:56.420 align:middle line:84% Those are actually not real energy levels, OK? 00:27:56.420 --> 00:27:58.940 align:middle line:84% So that's why they must have a very short lifetime dictated 00:27:58.940 --> 00:28:01.140 align:middle line:84% by essentially Heisenberg uncertainty principle. 00:28:01.140 --> 00:28:04.460 align:middle line:84% So within a very short period of time, it should relax back. 00:28:04.460 --> 00:28:07.740 align:middle line:84% Normally, it will relax back to the same starting level. 00:28:07.740 --> 00:28:09.520 align:middle line:84% So there's no change of photon energy. 00:28:09.520 --> 00:28:11.480 align:middle line:84% And that's basically the Rayleigh scattering, 00:28:11.480 --> 00:28:14.540 align:middle line:84% just all the scattering we talked about previously. 00:28:14.540 --> 00:28:17.300 align:middle line:84% Sometimes if you start out from a ground state 00:28:17.300 --> 00:28:19.870 align:middle line:84% and relax back to the excited state, 00:28:19.870 --> 00:28:22.350 align:middle line:84% then this is basically a Stokes scattering. 00:28:22.350 --> 00:28:24.690 align:middle line:84% It will emit a photon with a shorter wavelength. 00:28:24.690 --> 00:28:27.290 align:middle line:84% Vice versa, if you start from an excited state, 00:28:27.290 --> 00:28:29.750 align:middle line:84% go back to the ground state of the crystalline lattice, 00:28:29.750 --> 00:28:32.870 align:middle line:84% then you will end up having a anti-Stokes scattering. 00:28:32.870 --> 00:28:36.190 align:middle line:90% 00:28:36.190 --> 00:28:40.310 align:middle line:84% Now if you look at this here, because those scattering, 00:28:40.310 --> 00:28:44.630 align:middle line:84% it will interact with the solid that's in the ground state. 00:28:44.630 --> 00:28:49.550 align:middle line:84% Anti-Stokes interact with solid at excited state. 00:28:49.550 --> 00:28:50.310 align:middle line:90% OK. 00:28:50.310 --> 00:28:52.670 align:middle line:84% Now according to Bose Einstein distribution 00:28:52.670 --> 00:28:54.910 align:middle line:84% or Boltzmann distribution, either way, 00:28:54.910 --> 00:28:58.430 align:middle line:84% excited state population is always much smaller 00:28:58.430 --> 00:29:00.270 align:middle line:84% compared to a ground state population. 00:29:00.270 --> 00:29:02.228 align:middle line:84% Basically, they differ by the Boltzmann factor, 00:29:02.228 --> 00:29:04.990 align:middle line:90% e negative delta E kT. 00:29:04.990 --> 00:29:09.910 align:middle line:84% So that's why Stokes scattering is always 00:29:09.910 --> 00:29:14.110 align:middle line:84% a lot stronger compared to anti-Stokes scattering, 00:29:14.110 --> 00:29:17.390 align:middle line:84% because there are a lot more excitation at the ground state 00:29:17.390 --> 00:29:20.030 align:middle line:90% compared to the excited state. 00:29:20.030 --> 00:29:22.430 align:middle line:84% In fact, this actually gives give you 00:29:22.430 --> 00:29:24.990 align:middle line:84% a method to quantitatively measure 00:29:24.990 --> 00:29:28.030 align:middle line:84% the temperature of a sample in a non-contact manner. 00:29:28.030 --> 00:29:30.910 align:middle line:84% What you will do is you can essentially 00:29:30.910 --> 00:29:32.590 align:middle line:84% look at the Raman spectra and compare 00:29:32.590 --> 00:29:36.390 align:middle line:84% the intensity of the Stokes line and the anti-Stokes line. 00:29:36.390 --> 00:29:38.870 align:middle line:84% From the ratio of the two lines, you 00:29:38.870 --> 00:29:40.610 align:middle line:84% can then figure out the Boltzmann factor. 00:29:40.610 --> 00:29:43.750 align:middle line:84% And therefore infer the temperature. 00:29:43.750 --> 00:29:46.070 align:middle line:90% OK? 00:29:46.070 --> 00:29:48.850 align:middle line:84% So this is one unique capability of Raman spectroscopy. 00:29:48.850 --> 00:29:50.710 align:middle line:84% You can actually measure temperature 00:29:50.710 --> 00:29:53.923 align:middle line:90% in a non-contact way. 00:29:53.923 --> 00:29:56.590 align:middle line:84% I will talk about another method to actually measure temperature 00:29:56.590 --> 00:29:57.730 align:middle line:90% using Raman spectroscopy. 00:29:57.730 --> 00:30:00.397 align:middle line:84% There are actually multiple ways to measure temperature in Raman 00:30:00.397 --> 00:30:00.990 align:middle line:90% spectroscopy. 00:30:00.990 --> 00:30:03.230 align:middle line:84% This is one, by looking at the ratio of the Stokes 00:30:03.230 --> 00:30:04.590 align:middle line:90% and anti-Stokes lines. 00:30:04.590 --> 00:30:07.395 align:middle line:90% 00:30:07.395 --> 00:30:10.870 align:middle line:84% So now Raman is actually very useful for analyzing 00:30:10.870 --> 00:30:13.950 align:middle line:84% solids in general, crystalline and amorphous as well. 00:30:13.950 --> 00:30:17.560 align:middle line:84% Because as you can see here, the shift 00:30:17.560 --> 00:30:20.360 align:middle line:84% of the energy of the photons directly 00:30:20.360 --> 00:30:24.120 align:middle line:84% correlates with the phonon energy in the solid material, 00:30:24.120 --> 00:30:26.840 align:middle line:84% and phonon energy obviously correlates with the structure 00:30:26.840 --> 00:30:28.120 align:middle line:90% of the material. 00:30:28.120 --> 00:30:30.480 align:middle line:84% That's why Raman becomes a very useful technique 00:30:30.480 --> 00:30:32.280 align:middle line:90% for analyzing solid materials. 00:30:32.280 --> 00:30:33.400 align:middle line:90% OK? 00:30:33.400 --> 00:30:35.060 align:middle line:84% So what I'm showing in this slide here, 00:30:35.060 --> 00:30:37.227 align:middle line:84% these are the typical Raman setup you would actually 00:30:37.227 --> 00:30:39.560 align:middle line:90% use if you go to a lab. 00:30:39.560 --> 00:30:43.160 align:middle line:84% Most of the time people now use so-called micro-Raman systems 00:30:43.160 --> 00:30:46.120 align:middle line:84% essentially integrating Raman spectroscopy setup 00:30:46.120 --> 00:30:48.700 align:middle line:84% with a microscope, optical microscope OK. 00:30:48.700 --> 00:30:51.520 align:middle line:84% And the idea there is that you can essentially 00:30:51.520 --> 00:30:53.960 align:middle line:84% use the microscope as a way to examine 00:30:53.960 --> 00:30:56.720 align:middle line:84% the metrology of the sample, identify a region where you 00:30:56.720 --> 00:30:58.720 align:middle line:84% actually want to perform Raman spectroscopy, 00:30:58.720 --> 00:31:02.960 align:middle line:84% and then you can use the same microscope objective 00:31:02.960 --> 00:31:06.140 align:middle line:84% to focus the excitation laser beam onto the sample. 00:31:06.140 --> 00:31:08.320 align:middle line:84% And then collect the backscattered Raman signal 00:31:08.320 --> 00:31:11.560 align:middle line:84% also through a microscope objective. 00:31:11.560 --> 00:31:14.587 align:middle line:84% So you can very easily correlate morphology information 00:31:14.587 --> 00:31:16.920 align:middle line:84% with the local essentially structured information coming 00:31:16.920 --> 00:31:20.040 align:middle line:90% from Raman. 00:31:20.040 --> 00:31:24.480 align:middle line:84% It can perform a very high throughput analysis. 00:31:24.480 --> 00:31:27.360 align:middle line:84% A lot of the micro-Raman systems are now fully automated. 00:31:27.360 --> 00:31:29.700 align:middle line:84% You can essentially tell it to actually scan, 00:31:29.700 --> 00:31:31.960 align:middle line:84% for example, multiple spots on the sample surface. 00:31:31.960 --> 00:31:33.260 align:middle line:84% And it actually gives you, in the end, 00:31:33.260 --> 00:31:34.760 align:middle line:84% essentially a collection of spectrum 00:31:34.760 --> 00:31:37.177 align:middle line:84% that allows you to do, for example, structure or elemental 00:31:37.177 --> 00:31:39.560 align:middle line:90% mapping across a large area. 00:31:39.560 --> 00:31:43.200 align:middle line:84% So it's quite a convenient technique. 00:31:43.200 --> 00:31:46.840 align:middle line:84% Raman also gives you a pretty good spatial resolution 00:31:46.840 --> 00:31:49.520 align:middle line:84% in the in-plane direction, the spatial resolution 00:31:49.520 --> 00:31:53.360 align:middle line:84% is basically given by the size of the laser spot. 00:31:53.360 --> 00:31:55.740 align:middle line:84% So the size of the laser spot can be quite small 00:31:55.740 --> 00:31:59.800 align:middle line:84% if you have a high magnification microscope objective, 00:31:59.800 --> 00:32:02.960 align:middle line:84% you can have a sub-micron spot in the lateral direction. 00:32:02.960 --> 00:32:06.320 align:middle line:84% So you can have high lateral spatial resolution. 00:32:06.320 --> 00:32:09.040 align:middle line:84% You can also enhance the resolution 00:32:09.040 --> 00:32:12.480 align:middle line:84% in the depth direction or in the out-of-plane direction 00:32:12.480 --> 00:32:16.490 align:middle line:84% by using a so-called confocal setup. 00:32:16.490 --> 00:32:18.890 align:middle line:84% OK, so let me explain a little bit about how 00:32:18.890 --> 00:32:23.810 align:middle line:90% the confocal microscope works. 00:32:23.810 --> 00:32:38.770 align:middle line:84% So for confocal microscope, what you would do is say 00:32:38.770 --> 00:32:40.050 align:middle line:90% this is your objective. 00:32:40.050 --> 00:32:41.850 align:middle line:90% OK? 00:32:41.850 --> 00:32:44.570 align:middle line:84% It will focus the Raman excitation laser 00:32:44.570 --> 00:32:47.450 align:middle line:84% into a small spot and focusing on your sample. 00:32:47.450 --> 00:32:49.090 align:middle line:84% So let's say this is your sample. 00:32:49.090 --> 00:32:49.770 align:middle line:90% OK. 00:32:49.770 --> 00:32:53.210 align:middle line:84% Now in a confocal setup, you actually 00:32:53.210 --> 00:32:58.070 align:middle line:84% add a little extra in your path length of laser right 00:32:58.070 --> 00:32:59.770 align:middle line:84% at this point here, where the laser beam 00:32:59.770 --> 00:33:02.570 align:middle line:90% has the smallest diameter. 00:33:02.570 --> 00:33:03.490 align:middle line:90% OK? 00:33:03.490 --> 00:33:06.330 align:middle line:90% So now let's see what happens. 00:33:06.330 --> 00:33:08.570 align:middle line:84% Suppose you focus your microscope 00:33:08.570 --> 00:33:10.530 align:middle line:90% to write on the sample surface. 00:33:10.530 --> 00:33:12.910 align:middle line:84% Then any photon generated from sample surface, 00:33:12.910 --> 00:33:15.245 align:middle line:84% it will essentially retrace these light rays here, 00:33:15.245 --> 00:33:17.370 align:middle line:84% and then will be able to get through this pink hole 00:33:17.370 --> 00:33:18.950 align:middle line:90% or this little aperture easily. 00:33:18.950 --> 00:33:22.490 align:middle line:84% Now what about photons coming from, let's say here? 00:33:22.490 --> 00:33:26.970 align:middle line:84% Now keep in mind because your laser continues to diverge, 00:33:26.970 --> 00:33:30.570 align:middle line:84% it means that the sample here underneath the surface 00:33:30.570 --> 00:33:31.630 align:middle line:90% also can get excited. 00:33:31.630 --> 00:33:33.190 align:middle line:84% They can also emit Raman photons. 00:33:33.190 --> 00:33:38.970 align:middle line:84% But for these photons, it will also go through the objective. 00:33:38.970 --> 00:33:41.810 align:middle line:84% But then because this point is actually 00:33:41.810 --> 00:33:44.590 align:middle line:84% getting shifted along the optical axis to this direction, 00:33:44.590 --> 00:33:48.410 align:middle line:84% it means that they will now focus at the position, 00:33:48.410 --> 00:33:51.930 align:middle line:84% let's shift it towards the objective. 00:33:51.930 --> 00:33:53.490 align:middle line:90% Now you see what happens. 00:33:53.490 --> 00:33:56.570 align:middle line:84% Now most of the scattered photons 00:33:56.570 --> 00:33:59.210 align:middle line:84% will be blocked by this little aperture there. 00:33:59.210 --> 00:34:01.560 align:middle line:84% This is not a very good schematic. 00:34:01.560 --> 00:34:03.310 align:middle line:84% Let me try to draw it a little bit better. 00:34:03.310 --> 00:34:12.060 align:middle line:90% 00:34:12.060 --> 00:34:15.860 align:middle line:84% So using this method essentially allows you to selectively 00:34:15.860 --> 00:34:22.820 align:middle line:84% probe a thin layer within essentially the depth of focus 00:34:22.820 --> 00:34:23.880 align:middle line:90% of the system here. 00:34:23.880 --> 00:34:26.746 align:middle line:90% 00:34:26.746 --> 00:34:30.699 align:middle line:84% So a confocal setup improves the z direction 00:34:30.699 --> 00:34:33.940 align:middle line:84% or the out-of-plane direction resolution. 00:34:33.940 --> 00:34:36.900 align:middle line:84% STUDENT: The top line is like your viewing field? 00:34:36.900 --> 00:34:39.556 align:middle line:84% JUEJUN HU: Top line here, or even this one or this line? 00:34:39.556 --> 00:34:40.139 align:middle line:90% STUDENT: Yeah. 00:34:40.139 --> 00:34:41.639 align:middle line:84% JUEJUN HU: This line is an aperture. 00:34:41.639 --> 00:34:43.340 align:middle line:90% It's basically a little pinhole. 00:34:43.340 --> 00:34:46.880 align:middle line:84% It's mostly opaque with a little transparent hole in the middle. 00:34:46.880 --> 00:34:51.306 align:middle line:84% STUDENT: How if your focal point is below the surface-- 00:34:51.306 --> 00:34:53.139 align:middle line:84% JUEJUN HU: And your detector should be here. 00:34:53.139 --> 00:34:56.620 align:middle line:84% Detector should be like somewhere sitting here. 00:34:56.620 --> 00:34:59.020 align:middle line:84% This is where you actually receive the photons. 00:34:59.020 --> 00:35:00.060 align:middle line:90% STUDENT: OK. 00:35:00.060 --> 00:35:04.520 align:middle line:84% How does it, if it's not in focus at your aperture, 00:35:04.520 --> 00:35:07.340 align:middle line:84% how is it reaching your detector in focus, 00:35:07.340 --> 00:35:09.720 align:middle line:90% or is that not an issue? 00:35:09.720 --> 00:35:12.300 align:middle line:90% 00:35:12.300 --> 00:35:14.280 align:middle line:84% JUEJUN HU: It doesn't have to reach the-- 00:35:14.280 --> 00:35:17.100 align:middle line:90% 00:35:17.100 --> 00:35:20.890 align:middle line:84% STUDENT: Where are you losing information 00:35:20.890 --> 00:35:26.340 align:middle line:84% because your focal point is like in front of the aperture? 00:35:26.340 --> 00:35:28.940 align:middle line:84% I don't think I understand those lines. 00:35:28.940 --> 00:35:31.580 align:middle line:84% JUEJUN HU: Oh, these lines essentially are light rays. 00:35:31.580 --> 00:35:33.820 align:middle line:84% STUDENT: So you're losing some of your light rays 00:35:33.820 --> 00:35:36.232 align:middle line:84% or they're not crossing right at the aperture. 00:35:36.232 --> 00:35:36.940 align:middle line:90% JUEJUN HU: Right. 00:35:36.940 --> 00:35:38.420 align:middle line:90% Because then a lot of-- 00:35:38.420 --> 00:35:41.340 align:middle line:84% essentially, so think of it like the light comes out 00:35:41.340 --> 00:35:43.100 align:middle line:90% as like a cone. 00:35:43.100 --> 00:35:48.185 align:middle line:84% It essentially emits, basically, isotropically to all directions. 00:35:48.185 --> 00:35:49.560 align:middle line:84% Essentially, that's what happens. 00:35:49.560 --> 00:35:53.020 align:middle line:84% But the idea is that if your light source is right here, 00:35:53.020 --> 00:35:55.080 align:middle line:84% when it emits, it's going to get all the light. 00:35:55.080 --> 00:35:58.220 align:middle line:84% Essentially, the image of this point formed by the lens 00:35:58.220 --> 00:36:00.020 align:middle line:90% is right here. 00:36:00.020 --> 00:36:02.815 align:middle line:84% So effectively when your detector sees, 00:36:02.815 --> 00:36:04.440 align:middle line:84% it's not the light source sitting here. 00:36:04.440 --> 00:36:07.100 align:middle line:84% It's the light source sitting right at the pinhole. 00:36:07.100 --> 00:36:09.322 align:middle line:84% So then because it's sitting right 00:36:09.322 --> 00:36:11.030 align:middle line:84% at the pinhole, essentially all the light 00:36:11.030 --> 00:36:13.830 align:middle line:84% the emitted can actually get to the detector, 00:36:13.830 --> 00:36:18.550 align:middle line:84% versus if you have a source coming from this point here. 00:36:18.550 --> 00:36:20.690 align:middle line:84% Then the image will be right here. 00:36:20.690 --> 00:36:23.230 align:middle line:84% It's actually beneath the pinhole. 00:36:23.230 --> 00:36:25.870 align:middle line:84% So then only a very narrow range, 00:36:25.870 --> 00:36:28.550 align:middle line:84% angular range of the photons coming from here, 00:36:28.550 --> 00:36:30.350 align:middle line:84% could actually reach your detector. 00:36:30.350 --> 00:36:32.487 align:middle line:84% Everything else is going to get blocked by this. 00:36:32.487 --> 00:36:33.070 align:middle line:90% STUDENT: Yeah. 00:36:33.070 --> 00:36:36.108 align:middle line:84% How does that affect that information? 00:36:36.108 --> 00:36:37.650 align:middle line:84% JUEJUN HU: You just don't collect it. 00:36:37.650 --> 00:36:38.630 align:middle line:84% Essentially, it means that you're 00:36:38.630 --> 00:36:40.150 align:middle line:84% collecting very small amount of photons 00:36:40.150 --> 00:36:42.270 align:middle line:84% from anything that's actually not at the surface. 00:36:42.270 --> 00:36:44.310 align:middle line:84% STUDENT: So your very low signal. 00:36:44.310 --> 00:36:45.770 align:middle line:84% JUEJUN HU: You decrease the signal. 00:36:45.770 --> 00:36:46.770 align:middle line:90% You suppress the signal. 00:36:46.770 --> 00:36:48.478 align:middle line:84% Essentially, if you look at, for example, 00:36:48.478 --> 00:36:51.310 align:middle line:84% if you plot this is the intensity of photons 00:36:51.310 --> 00:36:52.530 align:middle line:90% you collect, right? 00:36:52.530 --> 00:36:53.870 align:middle line:90% This is the depth. 00:36:53.870 --> 00:36:56.030 align:middle line:84% You are collecting photons essentially only 00:36:56.030 --> 00:36:57.490 align:middle line:90% from near the surface. 00:36:57.490 --> 00:37:00.830 align:middle line:90% 00:37:00.830 --> 00:37:04.730 align:middle line:84% This is like the z direction, z direction. 00:37:04.730 --> 00:37:05.670 align:middle line:90% STUDENT: OK. 00:37:05.670 --> 00:37:08.693 align:middle line:90% And you want that? 00:37:08.693 --> 00:37:09.610 align:middle line:90% JUEJUN HU: It depends. 00:37:09.610 --> 00:37:12.590 align:middle line:84% Sometimes you want this kind of depth resolution. 00:37:12.590 --> 00:37:14.870 align:middle line:84% Suppose your sample is inhomogeneous 00:37:14.870 --> 00:37:16.050 align:middle line:90% in the depth direction. 00:37:16.050 --> 00:37:18.350 align:middle line:84% Like thin film, for example, you only 00:37:18.350 --> 00:37:20.990 align:middle line:84% want a signal from your thin film, not from the substrate. 00:37:20.990 --> 00:37:24.110 align:middle line:84% STUDENT: So it's not that you're getting two different spectra 00:37:24.110 --> 00:37:27.050 align:middle line:90% from the top surface and down. 00:37:27.050 --> 00:37:28.200 align:middle line:90% It's just you are-- 00:37:28.200 --> 00:37:29.450 align:middle line:90% JUEJUN HU: You're restricting. 00:37:29.450 --> 00:37:30.790 align:middle line:84% Yeah, you're restricting the z range 00:37:30.790 --> 00:37:32.457 align:middle line:84% where you're collecting the signal from. 00:37:32.457 --> 00:37:33.030 align:middle line:90% STUDENT: OK. 00:37:33.030 --> 00:37:35.390 align:middle line:90% Yeah. 00:37:35.390 --> 00:37:38.790 align:middle line:84% JUEJUN HU: At the expense that you get lower signal. 00:37:38.790 --> 00:37:42.530 align:middle line:84% So that's why this kind of confocal microscopy, 00:37:42.530 --> 00:37:44.317 align:middle line:84% confocal Raman microscopy is used 00:37:44.317 --> 00:37:46.150 align:middle line:84% when you're analyzing things like thin films 00:37:46.150 --> 00:37:48.110 align:middle line:84% or if you're trying to analyze surface. 00:37:48.110 --> 00:37:48.750 align:middle line:90% OK? 00:37:48.750 --> 00:37:50.810 align:middle line:84% If you're trying to analyze the bulk sample, 00:37:50.810 --> 00:37:52.990 align:middle line:84% the recommendation is to just use the regular Raman. 00:37:52.990 --> 00:37:54.990 align:middle line:84% Don't worry about confocal because otherwise you 00:37:54.990 --> 00:37:58.370 align:middle line:84% are essentially losing signal by just cutting off the light. 00:37:58.370 --> 00:37:58.870 align:middle line:90% OK? 00:37:58.870 --> 00:38:07.320 align:middle line:90% 00:38:07.320 --> 00:38:09.865 align:middle line:84% Now this is some examples that shows 00:38:09.865 --> 00:38:11.240 align:middle line:84% what the Raman structure actually 00:38:11.240 --> 00:38:13.640 align:middle line:84% looks like for actual amorphous materials. 00:38:13.640 --> 00:38:16.320 align:middle line:84% Left-hand side, this is for single crystalline silicon. 00:38:16.320 --> 00:38:19.200 align:middle line:84% It has a well-defined Raman peak centering 00:38:19.200 --> 00:38:21.620 align:middle line:90% about 520 inverse centimeter. 00:38:21.620 --> 00:38:23.520 align:middle line:90% Now notice the unit here. 00:38:23.520 --> 00:38:26.120 align:middle line:90% The unit is in Raman shift. 00:38:26.120 --> 00:38:30.120 align:middle line:84% It's defined as the change of wave number 00:38:30.120 --> 00:38:32.700 align:middle line:90% from the excitation source. 00:38:32.700 --> 00:38:37.840 align:middle line:90% 00:38:37.840 --> 00:38:40.240 align:middle line:84% So you can think of the horizontal axis 00:38:40.240 --> 00:38:43.960 align:middle line:84% basically as the frequency shift or effectively 00:38:43.960 --> 00:38:45.520 align:middle line:90% the wavelength shift. 00:38:45.520 --> 00:38:46.020 align:middle line:90% OK? 00:38:46.020 --> 00:38:49.920 align:middle line:90% 00:38:49.920 --> 00:38:53.520 align:middle line:84% So from the position of the peak what you can infer 00:38:53.520 --> 00:38:55.260 align:middle line:90% is basically the phonon energy. 00:38:55.260 --> 00:39:00.120 align:middle line:90% 00:39:00.120 --> 00:39:02.280 align:middle line:84% The larger the wave number, it means 00:39:02.280 --> 00:39:04.920 align:middle line:84% that there is larger energy difference between the incident 00:39:04.920 --> 00:39:07.680 align:middle line:84% photon and the scattered photon, and therefore, it 00:39:07.680 --> 00:39:11.360 align:middle line:84% means that the solid has a higher phonon energy. 00:39:11.360 --> 00:39:16.900 align:middle line:84% Essentially, this latter offset gives you the phonon energy. 00:39:16.900 --> 00:39:19.200 align:middle line:84% It's a measure of the phonon energy. 00:39:19.200 --> 00:39:22.680 align:middle line:84% So for single crystal solid silicon, 00:39:22.680 --> 00:39:25.440 align:middle line:84% it has a very well defined peak because it 00:39:25.440 --> 00:39:26.860 align:middle line:90% has this periodic structure. 00:39:26.860 --> 00:39:28.700 align:middle line:84% Its photon energy is also very well-defined. 00:39:28.700 --> 00:39:29.950 align:middle line:90% That's basically what it says. 00:39:29.950 --> 00:39:32.000 align:middle line:84% OK, versus amorphous material, this 00:39:32.000 --> 00:39:33.620 align:middle line:84% is in this case as in sulfide glass. 00:39:33.620 --> 00:39:36.840 align:middle line:84% You see this kind of broad peaks here. 00:39:36.840 --> 00:39:40.000 align:middle line:84% And that comes from multiple factors. 00:39:40.000 --> 00:39:43.560 align:middle line:84% So one is that, of course, you have this dispersion 00:39:43.560 --> 00:39:45.200 align:middle line:90% of local structures. 00:39:45.200 --> 00:39:47.720 align:middle line:84% Every location, the atomic arrangement 00:39:47.720 --> 00:39:49.560 align:middle line:84% is slightly different from others. 00:39:49.560 --> 00:39:52.300 align:middle line:84% And this gives rise to dispersion of phonon energy. 00:39:52.300 --> 00:39:52.800 align:middle line:90% OK? 00:39:52.800 --> 00:39:55.743 align:middle line:90% 00:39:55.743 --> 00:39:58.160 align:middle line:84% Another factor that contributes to this kind of complexity 00:39:58.160 --> 00:40:01.000 align:middle line:84% of Raman spectra is the breakdown of selection rules. 00:40:01.000 --> 00:40:04.450 align:middle line:84% So selection rules basically coming from Fermi's golden rule, 00:40:04.450 --> 00:40:08.290 align:middle line:84% essentially means that there are some certain transitions 00:40:08.290 --> 00:40:13.130 align:middle line:84% that despite that a transition exists but has a transition 00:40:13.130 --> 00:40:16.490 align:middle line:84% probability of zero because the transition matrix 00:40:16.490 --> 00:40:17.810 align:middle line:90% elements is zero. 00:40:17.810 --> 00:40:18.570 align:middle line:90% OK? 00:40:18.570 --> 00:40:20.850 align:middle line:84% Now usually that's caused by symmetry. 00:40:20.850 --> 00:40:23.588 align:middle line:90% 00:40:23.588 --> 00:40:26.130 align:middle line:84% It means that, for example, you cannot easily transition from 00:40:26.130 --> 00:40:28.130 align:middle line:84% a symmetric state into a mirror symmetric state 00:40:28.130 --> 00:40:31.050 align:middle line:84% because the overlap integral of that two-wave function is zero. 00:40:31.050 --> 00:40:34.050 align:middle line:84% That's what happens with selection rule. 00:40:34.050 --> 00:40:36.348 align:middle line:84% Now selection rule applies in crystalline solids 00:40:36.348 --> 00:40:37.890 align:middle line:84% because you have crystalline lattice, 00:40:37.890 --> 00:40:39.770 align:middle line:90% you have symmetry in place. 00:40:39.770 --> 00:40:41.410 align:middle line:84% In amorphous material, you no longer 00:40:41.410 --> 00:40:43.550 align:middle line:90% have lattice, no symmetry. 00:40:43.550 --> 00:40:45.610 align:middle line:84% So essentially, a lot of these selection rules 00:40:45.610 --> 00:40:46.970 align:middle line:90% will just break down. 00:40:46.970 --> 00:40:50.050 align:middle line:84% And what that means is that sometimes some of the inhibitor 00:40:50.050 --> 00:40:51.850 align:middle line:84% transitions in the crystalline solid 00:40:51.850 --> 00:40:55.290 align:middle line:84% now becomes allowable in amorphous materials. 00:40:55.290 --> 00:40:57.530 align:middle line:84% And those photon transitions will then 00:40:57.530 --> 00:41:00.290 align:middle line:84% show up on this spectrum here, which 00:41:00.290 --> 00:41:02.810 align:middle line:84% is another reason why this is a lot more complex compared 00:41:02.810 --> 00:41:04.470 align:middle line:84% to the case of a crystalline solid. 00:41:04.470 --> 00:41:12.930 align:middle line:90% 00:41:12.930 --> 00:41:13.430 align:middle line:90% OK. 00:41:13.430 --> 00:41:17.450 align:middle line:84% So now the question is what information can you 00:41:17.450 --> 00:41:21.310 align:middle line:84% extract from this seemingly again featureless spectrum? 00:41:21.310 --> 00:41:29.930 align:middle line:90% 00:41:29.930 --> 00:41:32.610 align:middle line:84% I'm not going to derive equations. 00:41:32.610 --> 00:41:35.330 align:middle line:84% Instead, I will show you one example about 00:41:35.330 --> 00:41:38.450 align:middle line:84% what are the information you can extract just 00:41:38.450 --> 00:41:39.630 align:middle line:90% looking at Raman spectra. 00:41:39.630 --> 00:41:41.430 align:middle line:84% So this is actually some example. 00:41:41.430 --> 00:41:42.810 align:middle line:84% This is actually something we did 00:41:42.810 --> 00:41:45.630 align:middle line:84% from my own group in collaboration with Lincoln Labs. 00:41:45.630 --> 00:41:47.210 align:middle line:84% What we are trying to do is we are 00:41:47.210 --> 00:41:49.190 align:middle line:84% trying to look at phase change materials. 00:41:49.190 --> 00:41:50.450 align:middle line:84% You know what phase change material is, right? 00:41:50.450 --> 00:41:52.658 align:middle line:84% They switch between amorphous and crystalline states. 00:41:52.658 --> 00:41:55.690 align:middle line:84% So we perform this kind of switching 00:41:55.690 --> 00:41:57.610 align:middle line:84% by using essentially in this case 00:41:57.610 --> 00:41:59.840 align:middle line:90% a microheater, resistive heater. 00:41:59.840 --> 00:42:02.520 align:middle line:84% We basically have this kind of silicon wafer structure. 00:42:02.520 --> 00:42:04.040 align:middle line:84% It's called silicon on insulator. 00:42:04.040 --> 00:42:06.860 align:middle line:84% It has a layer of single crystalline silicon sitting 00:42:06.860 --> 00:42:08.740 align:middle line:84% on top of silicon substrate, separated 00:42:08.740 --> 00:42:10.980 align:middle line:90% by a layer of silicon dioxide. 00:42:10.980 --> 00:42:13.280 align:middle line:84% And silicon, this is actually a doped silicon layer. 00:42:13.280 --> 00:42:15.530 align:middle line:84% Once you dope it, they become electrically conductive. 00:42:15.530 --> 00:42:17.700 align:middle line:84% We can pass current through it, and therefore, we 00:42:17.700 --> 00:42:20.900 align:middle line:84% can introduce a controllable crystallization of this layer 00:42:20.900 --> 00:42:23.460 align:middle line:90% of phase change materials. 00:42:23.460 --> 00:42:26.940 align:middle line:84% So now if you look at using Raman, 00:42:26.940 --> 00:42:28.540 align:middle line:84% I've schematically shown to you this 00:42:28.540 --> 00:42:31.940 align:middle line:84% is what the Raman excitation beam would look like. 00:42:31.940 --> 00:42:36.060 align:middle line:84% This is the volume where you have Raman interaction 00:42:36.060 --> 00:42:37.100 align:middle line:90% with the sample. 00:42:37.100 --> 00:42:40.280 align:middle line:84% Now notice here this interaction volume is actually pretty large. 00:42:40.280 --> 00:42:43.260 align:middle line:84% It covers the phase change material itself. 00:42:43.260 --> 00:42:45.920 align:middle line:84% It also covers this silicon layer here. 00:42:45.920 --> 00:42:46.860 align:middle line:90% That's a heater. 00:42:46.860 --> 00:42:51.180 align:middle line:84% And it also overlaps a little bit with the substrate. 00:42:51.180 --> 00:42:53.660 align:middle line:84% So now let's see what information we can get. 00:42:53.660 --> 00:42:58.420 align:middle line:84% First thing is that we can monitor the peak position 00:42:58.420 --> 00:43:01.490 align:middle line:84% from the silicon Raman peak, signal increase and silicon 00:43:01.490 --> 00:43:02.140 align:middle line:90% Raman peak. 00:43:02.140 --> 00:43:05.500 align:middle line:84% What we have noticed that is that initially you 00:43:05.500 --> 00:43:07.500 align:middle line:90% have one silicon Raman peak. 00:43:07.500 --> 00:43:11.038 align:middle line:84% As you increase the voltage through this two electrodes 00:43:11.038 --> 00:43:13.580 align:middle line:84% here, it essentially means that you're heating up the heater. 00:43:13.580 --> 00:43:18.500 align:middle line:84% As you heating up, you start to see a shift of the Raman peak. 00:43:18.500 --> 00:43:20.820 align:middle line:84% And then at some point, you see that the silicon Raman 00:43:20.820 --> 00:43:21.880 align:middle line:90% peak split into two. 00:43:21.880 --> 00:43:25.640 align:middle line:90% 00:43:25.640 --> 00:43:27.420 align:middle line:84% Now the shift can be explained by the fact 00:43:27.420 --> 00:43:29.740 align:middle line:84% that the position of the Raman peak 00:43:29.740 --> 00:43:31.765 align:middle line:84% is actually a function of temperature. 00:43:31.765 --> 00:43:33.140 align:middle line:84% So that's actually another method 00:43:33.140 --> 00:43:35.460 align:middle line:84% to use Raman to actually do a non-contact measurement 00:43:35.460 --> 00:43:36.687 align:middle line:90% of temperature on samples. 00:43:36.687 --> 00:43:38.520 align:middle line:84% If you have a crystalline silicon substrate, 00:43:38.520 --> 00:43:40.940 align:middle line:84% you can monitor temperature by just looking at the shift. 00:43:40.940 --> 00:43:44.380 align:middle line:84% Now, the reason there is actually a split here, 00:43:44.380 --> 00:43:48.540 align:middle line:84% it's actually because our probing beam overlaps 00:43:48.540 --> 00:43:52.980 align:middle line:84% with both this silicon layer as well as the silicon substrate. 00:43:52.980 --> 00:43:55.200 align:middle line:84% As you can imagine, when you pass current through it, 00:43:55.200 --> 00:43:57.410 align:middle line:84% this heater is going to go to much higher temperature. 00:43:57.410 --> 00:43:58.810 align:middle line:84% The substrate, on the other hand, 00:43:58.810 --> 00:44:00.185 align:middle line:84% will set a much lower temperature 00:44:00.185 --> 00:44:01.870 align:middle line:84% because it's basically a heat sink. 00:44:01.870 --> 00:44:04.370 align:middle line:84% And that's why you see that at some point, 00:44:04.370 --> 00:44:06.490 align:middle line:84% these two silicon peaks will split, 00:44:06.490 --> 00:44:08.750 align:middle line:84% indicating that this layer of silicon 00:44:08.750 --> 00:44:10.590 align:middle line:84% is now at a much higher temperature compared 00:44:10.590 --> 00:44:12.630 align:middle line:90% to the silicon substrate. 00:44:12.630 --> 00:44:15.350 align:middle line:84% So now we can essentially now determine 00:44:15.350 --> 00:44:18.028 align:middle line:84% what is the temperature of the heater 00:44:18.028 --> 00:44:19.570 align:middle line:84% as well as the phase change material. 00:44:19.570 --> 00:44:22.550 align:middle line:90% 00:44:22.550 --> 00:44:23.700 align:middle line:90% So we can know temperature. 00:44:23.700 --> 00:44:24.450 align:middle line:90% This is one thing. 00:44:24.450 --> 00:44:27.150 align:middle line:90% 00:44:27.150 --> 00:44:29.470 align:middle line:84% This is actually an actual experimental data. 00:44:29.470 --> 00:44:32.590 align:middle line:84% The line is basically our simulation results 00:44:32.590 --> 00:44:34.210 align:middle line:90% using finite element methods. 00:44:34.210 --> 00:44:35.870 align:middle line:84% The thoughts actually experimentally measure data, 00:44:35.870 --> 00:44:37.953 align:middle line:84% showing that how we actually increase the voltage, 00:44:37.953 --> 00:44:41.530 align:middle line:84% how the temperature of the heater actually increases. 00:44:41.530 --> 00:44:43.990 align:middle line:84% So now you know temperature, we can now 00:44:43.990 --> 00:44:45.790 align:middle line:84% try to analyze the temperature dependent 00:44:45.790 --> 00:44:48.150 align:middle line:84% structural transformation as well as the kinetics 00:44:48.150 --> 00:44:49.870 align:middle line:90% of the transformation. 00:44:49.870 --> 00:44:53.590 align:middle line:84% So to analyze the Raman spectra what I'm showing here, 00:44:53.590 --> 00:44:55.030 align:middle line:84% this is the raw spectra that's is 00:44:55.030 --> 00:44:58.050 align:middle line:84% collected for amorphous phase of the phase change material. 00:44:58.050 --> 00:45:00.590 align:middle line:84% This is for crystalline phase of the phase change material. 00:45:00.590 --> 00:45:02.570 align:middle line:84% OK, again, seems quite like featureless. 00:45:02.570 --> 00:45:04.237 align:middle line:84% You all this kind of featureless things. 00:45:04.237 --> 00:45:06.870 align:middle line:84% OK, but some general features you can tell 00:45:06.870 --> 00:45:08.950 align:middle line:84% is that if it's a crystalline phase, 00:45:08.950 --> 00:45:12.430 align:middle line:84% there's a dominant peak at this wave number here. 00:45:12.430 --> 00:45:16.270 align:middle line:84% This is actually about 100 and I think this 00:45:16.270 --> 00:45:18.730 align:middle line:84% was 120 inverse centimeter wave number. 00:45:18.730 --> 00:45:20.790 align:middle line:84% But for amorphous space, there's another peak 00:45:20.790 --> 00:45:24.230 align:middle line:84% coming up at around 160 inverse centimeter. 00:45:24.230 --> 00:45:26.670 align:middle line:84% So if you want to get more quantitative information, what 00:45:26.670 --> 00:45:29.150 align:middle line:84% you have to do is you have to first correct the spectrum 00:45:29.150 --> 00:45:30.450 align:middle line:90% and then do some fitting there. 00:45:30.450 --> 00:45:32.910 align:middle line:84% The first correction you have to do 00:45:32.910 --> 00:45:35.670 align:middle line:84% is to correct for absorption and scattering. 00:45:35.670 --> 00:45:39.050 align:middle line:84% So this comes into play because similar to X-ray, 00:45:39.050 --> 00:45:42.430 align:middle line:84% when the excitation laser goes through the sample it gets 00:45:42.430 --> 00:45:43.050 align:middle line:90% absorbed. 00:45:43.050 --> 00:45:43.890 align:middle line:90% It gets scattered. 00:45:43.890 --> 00:45:45.557 align:middle line:84% So its intensity actually changes as you 00:45:45.557 --> 00:45:46.790 align:middle line:90% penetrate into the sample. 00:45:46.790 --> 00:45:49.590 align:middle line:84% So this is a factor that has to be corrected 00:45:49.590 --> 00:45:51.930 align:middle line:90% to get the Raman spectra there. 00:45:51.930 --> 00:45:53.960 align:middle line:84% So you first perform this correction here 00:45:53.960 --> 00:45:55.600 align:middle line:90% to get this corrected structure. 00:45:55.600 --> 00:45:59.560 align:middle line:84% Next part is then we need to eliminate this broad background 00:45:59.560 --> 00:46:00.280 align:middle line:90% here. 00:46:00.280 --> 00:46:05.680 align:middle line:84% The broad background is caused by so-called a Boson peak. 00:46:05.680 --> 00:46:09.380 align:middle line:84% The origin of the Boson peak is still somewhat under debate. 00:46:09.380 --> 00:46:12.600 align:middle line:84% But in general, people agree that this is a common phenomena 00:46:12.600 --> 00:46:13.860 align:middle line:90% in amorphous materials. 00:46:13.860 --> 00:46:16.520 align:middle line:84% It's a consequence of the medium range order in the solids 00:46:16.520 --> 00:46:18.240 align:middle line:90% that lead to this Boson peak. 00:46:18.240 --> 00:46:20.680 align:middle line:84% Now, fortunately, people already have 00:46:20.680 --> 00:46:24.280 align:middle line:84% a pretty well-defined function for this Boson peak here. 00:46:24.280 --> 00:46:27.360 align:middle line:84% So you can essentially use that function to actually subtract 00:46:27.360 --> 00:46:29.960 align:middle line:84% this background and leaving behind this information 00:46:29.960 --> 00:46:33.560 align:middle line:84% did actually come from the Raman scattering of the sample. 00:46:33.560 --> 00:46:38.120 align:middle line:84% So then next step is that you can perform a peak decomposition 00:46:38.120 --> 00:46:43.480 align:middle line:84% to decompose the Raman spectra into a few discrete peaks. 00:46:43.480 --> 00:46:47.043 align:middle line:84% Now to further analyze what are causing these discrete peaks, 00:46:47.043 --> 00:46:48.960 align:middle line:84% what you have to do now is to actually perform 00:46:48.960 --> 00:46:50.400 align:middle line:90% some simulation. 00:46:50.400 --> 00:46:52.740 align:middle line:84% So we did some density functional theory, 00:46:52.740 --> 00:46:54.380 align:middle line:84% first principle atomic calculations. 00:46:54.380 --> 00:46:59.100 align:middle line:84% And according to the density functional theory, 00:46:59.100 --> 00:47:01.380 align:middle line:84% there are many, many vibrational modes. 00:47:01.380 --> 00:47:03.640 align:middle line:84% Each is represented by essentially one of these peaks 00:47:03.640 --> 00:47:05.080 align:middle line:90% here 00:47:05.080 --> 00:47:07.320 align:middle line:84% So the peak position basically indicates 00:47:07.320 --> 00:47:10.320 align:middle line:84% the vibrational frequency of each of the vibrational modes 00:47:10.320 --> 00:47:11.520 align:middle line:90% of the lattice. 00:47:11.520 --> 00:47:17.160 align:middle line:84% And the width of these peaks indicates structural disorder. 00:47:17.160 --> 00:47:18.900 align:middle line:84% The more structural disorder you have, 00:47:18.900 --> 00:47:21.358 align:middle line:84% the larger the dispersion of the local structure, the wider 00:47:21.358 --> 00:47:22.960 align:middle line:90% the peak gets. 00:47:22.960 --> 00:47:28.040 align:middle line:84% So you can see that our simulation actually 00:47:28.040 --> 00:47:30.280 align:middle line:84% gives pretty good agreement compared to experiment. 00:47:30.280 --> 00:47:31.800 align:middle line:90% There are actually two peaks. 00:47:31.800 --> 00:47:34.400 align:middle line:84% The blue curve is actually what's 00:47:34.400 --> 00:47:36.340 align:middle line:84% predicted by density functional theory. 00:47:36.340 --> 00:47:38.720 align:middle line:84% The black curve is what we actually get from experiment. 00:47:38.720 --> 00:47:39.100 align:middle line:90% OK. 00:47:39.100 --> 00:47:40.475 align:middle line:84% So you get pretty nice agreement. 00:47:40.475 --> 00:47:42.800 align:middle line:84% So now you can unequivocally start 00:47:42.800 --> 00:47:47.680 align:middle line:84% to assign structural entities to each of the corresponding peaks. 00:47:47.680 --> 00:47:49.880 align:middle line:84% So for example, this green one actually 00:47:49.880 --> 00:47:53.290 align:middle line:84% is associated with germanium 6 selenium octahedral structure. 00:47:53.290 --> 00:47:55.090 align:middle line:84% This one is actually germanium sitting 00:47:55.090 --> 00:47:57.630 align:middle line:84% in tetrahedral, selenium tetrahedra. 00:47:57.630 --> 00:48:00.730 align:middle line:84% This one is antimony sitting in selenium octahedral. 00:48:00.730 --> 00:48:02.970 align:middle line:84% OK, so now you will be able to identify 00:48:02.970 --> 00:48:05.970 align:middle line:84% what is the structure entity that caused all the peaks. 00:48:05.970 --> 00:48:07.790 align:middle line:84% You also see some useful information here. 00:48:07.790 --> 00:48:09.930 align:middle line:84% So for example as you go from crystalline phase 00:48:09.930 --> 00:48:12.330 align:middle line:84% to amorphous phase, you are seeing that germanium 00:48:12.330 --> 00:48:13.930 align:middle line:90% is actually shifting location. 00:48:13.930 --> 00:48:15.610 align:middle line:84% Initially, most germanium actually 00:48:15.610 --> 00:48:17.190 align:middle line:90% sits in octahedral site. 00:48:17.190 --> 00:48:18.930 align:middle line:84% Now they move to a tetrahedral site 00:48:18.930 --> 00:48:21.890 align:middle line:90% as you move to amorphous phase. 00:48:21.890 --> 00:48:24.030 align:middle line:84% OK, so that's the useful information. 00:48:24.030 --> 00:48:26.930 align:middle line:84% Now you can actually extract from this kind of a data here. 00:48:26.930 --> 00:48:27.430 align:middle line:90% OK. 00:48:27.430 --> 00:48:29.557 align:middle line:90% 00:48:29.557 --> 00:48:31.890 align:middle line:84% But basically, that's how you actually analyze the Raman 00:48:31.890 --> 00:48:34.570 align:middle line:90% spectra quantitatively. 00:48:34.570 --> 00:48:36.610 align:middle line:84% You have to compare it with literature 00:48:36.610 --> 00:48:38.650 align:middle line:84% or with first principle simulations 00:48:38.650 --> 00:48:43.570 align:middle line:84% to identify the specific nature, the origin for all 00:48:43.570 --> 00:48:46.770 align:middle line:90% the Raman scattering peaks. 00:48:46.770 --> 00:48:47.390 align:middle line:90% All right. 00:48:47.390 --> 00:48:49.730 align:middle line:84% So now you can identify essentially the temperature 00:48:49.730 --> 00:48:51.877 align:middle line:84% dependent structure of the material. 00:48:51.877 --> 00:48:54.210 align:middle line:84% Next thing you can also do is that it actually gives you 00:48:54.210 --> 00:48:58.010 align:middle line:84% a way to actually measure the phase transition kinetics. 00:48:58.010 --> 00:49:02.810 align:middle line:84% So phase transition kinetics is captured by this TTT diagram. 00:49:02.810 --> 00:49:04.850 align:middle line:84% So to do a TTT diagram, what you have to do 00:49:04.850 --> 00:49:07.195 align:middle line:84% is you have to perform a set of isothermal experiments, 00:49:07.195 --> 00:49:09.070 align:middle line:84% if you remember how a TTT diagram is derived. 00:49:09.070 --> 00:49:10.070 align:middle line:90% You fix the temperature. 00:49:10.070 --> 00:49:12.237 align:middle line:84% You look at how long does it take to actually induce 00:49:12.237 --> 00:49:13.250 align:middle line:90% some phase transition. 00:49:13.250 --> 00:49:16.590 align:middle line:84% And then you connect all those points on the graph. 00:49:16.590 --> 00:49:18.895 align:middle line:90% Then you get a diagram. 00:49:18.895 --> 00:49:21.270 align:middle line:84% So that's exactly what we can do now with this technique. 00:49:21.270 --> 00:49:24.730 align:middle line:84% Because we know temperature from the Raman peak shift of silicon. 00:49:24.730 --> 00:49:25.647 align:middle line:90% We know the structure. 00:49:25.647 --> 00:49:27.897 align:middle line:84% So we can know exactly what's the fraction of material 00:49:27.897 --> 00:49:30.530 align:middle line:84% we have actually crystallized by analyzing Raman spectra there. 00:49:30.530 --> 00:49:33.210 align:middle line:84% So then if you collect those data, 00:49:33.210 --> 00:49:35.637 align:middle line:84% you can generate this TTT diagram here. 00:49:35.637 --> 00:49:37.970 align:middle line:84% It may look a little bit different from the TTT diagram, 00:49:37.970 --> 00:49:40.290 align:middle line:84% because what we do, this is actually a discrete version 00:49:40.290 --> 00:49:41.830 align:middle line:90% of the diagram. 00:49:41.830 --> 00:49:44.190 align:middle line:84% What we did is we have the heater. 00:49:44.190 --> 00:49:46.990 align:middle line:84% We can turn on the heater, heat up to certain temperature, 00:49:46.990 --> 00:49:49.397 align:middle line:84% hold it there for some period of time. 00:49:49.397 --> 00:49:50.980 align:middle line:84% And we're now examining whether or not 00:49:50.980 --> 00:49:53.780 align:middle line:84% the material has crystallized or not. 00:49:53.780 --> 00:49:56.820 align:middle line:84% So each data point essentially corresponds to one 00:49:56.820 --> 00:49:58.380 align:middle line:90% of these experiments. 00:49:58.380 --> 00:50:00.740 align:middle line:84% And what we are seeing here is that you're only 00:50:00.740 --> 00:50:03.180 align:middle line:84% introducing crystallization when you actually 00:50:03.180 --> 00:50:05.980 align:middle line:84% force within this dotted line range here. 00:50:05.980 --> 00:50:08.820 align:middle line:84% This is when you actually see crystallization of the PCM. 00:50:08.820 --> 00:50:12.420 align:middle line:84% So this total line basically then corresponds 00:50:12.420 --> 00:50:16.520 align:middle line:84% to the crystalline region that you normally see in 3D diagram. 00:50:16.520 --> 00:50:18.740 align:middle line:84% And this is where essentially the noise temperature 00:50:18.740 --> 00:50:20.780 align:middle line:90% is basically. 00:50:20.780 --> 00:50:24.860 align:middle line:84% It's like a discrete version of a normal TTT diagram. 00:50:24.860 --> 00:50:27.820 align:middle line:90% Does that make sense? 00:50:27.820 --> 00:50:30.980 align:middle line:84% So this is in fact, I believe this is actually 00:50:30.980 --> 00:50:34.620 align:middle line:84% the first time a true TTT diagram was actually 00:50:34.620 --> 00:50:36.380 align:middle line:90% measured in PCM. 00:50:36.380 --> 00:50:38.200 align:middle line:84% Otherwise, it can be pretty tricky, right? 00:50:38.200 --> 00:50:39.882 align:middle line:90% Because it crystallizes so fast. 00:50:39.882 --> 00:50:41.340 align:middle line:84% And you also need a way to actually 00:50:41.340 --> 00:50:43.220 align:middle line:84% accurately identify temperature and also 00:50:43.220 --> 00:50:44.700 align:middle line:90% identify the structure there. 00:50:44.700 --> 00:50:46.940 align:middle line:84% So Raman is actually a pretty perfect candidate 00:50:46.940 --> 00:50:49.900 align:middle line:84% to do both things, killing two birds with one stone. 00:50:49.900 --> 00:50:51.700 align:middle line:90% OK. 00:50:51.700 --> 00:50:53.260 align:middle line:90% All right. 00:50:53.260 --> 00:50:54.740 align:middle line:90% So that's Raman. 00:50:54.740 --> 00:50:57.820 align:middle line:84% Now, last technique I'm going to discuss here 00:50:57.820 --> 00:51:01.640 align:middle line:84% is thermal analysis or basically a calorimetry. 00:51:01.640 --> 00:51:08.060 align:middle line:90% 00:51:08.060 --> 00:51:11.860 align:middle line:84% So you're probably all familiar with calorie numbers 00:51:11.860 --> 00:51:14.100 align:middle line:84% that you normally see in essentially any kind of food 00:51:14.100 --> 00:51:14.680 align:middle line:90% packages. 00:51:14.680 --> 00:51:17.020 align:middle line:84% You will see all those numbers listing calories. 00:51:17.020 --> 00:51:20.620 align:middle line:84% Have you ever wondered how those numbers come from? 00:51:20.620 --> 00:51:23.280 align:middle line:84% They come from calorimetry measurements. 00:51:23.280 --> 00:51:24.780 align:middle line:84% And there's actually an equation I'm 00:51:24.780 --> 00:51:27.940 align:middle line:84% listing down here that actually defines rigorously 00:51:27.940 --> 00:51:31.360 align:middle line:84% how those calorie numbers are actually calculated or measured. 00:51:31.360 --> 00:51:34.700 align:middle line:84% So it should be equalling to the energy 00:51:34.700 --> 00:51:39.340 align:middle line:84% in the food minus the energy that gets carried away 00:51:39.340 --> 00:51:42.820 align:middle line:90% in basically a human waste. 00:51:42.820 --> 00:51:45.710 align:middle line:84% So now if you want to actually measure 00:51:45.710 --> 00:51:50.367 align:middle line:84% the actual calories contained in food ingredient, what you have 00:51:50.367 --> 00:51:51.950 align:middle line:84% to do is you have to perform this kind 00:51:51.950 --> 00:51:53.550 align:middle line:90% of calorimetric measurements. 00:51:53.550 --> 00:51:57.190 align:middle line:84% So a calorimeter basically is you have your chamber here. 00:51:57.190 --> 00:52:00.550 align:middle line:84% You then perform oxidation of food 00:52:00.550 --> 00:52:06.135 align:middle line:84% or whatever sample it is, basically burning it. 00:52:06.135 --> 00:52:07.510 align:middle line:84% So when you burn it, it generates 00:52:07.510 --> 00:52:09.130 align:middle line:90% heat coming from oxidation. 00:52:09.130 --> 00:52:12.310 align:middle line:84% The heat is passed around to this water bath here 00:52:12.310 --> 00:52:14.950 align:middle line:84% and everything is enclosed in thermally 00:52:14.950 --> 00:52:17.050 align:middle line:90% insulating containment. 00:52:17.050 --> 00:52:20.190 align:middle line:84% So then the temperature rise of the water 00:52:20.190 --> 00:52:24.190 align:middle line:84% will indicate how much heat is generated in oxidation process. 00:52:24.190 --> 00:52:27.190 align:middle line:84% So to complete the equation, you need 00:52:27.190 --> 00:52:29.630 align:middle line:84% to measure the energy contained in food. 00:52:29.630 --> 00:52:33.310 align:middle line:84% You also need to burn human waste 00:52:33.310 --> 00:52:36.990 align:middle line:84% to get the actual energy carried away by those materials. 00:52:36.990 --> 00:52:40.010 align:middle line:84% So that's not a particularly pleasant experiment. 00:52:40.010 --> 00:52:42.010 align:middle line:84% And as you can imagine, people will not do that. 00:52:42.010 --> 00:52:44.870 align:middle line:84% I mean, like will McDonald's try to actually burn 00:52:44.870 --> 00:52:47.430 align:middle line:84% the burger to actually measure it, the actual heat? 00:52:47.430 --> 00:52:49.013 align:middle line:90% No. 00:52:49.013 --> 00:52:50.430 align:middle line:84% Most of the time when you actually 00:52:50.430 --> 00:52:52.650 align:middle line:84% see those numbers on food packages, what they did, 00:52:52.650 --> 00:52:53.990 align:middle line:90% they took a shortcut. 00:52:53.990 --> 00:52:56.150 align:middle line:84% They just look at how much protein, 00:52:56.150 --> 00:53:00.830 align:middle line:84% how much fiber, how much fat is contained in each kind of food. 00:53:00.830 --> 00:53:02.670 align:middle line:84% And there's a standard conversion table 00:53:02.670 --> 00:53:04.870 align:middle line:84% that tells you that this amount of fat 00:53:04.870 --> 00:53:07.030 align:middle line:84% corresponds to this amount of calories. 00:53:07.030 --> 00:53:09.110 align:middle line:84% They simply add it together and that's the number 00:53:09.110 --> 00:53:10.990 align:middle line:90% they actually reported. 00:53:10.990 --> 00:53:15.830 align:middle line:84% So now actually you can imagine that's grossly inaccurate 00:53:15.830 --> 00:53:16.930 align:middle line:90% that kind of method. 00:53:16.930 --> 00:53:19.910 align:middle line:84% It completely ignores any kind of difference 00:53:19.910 --> 00:53:22.110 align:middle line:84% in terms of how you actually process the food. 00:53:22.110 --> 00:53:24.530 align:middle line:84% As you can imagine, if you have a steak, 00:53:24.530 --> 00:53:29.110 align:middle line:84% you have basically a raw steak compared to something 00:53:29.110 --> 00:53:30.710 align:middle line:90% that's perfectly well done. 00:53:30.710 --> 00:53:32.590 align:middle line:84% The amount of energy human body can extract 00:53:32.590 --> 00:53:35.630 align:middle line:90% is completely different. 00:53:35.630 --> 00:53:38.110 align:middle line:84% The human body requires a lot more energy 00:53:38.110 --> 00:53:39.830 align:middle line:84% to assimilate, essentially a raw steak 00:53:39.830 --> 00:53:41.590 align:middle line:90% compared to well-done steak. 00:53:41.590 --> 00:53:44.120 align:middle line:84% But that difference is completely 00:53:44.120 --> 00:53:47.320 align:middle line:84% ignored in this kind of calculation. 00:53:47.320 --> 00:53:49.120 align:middle line:84% So now you realize you should not really 00:53:49.120 --> 00:53:51.000 align:middle line:90% trust those numbers too much. 00:53:51.000 --> 00:53:53.240 align:middle line:84% They are just simply not very accurate. 00:53:53.240 --> 00:53:54.600 align:middle line:90% OK? 00:53:54.600 --> 00:53:56.880 align:middle line:84% Now as scientists, we want to be a bit more 00:53:56.880 --> 00:54:00.240 align:middle line:84% accurate when it comes to analyzing amorphous materials. 00:54:00.240 --> 00:54:03.680 align:middle line:84% So that's why we are introducing two techniques here-- 00:54:03.680 --> 00:54:06.360 align:middle line:84% differential scanning calorimetry or DSC 00:54:06.360 --> 00:54:08.960 align:middle line:84% or differential thermal analysis, DTA. 00:54:08.960 --> 00:54:11.680 align:middle line:90% 00:54:11.680 --> 00:54:15.680 align:middle line:84% First of all, these two methods, they basically more or less 00:54:15.680 --> 00:54:19.360 align:middle line:90% reveal similar information. 00:54:19.360 --> 00:54:22.400 align:middle line:84% DTA was the first technique that was developed 00:54:22.400 --> 00:54:24.838 align:middle line:84% because it's configurationally a lot easier, 00:54:24.838 --> 00:54:26.380 align:middle line:84% and that's why people like to use it, 00:54:26.380 --> 00:54:27.800 align:middle line:90% especially in early days. 00:54:27.800 --> 00:54:31.880 align:middle line:84% But as I'll show you later, DSC can be a lot more quantitative. 00:54:31.880 --> 00:54:36.480 align:middle line:84% And that's why people are basically progressively 00:54:36.480 --> 00:54:38.640 align:middle line:90% transitioning from DTA to DSC. 00:54:38.640 --> 00:54:40.667 align:middle line:84% But if you read all the literature, 00:54:40.667 --> 00:54:42.500 align:middle line:84% you're still going to see a lot of DTA data. 00:54:42.500 --> 00:54:44.625 align:middle line:84% So that's why you need to understand the technique. 00:54:44.625 --> 00:54:47.520 align:middle line:90% So what does the DSC measure? 00:54:47.520 --> 00:54:50.760 align:middle line:84% A DSC essentially you put your sample along 00:54:50.760 --> 00:54:54.720 align:middle line:84% with a reference in two separate heating ovens, OK, 00:54:54.720 --> 00:54:58.240 align:middle line:90% or two separate heaters. 00:54:58.240 --> 00:55:01.600 align:middle line:84% The reference should be an inert material with known 00:55:01.600 --> 00:55:03.400 align:middle line:90% thermal characteristics. 00:55:03.400 --> 00:55:06.720 align:middle line:84% So for inert, it means that the reference should not 00:55:06.720 --> 00:55:08.840 align:middle line:84% undergo any kind of phase transition 00:55:08.840 --> 00:55:13.000 align:middle line:84% in the entire temperature range of interest. 00:55:13.000 --> 00:55:16.020 align:middle line:84% Its thermal properties, which basically is the heat capacity, 00:55:16.020 --> 00:55:17.840 align:middle line:84% should also be very well calibrated 00:55:17.840 --> 00:55:19.340 align:middle line:84% across the entire temperature range. 00:55:19.340 --> 00:55:22.120 align:middle line:90% 00:55:22.120 --> 00:55:23.540 align:middle line:90% OK, that's for the reference. 00:55:23.540 --> 00:55:27.080 align:middle line:90% 00:55:27.080 --> 00:55:29.180 align:middle line:84% Now in your actual analysis, what you will do, 00:55:29.180 --> 00:55:36.360 align:middle line:84% you create two identical ovens with two identical heaters. 00:55:36.360 --> 00:55:39.060 align:middle line:84% You put your sample on one, you put the reference on the other. 00:55:39.060 --> 00:55:40.435 align:middle line:84% And they are thermally insulated. 00:55:40.435 --> 00:55:42.570 align:middle line:84% There is no crosstalk in between the two. 00:55:42.570 --> 00:55:45.090 align:middle line:84% You now start to pass current through the heaters 00:55:45.090 --> 00:55:46.650 align:middle line:90% to heat them up. 00:55:46.650 --> 00:55:51.770 align:middle line:84% For DSC, you essentially ensure that the temperature 00:55:51.770 --> 00:55:54.010 align:middle line:84% of the sample and the reference is always 00:55:54.010 --> 00:55:56.810 align:middle line:84% the same throughout the entire heating cycle. 00:55:56.810 --> 00:56:00.570 align:middle line:84% And you do this through a feedback loop computer control. 00:56:00.570 --> 00:56:03.090 align:middle line:84% You change the instantaneous power 00:56:03.090 --> 00:56:06.530 align:middle line:84% you feed into the two heaters, just so that the temperature is 00:56:06.530 --> 00:56:09.110 align:middle line:84% always the same for the reference and for your sample. 00:56:09.110 --> 00:56:16.340 align:middle line:90% 00:56:16.340 --> 00:56:19.010 align:middle line:84% So what you are measuring here for DSC 00:56:19.010 --> 00:56:23.290 align:middle line:84% is basically the difference of heat flow into the sample 00:56:23.290 --> 00:56:24.670 align:middle line:90% versus into reference. 00:56:24.670 --> 00:56:31.650 align:middle line:90% 00:56:31.650 --> 00:56:34.770 align:middle line:84% Now for DTA, DTA is a lot easier. 00:56:34.770 --> 00:56:38.010 align:middle line:90% DTA you only have one oven. 00:56:38.010 --> 00:56:40.810 align:middle line:84% You have this kind of symmetrically configured oven. 00:56:40.810 --> 00:56:42.283 align:middle line:84% You have one heater, single heater. 00:56:42.283 --> 00:56:43.950 align:middle line:84% You have a sample, you have a reference. 00:56:43.950 --> 00:56:46.810 align:middle line:84% You put it in this mirror symmetric configuration, 00:56:46.810 --> 00:56:50.490 align:middle line:84% so that the assumption is that the thermal conductance 00:56:50.490 --> 00:56:53.450 align:middle line:84% from the heater to the sample and to reference 00:56:53.450 --> 00:56:56.810 align:middle line:84% is the same, more or less identical. 00:56:56.810 --> 00:57:01.250 align:middle line:84% So then if you assume the heat conductance is same, 00:57:01.250 --> 00:57:03.650 align:middle line:84% it means that the heat flux going from the heater 00:57:03.650 --> 00:57:04.310 align:middle line:90% to the sample. 00:57:04.310 --> 00:57:06.130 align:middle line:84% And from the heater to the reference 00:57:06.130 --> 00:57:08.170 align:middle line:90% is more or less the same. 00:57:08.170 --> 00:57:11.303 align:middle line:84% So if heat flux is same, the sample and the reference, 00:57:11.303 --> 00:57:12.970 align:middle line:84% they may have different heat capacities. 00:57:12.970 --> 00:57:15.530 align:middle line:84% So different heat capacities will then 00:57:15.530 --> 00:57:18.130 align:middle line:90% lead to a different temperature. 00:57:18.130 --> 00:57:21.090 align:middle line:84% So what DTA measures is the temperature difference 00:57:21.090 --> 00:57:22.950 align:middle line:84% between the sample and the reference. 00:57:22.950 --> 00:57:25.970 align:middle line:90% 00:57:25.970 --> 00:57:29.388 align:middle line:84% So now you can see why DTA is a lot easier to prepare 00:57:29.388 --> 00:57:30.430 align:middle line:90% because it's very simple. 00:57:30.430 --> 00:57:32.382 align:middle line:90% It's just one single furnace. 00:57:32.382 --> 00:57:34.590 align:middle line:84% Put things in there and just measure the temperature, 00:57:34.590 --> 00:57:35.650 align:middle line:90% very straightforward. 00:57:35.650 --> 00:57:40.500 align:middle line:84% Versus DSC, you need actually some pretty complicated computer 00:57:40.500 --> 00:57:42.500 align:middle line:84% control to ensure that you always 00:57:42.500 --> 00:57:44.660 align:middle line:84% have the same temperature between the sample 00:57:44.660 --> 00:57:46.940 align:middle line:90% and the reference. 00:57:46.940 --> 00:57:51.340 align:middle line:84% Now let's start by taking a look at DSC first, 00:57:51.340 --> 00:57:53.580 align:middle line:90% and I'll explain DTA. 00:57:53.580 --> 00:57:57.780 align:middle line:84% So in a DSC structure essentially the vertical axis 00:57:57.780 --> 00:58:00.780 align:middle line:84% will be the difference of the heat flow to the sample 00:58:00.780 --> 00:58:01.940 align:middle line:90% versus to the reference. 00:58:01.940 --> 00:58:02.700 align:middle line:90% OK? 00:58:02.700 --> 00:58:04.940 align:middle line:84% There are different conventions as to which 00:58:04.940 --> 00:58:07.860 align:middle line:84% side is the positive axis, which side is negative axis. 00:58:07.860 --> 00:58:10.280 align:middle line:84% What I'm assuming here is that if you go along, 00:58:10.280 --> 00:58:12.500 align:middle line:84% the positive axis essentially correspond 00:58:12.500 --> 00:58:14.205 align:middle line:84% to endothermic reaction in your sample. 00:58:14.205 --> 00:58:16.580 align:middle line:84% Endothermic essentially means that the sample is actually 00:58:16.580 --> 00:58:18.140 align:middle line:90% absorbing heat. 00:58:18.140 --> 00:58:21.460 align:middle line:84% If you go in the negative axis, it's an exothermic reaction. 00:58:21.460 --> 00:58:23.780 align:middle line:84% It means your sample is releasing heat. 00:58:23.780 --> 00:58:30.580 align:middle line:84% So effectively, if you have a curve that 00:58:30.580 --> 00:58:34.100 align:middle line:84% goes somewhere up here, it means that either your sample 00:58:34.100 --> 00:58:38.060 align:middle line:84% is releasing heat or your sample has a very small heat capacity, 00:58:38.060 --> 00:58:40.380 align:middle line:84% or smaller heat capacity compared to the reference. 00:58:40.380 --> 00:58:44.500 align:middle line:90% 00:58:44.500 --> 00:58:45.000 align:middle line:90% All right. 00:58:45.000 --> 00:58:46.700 align:middle line:84% So now we can take a look at the spectra here. 00:58:46.700 --> 00:58:48.820 align:middle line:84% So if you have a glass sample, amorphous sample, 00:58:48.820 --> 00:58:49.920 align:middle line:90% you go through DSC. 00:58:49.920 --> 00:58:53.260 align:middle line:84% Initially, you get more or less a flat line. 00:58:53.260 --> 00:58:58.380 align:middle line:84% What a flat line represents, in a steady state 00:58:58.380 --> 00:59:00.700 align:middle line:84% we are measuring the heat flux difference. 00:59:00.700 --> 00:59:03.800 align:middle line:84% The heat flux in an isobaric experiment, 00:59:03.800 --> 00:59:05.660 align:middle line:84% which means the constant pressure that's 00:59:05.660 --> 00:59:07.900 align:middle line:84% the case for most experiments, is basically 00:59:07.900 --> 00:59:09.680 align:middle line:90% the change of enthalpy. 00:59:09.680 --> 00:59:11.380 align:middle line:84% The heat flux is basically a change 00:59:11.380 --> 00:59:13.140 align:middle line:90% of enthalpy of the sample. 00:59:13.140 --> 00:59:15.900 align:middle line:84% So the heat flux is basically this differential 00:59:15.900 --> 00:59:20.460 align:middle line:84% here, dH dT That's enthalpy change as a change 00:59:20.460 --> 00:59:21.538 align:middle line:90% rate in your sample. 00:59:21.538 --> 00:59:23.580 align:middle line:84% You're looking at a difference between the sample 00:59:23.580 --> 00:59:24.500 align:middle line:90% and the reference. 00:59:24.500 --> 00:59:26.520 align:middle line:84% So subscript S is basically your sample. 00:59:26.520 --> 00:59:29.660 align:middle line:84% Subscript R is basically reference. 00:59:29.660 --> 00:59:32.580 align:middle line:84% Now we also know that enthalpy change 00:59:32.580 --> 00:59:36.190 align:middle line:84% can be directly correlated with heat capacity of the material. 00:59:36.190 --> 00:59:40.870 align:middle line:84% So essentially this heat flux difference 00:59:40.870 --> 00:59:43.250 align:middle line:84% can be trivially connected to this equation here. 00:59:43.250 --> 00:59:45.870 align:middle line:84% It's the difference of heat capacity between the two samples 00:59:45.870 --> 00:59:47.710 align:middle line:84% here, between the sample and the reference, 00:59:47.710 --> 00:59:50.010 align:middle line:84% as well as times the heating rate. 00:59:50.010 --> 00:59:52.660 align:middle line:90% 00:59:52.660 --> 00:59:55.210 align:middle line:84% So now you can tell why people like DSC, right? 00:59:55.210 --> 00:59:58.790 align:middle line:84% You have this very clean, simple expression. 00:59:58.790 --> 01:00:03.350 align:middle line:84% You can directly extract what is the heat capacity just 01:00:03.350 --> 01:00:05.470 align:middle line:90% from this measurement here. 01:00:05.470 --> 01:00:12.543 align:middle line:84% STUDENT: So the dHS dT minus dHR dT, that's just the y-axis? 01:00:12.543 --> 01:00:14.210 align:middle line:84% JUEJUN HU: This is basically the y-axis. 01:00:14.210 --> 01:00:15.410 align:middle line:90% It's a heat flux difference. 01:00:15.410 --> 01:00:16.785 align:middle line:84% The y-axis is basically measuring 01:00:16.785 --> 01:00:19.590 align:middle line:84% the difference of heat flow to the sample and to the reference. 01:00:19.590 --> 01:00:26.310 align:middle line:90% 01:00:26.310 --> 01:00:29.430 align:middle line:84% If your sample doesn't undergo any kind of phase transition 01:00:29.430 --> 01:00:34.390 align:middle line:84% then you expect this DSC trace will pretty much be a flat line. 01:00:34.390 --> 01:00:36.348 align:middle line:84% It just gives you the heat capacity difference 01:00:36.348 --> 01:00:37.890 align:middle line:84% between the sample and the reference. 01:00:37.890 --> 01:00:42.070 align:middle line:90% 01:00:42.070 --> 01:00:42.810 align:middle line:90% All right. 01:00:42.810 --> 01:00:46.190 align:middle line:90% Now go to the first step here. 01:00:46.190 --> 01:00:50.090 align:middle line:84% This first step corresponds to glass transition. 01:00:50.090 --> 01:00:53.030 align:middle line:90% 01:00:53.030 --> 01:00:55.310 align:middle line:84% The reason there's a step there is 01:00:55.310 --> 01:00:57.430 align:middle line:84% because as you go from glassy state 01:00:57.430 --> 01:01:01.390 align:middle line:84% to go to a supercooled liquid state, 01:01:01.390 --> 01:01:04.630 align:middle line:90% the heat capacity changes. 01:01:04.630 --> 01:01:08.070 align:middle line:84% The supercooled liquid state, the material 01:01:08.070 --> 01:01:09.870 align:middle line:84% has access to more degrees of freedom, 01:01:09.870 --> 01:01:12.950 align:middle line:84% and therefore, it should have a high heat capacity. 01:01:12.950 --> 01:01:15.310 align:middle line:84% This can also be explained by looking 01:01:15.310 --> 01:01:17.950 align:middle line:84% in how the enthalpy changes as a function of temperature 01:01:17.950 --> 01:01:20.733 align:middle line:84% for glass materials, if you remember. 01:01:20.733 --> 01:01:22.650 align:middle line:84% And so we change as a function of temperature. 01:01:22.650 --> 01:01:24.942 align:middle line:84% Essentially, the curve starts out with a smaller slope. 01:01:24.942 --> 01:01:28.750 align:middle line:84% As you go through glass transition, it becomes steeper. 01:01:28.750 --> 01:01:29.470 align:middle line:90% Right? 01:01:29.470 --> 01:01:32.560 align:middle line:84% That's basically showing up in essentially the different heat 01:01:32.560 --> 01:01:33.340 align:middle line:90% capacities here. 01:01:33.340 --> 01:01:34.700 align:middle line:90% That's the two plateaus. 01:01:34.700 --> 01:01:36.900 align:middle line:84% This is basically heat capacity of the glass. 01:01:36.900 --> 01:01:38.900 align:middle line:84% This is the heat capacity of supercooled liquid. 01:01:38.900 --> 01:01:49.280 align:middle line:90% 01:01:49.280 --> 01:01:51.440 align:middle line:84% Now if you continue to heat up, there's 01:01:51.440 --> 01:01:55.600 align:middle line:84% going to be a dip or negative peak that actually comes up. 01:01:55.600 --> 01:01:59.840 align:middle line:84% This corresponds to crystallization. 01:01:59.840 --> 01:02:02.080 align:middle line:84% So when the amorphous sample crystallizes, 01:02:02.080 --> 01:02:05.400 align:middle line:84% the crystalline state actually has a lower enthalpy compared 01:02:05.400 --> 01:02:06.540 align:middle line:90% to the amorphous state. 01:02:06.540 --> 01:02:09.072 align:middle line:90% 01:02:09.072 --> 01:02:12.800 align:middle line:84% So therefore in the crystallization process, 01:02:12.800 --> 01:02:15.800 align:middle line:84% the sample actually releases heat 01:02:15.800 --> 01:02:19.920 align:middle line:84% when it transitions to this low enthalpy crystalline state. 01:02:19.920 --> 01:02:23.200 align:middle line:84% So that's why that's basically an exothermic peak that 01:02:23.200 --> 01:02:23.860 align:middle line:90% comes up. 01:02:23.860 --> 01:02:27.200 align:middle line:90% 01:02:27.200 --> 01:02:29.263 align:middle line:84% There's excess amount of all enthalpy that's 01:02:29.263 --> 01:02:30.680 align:middle line:84% released to the environment as you 01:02:30.680 --> 01:02:33.760 align:middle line:90% go through this enthalpy state. 01:02:33.760 --> 01:02:36.400 align:middle line:84% Then if you keep going to high temperature, at some point 01:02:36.400 --> 01:02:40.920 align:middle line:84% you go to essentially a melting point. 01:02:40.920 --> 01:02:43.260 align:middle line:84% And in order to melt a crystalline material, 01:02:43.260 --> 01:02:45.000 align:middle line:84% you need to supply the latent heat. 01:02:45.000 --> 01:02:51.320 align:middle line:84% And that's why it shows up as a endothermic peak. 01:02:51.320 --> 01:02:53.080 align:middle line:84% And you need to absorb heat in order 01:02:53.080 --> 01:02:57.920 align:middle line:84% to transition it from solid state to liquid state. 01:02:57.920 --> 01:02:59.840 align:middle line:84% So this is typically what the DSC trace 01:02:59.840 --> 01:03:01.920 align:middle line:84% is going to look like for an amorphous material, 01:03:01.920 --> 01:03:02.940 align:middle line:90% for glassy material. 01:03:02.940 --> 01:03:06.805 align:middle line:90% 01:03:06.805 --> 01:03:09.360 align:middle line:84% STUDENT: That first piece that would have been a lot easier 01:03:09.360 --> 01:03:10.108 align:middle line:90% with this. 01:03:10.108 --> 01:03:10.900 align:middle line:90% JUEJUN HU: Oh Yeah. 01:03:10.900 --> 01:03:12.020 align:middle line:90% Now you remember that one. 01:03:12.020 --> 01:03:13.600 align:middle line:90% Yes, exactly. 01:03:13.600 --> 01:03:15.860 align:middle line:84% I'm trying to prepare you for this. 01:03:15.860 --> 01:03:16.818 align:middle line:90% OK. 01:03:16.818 --> 01:03:18.860 align:middle line:84% Maybe I should have done this after this lecture. 01:03:18.860 --> 01:03:21.700 align:middle line:84% But now, one thing I also want to quickly mention here, 01:03:21.700 --> 01:03:24.000 align:middle line:84% the reason I said DSC people like it is 01:03:24.000 --> 01:03:25.720 align:middle line:90% because it's very quantitative. 01:03:25.720 --> 01:03:28.250 align:middle line:84% The area under each of these peaks 01:03:28.250 --> 01:03:33.210 align:middle line:84% can be directly correlated with the enthalpy change. 01:03:33.210 --> 01:03:36.183 align:middle line:84% You can, for example, from the area under the peak, 01:03:36.183 --> 01:03:37.850 align:middle line:84% under the melting peak, you can directly 01:03:37.850 --> 01:03:39.225 align:middle line:84% calculate what is the latent heat 01:03:39.225 --> 01:03:41.530 align:middle line:84% or what is the enthalpy of melting. 01:03:41.530 --> 01:03:44.370 align:middle line:84% Same thing, area under the crystallization peak 01:03:44.370 --> 01:03:46.207 align:middle line:84% gives you the enthalpy of crystallization 01:03:46.207 --> 01:03:48.290 align:middle line:84% or the enthalpy difference between crystalline and 01:03:48.290 --> 01:03:50.290 align:middle line:90% amorphous state. 01:03:50.290 --> 01:03:55.850 align:middle line:84% So you can not only measure the crystallization temperature, 01:03:55.850 --> 01:03:58.970 align:middle line:84% the melting point, or the glass transition temperature, 01:03:58.970 --> 01:04:00.770 align:middle line:84% you can also quantitatively determine 01:04:00.770 --> 01:04:03.230 align:middle line:84% some thermodynamic parameters of your material. 01:04:03.230 --> 01:04:09.330 align:middle line:90% 01:04:09.330 --> 01:04:12.090 align:middle line:84% And that's why I said people like DSC, exactly 01:04:12.090 --> 01:04:12.870 align:middle line:90% for that reason. 01:04:12.870 --> 01:04:15.490 align:middle line:84% Because you can quantitatively determine your sample 01:04:15.490 --> 01:04:16.230 align:middle line:90% parameters. 01:04:16.230 --> 01:04:23.530 align:middle line:90% 01:04:23.530 --> 01:04:25.430 align:middle line:84% Now I want to also mention one caveat here. 01:04:25.430 --> 01:04:29.170 align:middle line:84% This is basically your p set, your first p set. 01:04:29.170 --> 01:04:31.050 align:middle line:84% About this part of the curve, so I 01:04:31.050 --> 01:04:32.730 align:middle line:84% have used this very simple curve here 01:04:32.730 --> 01:04:34.290 align:middle line:84% just a smooth curve just to connect 01:04:34.290 --> 01:04:36.850 align:middle line:84% the glass regime and the supercooied liquid regime. 01:04:36.850 --> 01:04:38.970 align:middle line:84% In reality, usually you don't get 01:04:38.970 --> 01:04:40.890 align:middle line:90% this kind of very simple curve. 01:04:40.890 --> 01:04:42.330 align:middle line:84% In fact, what you're going to get 01:04:42.330 --> 01:04:46.917 align:middle line:84% is a curve more like this, because you have a relaxation. 01:04:46.917 --> 01:04:48.750 align:middle line:84% As you go through a glass transition regime, 01:04:48.750 --> 01:04:50.730 align:middle line:84% we know that it's going to relax towards a supercooled liquid 01:04:50.730 --> 01:04:51.450 align:middle line:90% state. 01:04:51.450 --> 01:04:54.690 align:middle line:84% And the slope of this line basically 01:04:54.690 --> 01:05:00.370 align:middle line:84% gives you the heat flux, exactly the p set OK. 01:05:00.370 --> 01:05:04.290 align:middle line:84% And that's why you will have this kind of complicated shape 01:05:04.290 --> 01:05:06.730 align:middle line:90% of the heat flow there. 01:05:06.730 --> 01:05:11.450 align:middle line:84% So this is what our DSC trace is actually going to look like. 01:05:11.450 --> 01:05:14.050 align:middle line:84% Now one immediate consequence here 01:05:14.050 --> 01:05:18.170 align:middle line:84% is that it becomes quite difficult to unequivocally 01:05:18.170 --> 01:05:20.930 align:middle line:84% determine a glass transition temperature just 01:05:20.930 --> 01:05:23.050 align:middle line:84% by looking at the DSC trace here. 01:05:23.050 --> 01:05:24.740 align:middle line:84% I mentioned about this kind of ambiguity 01:05:24.740 --> 01:05:26.965 align:middle line:84% there, that Tg, glass transition temperature, 01:05:26.965 --> 01:05:28.340 align:middle line:84% has different definitions when we 01:05:28.340 --> 01:05:29.670 align:middle line:90% talk to different communities. 01:05:29.670 --> 01:05:30.920 align:middle line:90% You talk to a glass community. 01:05:30.920 --> 01:05:33.545 align:middle line:84% People will tell you that Tg is basically when viscosity equals 01:05:33.545 --> 01:05:36.900 align:middle line:84% 10 to the 12th Pascal-seconds-- simple, very well defined. 01:05:36.900 --> 01:05:40.900 align:middle line:84% If you talk to people working on the thermal analysis community, 01:05:40.900 --> 01:05:42.540 align:middle line:90% things become a bit fuzzy there. 01:05:42.540 --> 01:05:45.660 align:middle line:84% They try to measure the glass transition temperature 01:05:45.660 --> 01:05:48.220 align:middle line:84% by essentially looking at when this transition happens 01:05:48.220 --> 01:05:50.060 align:middle line:90% on the DSC trace. 01:05:50.060 --> 01:05:52.597 align:middle line:84% Now you can tell it's quite difficult to determine. 01:05:52.597 --> 01:05:54.180 align:middle line:84% In fact, what people would normally do 01:05:54.180 --> 01:05:56.980 align:middle line:84% is they try to extend some of these two lines 01:05:56.980 --> 01:05:59.140 align:middle line:84% here and look at the crossover point, 01:05:59.140 --> 01:06:01.480 align:middle line:84% and then use that crossover point to define the Tg. 01:06:01.480 --> 01:06:04.980 align:middle line:90% 01:06:04.980 --> 01:06:06.980 align:middle line:84% It's not very rigorous, as you can tell. 01:06:06.980 --> 01:06:09.340 align:middle line:84% If you have different heating rates, different sample 01:06:09.340 --> 01:06:11.460 align:middle line:84% preparation conditions, it's going 01:06:11.460 --> 01:06:13.460 align:middle line:90% to be very, very different. 01:06:13.460 --> 01:06:16.580 align:middle line:84% So that's why Tg determined from DSC, 01:06:16.580 --> 01:06:20.520 align:middle line:84% it's at best, maybe a semi-quantitative measure. 01:06:20.520 --> 01:06:23.020 align:middle line:84% If you fix your experimental condition like the same heating 01:06:23.020 --> 01:06:25.720 align:middle line:84% rate, you can use it to compare different samples, 01:06:25.720 --> 01:06:27.700 align:middle line:84% but you should be very, very careful 01:06:27.700 --> 01:06:32.020 align:middle line:84% not to compare your Tg to some other people's Tg measured 01:06:32.020 --> 01:06:33.540 align:middle line:90% on two different DSC machines. 01:06:33.540 --> 01:06:34.760 align:middle line:90% That may not be comparable. 01:06:34.760 --> 01:06:37.300 align:middle line:90% 01:06:37.300 --> 01:06:38.700 align:middle line:90% No, no, no, no, no. 01:06:38.700 --> 01:06:41.960 align:middle line:84% As long as you are consistent using the same DSC machine, 01:06:41.960 --> 01:06:44.240 align:middle line:84% compare different things, try the same heating rate, 01:06:44.240 --> 01:06:44.860 align:middle line:90% that's OK. 01:06:44.860 --> 01:06:46.400 align:middle line:90% Don't worry too much about it. 01:06:46.400 --> 01:06:50.345 align:middle line:84% Or if your Tg differs by a much larger temperature 01:06:50.345 --> 01:06:52.220 align:middle line:84% window than what I'm showing here, then maybe 01:06:52.220 --> 01:06:53.900 align:middle line:90% you don't even care. 01:06:53.900 --> 01:06:56.280 align:middle line:84% Anyway, that's just a caveat there. 01:06:56.280 --> 01:07:00.260 align:middle line:84% So just be careful when you're actually interpreting DSC data. 01:07:00.260 --> 01:07:00.760 align:middle line:90% All right. 01:07:00.760 --> 01:07:02.780 align:middle line:90% Now switch over to DTA. 01:07:02.780 --> 01:07:04.692 align:middle line:84% So DTA, as I mentioned, now we are 01:07:04.692 --> 01:07:06.900 align:middle line:84% looking at the temperature difference between the two 01:07:06.900 --> 01:07:07.500 align:middle line:90% samples. 01:07:07.500 --> 01:07:10.900 align:middle line:90% 01:07:10.900 --> 01:07:16.180 align:middle line:84% So quantitatively, we can look at the DTA 01:07:16.180 --> 01:07:17.720 align:middle line:84% by looking at this equation here. 01:07:17.720 --> 01:07:20.380 align:middle line:84% Let me explain what this equation means. 01:07:20.380 --> 01:07:22.710 align:middle line:90% So K is the thermal conductance. 01:07:22.710 --> 01:07:26.710 align:middle line:84% K is the thermal conductance from your heater to your sample 01:07:26.710 --> 01:07:27.550 align:middle line:90% or to the reference. 01:07:27.550 --> 01:07:29.310 align:middle line:84% Because it's symmetric, basically, the K 01:07:29.310 --> 01:07:33.030 align:middle line:84% is the same for the sample and the reference. 01:07:33.030 --> 01:07:36.390 align:middle line:84% So according to Fourier's law of conduction, 01:07:36.390 --> 01:07:39.510 align:middle line:84% the amount of heat flux to the sample or to the reference 01:07:39.510 --> 01:07:42.390 align:middle line:84% is given by K thermal conductance times 01:07:42.390 --> 01:07:44.670 align:middle line:84% the temperature difference between your heater, which 01:07:44.670 --> 01:07:49.710 align:middle line:84% is Tf minus the temperature of your sample, or the reference. 01:07:49.710 --> 01:07:51.990 align:middle line:84% It's basically delta T times thermal conductance. 01:07:51.990 --> 01:07:53.430 align:middle line:90% That gives you a heat flux. 01:07:53.430 --> 01:07:56.790 align:middle line:84% And the heat flux should equal to basically dH 01:07:56.790 --> 01:07:58.850 align:middle line:90% dT, the enthalpy change. 01:07:58.850 --> 01:08:03.230 align:middle line:90% 01:08:03.230 --> 01:08:05.750 align:middle line:84% So you can take the difference of these two equations. 01:08:05.750 --> 01:08:07.330 align:middle line:90% I'm going to skip the math here. 01:08:07.330 --> 01:08:11.270 align:middle line:84% We end up getting is that the temperature 01:08:11.270 --> 01:08:13.510 align:middle line:84% difference between the sample and reference 01:08:13.510 --> 01:08:17.550 align:middle line:84% should also correlate with the heat capacity 01:08:17.550 --> 01:08:19.810 align:middle line:84% difference between the sample and the reference. 01:08:19.810 --> 01:08:22.590 align:middle line:90% 01:08:22.590 --> 01:08:27.710 align:middle line:84% But notice the sign difference here is CR minus CS. 01:08:27.710 --> 01:08:31.149 align:middle line:90% Here is CS minus CR. 01:08:31.149 --> 01:08:34.390 align:middle line:90% CS minus CR, CR minus CS. 01:08:34.390 --> 01:08:36.310 align:middle line:84% So to the first order, you will see 01:08:36.310 --> 01:08:38.910 align:middle line:84% that the DTA curve essentially looks 01:08:38.910 --> 01:08:44.590 align:middle line:84% like a DSC curve flipped, flipped upside down because 01:08:44.590 --> 01:08:46.843 align:middle line:90% of the negative sign. 01:08:46.843 --> 01:08:48.510 align:middle line:84% Now second thing, I also want to mention 01:08:48.510 --> 01:08:50.990 align:middle line:84% that DTA is a lot more difficult to quantify 01:08:50.990 --> 01:08:54.390 align:middle line:84% because of the presence of this K in your equation there. 01:08:54.390 --> 01:08:56.750 align:middle line:84% K is the thermal conductance from your heater 01:08:56.750 --> 01:08:59.750 align:middle line:84% to your sample, which is very difficult to measure. 01:08:59.750 --> 01:09:02.210 align:middle line:84% And it's different from one machine to the other machine. 01:09:02.210 --> 01:09:05.250 align:middle line:90% 01:09:05.250 --> 01:09:08.430 align:middle line:84% So that's why most of the time when people are using DTA, 01:09:08.430 --> 01:09:11.710 align:middle line:84% people are not trying to extract quantitative, thermodynamic 01:09:11.710 --> 01:09:13.790 align:middle line:90% parameters like enthalpy. 01:09:13.790 --> 01:09:17.310 align:middle line:90% If you want to do that, use DSC. 01:09:17.310 --> 01:09:20.800 align:middle line:84% What people use DTA for is just to determine the temperature. 01:09:20.800 --> 01:09:22.319 align:middle line:84% Determine, for example, what's Tg, 01:09:22.319 --> 01:09:24.760 align:middle line:84% what's Tx, the crystallization temperature, or what's 01:09:24.760 --> 01:09:26.520 align:middle line:90% Tm, what's the melting point. 01:09:26.520 --> 01:09:28.080 align:middle line:90% So that's what DTA is used for. 01:09:28.080 --> 01:09:36.319 align:middle line:90% 01:09:36.319 --> 01:09:38.720 align:middle line:84% So the interpretation of the DTA curve 01:09:38.720 --> 01:09:40.473 align:middle line:84% is actually really pretty straightforward. 01:09:40.473 --> 01:09:42.640 align:middle line:84% As I said, it's basically the DSC curve more or less 01:09:42.640 --> 01:09:44.100 align:middle line:90% flipped upside down. 01:09:44.100 --> 01:09:45.880 align:middle line:90% You will see a glass transition. 01:09:45.880 --> 01:09:47.720 align:middle line:84% You will similarly now see a positive peak 01:09:47.720 --> 01:09:49.920 align:middle line:84% for crystallization and then a dip 01:09:49.920 --> 01:09:52.040 align:middle line:90% or negative peak for melting. 01:09:52.040 --> 01:09:55.160 align:middle line:84% And you can again use whatever trick 01:09:55.160 --> 01:09:57.940 align:middle line:84% you like to do to try to fit the different temperatures there. 01:09:57.940 --> 01:10:09.000 align:middle line:90% 01:10:09.000 --> 01:10:09.500 align:middle line:90% All right. 01:10:09.500 --> 01:10:11.600 align:middle line:84% Now, one real example of how people actually 01:10:11.600 --> 01:10:17.385 align:middle line:84% use DTA to analyze glass materials, so in this case 01:10:17.385 --> 01:10:18.760 align:middle line:84% here, people are basically trying 01:10:18.760 --> 01:10:22.920 align:middle line:84% to gauge the impact of silicon addition 01:10:22.920 --> 01:10:29.240 align:middle line:84% in the amorphous phase stability of arsenic telluride glass. 01:10:29.240 --> 01:10:31.220 align:middle line:84% So you can see that you have two decay curves, 01:10:31.220 --> 01:10:35.480 align:middle line:84% one without silicon, one with silicon. 01:10:35.480 --> 01:10:37.440 align:middle line:84% And you can now start trying to fit 01:10:37.440 --> 01:10:39.340 align:middle line:84% all these different temperature points here. 01:10:39.340 --> 01:10:42.560 align:middle line:90% 01:10:42.560 --> 01:10:44.280 align:middle line:84% By essentially extending the lines 01:10:44.280 --> 01:10:46.160 align:middle line:84% and see where they cross over, and this 01:10:46.160 --> 01:10:48.618 align:middle line:84% is how you actually determine all the different temperature 01:10:48.618 --> 01:10:50.080 align:middle line:90% points. 01:10:50.080 --> 01:10:56.600 align:middle line:84% Again, as I said, this is only semi-quantitative at best. 01:10:56.600 --> 01:11:00.010 align:middle line:84% However, what is legit is that you can actually still look at, 01:11:00.010 --> 01:11:01.760 align:middle line:84% if you compare these two samples, measured 01:11:01.760 --> 01:11:04.760 align:middle line:84% in the same DTA machine, the relative difference 01:11:04.760 --> 01:11:07.183 align:middle line:84% of the temperature still makes sense. 01:11:07.183 --> 01:11:09.600 align:middle line:84% In this particular case, what they are trying to determine 01:11:09.600 --> 01:11:11.208 align:middle line:84% is the amorphous phase stability. 01:11:11.208 --> 01:11:13.000 align:middle line:84% We mentioned that amorphous phase stability 01:11:13.000 --> 01:11:15.160 align:middle line:84% can be gauged using different kind figure of merit. 01:11:15.160 --> 01:11:18.818 align:middle line:84% For example, the most common one is delta T. Tx minus Tg, where 01:11:18.818 --> 01:11:20.610 align:middle line:84% Tx is [? supercooled ?] liquid temperature, 01:11:20.610 --> 01:11:23.410 align:middle line:84% Tg is the glass transition temperature. 01:11:23.410 --> 01:11:25.730 align:middle line:84% So essentially, in this case, you 01:11:25.730 --> 01:11:27.610 align:middle line:84% can see that you have two samples. 01:11:27.610 --> 01:11:28.450 align:middle line:90% Let's see. 01:11:28.450 --> 01:11:30.610 align:middle line:84% So this is basically Tx minus Tg. 01:11:30.610 --> 01:11:32.490 align:middle line:90% This is Tm minus Tx. 01:11:32.490 --> 01:11:35.650 align:middle line:84% So this window essentially tells you 01:11:35.650 --> 01:11:37.450 align:middle line:84% which sample is actually more stable. 01:11:37.450 --> 01:11:40.290 align:middle line:84% In this case, it seems like the one doped with silicon 01:11:40.290 --> 01:11:42.388 align:middle line:84% has a larger difference between Tx minus Tg, 01:11:42.388 --> 01:11:44.430 align:middle line:84% and therefore, it should be actually more stable. 01:11:44.430 --> 01:11:46.222 align:middle line:84% So the argument is that if you add silicon, 01:11:46.222 --> 01:11:48.210 align:middle line:84% you make this glass actually more stable. 01:11:48.210 --> 01:11:50.490 align:middle line:84% That's the conclusion you can draw legitimately 01:11:50.490 --> 01:11:55.770 align:middle line:90% from this analysis here 01:11:55.770 --> 01:11:57.770 align:middle line:90% All right. 01:11:57.770 --> 01:12:00.475 align:middle line:84% So in the remaining five minutes, 01:12:00.475 --> 01:12:02.850 align:middle line:84% I just also want to quickly mention that this is actually 01:12:02.850 --> 01:12:05.970 align:middle line:84% a new technique people are now developing here called the flash 01:12:05.970 --> 01:12:08.970 align:middle line:90% DSC, or ultrafast DSC. 01:12:08.970 --> 01:12:11.050 align:middle line:84% The motivation there is that people sometimes 01:12:11.050 --> 01:12:13.530 align:middle line:84% want to characterize some material transformation that 01:12:13.530 --> 01:12:15.210 align:middle line:90% is very, very fast. 01:12:15.210 --> 01:12:17.085 align:middle line:84% And if you use a normal DSC, you will not 01:12:17.085 --> 01:12:19.210 align:middle line:84% be able to actually capture that because the sample 01:12:19.210 --> 01:12:22.510 align:middle line:84% itself has a finite volume heating up or cooling it down, 01:12:22.510 --> 01:12:25.250 align:middle line:84% it all takes time because of the large thermal mass. 01:12:25.250 --> 01:12:27.450 align:middle line:84% So you will actually miss a lot of this kind 01:12:27.450 --> 01:12:30.370 align:middle line:84% of transient transitions that happens actually in materials. 01:12:30.370 --> 01:12:33.450 align:middle line:84% So in a flash DSC, what people are doing here 01:12:33.450 --> 01:12:36.430 align:middle line:84% is they essentially use a special kind of sample data. 01:12:36.430 --> 01:12:38.770 align:middle line:84% Instead of being a bulk sample, they essentially 01:12:38.770 --> 01:12:40.850 align:middle line:84% use a microfabrication technology 01:12:40.850 --> 01:12:44.570 align:middle line:84% to fabricate micro heaters on a silicon substrate. 01:12:44.570 --> 01:12:46.153 align:middle line:84% And then they use those micro heaters. 01:12:46.153 --> 01:12:48.612 align:middle line:84% They pass current essentially through those resistive micro 01:12:48.612 --> 01:12:50.570 align:middle line:84% heaters, and use that to actually quickly heat 01:12:50.570 --> 01:12:52.110 align:middle line:90% up and cool down the material. 01:12:52.110 --> 01:12:54.290 align:middle line:84% Because a very small sample volume, 01:12:54.290 --> 01:12:56.662 align:middle line:84% you can realize much higher heating and cooling rate 01:12:56.662 --> 01:12:58.370 align:middle line:84% compared to what you were able to achieve 01:12:58.370 --> 01:12:59.930 align:middle line:90% using conventional DSC. 01:12:59.930 --> 01:13:04.366 align:middle line:84% OK, so let me just play that video. 01:13:04.366 --> 01:13:05.362 align:middle line:90% [VIDEO PLAYBACK] 01:13:05.362 --> 01:13:07.852 align:middle line:90% [MUSIC PLAYING] 01:13:07.852 --> 01:13:16.340 align:middle line:90% 01:13:16.340 --> 01:13:19.780 align:middle line:84% - Up until now, many physical transitions and chemical 01:13:19.780 --> 01:13:23.060 align:middle line:84% reactions could not be investigated simply 01:13:23.060 --> 01:13:25.220 align:middle line:84% because no instrument was fast enough 01:13:25.220 --> 01:13:27.320 align:middle line:84% to measure the processes involved. 01:13:27.320 --> 01:13:31.100 align:middle line:90% 01:13:31.100 --> 01:13:35.180 align:middle line:84% The new revolutionary Mettler Toledo Flash DSC, 01:13:35.180 --> 01:13:38.420 align:middle line:84% opens up new frontiers in thermal analysis 01:13:38.420 --> 01:13:43.020 align:middle line:84% and gives you access to a complete whole new world. 01:13:43.020 --> 01:13:47.420 align:middle line:84% Differential scanning calorimetry, or DSC for short, 01:13:47.420 --> 01:13:51.140 align:middle line:84% is a technique that allows you to determine the energy absorbed 01:13:51.140 --> 01:13:55.700 align:middle line:84% or released by a sample over a wide temperature range. 01:13:55.700 --> 01:13:58.500 align:middle line:84% The standard DSC from Mettler Toledo 01:13:58.500 --> 01:14:03.220 align:middle line:84% has a maximum heating rate of 400 Kelvin per minute. 01:14:03.220 --> 01:14:07.620 align:middle line:84% In contrast, the new Flash DSC provides heating rates of up 01:14:07.620 --> 01:14:12.900 align:middle line:84% to 2,400,000 Kelvin per minute and cooling rates of up 01:14:12.900 --> 01:14:16.660 align:middle line:90% to 240,000 Kelvin per minute. 01:14:16.660 --> 01:14:19.500 align:middle line:84% These incredibly high heating and cooling rates 01:14:19.500 --> 01:14:22.740 align:middle line:84% present exciting new application possibilities that 01:14:22.740 --> 01:14:25.740 align:middle line:90% were previously undreamt of. 01:14:25.740 --> 01:14:29.020 align:middle line:84% For example, materials used for injection molding 01:14:29.020 --> 01:14:33.380 align:middle line:84% can now be studied under actual processing conditions. 01:14:33.380 --> 01:14:35.740 align:middle line:84% The Flash DSC's cooling rates are 01:14:35.740 --> 01:14:38.180 align:middle line:84% so high that a sample can be cooled 01:14:38.180 --> 01:14:41.020 align:middle line:84% under exactly the same conditions as occur 01:14:41.020 --> 01:14:43.620 align:middle line:90% in the process. 01:14:43.620 --> 01:14:47.380 align:middle line:84% The heart of the Flash DSC is the innovative sensor chip 01:14:47.380 --> 01:14:49.940 align:middle line:90% based on MEMS technology. 01:14:49.940 --> 01:14:52.300 align:middle line:84% This sensor has a very small mass 01:14:52.300 --> 01:14:54.940 align:middle line:84% and combines unsurpassed sensitivity 01:14:54.940 --> 01:14:56.940 align:middle line:90% with excellent resolution, and-- 01:14:56.940 --> 01:14:57.660 align:middle line:84% JUEJUN HU: You see the [? better ?] traces. 01:14:57.660 --> 01:14:59.340 align:middle line:90% That's actually how you apply-- 01:14:59.340 --> 01:15:01.660 align:middle line:84% - On a Flash DSC measurement, the sample 01:15:01.660 --> 01:15:05.380 align:middle line:84% is placed directly onto the replaceable sensor. 01:15:05.380 --> 01:15:08.340 align:middle line:84% The ergonomic design of the instrument, the touch screen 01:15:08.340 --> 01:15:12.310 align:middle line:84% display, and the microscope ensure complete ease of use 01:15:12.310 --> 01:15:16.230 align:middle line:84% when working with such very small samples. 01:15:16.230 --> 01:15:18.670 align:middle line:84% The very high heating and cooling rates 01:15:18.670 --> 01:15:23.430 align:middle line:84% enable many measurements to be performed in just a few seconds. 01:15:23.430 --> 01:15:25.510 align:middle line:84% This generates an enormous amount 01:15:25.510 --> 01:15:28.510 align:middle line:90% of new data for evaluation. 01:15:28.510 --> 01:15:31.710 align:middle line:84% Mettler Toledo's powerful STARe software 01:15:31.710 --> 01:15:36.150 align:middle line:84% offers unrivaled flexibility and almost unlimited evaluation 01:15:36.150 --> 01:15:40.470 align:middle line:84% possibilities, and allows you to explore a completely new world 01:15:40.470 --> 01:15:41.670 align:middle line:90% with Flash DSC. 01:15:41.670 --> 01:15:43.350 align:middle line:84% JUEJUN HU: That's [INAUDIBLE] peaks. 01:15:43.350 --> 01:15:45.070 align:middle line:90% - --innovative technology. 01:15:45.070 --> 01:15:47.470 align:middle line:84% JUEJUN HU: So now we know what you have on your T-shirt. 01:15:47.470 --> 01:15:50.270 align:middle line:90% 01:15:50.270 --> 01:15:54.430 align:middle line:84% - The Mettler Toledo Flash DSC represents a quantum leap 01:15:54.430 --> 01:15:57.630 align:middle line:84% in thermal analysis and revolutionizes 01:15:57.630 --> 01:15:59.567 align:middle line:90% fast scanning DSC. 01:15:59.567 --> 01:16:00.150 align:middle line:90% [END PLAYBACK] 01:16:00.150 --> 01:16:00.733 align:middle line:90% JUEJUN HU: OK. 01:16:00.733 --> 01:16:03.710 align:middle line:90% 01:16:03.710 --> 01:16:04.470 align:middle line:90% All right. 01:16:04.470 --> 01:16:06.830 align:middle line:84% I show this is just one quick example reference 01:16:06.830 --> 01:16:08.230 align:middle line:90% from this paper there. 01:16:08.230 --> 01:16:10.480 align:middle line:84% Essentially, this is one example where people actually 01:16:10.480 --> 01:16:11.877 align:middle line:90% used ultrafast DSC. 01:16:11.877 --> 01:16:13.710 align:middle line:84% In this case is actually the crystallization 01:16:13.710 --> 01:16:14.752 align:middle line:90% of phase change material. 01:16:14.752 --> 01:16:16.543 align:middle line:84% We know this phase change material actually 01:16:16.543 --> 01:16:17.770 align:middle line:90% are essentially poor gasses. 01:16:17.770 --> 01:16:19.687 align:middle line:84% They crystallize in very short period of time. 01:16:19.687 --> 01:16:21.690 align:middle line:84% You cannot analyze it using conventional DSC. 01:16:21.690 --> 01:16:24.630 align:middle line:84% But now you can actually do it with this ultrafast DSC. 01:16:24.630 --> 01:16:27.830 align:middle line:90% So we are right on time. 01:16:27.830 --> 01:16:30.290 align:middle line:84% And I'm actually going to conclude here. 01:16:30.290 --> 01:16:33.400 align:middle line:90% Any last minute questions? 01:16:33.400 --> 01:17:09.000 align:middle line:90%