WEBVTT 00:00:00.000 --> 00:00:02.500 align:middle line:90% [SQUEAKING] 00:00:02.500 --> 00:00:04.000 align:middle line:90% [RUSTLING] 00:00:04.000 --> 00:00:07.500 align:middle line:90% [CLICKING] 00:00:07.500 --> 00:00:15.560 align:middle line:90% 00:00:15.560 --> 00:00:17.560 align:middle line:84% JUEJUN HU: OK, so in this lecture, what we'll do 00:00:17.560 --> 00:00:20.200 align:middle line:84% is we'll focus on a unique class of amorphous materials 00:00:20.200 --> 00:00:24.080 align:middle line:90% basically, metallic glasses. 00:00:24.080 --> 00:00:26.000 align:middle line:84% So metallic glasses is pretty much not 00:00:26.000 --> 00:00:29.200 align:middle line:84% included the reference text I recommended 00:00:29.200 --> 00:00:30.880 align:middle line:84% at the beginning of semester, so that's 00:00:30.880 --> 00:00:32.479 align:middle line:84% why I have included a few, I think, 00:00:32.479 --> 00:00:35.160 align:middle line:84% very nice papers here that discusses 00:00:35.160 --> 00:00:38.040 align:middle line:84% about structural or mechanical behavior of these metallic 00:00:38.040 --> 00:00:41.160 align:middle line:90% glasses as references. 00:00:41.160 --> 00:00:43.440 align:middle line:84% All right, so to start with, this slide basically 00:00:43.440 --> 00:00:46.320 align:middle line:84% summarizes the historic timeline of the development 00:00:46.320 --> 00:00:49.440 align:middle line:84% for amorphous metals or metallic glasses. 00:00:49.440 --> 00:00:53.160 align:middle line:84% For a long time, people do not believe that you can actually 00:00:53.160 --> 00:00:54.960 align:middle line:84% prepare metal in an amorphous form, 00:00:54.960 --> 00:00:57.300 align:middle line:84% because they tend to crystallize very, very quickly. 00:00:57.300 --> 00:01:00.690 align:middle line:84% So it's very hard to prevent essentially a crystallization 00:01:00.690 --> 00:01:02.130 align:middle line:90% of this material. 00:01:02.130 --> 00:01:05.209 align:middle line:84% It's only until like 1960s, where people actually start 00:01:05.209 --> 00:01:08.050 align:middle line:84% to discover that you can actually prepare essentially 00:01:08.050 --> 00:01:12.090 align:middle line:84% a very thin membrane form of metallic glasses or amorphous 00:01:12.090 --> 00:01:16.050 align:middle line:84% metals in this binary gold silicon alloy. 00:01:16.050 --> 00:01:18.570 align:middle line:84% So for that particular alloy, the critical cooling rate 00:01:18.570 --> 00:01:20.650 align:middle line:84% you need to actually prevent crystallization 00:01:20.650 --> 00:01:25.755 align:middle line:84% is of the order of 1 MIG degree Celsius per second. 00:01:25.755 --> 00:01:27.130 align:middle line:84% So you still need very, very fast 00:01:27.130 --> 00:01:29.450 align:middle line:84% cooling in order to be able to actually amorphize it. 00:01:29.450 --> 00:01:32.050 align:middle line:84% And you may also recall that this kind of fast cooling rate 00:01:32.050 --> 00:01:34.690 align:middle line:84% essentially also corresponds to a very small thickness, where 00:01:34.690 --> 00:01:37.130 align:middle line:84% you can get efficient thermal extraction from the interior 00:01:37.130 --> 00:01:38.970 align:middle line:84% to prevent essentially crystallization. 00:01:38.970 --> 00:01:42.850 align:middle line:84% So that's why in the early days, these metallic glasses can only 00:01:42.850 --> 00:01:48.250 align:middle line:84% be prepared in a thin film or thin membrane form. 00:01:48.250 --> 00:01:49.930 align:middle line:84% The technique that people actually 00:01:49.930 --> 00:01:54.530 align:middle line:84% use to actually prepare them is mostly 00:01:54.530 --> 00:01:56.530 align:middle line:90% so-called the melt spinning. 00:01:56.530 --> 00:01:58.930 align:middle line:84% I have briefly mentioned about it earlier before, 00:01:58.930 --> 00:02:01.310 align:middle line:84% but the whole idea is that you have a big drum that's 00:02:01.310 --> 00:02:02.275 align:middle line:90% essentially rotating. 00:02:02.275 --> 00:02:03.650 align:middle line:84% You keep it at a low temperature. 00:02:03.650 --> 00:02:05.130 align:middle line:84% You then put the crucible on top. 00:02:05.130 --> 00:02:08.650 align:middle line:84% At the bottom of crucible, then the melt of the metal comes out. 00:02:08.650 --> 00:02:11.130 align:middle line:84% So then when it comes into contact with this cold drum, 00:02:11.130 --> 00:02:12.290 align:middle line:90% it then quickly cools down. 00:02:12.290 --> 00:02:14.010 align:middle line:84% And then due to the centrifugal force, 00:02:14.010 --> 00:02:16.710 align:middle line:84% it essentially comes out as like a continuous ribbon. 00:02:16.710 --> 00:02:21.110 align:middle line:84% So starting in the 1970s, people started looking 00:02:21.110 --> 00:02:24.390 align:middle line:84% into applications for these kinds of amorphous metals. 00:02:24.390 --> 00:02:27.990 align:middle line:84% Their first area where they get commercial adoption 00:02:27.990 --> 00:02:31.370 align:middle line:84% is in the field of magnetic applications, 00:02:31.370 --> 00:02:34.750 align:middle line:84% mostly to use as essentially the core for transformers 00:02:34.750 --> 00:02:35.850 align:middle line:90% or generators. 00:02:35.850 --> 00:02:40.670 align:middle line:84% So the reason they have become attractive 00:02:40.670 --> 00:02:43.870 align:middle line:84% is because in amorphous metal, unlike crystalline metal, 00:02:43.870 --> 00:02:45.510 align:middle line:84% you have no crystalline boundaries. 00:02:45.510 --> 00:02:49.390 align:middle line:84% So when the magnetic domains, they try to move around, 00:02:49.390 --> 00:02:52.190 align:middle line:84% they have much less resistance in amorphous metal 00:02:52.190 --> 00:02:53.910 align:middle line:90% compared to crystalline metal. 00:02:53.910 --> 00:02:55.910 align:middle line:84% So magnetically, what they correspond to 00:02:55.910 --> 00:02:59.200 align:middle line:84% is that the magnetic coercivity for amorphous metal 00:02:59.200 --> 00:03:00.800 align:middle line:90% tends to be very, very low. 00:03:00.800 --> 00:03:03.040 align:middle line:84% So in other words, they tend to be very good 00:03:03.040 --> 00:03:04.620 align:middle line:90% soft magnetic materials. 00:03:04.620 --> 00:03:07.800 align:middle line:84% There's very little residual magnetic polarization 00:03:07.800 --> 00:03:10.688 align:middle line:84% or magnetization once you remove the magnetic field. 00:03:10.688 --> 00:03:12.480 align:middle line:84% And that kind of characteristic is actually 00:03:12.480 --> 00:03:16.520 align:middle line:84% quite useful for things like transformers. 00:03:16.520 --> 00:03:18.200 align:middle line:84% On top of that, the other advantage 00:03:18.200 --> 00:03:20.600 align:middle line:84% is that these amorphous metals tend 00:03:20.600 --> 00:03:22.880 align:middle line:84% to be electrically a bit more resistive compared 00:03:22.880 --> 00:03:25.490 align:middle line:84% to their crystalline counterpart, basically, 00:03:25.490 --> 00:03:27.240 align:middle line:84% because when the electronic carriers, when 00:03:27.240 --> 00:03:30.080 align:middle line:84% they are moving around because of amorphous structure, 00:03:30.080 --> 00:03:32.480 align:middle line:84% you basically get more scattering because of the lack 00:03:32.480 --> 00:03:33.800 align:middle line:90% of long-range order. 00:03:33.800 --> 00:03:36.800 align:middle line:84% So that leads to a reduced mobility and therefore 00:03:36.800 --> 00:03:38.462 align:middle line:90% higher electrical resistance. 00:03:38.462 --> 00:03:39.920 align:middle line:84% Now higher electrical resistance is 00:03:39.920 --> 00:03:43.160 align:middle line:84% beneficial for these kinds of magnetic applications 00:03:43.160 --> 00:03:47.120 align:middle line:84% because electrical current, or eddy current, basically 00:03:47.120 --> 00:03:49.400 align:middle line:84% is a parasitic current that's getting 00:03:49.400 --> 00:03:52.900 align:middle line:84% generated if you have an oscillating magnetic field, 00:03:52.900 --> 00:03:54.460 align:middle line:84% they can actually dissipate energy, 00:03:54.460 --> 00:03:56.910 align:middle line:84% leading to unnecessary power consumption. 00:03:56.910 --> 00:03:59.210 align:middle line:84% So that's why people were interested in looking 00:03:59.210 --> 00:04:02.370 align:middle line:84% at them for soft magnetic materials essentially. 00:04:02.370 --> 00:04:04.930 align:middle line:84% In 1980s, people start to discover that they can actually 00:04:04.930 --> 00:04:08.610 align:middle line:84% make what's called a bulk metallic glasses, BMG, 00:04:08.610 --> 00:04:11.290 align:middle line:84% with a much better glass forming ability. 00:04:11.290 --> 00:04:14.770 align:middle line:84% Now going to the range of maybe like a few hundred 00:04:14.770 --> 00:04:17.084 align:middle line:84% Kelvin per second, critical cooling rate. 00:04:17.084 --> 00:04:18.709 align:middle line:84% For that kind of critical cooling rate, 00:04:18.709 --> 00:04:20.690 align:middle line:84% you can start to make macroscopic size 00:04:20.690 --> 00:04:23.050 align:middle line:84% pieces of this kind of metallic glasses, 00:04:23.050 --> 00:04:26.690 align:middle line:84% with millimeters or even thicker, centimeter thickness. 00:04:26.690 --> 00:04:29.650 align:middle line:84% 1990s, that's when you start to get more and more companies 00:04:29.650 --> 00:04:31.730 align:middle line:90% start to jump into this field. 00:04:31.730 --> 00:04:34.010 align:middle line:84% There's a very famous group in Caltech. 00:04:34.010 --> 00:04:39.370 align:middle line:84% They actually developed this Vitreloy amorphous metal series. 00:04:39.370 --> 00:04:42.410 align:middle line:84% They actually get quite a bit of commercial traction. 00:04:42.410 --> 00:04:46.310 align:middle line:84% And then in they also get a lot-- 00:04:46.310 --> 00:04:49.370 align:middle line:90% I put a quotation mark "cheap." 00:04:49.370 --> 00:04:51.710 align:middle line:84% Cheap, this is a relative term, right? 00:04:51.710 --> 00:04:53.867 align:middle line:84% The Vitreloy is actually still pretty expensive. 00:04:53.867 --> 00:04:56.450 align:middle line:84% The little piece of Vitreloy I showed you in the last lecture, 00:04:56.450 --> 00:04:58.510 align:middle line:90% that one cost me $200. 00:04:58.510 --> 00:05:02.030 align:middle line:84% But still, in terms of cost, this 00:05:02.030 --> 00:05:04.390 align:middle line:84% is much lower compared to a lot of the amorphous metal 00:05:04.390 --> 00:05:06.710 align:middle line:84% in early days because they tend to contain 00:05:06.710 --> 00:05:10.292 align:middle line:90% a noble metal like gold. 00:05:10.292 --> 00:05:12.250 align:middle line:84% So yeah, they are at least relatively low cost. 00:05:12.250 --> 00:05:15.550 align:middle line:84% And that's why we start to see some commercial adoptions there. 00:05:15.550 --> 00:05:17.070 align:middle line:84% Besides magnetic applications, they 00:05:17.070 --> 00:05:20.670 align:middle line:84% are mostly used because of their superior mechanical properties. 00:05:20.670 --> 00:05:25.950 align:middle line:84% So they're used in things like high-end sports gears 00:05:25.950 --> 00:05:30.870 align:middle line:90% like skis, golf clubs. 00:05:30.870 --> 00:05:34.372 align:middle line:84% They are also used in critical components like in sensors 00:05:34.372 --> 00:05:36.830 align:middle line:84% or automotive applications, where you need high temperature 00:05:36.830 --> 00:05:40.910 align:middle line:84% stability, minimal amount of degradation and plastic 00:05:40.910 --> 00:05:42.110 align:middle line:90% deformation. 00:05:42.110 --> 00:05:46.550 align:middle line:84% So that's where they see a commercial options there. 00:05:46.550 --> 00:05:51.150 align:middle line:84% In this next slide, I'm showing you 00:05:51.150 --> 00:05:54.440 align:middle line:84% a table of different metallic glass composition 00:05:54.440 --> 00:05:57.560 align:middle line:84% or metallic glass compositions people have developed. 00:05:57.560 --> 00:06:00.960 align:middle line:84% This table, horizontal axis is basically 00:06:00.960 --> 00:06:04.080 align:middle line:84% the normalized Gaussian tradition temperature 00:06:04.080 --> 00:06:06.000 align:middle line:90% for various compositions here. 00:06:06.000 --> 00:06:08.440 align:middle line:84% Vertical axis, I have two vertical axis here. 00:06:08.440 --> 00:06:10.540 align:middle line:84% Left-hand side is basically critical cooling rate. 00:06:10.540 --> 00:06:12.623 align:middle line:84% We know that the critical cooling rate corresponds 00:06:12.623 --> 00:06:13.700 align:middle line:90% to the maximum thickness. 00:06:13.700 --> 00:06:16.740 align:middle line:84% You can prepare a sample while still staying in amorphous form. 00:06:16.740 --> 00:06:19.880 align:middle line:84% So we can see how this material is actually 00:06:19.880 --> 00:06:22.760 align:middle line:84% evolved from the ones that actually 00:06:22.760 --> 00:06:25.623 align:middle line:84% have a high critical cooling rate, small thickness, 00:06:25.623 --> 00:06:28.040 align:middle line:84% all the way down to essentially on this end, where we have 00:06:28.040 --> 00:06:30.300 align:middle line:84% actual bulk metallic glasses that can be centimeters 00:06:30.300 --> 00:06:30.800 align:middle line:90% thickness. 00:06:30.800 --> 00:06:32.440 align:middle line:84% So what I will do in this lecture 00:06:32.440 --> 00:06:34.700 align:middle line:84% is I will divide it roughly in two parts. 00:06:34.700 --> 00:06:36.800 align:middle line:84% I will start by talking about structural model. 00:06:36.800 --> 00:06:39.580 align:middle line:84% How do we actually engineer the constitutive atoms 00:06:39.580 --> 00:06:41.980 align:middle line:84% so you maximize the glass forming ability. 00:06:41.980 --> 00:06:43.200 align:middle line:84% And then in the second part, I will then based 00:06:43.200 --> 00:06:44.400 align:middle line:84% on structural model let's discuss 00:06:44.400 --> 00:06:46.525 align:middle line:84% a little bit about their mechanical behavior, which 00:06:46.525 --> 00:06:50.840 align:middle line:84% is the main attribute that draws most of the commercial interest. 00:06:50.840 --> 00:06:55.290 align:middle line:84% So in terms of structure of metallic glass, 00:06:55.290 --> 00:06:57.530 align:middle line:84% there are two key things I want to mention here. 00:06:57.530 --> 00:06:59.850 align:middle line:84% One is that the chemical bond in them 00:06:59.850 --> 00:07:01.930 align:middle line:90% is essentially metallic bonds. 00:07:01.930 --> 00:07:03.770 align:middle line:84% Metallic bonds, unlike covalent bonds 00:07:03.770 --> 00:07:06.190 align:middle line:84% that you find in other inorganic glasses, 00:07:06.190 --> 00:07:08.330 align:middle line:90% they are nondirectional. 00:07:08.330 --> 00:07:14.575 align:middle line:84% And also in order to stabilize metallic glass, 00:07:14.575 --> 00:07:16.450 align:middle line:84% the criterion is also a little bit different. 00:07:16.450 --> 00:07:20.610 align:middle line:84% In organic network glasses we talk about essentially topology 00:07:20.610 --> 00:07:23.770 align:middle line:84% or the connectivity of the network being the key criteria 00:07:23.770 --> 00:07:25.110 align:middle line:90% that influence stability. 00:07:25.110 --> 00:07:27.233 align:middle line:84% In metallic glasses, on the other hand, 00:07:27.233 --> 00:07:28.650 align:middle line:84% what we are trying to do is we are 00:07:28.650 --> 00:07:30.810 align:middle line:84% trying to lower the Gibbs-free energy 00:07:30.810 --> 00:07:34.130 align:middle line:90% of the amorphous structure. 00:07:34.130 --> 00:07:35.980 align:middle line:84% To lower the Gibbs-free energy, you 00:07:35.980 --> 00:07:37.730 align:middle line:84% need to essentially lower the total energy 00:07:37.730 --> 00:07:40.830 align:middle line:90% of all the metallic bonds. 00:07:40.830 --> 00:07:44.530 align:middle line:84% And that's directly correlated with packing density. 00:07:44.530 --> 00:07:47.530 align:middle line:84% If you can pack essentially atoms more close to each other, 00:07:47.530 --> 00:07:50.130 align:middle line:84% you get stronger interaction between the outer shell 00:07:50.130 --> 00:07:52.420 align:middle line:90% electrons and the atomic nuclei. 00:07:52.420 --> 00:07:56.740 align:middle line:84% And as a result, you reduce the overall energy of the system. 00:07:56.740 --> 00:07:58.580 align:middle line:84% So the key point I want to make here 00:07:58.580 --> 00:08:01.860 align:middle line:84% is that in order to get a stable metallic glass, 00:08:01.860 --> 00:08:04.180 align:middle line:84% you need to try to achieve structures that have 00:08:04.180 --> 00:08:05.800 align:middle line:90% as high density as possible. 00:08:05.800 --> 00:08:09.612 align:middle line:90% 00:08:09.612 --> 00:08:14.780 align:middle line:84% So that's why Inoue, who is actually 00:08:14.780 --> 00:08:17.980 align:middle line:84% a pioneer in the area of bulk metallic glasses, 00:08:17.980 --> 00:08:20.760 align:middle line:84% when he actually summarized the three empirical rules here, 00:08:20.760 --> 00:08:24.300 align:middle line:84% you can clearly see the role that 00:08:24.300 --> 00:08:26.580 align:middle line:84% this close-packing structure actually kind of plays 00:08:26.580 --> 00:08:28.580 align:middle line:84% in dictating the glass forming ability 00:08:28.580 --> 00:08:30.660 align:middle line:90% in bulk metallic materials. 00:08:30.660 --> 00:08:33.723 align:middle line:84% So I've already talked about this before. 00:08:33.723 --> 00:08:34.640 align:middle line:90% There are three rules. 00:08:34.640 --> 00:08:37.659 align:middle line:84% First one is that you need to have 00:08:37.659 --> 00:08:40.148 align:middle line:84% at least three constituent atoms or even more. 00:08:40.148 --> 00:08:42.440 align:middle line:84% And they also need to have significant size difference. 00:08:42.440 --> 00:08:45.900 align:middle line:84% Usually the size difference has to be greater than 15%. 00:08:45.900 --> 00:08:48.900 align:middle line:84% So that you can actually pack them together 00:08:48.900 --> 00:08:52.572 align:middle line:84% in a close packed manner without introducing structural order. 00:08:52.572 --> 00:08:53.780 align:middle line:90% The argument is quite simple. 00:08:53.780 --> 00:08:56.578 align:middle line:84% If you have all the atoms within the same size, 00:08:56.578 --> 00:08:58.620 align:middle line:84% you can easily achieve a close packing structure, 00:08:58.620 --> 00:09:00.760 align:middle line:90% go to FCC or HCP. 00:09:00.760 --> 00:09:03.620 align:middle line:84% It's very easy to look at form local structures like that. 00:09:03.620 --> 00:09:07.120 align:middle line:84% But then you are not able to realize amorphous stacking. 00:09:07.120 --> 00:09:12.200 align:middle line:84% The first two points here, both actually 00:09:12.200 --> 00:09:17.302 align:middle line:84% has to do with the topology of metallic glass. 00:09:17.302 --> 00:09:19.760 align:middle line:84% The first two points that we have not talked about anything 00:09:19.760 --> 00:09:21.480 align:middle line:84% about the specific chemical properties 00:09:21.480 --> 00:09:22.983 align:middle line:90% of the constituent atoms. 00:09:22.983 --> 00:09:24.400 align:middle line:84% The only thing that really matters 00:09:24.400 --> 00:09:30.520 align:middle line:84% there is essentially size, which is a geometric parameter. 00:09:30.520 --> 00:09:32.850 align:middle line:84% The last point here, negative enthalpy of mixing, this 00:09:32.850 --> 00:09:34.600 align:middle line:84% is just to prevent essentially segregation 00:09:34.600 --> 00:09:35.683 align:middle line:90% of different compositions. 00:09:35.683 --> 00:09:37.420 align:middle line:84% They have to be thermodynamically stable. 00:09:37.420 --> 00:09:40.003 align:middle line:84% They need to be happy when they are actually staying together. 00:09:40.003 --> 00:09:42.755 align:middle line:90% 00:09:42.755 --> 00:09:44.663 align:middle line:84% So these are the empirical rules. 00:09:44.663 --> 00:09:46.080 align:middle line:84% What I'll do next, I will give you 00:09:46.080 --> 00:09:49.650 align:middle line:84% a more quantitative description about the structural model 00:09:49.650 --> 00:09:51.570 align:middle line:90% for bulk metallic glasses. 00:09:51.570 --> 00:09:53.870 align:middle line:84% In this regard, if you think about the network 00:09:53.870 --> 00:09:56.810 align:middle line:84% in inorganic glasses, we talk about essentially Zachariasen's 00:09:56.810 --> 00:09:58.390 align:middle line:90% rules, the empirical rules. 00:09:58.390 --> 00:10:01.010 align:middle line:84% And then we talk about the topological constraint theory. 00:10:01.010 --> 00:10:03.950 align:middle line:84% So in the world of metallic glasses, 00:10:03.950 --> 00:10:05.930 align:middle line:84% this Inoue's empirical rule plays 00:10:05.930 --> 00:10:09.850 align:middle line:84% the role of Zachariasen's rules And then what I'll talk to you 00:10:09.850 --> 00:10:12.530 align:middle line:84% about is essentially this topological model 00:10:12.530 --> 00:10:16.410 align:middle line:84% that allows us to achieve maximum packing density using 00:10:16.410 --> 00:10:18.410 align:middle line:84% different kinds of metallic atoms. 00:10:18.410 --> 00:10:20.770 align:middle line:84% Now, before I go to that, I just also want 00:10:20.770 --> 00:10:23.010 align:middle line:84% to mention that this theory, this is not just 00:10:23.010 --> 00:10:26.510 align:middle line:90% a speculation by scientists. 00:10:26.510 --> 00:10:29.010 align:middle line:84% This is something now people were able to essentially verify 00:10:29.010 --> 00:10:30.010 align:middle line:90% experimentally. 00:10:30.010 --> 00:10:31.350 align:middle line:90% So this is actually one example. 00:10:31.350 --> 00:10:33.058 align:middle line:84% This is a paper published a few years ago 00:10:33.058 --> 00:10:36.090 align:middle line:84% where people were able to do essentially an electron 00:10:36.090 --> 00:10:37.395 align:middle line:90% tomography. 00:10:37.395 --> 00:10:39.770 align:middle line:84% So tomography essentially means that you're looking at 3D 00:10:39.770 --> 00:10:42.730 align:middle line:84% structures rather than these 2D sections or 2D images 00:10:42.730 --> 00:10:44.710 align:middle line:90% of materials. 00:10:44.710 --> 00:10:48.020 align:middle line:84% They were able to actually look at an amorphous metallic 00:10:48.020 --> 00:10:50.260 align:middle line:84% nanoparticle that actually determines 00:10:50.260 --> 00:10:52.980 align:middle line:84% the coordinates of all the constituent atoms 00:10:52.980 --> 00:10:54.700 align:middle line:84% within that nanoparticle, which then 00:10:54.700 --> 00:10:57.460 align:middle line:84% allows them to verify this kind of topological structural 00:10:57.460 --> 00:10:58.040 align:middle line:90% models. 00:10:58.040 --> 00:11:00.080 align:middle line:84% So if you actually go and read the Nature paper, 00:11:00.080 --> 00:11:01.872 align:middle line:84% what they spend a lot of time talking about 00:11:01.872 --> 00:11:06.060 align:middle line:84% is how they actually verified the topological local structures 00:11:06.060 --> 00:11:08.660 align:middle line:84% that people have predicted, and that eventually 00:11:08.660 --> 00:11:11.380 align:middle line:84% shows up in the experimental characterization. 00:11:11.380 --> 00:11:13.940 align:middle line:84% All right, so now let's start by talking 00:11:13.940 --> 00:11:15.500 align:middle line:90% about topological theory. 00:11:15.500 --> 00:11:17.980 align:middle line:84% So the whole assumption is that we 00:11:17.980 --> 00:11:22.180 align:middle line:84% want to approximate all the constituent atoms essentially 00:11:22.180 --> 00:11:24.860 align:middle line:90% as hard spheres. 00:11:24.860 --> 00:11:30.300 align:middle line:84% So then the problem becomes a pure geometric construction. 00:11:30.300 --> 00:11:32.780 align:middle line:84% We want to find some hard spheres 00:11:32.780 --> 00:11:35.740 align:middle line:84% with different sizes and different fractions 00:11:35.740 --> 00:11:37.540 align:middle line:84% or different compositions, basically. 00:11:37.540 --> 00:11:41.020 align:middle line:84% We want to put them together so we can achieve maximum packing 00:11:41.020 --> 00:11:42.260 align:middle line:90% density. 00:11:42.260 --> 00:11:46.300 align:middle line:84% The hypothesis is that the glass composition that's most stable 00:11:46.300 --> 00:11:49.600 align:middle line:84% would also correspond to the compositions that gives us 00:11:49.600 --> 00:11:51.340 align:middle line:90% the highest packing density. 00:11:51.340 --> 00:11:55.040 align:middle line:90% 00:11:55.040 --> 00:11:58.260 align:middle line:84% So let's start by looking at the most simple example here. 00:11:58.260 --> 00:11:59.780 align:middle line:84% Instead of looking at 3D packing, 00:11:59.780 --> 00:12:01.920 align:middle line:90% let's think about 2D packing. 00:12:01.920 --> 00:12:06.360 align:middle line:84% So a hard sphere in 2D basically means essentially a hard circle. 00:12:06.360 --> 00:12:09.920 align:middle line:84% And to make things even simpler, let's consider a binary 2D 00:12:09.920 --> 00:12:10.420 align:middle line:90% packing. 00:12:10.420 --> 00:12:11.972 align:middle line:84% We have only two kinds of circles 00:12:11.972 --> 00:12:13.180 align:middle line:90% that we want to put together. 00:12:13.180 --> 00:12:15.480 align:middle line:84% So what I'm showing you here, this 00:12:15.480 --> 00:12:19.960 align:middle line:84% is a local cluster where we have two kind of circles here. 00:12:19.960 --> 00:12:22.040 align:middle line:84% And the horizontal axis on this plot 00:12:22.040 --> 00:12:24.857 align:middle line:84% is basically a radius ratio of these two kind of circles. 00:12:24.857 --> 00:12:27.440 align:middle line:84% Now if you only have two kind of circles, what you can imagine 00:12:27.440 --> 00:12:30.040 align:middle line:84% there is that there are some specific radius 00:12:30.040 --> 00:12:32.200 align:middle line:90% ratios of the two spheres. 00:12:32.200 --> 00:12:34.380 align:middle line:84% Once you meet those critical ratios, 00:12:34.380 --> 00:12:38.440 align:middle line:84% you can essentially put one kind of sphere right around the other 00:12:38.440 --> 00:12:40.380 align:middle line:84% without leaving any gaps in between. 00:12:40.380 --> 00:12:42.960 align:middle line:90% 00:12:42.960 --> 00:12:45.680 align:middle line:84% And what we argue is that that kind of configuration, 00:12:45.680 --> 00:12:47.730 align:middle line:84% or that kind of critical radius ratio, 00:12:47.730 --> 00:12:50.730 align:middle line:84% is what gives you the maximum packing density. 00:12:50.730 --> 00:12:53.463 align:middle line:84% So that's what we are plotting on this plot here. 00:12:53.463 --> 00:12:55.630 align:middle line:84% The vertical axis, there are two vertical axes here. 00:12:55.630 --> 00:12:57.570 align:middle line:84% Let's look at the one on the right-hand side. 00:12:57.570 --> 00:13:01.250 align:middle line:90% 00:13:01.250 --> 00:13:04.170 align:middle line:84% So what's on the right axis is what 00:13:04.170 --> 00:13:06.410 align:middle line:90% we call the packing efficiency. 00:13:06.410 --> 00:13:11.330 align:middle line:84% I mean you can consider it as the packing density, the ratio 00:13:11.330 --> 00:13:13.770 align:middle line:84% of the actual packing density over the theoretical maximum 00:13:13.770 --> 00:13:16.370 align:middle line:90% packing density you can get. 00:13:16.370 --> 00:13:19.570 align:middle line:84% And for the right axis, the plot actually 00:13:19.570 --> 00:13:21.818 align:middle line:90% goes by these kind of dots. 00:13:21.818 --> 00:13:23.610 align:middle line:84% And what you're seeing here is that you see 00:13:23.610 --> 00:13:26.210 align:middle line:90% this kind of a zigzag pattern. 00:13:26.210 --> 00:13:27.810 align:middle line:84% What happens is that when you actually 00:13:27.810 --> 00:13:30.210 align:middle line:84% hit one of these critical ratios here, 00:13:30.210 --> 00:13:32.690 align:middle line:84% you can fill one kind of sphere around the other 00:13:32.690 --> 00:13:33.990 align:middle line:90% without leaving any gaps. 00:13:33.990 --> 00:13:36.950 align:middle line:84% So this corresponds to a peak in terms of packing efficiency. 00:13:36.950 --> 00:13:38.730 align:middle line:84% You get unity packing efficiency. 00:13:38.730 --> 00:13:40.650 align:middle line:84% And as you deviate from that point, 00:13:40.650 --> 00:13:43.450 align:middle line:84% you start to get a decrease of packing efficiency 00:13:43.450 --> 00:13:46.180 align:middle line:84% until you go to the next point here where the coordination 00:13:46.180 --> 00:13:47.627 align:middle line:84% number essentially increases by 1, 00:13:47.627 --> 00:13:48.960 align:middle line:90% you can fit in one extra sphere. 00:13:48.960 --> 00:13:51.300 align:middle line:84% So again, the packing density peaks. 00:13:51.300 --> 00:13:54.560 align:middle line:84% On the left-hand side this is basically coordination number. 00:13:54.560 --> 00:13:57.260 align:middle line:84% Coordination number actually goes essentially monotonically 00:13:57.260 --> 00:13:58.780 align:middle line:90% in a large 2D array there. 00:13:58.780 --> 00:14:02.260 align:middle line:84% It's talking about average coordination number. 00:14:02.260 --> 00:14:04.020 align:middle line:84% So take-away message, dense packing 00:14:04.020 --> 00:14:07.900 align:middle line:84% is only achieved at certain critical radius ratios. 00:14:07.900 --> 00:14:11.080 align:middle line:84% So we can translate this conclusion into 3D. 00:14:11.080 --> 00:14:12.840 align:middle line:84% It's actually very, very similar. 00:14:12.840 --> 00:14:14.440 align:middle line:90% So the plot is exactly the same. 00:14:14.440 --> 00:14:17.940 align:middle line:84% We still have only two kinds of hard spheres now in 3D, 00:14:17.940 --> 00:14:20.800 align:middle line:84% horizontal axis radius ratio, this is packing efficiency. 00:14:20.800 --> 00:14:23.820 align:middle line:84% You see a very similar kind of zigzag patterns. 00:14:23.820 --> 00:14:25.660 align:middle line:84% Left-hand side is coordination number. 00:14:25.660 --> 00:14:28.700 align:middle line:84% Now you do notice that for the average coordination number, 00:14:28.700 --> 00:14:31.135 align:middle line:84% there's a little discontinuity right here. 00:14:31.135 --> 00:14:33.260 align:middle line:84% That's actually because we have two different kinds 00:14:33.260 --> 00:14:34.480 align:middle line:90% of configurations here. 00:14:34.480 --> 00:14:37.070 align:middle line:84% On the left-hand side, one of the spheres 00:14:37.070 --> 00:14:38.820 align:middle line:84% is actually fitting into interstitial size 00:14:38.820 --> 00:14:40.380 align:middle line:90% between the other spheres. 00:14:40.380 --> 00:14:41.980 align:middle line:84% And on the right side, is basically 00:14:41.980 --> 00:14:44.517 align:middle line:90% going to a substitutional site. 00:14:44.517 --> 00:14:46.100 align:middle line:84% So because of change of configuration, 00:14:46.100 --> 00:14:48.400 align:middle line:84% that's why that little discontinuity there. 00:14:48.400 --> 00:14:51.260 align:middle line:84% Anyway, regardless of that detail, 00:14:51.260 --> 00:14:53.640 align:middle line:84% we see the very similar features here 00:14:53.640 --> 00:14:56.520 align:middle line:84% that if you want to achieve maximum packing density, 00:14:56.520 --> 00:15:00.040 align:middle line:84% the two spheres also need to fulfill specific critical radius 00:15:00.040 --> 00:15:01.720 align:middle line:90% ratios. 00:15:01.720 --> 00:15:04.840 align:middle line:84% So now what we hypothesize, if we translate it 00:15:04.840 --> 00:15:10.960 align:middle line:84% into actual metallic systems, we expect to find pairs of atoms. 00:15:10.960 --> 00:15:16.120 align:middle line:84% If those atom pairs fulfill their critical radius ratio, 00:15:16.120 --> 00:15:19.060 align:middle line:84% you'll be able to maximize the atomic packing density. 00:15:19.060 --> 00:15:23.080 align:middle line:84% and we then postulate that those atoms will then 00:15:23.080 --> 00:15:28.600 align:middle line:84% give rise to the most stable binary metallic glasses. 00:15:28.600 --> 00:15:32.860 align:middle line:84% So this is what they actually did in this paper here. 00:15:32.860 --> 00:15:34.740 align:middle line:90% So let me explain what they did. 00:15:34.740 --> 00:15:36.920 align:middle line:84% So horizontal axis, this is again 00:15:36.920 --> 00:15:42.890 align:middle line:84% the radius ratio of atoms in binary metallic glasses. 00:15:42.890 --> 00:15:46.530 align:middle line:84% The vertical lines here, each of these vertical lines 00:15:46.530 --> 00:15:49.930 align:middle line:84% essentially correspond to one of these critical radius ratios 00:15:49.930 --> 00:15:53.130 align:middle line:84% that give you the highest packing efficiency. 00:15:53.130 --> 00:15:56.850 align:middle line:84% And the vertical axis here, this is basically a histogram. 00:15:56.850 --> 00:15:59.770 align:middle line:84% So what the authors did is they essentially survey 00:15:59.770 --> 00:16:02.730 align:middle line:84% all the literature published up to that time on binary 00:16:02.730 --> 00:16:04.810 align:middle line:84% metallic glasses, and then they essentially 00:16:04.810 --> 00:16:11.770 align:middle line:84% count the frequency of one particular atomic radius ratio 00:16:11.770 --> 00:16:13.450 align:middle line:90% that appears in literature. 00:16:13.450 --> 00:16:16.570 align:middle line:84% So if you see a peak, for example here, 00:16:16.570 --> 00:16:18.410 align:middle line:84% essentially it means that there's actually 00:16:18.410 --> 00:16:22.170 align:middle line:84% more literature reporting metallic glasses that 00:16:22.170 --> 00:16:25.370 align:middle line:84% are having atomic ratio right at this point there. 00:16:25.370 --> 00:16:28.770 align:middle line:84% Now if you look at this line here, 00:16:28.770 --> 00:16:30.250 align:middle line:90% you clearly see the correlation. 00:16:30.250 --> 00:16:32.930 align:middle line:84% Whenever there's actually one vertical line that corresponds 00:16:32.930 --> 00:16:36.210 align:middle line:84% to one critical radius ratio, that tends to be a peak, 00:16:36.210 --> 00:16:38.210 align:middle line:84% meaning that there are more binary metallic 00:16:38.210 --> 00:16:43.540 align:middle line:84% glasses that assumes the particular atomic radius ratio. 00:16:43.540 --> 00:16:48.100 align:middle line:84% OK, now one exception, you look at this line here. 00:16:48.100 --> 00:16:51.040 align:middle line:84% This line R equals 12 around R equals 12, 00:16:51.040 --> 00:16:52.780 align:middle line:84% you see that this actually corresponds 00:16:52.780 --> 00:16:55.420 align:middle line:90% like a local minimum. 00:16:55.420 --> 00:16:57.340 align:middle line:90% Why is that? 00:16:57.340 --> 00:17:00.980 align:middle line:84% AUDIENCE: Because it's the atoms are the same size so they just 00:17:00.980 --> 00:17:01.940 align:middle line:90% form a crystal. 00:17:01.940 --> 00:17:05.260 align:middle line:84% JUEJUN HU: Yeah, so essentially when I say the R12 here 00:17:05.260 --> 00:17:07.619 align:middle line:84% this is basically the coordination 00:17:07.619 --> 00:17:09.020 align:middle line:90% number nearest neighbor. 00:17:09.020 --> 00:17:11.720 align:middle line:84% So R12 corresponds to a what kind of structure? 00:17:11.720 --> 00:17:12.260 align:middle line:90% FCC? 00:17:12.260 --> 00:17:13.740 align:middle line:90% Exactly FCC or HCP. 00:17:13.740 --> 00:17:15.282 align:middle line:90% Both FCC and HCP have 12. 00:17:15.282 --> 00:17:16.740 align:middle line:84% So essentially what it says is like 00:17:16.740 --> 00:17:18.365 align:middle line:84% even though you can form close packing, 00:17:18.365 --> 00:17:21.980 align:middle line:84% but it will crystallize if they are exactly the same size. 00:17:21.980 --> 00:17:24.897 align:middle line:84% And that's why when the atomic radius ratio is close to 1, 00:17:24.897 --> 00:17:26.980 align:middle line:84% that's why despite you have a high packing density 00:17:26.980 --> 00:17:29.660 align:middle line:84% it's a poor choice for bulk metallic glasses. 00:17:29.660 --> 00:17:33.900 align:middle line:90% 00:17:33.900 --> 00:17:37.933 align:middle line:84% So that's for binary metallic glasses. 00:17:37.933 --> 00:17:40.100 align:middle line:84% Now what we want to do is we want to actually extend 00:17:40.100 --> 00:17:45.040 align:middle line:84% the theory into a ternary, quaternary, multi-component bulk 00:17:45.040 --> 00:17:47.200 align:middle line:90% metallic glasses. 00:17:47.200 --> 00:17:48.840 align:middle line:84% Now for those, we will be looking 00:17:48.840 --> 00:17:51.320 align:middle line:84% at packing of hard spheres, but more specifically, we 00:17:51.320 --> 00:17:53.070 align:middle line:84% will be essentially looking at essentially 00:17:53.070 --> 00:17:56.200 align:middle line:90% this tiered structure. 00:17:56.200 --> 00:17:58.200 align:middle line:84% We're looking at two structure tiers, 00:17:58.200 --> 00:18:03.145 align:middle line:84% first, by starting looking at clusters A cluster is defined, 00:18:03.145 --> 00:18:04.520 align:middle line:84% so what I'm showing here, this is 00:18:04.520 --> 00:18:09.253 align:middle line:84% a cartoon of the multi-component bulk metallic glass. 00:18:09.253 --> 00:18:10.920 align:middle line:84% Different spheres essentially correspond 00:18:10.920 --> 00:18:12.263 align:middle line:90% with different kinds of atoms. 00:18:12.263 --> 00:18:14.180 align:middle line:84% We are looking at essentially clusters, right? 00:18:14.180 --> 00:18:15.597 align:middle line:84% So a cluster is I will defined, is 00:18:15.597 --> 00:18:18.760 align:middle line:84% as you have a center atom in this case labeled as alpha. 00:18:18.760 --> 00:18:21.040 align:middle line:84% You then have some surrounding atoms. 00:18:21.040 --> 00:18:23.760 align:middle line:84% That's basically like the solute. 00:18:23.760 --> 00:18:27.120 align:middle line:84% So each of these essentially is one cluster. 00:18:27.120 --> 00:18:29.560 align:middle line:84% These clusters then stack together 00:18:29.560 --> 00:18:33.060 align:middle line:84% to form the three-dimensional structure 00:18:33.060 --> 00:18:34.880 align:middle line:84% So there are two structures here. 00:18:34.880 --> 00:18:36.880 align:middle line:84% Now in order to maximize the packing density, 00:18:36.880 --> 00:18:38.440 align:middle line:90% we need to do two things. 00:18:38.440 --> 00:18:41.130 align:middle line:84% First thing we need to maximize the packing density 00:18:41.130 --> 00:18:43.410 align:middle line:90% within a cluster. 00:18:43.410 --> 00:18:47.370 align:middle line:84% And this is a problem we already solved. 00:18:47.370 --> 00:18:50.190 align:middle line:84% We know that if the two atoms forming the cluster, 00:18:50.190 --> 00:18:53.570 align:middle line:84% they fulfill a certain radius ratio, then one kind of atom 00:18:53.570 --> 00:18:57.980 align:middle line:84% can surround the other without leaving any gaps. 00:18:57.980 --> 00:19:02.010 align:middle line:84% So this gives rise now to essentially a specific radius 00:19:02.010 --> 00:19:05.410 align:middle line:84% ratio between the two atoms, and also a specific competition 00:19:05.410 --> 00:19:06.110 align:middle line:90% ratio. 00:19:06.110 --> 00:19:09.570 align:middle line:84% Because once the specific radius ratio 00:19:09.570 --> 00:19:11.790 align:middle line:84% it also gives you the coordination number. 00:19:11.790 --> 00:19:13.290 align:middle line:84% If you know the coordination number, 00:19:13.290 --> 00:19:15.623 align:middle line:84% it actually corresponds to a specific composition ratio. 00:19:15.623 --> 00:19:17.570 align:middle line:84% So they can essentially form these clusters 00:19:17.570 --> 00:19:21.693 align:middle line:84% without leaving any atoms behind. 00:19:21.693 --> 00:19:23.610 align:middle line:84% So that's how you maximize the packing density 00:19:23.610 --> 00:19:24.850 align:middle line:90% within a cluster. 00:19:24.850 --> 00:19:27.850 align:middle line:84% Now to maximize packing density between the clusters, 00:19:27.850 --> 00:19:32.410 align:middle line:84% the strategy what nature will actually take 00:19:32.410 --> 00:19:34.210 align:middle line:84% is you can actually fill in smaller atoms 00:19:34.210 --> 00:19:38.760 align:middle line:84% in between the interstitials between the clusters 00:19:38.760 --> 00:19:40.920 align:middle line:84% So you start by essentially packing the clusters. 00:19:40.920 --> 00:19:43.940 align:middle line:84% And then in the interstitial side in between the clusters, 00:19:43.940 --> 00:19:46.880 align:middle line:84% you're squeezing atoms with smaller sizes. 00:19:46.880 --> 00:19:49.900 align:middle line:90% 00:19:49.900 --> 00:19:53.660 align:middle line:84% Now this strategy also specifies an optimal size 00:19:53.660 --> 00:19:56.860 align:middle line:84% for those interstitial atoms, right? 00:19:56.860 --> 00:19:59.140 align:middle line:84% So from crystallography classes you 00:19:59.140 --> 00:20:01.802 align:middle line:84% have taken, structured classes 3010, 00:20:01.802 --> 00:20:03.260 align:middle line:84% you know that all the interstitials 00:20:03.260 --> 00:20:04.480 align:middle line:90% have a specific size, right? 00:20:04.480 --> 00:20:06.438 align:middle line:84% There's a maximum radius where you can actually 00:20:06.438 --> 00:20:10.020 align:middle line:84% squeeze an atom into this particular interstitial, 00:20:10.020 --> 00:20:12.800 align:middle line:84% whether it's octahedral or tetrahedral. 00:20:12.800 --> 00:20:18.280 align:middle line:84% So if you have an atom that meets that critical size, 00:20:18.280 --> 00:20:21.400 align:middle line:84% it can be just squeezed into that interstitial. 00:20:21.400 --> 00:20:24.460 align:middle line:84% It will also maximize the packing density. 00:20:24.460 --> 00:20:27.597 align:middle line:84% So then what this model essentially assumes 00:20:27.597 --> 00:20:29.180 align:middle line:84% is it basically assumes different kind 00:20:29.180 --> 00:20:32.060 align:middle line:84% of topological functions or topological roles 00:20:32.060 --> 00:20:33.900 align:middle line:84% to different kind of constituent atoms. 00:20:33.900 --> 00:20:36.400 align:middle line:84% They label it in different kind of letters. 00:20:36.400 --> 00:20:40.670 align:middle line:84% They have alpha, which is the center atom in the cluster. 00:20:40.670 --> 00:20:45.070 align:middle line:84% omega, as I said is maybe the solvent. 00:20:45.070 --> 00:20:48.910 align:middle line:84% It surrounds the center atoms to form the atomic clusters. 00:20:48.910 --> 00:20:51.510 align:middle line:84% And then beta is the interstitial atom 00:20:51.510 --> 00:20:54.903 align:middle line:84% that goes in between clusters to maximize packing density. 00:20:54.903 --> 00:20:56.570 align:middle line:84% If you look at the original paper there, 00:20:56.570 --> 00:20:59.153 align:middle line:84% they actually also say there's some kind of atom called gamma. 00:20:59.153 --> 00:21:01.150 align:middle line:84% But gamma is basically equivalent as beta. 00:21:01.150 --> 00:21:03.030 align:middle line:84% Essentially, beta goes into octahedral 00:21:03.030 --> 00:21:04.550 align:middle line:90% like interstitial sites. 00:21:04.550 --> 00:21:07.610 align:middle line:84% Gamma goes into essentially tetrahedral interstitial sites, 00:21:07.610 --> 00:21:10.030 align:middle line:84% and tetrahedral interstitial is smaller [INAUDIBLE] 00:21:10.030 --> 00:21:11.090 align:middle line:90% interstitial site. 00:21:11.090 --> 00:21:13.010 align:middle line:84% So that's why there are two labels, 00:21:13.010 --> 00:21:15.630 align:middle line:84% but it's basically the same idea. 00:21:15.630 --> 00:21:19.230 align:middle line:84% So what this theory predicts now is that it can predict, 00:21:19.230 --> 00:21:22.950 align:middle line:84% give you essentially the atomic radius ratio of all [INAUDIBLE] 00:21:22.950 --> 00:21:23.490 align:middle line:90% atoms. 00:21:23.490 --> 00:21:26.330 align:middle line:90% 00:21:26.330 --> 00:21:31.510 align:middle line:84% It also tells you what is the optimum composition. 00:21:31.510 --> 00:21:34.790 align:middle line:84% For example, if you look at cluster for optimal packing 00:21:34.790 --> 00:21:37.450 align:middle line:84% density for a given atomic radius ratio, 00:21:37.450 --> 00:21:41.290 align:middle line:84% the number of omega atoms you can fit around alpha is fixed. 00:21:41.290 --> 00:21:43.890 align:middle line:84% So it means that there's actually optimum composition. 00:21:43.890 --> 00:21:46.045 align:middle line:84% Same thing, once you determine the cluster, 00:21:46.045 --> 00:21:48.170 align:middle line:84% the number of interstitial sites around the cluster 00:21:48.170 --> 00:21:50.050 align:middle line:90% is also fixed. 00:21:50.050 --> 00:21:52.690 align:middle line:84% You want to have a sufficient number of beta atoms 00:21:52.690 --> 00:21:54.270 align:middle line:84% or the right number of beta atoms. 00:21:54.270 --> 00:21:57.910 align:middle line:84% So you fill in all those interstitial sites, but no more. 00:21:57.910 --> 00:22:01.730 align:middle line:90% 00:22:01.730 --> 00:22:04.770 align:middle line:84% So this geometric theory essentially 00:22:04.770 --> 00:22:08.370 align:middle line:84% allows you to predict the optimal size and also 00:22:08.370 --> 00:22:12.370 align:middle line:84% the optimal composition for achieving maximum packing 00:22:12.370 --> 00:22:13.770 align:middle line:90% density. 00:22:13.770 --> 00:22:19.610 align:middle line:84% So then what we postulate is that these compositions 00:22:19.610 --> 00:22:21.490 align:middle line:84% and those kind of atomic size ratios 00:22:21.490 --> 00:22:26.288 align:middle line:84% correspond to the most stable bulk metallic glasses. 00:22:26.288 --> 00:22:27.330 align:middle line:90% So now what you see here? 00:22:27.330 --> 00:22:28.810 align:middle line:84% This is a purely topological theory. 00:22:28.810 --> 00:22:30.977 align:middle line:84% We have not talked about any kind of chemical nature 00:22:30.977 --> 00:22:31.870 align:middle line:90% of the atoms. 00:22:31.870 --> 00:22:36.620 align:middle line:84% The only parameter that matters, just the atomic size. 00:22:36.620 --> 00:22:39.302 align:middle line:84% So then if you read the paper, they actually then there 00:22:39.302 --> 00:22:41.760 align:middle line:84% are many graphs like what I'm showing you on the plot here. 00:22:41.760 --> 00:22:44.300 align:middle line:84% It's actually examining many, many bulk metallic composition 00:22:44.300 --> 00:22:46.220 align:middle line:84% groups and compare the predicted composition 00:22:46.220 --> 00:22:47.760 align:middle line:84% with what you get experimentally. 00:22:47.760 --> 00:22:51.500 align:middle line:84% So the plot essentially, for example, for this one, 00:22:51.500 --> 00:22:54.780 align:middle line:84% they are looking into a five-component bulk metallic 00:22:54.780 --> 00:22:58.000 align:middle line:84% glass-- zirconium, titanium, copper-nickel, beryllium. 00:22:58.000 --> 00:23:02.702 align:middle line:84% Now you notice that they group copper-nickel together. 00:23:02.702 --> 00:23:04.660 align:middle line:84% Because what happens is that copper and nickel, 00:23:04.660 --> 00:23:06.820 align:middle line:84% they have very similar atomic radius. 00:23:06.820 --> 00:23:08.740 align:middle line:84% So topologically, they essentially 00:23:08.740 --> 00:23:11.140 align:middle line:90% serve the same function. 00:23:11.140 --> 00:23:15.140 align:middle line:84% That's why they group them together 00:23:15.140 --> 00:23:17.140 align:middle line:84% And then these four essentially correspond 00:23:17.140 --> 00:23:22.100 align:middle line:84% to essentially the omega, alpha, and then 00:23:22.100 --> 00:23:24.460 align:middle line:84% this is the beta and the gamma, the four 00:23:24.460 --> 00:23:26.340 align:middle line:84% kind of topological roles we talk about 00:23:26.340 --> 00:23:28.060 align:middle line:90% in the previous slide. 00:23:28.060 --> 00:23:32.700 align:middle line:84% And the closest are the predictions 00:23:32.700 --> 00:23:34.842 align:middle line:84% based on this kind of a topological theory that 00:23:34.842 --> 00:23:36.550 align:middle line:84% will achieve the maximum packing density. 00:23:36.550 --> 00:23:41.170 align:middle line:84% The square and the diamond symbols, 00:23:41.170 --> 00:23:43.393 align:middle line:84% these are actually the experimentally prepared bulk 00:23:43.393 --> 00:23:45.810 align:middle line:84% metallic glasses that people have actually commercialized, 00:23:45.810 --> 00:23:47.650 align:middle line:84% in this case Vitreloy 1 and Vitreloy 4. 00:23:47.650 --> 00:23:50.550 align:middle line:84% So those actually correspond to what people have empirically 00:23:50.550 --> 00:23:53.910 align:middle line:84% derived, computations that give you the best stability. 00:23:53.910 --> 00:23:56.710 align:middle line:84% Now you see this kind of striking agreement 00:23:56.710 --> 00:23:59.130 align:middle line:84% here, the prediction and the actual competition. 00:23:59.130 --> 00:24:00.510 align:middle line:90% They are really quite close. 00:24:00.510 --> 00:24:02.730 align:middle line:90% Similarly, this is another one. 00:24:02.730 --> 00:24:04.870 align:middle line:84% This is calcium, magnesium, zinc, copper. 00:24:04.870 --> 00:24:08.333 align:middle line:84% Again, you see a remarkable similarity 00:24:08.333 --> 00:24:10.750 align:middle line:84% or remarkable agreement between the theoretical prediction 00:24:10.750 --> 00:24:17.310 align:middle line:84% and the actual competition your derive experimentally. 00:24:17.310 --> 00:24:21.265 align:middle line:84% So I always find this paper being quite remarkable there 00:24:21.265 --> 00:24:23.390 align:middle line:84% because it essentially starts from this very simple 00:24:23.390 --> 00:24:24.670 align:middle line:90% assumption. 00:24:24.670 --> 00:24:27.590 align:middle line:84% You reduce this very complex problem of amorphous phase 00:24:27.590 --> 00:24:31.130 align:middle line:84% stability into essentially packing density of hard spheres. 00:24:31.130 --> 00:24:33.050 align:middle line:84% And in the end, you can get results 00:24:33.050 --> 00:24:35.730 align:middle line:84% that you can actually predict the most stable competition 00:24:35.730 --> 00:24:38.490 align:middle line:84% with external agreement with experiments. 00:24:38.490 --> 00:24:42.610 align:middle line:84% So that's why I always find this paper as a miracle, the fact 00:24:42.610 --> 00:24:44.930 align:middle line:84% that if you look at the last name of the author, 00:24:44.930 --> 00:24:45.790 align:middle line:90% it's also Miracle. 00:24:45.790 --> 00:24:51.950 align:middle line:84% So it is indeed a miracle, miraculous paper. 00:24:51.950 --> 00:24:53.730 align:middle line:84% AUDIENCE: For the left-hand part, 00:24:53.730 --> 00:24:57.870 align:middle line:84% why is its prediction selection higher? 00:24:57.870 --> 00:24:59.370 align:middle line:90% JUEJUN HU: This one? 00:24:59.370 --> 00:25:03.770 align:middle line:90% AUDIENCE: Yeah, at [INAUDIBLE]. 00:25:03.770 --> 00:25:06.330 align:middle line:84% Yeah like, why is that one noticeably-- 00:25:06.330 --> 00:25:07.090 align:middle line:90% JUEJUN HU: Higher? 00:25:07.090 --> 00:25:08.273 align:middle line:90% AUDIENCE: Higher, yeah. 00:25:08.273 --> 00:25:10.190 align:middle line:84% JUEJUN HU: I don't have a good answer to that. 00:25:10.190 --> 00:25:13.210 align:middle line:84% I mean, I consider this already as a remarkable agreement, 00:25:13.210 --> 00:25:15.130 align:middle line:84% quite close to what you will get. 00:25:15.130 --> 00:25:16.850 align:middle line:84% But again, this is still, you can 00:25:16.850 --> 00:25:18.670 align:middle line:84% see that this is vastly simplified theory. 00:25:18.670 --> 00:25:20.910 align:middle line:84% Essentially you're treating-- the first thing, 00:25:20.910 --> 00:25:23.490 align:middle line:84% the atoms are not like hard spheres. 00:25:23.490 --> 00:25:25.970 align:middle line:84% The electron clouds can actually deform. 00:25:25.970 --> 00:25:28.810 align:middle line:84% They are more like squishy balls rather than hard spheres. 00:25:28.810 --> 00:25:30.830 align:middle line:84% So that's already one degree of error, 00:25:30.830 --> 00:25:33.120 align:middle line:84% even just looking at a simple topological model. 00:25:33.120 --> 00:25:35.620 align:middle line:84% And two is that this model completely 00:25:35.620 --> 00:25:38.700 align:middle line:84% neglects any kind of chemical information, which 00:25:38.700 --> 00:25:42.060 align:middle line:84% should have at least some impacts on the final glass 00:25:42.060 --> 00:25:42.580 align:middle line:90% stability. 00:25:42.580 --> 00:25:44.440 align:middle line:84% Different atoms, how they form different chemical bonds, 00:25:44.440 --> 00:25:46.520 align:middle line:84% all those things, it impacts actually the glass formability. 00:25:46.520 --> 00:25:47.960 align:middle line:84% Again, that's completely ignored here. 00:25:47.960 --> 00:25:50.002 align:middle line:84% So the fact that they can achieve this agreement, 00:25:50.002 --> 00:25:53.340 align:middle line:84% I already consider as quite remarkable. 00:25:53.340 --> 00:25:55.580 align:middle line:84% If you look, they actually predict two things. 00:25:55.580 --> 00:25:57.620 align:middle line:84% Essentially the atomic size ratio, 00:25:57.620 --> 00:26:00.580 align:middle line:84% which is the horizontal position of the crosses 00:26:00.580 --> 00:26:03.220 align:middle line:84% and the vertical position is the actual concentration. 00:26:03.220 --> 00:26:06.900 align:middle line:84% You see that the size almost agrees perfectly 00:26:06.900 --> 00:26:10.340 align:middle line:90% in this particular case. 00:26:10.340 --> 00:26:13.500 align:middle line:84% So yeah, I think that's already a miracle to me. 00:26:13.500 --> 00:26:15.500 align:middle line:84% It's such a simple assumption, already gives 00:26:15.500 --> 00:26:19.540 align:middle line:84% something that so closely agree with experiment. 00:26:19.540 --> 00:26:23.120 align:middle line:84% It's also similar to a topological constraint theory. 00:26:23.120 --> 00:26:23.900 align:middle line:90% So that's why. 00:26:23.900 --> 00:26:26.275 align:middle line:84% I think bottom line here is that if you think about glass 00:26:26.275 --> 00:26:32.110 align:middle line:84% formation, topology really plays a very significant role here. 00:26:32.110 --> 00:26:32.610 align:middle line:90% OK. 00:26:32.610 --> 00:26:35.830 align:middle line:90% Any more questions? 00:26:35.830 --> 00:26:37.850 align:middle line:84% OK, now let's switch gears a little bit. 00:26:37.850 --> 00:26:39.590 align:middle line:84% I want to talk a bit about essentially 00:26:39.590 --> 00:26:42.430 align:middle line:84% the mechanical properties of metallic glasses 00:26:42.430 --> 00:26:45.790 align:middle line:84% that derive from their unique structures. 00:26:45.790 --> 00:26:48.390 align:middle line:84% So in this slide, this slide I think 00:26:48.390 --> 00:26:50.250 align:middle line:84% I showed that in previous lectures. 00:26:50.250 --> 00:26:52.950 align:middle line:84% I'm just trying to summarize key structural differences 00:26:52.950 --> 00:26:55.990 align:middle line:84% of crystalline versus amorphous metals. 00:26:55.990 --> 00:26:57.130 align:middle line:90% For crystalline metal. 00:26:57.130 --> 00:27:00.770 align:middle line:84% We know that you can essentially induce plastic deformations. 00:27:00.770 --> 00:27:04.310 align:middle line:84% And most of the time plastic deformation in crystalline metal 00:27:04.310 --> 00:27:07.790 align:middle line:84% occurs through the motion of dislocations. 00:27:07.790 --> 00:27:10.790 align:middle line:84% So this is what actually results in many phenomena 00:27:10.790 --> 00:27:14.190 align:middle line:84% such as essentially like work hardening. 00:27:14.190 --> 00:27:16.330 align:middle line:84% The more you actually drive plastic deformation, 00:27:16.330 --> 00:27:18.050 align:middle line:84% the more you generate [? dislocations. ?] 00:27:18.050 --> 00:27:19.610 align:middle line:84% You have the more interaction between them. 00:27:19.610 --> 00:27:21.250 align:middle line:84% Therefore, essentially, you impede the motion. 00:27:21.250 --> 00:27:22.875 align:middle line:84% Therefore, they actually become harder. 00:27:22.875 --> 00:27:25.728 align:middle line:84% You also have crystalline planes. 00:27:25.728 --> 00:27:28.270 align:middle line:84% Those are the planes where you these [INAUDIBLE] can actually 00:27:28.270 --> 00:27:29.930 align:middle line:90% glide along those planes. 00:27:29.930 --> 00:27:33.650 align:middle line:84% So that also facilitates this kind of plastic deformation. 00:27:33.650 --> 00:27:36.650 align:middle line:84% Now all of those defects is absent in amorphous metal. 00:27:36.650 --> 00:27:39.290 align:middle line:84% So that's why we expect that amorphous metal tends 00:27:39.290 --> 00:27:42.250 align:middle line:84% to have much smaller plastic deformation compared 00:27:42.250 --> 00:27:44.625 align:middle line:90% to crystalline metals. 00:27:44.625 --> 00:27:46.250 align:middle line:84% And that's why in the demo I showed you 00:27:46.250 --> 00:27:49.550 align:middle line:84% in the last lecture, the little steel ball, 00:27:49.550 --> 00:27:52.890 align:middle line:84% they will bounce back many, many times on the metallic glass 00:27:52.890 --> 00:27:55.690 align:middle line:84% sheet because you don't have essentially plastic deformation 00:27:55.690 --> 00:27:58.470 align:middle line:84% that actually absorbs this kind of mechanical energy. 00:27:58.470 --> 00:28:02.090 align:middle line:84% So this is what accounts for large elastic limit 00:28:02.090 --> 00:28:04.650 align:middle line:84% and the high-yield strength in metallic glasses. 00:28:04.650 --> 00:28:08.530 align:middle line:84% But the downside is that you cannot use a co-working as a way 00:28:08.530 --> 00:28:11.450 align:middle line:84% to actually shape this bulk metallic glasses because of this 00:28:11.450 --> 00:28:14.730 align:middle line:84% very poor, what we call, the global plasticity. 00:28:14.730 --> 00:28:17.210 align:middle line:84% So metallic glasses, you cannot induce plastic deformation 00:28:17.210 --> 00:28:19.610 align:middle line:84% uniformly across the entire material. 00:28:19.610 --> 00:28:24.730 align:middle line:84% Instead, what happens is that there are always local regions 00:28:24.730 --> 00:28:26.210 align:middle line:90% for whatever reason. 00:28:26.210 --> 00:28:28.340 align:middle line:84% I mean, metallic amorphous structure network 00:28:28.340 --> 00:28:31.220 align:middle line:84% is not going to be homogeneous in the atomic scale. 00:28:31.220 --> 00:28:34.220 align:middle line:84% There are always certain regions that essentially initiates 00:28:34.220 --> 00:28:37.020 align:middle line:84% this kind of plastic deformation when you exceed your stress. 00:28:37.020 --> 00:28:40.140 align:middle line:84% Now when that happens, this plastic deformation process 00:28:40.140 --> 00:28:42.900 align:middle line:84% always involves relative motion of atoms with respect 00:28:42.900 --> 00:28:44.260 align:middle line:90% to each other. 00:28:44.260 --> 00:28:47.340 align:middle line:84% So in that process, it inevitably 00:28:47.340 --> 00:28:52.740 align:middle line:84% results in the generation and redistribution of free volume. 00:28:52.740 --> 00:28:55.180 align:middle line:84% If you generate more free volume, 00:28:55.180 --> 00:28:57.940 align:middle line:84% you have more wiggle room for atoms 00:28:57.940 --> 00:29:01.300 align:middle line:84% and plastic deformation essentially becomes easier. 00:29:01.300 --> 00:29:03.900 align:middle line:84% So what that means is that when you actually 00:29:03.900 --> 00:29:06.380 align:middle line:84% have in some specific location where you already 00:29:06.380 --> 00:29:09.040 align:middle line:84% induce plastic deformation, it becomes softer. 00:29:09.040 --> 00:29:11.940 align:middle line:84% It becomes more amenable to further plastic deformation. 00:29:11.940 --> 00:29:14.140 align:middle line:84% So eventually, all the plastic deformation 00:29:14.140 --> 00:29:16.340 align:middle line:84% is going to get localized in the region 00:29:16.340 --> 00:29:18.960 align:middle line:84% where you already initiate some plastic deformation. 00:29:18.960 --> 00:29:21.880 align:middle line:84% So this is a phenomenon known as shear localization. 00:29:21.880 --> 00:29:24.380 align:middle line:84% And that's why this is the image I showed you previously. 00:29:24.380 --> 00:29:26.080 align:middle line:90% You have a metallic glass rod. 00:29:26.080 --> 00:29:28.390 align:middle line:84% You try to compress it until it fails. 00:29:28.390 --> 00:29:31.590 align:middle line:84% What you see is that they tend to fail in some local region 00:29:31.590 --> 00:29:34.590 align:middle line:84% here, and you can clearly see this kind of shear 00:29:34.590 --> 00:29:36.590 align:middle line:84% bend actually forms, indicating large shear 00:29:36.590 --> 00:29:41.350 align:middle line:84% deformation occurs only in those kind of very narrow planes. 00:29:41.350 --> 00:29:43.990 align:middle line:84% All right, so more quantitatively 00:29:43.990 --> 00:29:46.830 align:middle line:84% we can describe this kind of a mechanical behavior 00:29:46.830 --> 00:29:50.910 align:middle line:84% of bulk metallic glasses using what we call the a deformation 00:29:50.910 --> 00:29:52.410 align:middle line:90% map, in this case. 00:29:52.410 --> 00:29:56.350 align:middle line:84% So for this deformation map, we have two axes. 00:29:56.350 --> 00:29:59.510 align:middle line:84% Horizontal axis is the temperature 00:29:59.510 --> 00:30:02.510 align:middle line:84% normalized against the glass transition temperature. 00:30:02.510 --> 00:30:06.630 align:middle line:84% Vertical axis is basically the normalized stress. 00:30:06.630 --> 00:30:09.230 align:middle line:84% So you see there are several regimes 00:30:09.230 --> 00:30:12.230 align:middle line:84% we can define in this kind of deformation map here. 00:30:12.230 --> 00:30:14.950 align:middle line:84% So if you have a low temperature, 00:30:14.950 --> 00:30:17.470 align:middle line:90% you also have a smaller stress. 00:30:17.470 --> 00:30:20.310 align:middle line:84% This is the regime where the deformation 00:30:20.310 --> 00:30:23.390 align:middle line:90% is completely elastic. 00:30:23.390 --> 00:30:26.680 align:middle line:84% So there's no essentially permanent deformation 00:30:26.680 --> 00:30:27.960 align:middle line:90% in this region here. 00:30:27.960 --> 00:30:30.440 align:middle line:84% Now, if you exceed this point, this point 00:30:30.440 --> 00:30:32.640 align:middle line:90% basically is your stress. 00:30:32.640 --> 00:30:36.573 align:middle line:84% Above that, you start to get shear deformation. 00:30:36.573 --> 00:30:38.240 align:middle line:84% And more specifically, this is basically 00:30:38.240 --> 00:30:40.160 align:middle line:84% shear localization that actually takes place that 00:30:40.160 --> 00:30:41.460 align:middle line:90% lead to catastrophic failure. 00:30:41.460 --> 00:30:45.600 align:middle line:84% So that's why this regime is called 00:30:45.600 --> 00:30:47.880 align:middle line:84% inhomogeneous deformation, essentially 00:30:47.880 --> 00:30:50.860 align:middle line:84% indicating that this deformation is spatially inhomogeneous. 00:30:50.860 --> 00:30:53.200 align:middle line:84% They are localized only in certain regions. 00:30:53.200 --> 00:30:55.920 align:middle line:90% 00:30:55.920 --> 00:30:58.800 align:middle line:84% If you go along the other axis, so that's 00:30:58.800 --> 00:31:04.840 align:middle line:84% actually what happens if you apply stress 00:31:04.840 --> 00:31:06.400 align:middle line:90% at relatively low temperature. 00:31:06.400 --> 00:31:09.560 align:middle line:84% So then you will introduce essentially shear localization. 00:31:09.560 --> 00:31:16.960 align:middle line:84% Now if you look at the stress strain plot, 00:31:16.960 --> 00:31:19.480 align:middle line:84% these lines indicate the behavior 00:31:19.480 --> 00:31:22.800 align:middle line:84% of this metallic glasses under low temperature. 00:31:22.800 --> 00:31:27.220 align:middle line:84% And low temperature, you see essentially elastic deformation. 00:31:27.220 --> 00:31:30.060 align:middle line:84% And then once you introduce shear deformation, 00:31:30.060 --> 00:31:32.320 align:middle line:84% it quickly fails because shear localization. 00:31:32.320 --> 00:31:34.720 align:middle line:84% So the curve abruptly terminates. 00:31:34.720 --> 00:31:36.993 align:middle line:90% 00:31:36.993 --> 00:31:39.660 align:middle line:84% So that's what the strain stress curve looks like in this region 00:31:39.660 --> 00:31:41.300 align:middle line:90% here, inhomogeneous deformation. 00:31:41.300 --> 00:31:44.220 align:middle line:84% Now if you go along this axis, if you go to this part 00:31:44.220 --> 00:31:47.660 align:middle line:84% here, go to high temperature, if you go to higher temperature 00:31:47.660 --> 00:31:51.780 align:middle line:84% such that temperature becomes comparable to the TG, 00:31:51.780 --> 00:31:55.600 align:middle line:84% then the material essentially becomes viscoelastic. 00:31:55.600 --> 00:31:58.260 align:middle line:84% You have a lot more viscous flow contribution 00:31:58.260 --> 00:32:00.700 align:middle line:84% when it comes to mechanical deformation. 00:32:00.700 --> 00:32:05.900 align:middle line:84% So if you apply a small stress, then the material basically 00:32:05.900 --> 00:32:07.880 align:middle line:90% behaves like a Newtonian fluid. 00:32:07.880 --> 00:32:12.060 align:middle line:90% 00:32:12.060 --> 00:32:15.700 align:middle line:84% If it is a Newtonian fluid, the shear rate 00:32:15.700 --> 00:32:19.460 align:middle line:84% will now be proportional to the applied stress. 00:32:19.460 --> 00:32:20.700 align:middle line:90% OK? 00:32:20.700 --> 00:32:22.740 align:middle line:84% So this is the regime that people 00:32:22.740 --> 00:32:26.230 align:middle line:84% like to use for thermoplastic forming to shaping this bulk 00:32:26.230 --> 00:32:27.830 align:middle line:90% metallic glasses. 00:32:27.830 --> 00:32:30.830 align:middle line:84% So if you look at all the strain stress curve, 00:32:30.830 --> 00:32:32.602 align:middle line:84% this curves at the bottom, this one. 00:32:32.602 --> 00:32:34.310 align:middle line:84% Forget about this one with a little bump. 00:32:34.310 --> 00:32:34.810 align:middle line:90% OK. 00:32:34.810 --> 00:32:37.710 align:middle line:84% Just look at this one at the bottom. 00:32:37.710 --> 00:32:41.590 align:middle line:84% So this one is at the bottom is the Newtonian fluid ones. 00:32:41.590 --> 00:32:43.390 align:middle line:84% You see the curve start to come up 00:32:43.390 --> 00:32:45.350 align:middle line:84% and then eventually they plateau. 00:32:45.350 --> 00:32:48.070 align:middle line:84% The regime where they plateau, essentially it 00:32:48.070 --> 00:32:50.350 align:middle line:84% corresponds to a constant shear rate. 00:32:50.350 --> 00:32:54.750 align:middle line:84% So a constant stress correspond to constant shear rate. 00:32:54.750 --> 00:32:57.990 align:middle line:84% So that's why you see this strain essentially monotonically 00:32:57.990 --> 00:33:01.870 align:middle line:84% increases while you keep the constant stress. 00:33:01.870 --> 00:33:04.390 align:middle line:84% So this is also a regime where you can essentially 00:33:04.390 --> 00:33:07.350 align:middle line:84% introduce a very large plastic deformation 00:33:07.350 --> 00:33:10.630 align:middle line:84% of bulk metallic glasses in a thermoplastic forming. 00:33:10.630 --> 00:33:12.550 align:middle line:84% So this is actually just one example on top 00:33:12.550 --> 00:33:15.790 align:middle line:84% what I'm showing here, there's essentially a little thin wire 00:33:15.790 --> 00:33:17.530 align:middle line:90% made of bulk metallic glass. 00:33:17.530 --> 00:33:21.650 align:middle line:84% You can actually introduce a very large strain. 00:33:21.650 --> 00:33:24.680 align:middle line:84% In this case, the deformation is actually more than 1,200, 00:33:24.680 --> 00:33:26.300 align:middle line:90% so huge deformation. 00:33:26.300 --> 00:33:28.840 align:middle line:84% You can introduce this very large elongation 00:33:28.840 --> 00:33:30.480 align:middle line:84% without actually breaking the material. 00:33:30.480 --> 00:33:32.200 align:middle line:84% The reason this material doesn't break 00:33:32.200 --> 00:33:34.820 align:middle line:84% is because you have essentially uniform stress across it, 00:33:34.820 --> 00:33:37.320 align:middle line:84% which also in a Newtonian regime this is according 00:33:37.320 --> 00:33:40.233 align:middle line:90% to a uniform strain rate. 00:33:40.233 --> 00:33:42.400 align:middle line:84% So if it's uniform strain rate, essentially diameter 00:33:42.400 --> 00:33:44.975 align:middle line:84% across the whole wire reduces uniformly. 00:33:44.975 --> 00:33:46.600 align:middle line:84% And that's why you can essentially draw 00:33:46.600 --> 00:33:47.920 align:middle line:90% this kind of long wires here. 00:33:47.920 --> 00:33:53.600 align:middle line:84% It's similar to cane drawing in like inorganic network glasses. 00:33:53.600 --> 00:33:56.600 align:middle line:84% All right, now last one, at high temperature, 00:33:56.600 --> 00:33:59.320 align:middle line:84% where you actually increase the stress, 00:33:59.320 --> 00:34:01.700 align:middle line:84% higher stress corresponds to higher strain rate. 00:34:01.700 --> 00:34:04.240 align:middle line:84% And this is where the nonlinearity would actually 00:34:04.240 --> 00:34:05.080 align:middle line:90% come into play. 00:34:05.080 --> 00:34:06.840 align:middle line:84% So now in this case, the metallic glass 00:34:06.840 --> 00:34:11.280 align:middle line:84% essentially behave like a non-Newtonian fluid. 00:34:11.280 --> 00:34:15.120 align:middle line:84% On the strain stress curve, this curve with a little bump, 00:34:15.120 --> 00:34:17.719 align:middle line:84% this is indicative of non-Newtonian behavior. 00:34:17.719 --> 00:34:19.000 align:middle line:90% So you increase the stress. 00:34:19.000 --> 00:34:20.820 align:middle line:90% Strain rate starts to increase. 00:34:20.820 --> 00:34:22.699 align:middle line:84% And at some point, because the increase 00:34:22.699 --> 00:34:26.820 align:middle line:84% of the strain rate or the shear rate, 00:34:26.820 --> 00:34:29.060 align:middle line:84% the stress actually decreases because 00:34:29.060 --> 00:34:33.360 align:middle line:84% of the change of viscosity as a function of the strain rate. 00:34:33.360 --> 00:34:35.520 align:middle line:84% And that's why you see a little bump here, 00:34:35.520 --> 00:34:39.179 align:middle line:84% essentially indicating the variation of viscosity 00:34:39.179 --> 00:34:43.460 align:middle line:84% as a function of the stress or strain rate. 00:34:43.460 --> 00:34:45.460 align:middle line:84% OK, so this is the regime you probably 00:34:45.460 --> 00:34:47.940 align:middle line:84% don't want to perform your process at, 00:34:47.940 --> 00:34:49.940 align:middle line:84% because it becomes very difficult to control 00:34:49.940 --> 00:34:51.699 align:middle line:90% the process uniformly. 00:34:51.699 --> 00:34:54.980 align:middle line:90% 00:34:54.980 --> 00:34:58.820 align:middle line:84% So that's about the high level overview of the deformation 00:34:58.820 --> 00:34:59.980 align:middle line:90% behavior. 00:34:59.980 --> 00:35:01.820 align:middle line:84% Now next we'll take a look at how 00:35:01.820 --> 00:35:03.620 align:middle line:84% the microscopic structure impacts 00:35:03.620 --> 00:35:05.620 align:middle line:90% their mechanical attributes. 00:35:05.620 --> 00:35:08.900 align:middle line:84% So starting from the simple elastic constants, 00:35:08.900 --> 00:35:10.980 align:middle line:84% for elastic constants, metallic glasses, 00:35:10.980 --> 00:35:12.478 align:middle line:90% they tend to be isotropic. 00:35:12.478 --> 00:35:13.520 align:middle line:90% Which makes sense, right? 00:35:13.520 --> 00:35:15.620 align:middle line:84% Because there's no particular grain orientation 00:35:15.620 --> 00:35:17.620 align:middle line:90% or crystalline orientation. 00:35:17.620 --> 00:35:20.710 align:middle line:84% The elastic moduli in metallic glasses 00:35:20.710 --> 00:35:23.830 align:middle line:84% tend to be lower compared to a crystalline counterpart. 00:35:23.830 --> 00:35:26.750 align:middle line:84% So the bulk modulus typically is about 6% lower. 00:35:26.750 --> 00:35:29.430 align:middle line:84% Shear/Young's modulus is 30% smaller. 00:35:29.430 --> 00:35:31.810 align:middle line:84% The reason it's lower come from a few facts. 00:35:31.810 --> 00:35:33.750 align:middle line:84% One is that the packing density is lower. 00:35:33.750 --> 00:35:35.990 align:middle line:84% You have free volume, so the density of glasses 00:35:35.990 --> 00:35:37.670 align:middle line:84% is lower than crystalline counterpart. 00:35:37.670 --> 00:35:39.830 align:middle line:84% So that means on average the atoms are actually 00:35:39.830 --> 00:35:41.870 align:middle line:90% further apart from each other. 00:35:41.870 --> 00:35:44.910 align:middle line:84% So this leads to a weaker interatomic interactions 00:35:44.910 --> 00:35:46.782 align:middle line:84% which then accounts for the reduced modulus. 00:35:46.782 --> 00:35:48.990 align:middle line:84% The modulus, essentially is the ability of a material 00:35:48.990 --> 00:35:50.310 align:middle line:90% to resist deformation. 00:35:50.310 --> 00:35:53.310 align:middle line:84% And it has to do essentially with stiffness of the chemical 00:35:53.310 --> 00:35:55.270 align:middle line:90% bonds in between the atoms. 00:35:55.270 --> 00:35:59.230 align:middle line:84% So low density means a low interaction, low stiffness. 00:35:59.230 --> 00:36:04.330 align:middle line:84% Also, because you don't have this long-range atomic order, 00:36:04.330 --> 00:36:07.910 align:middle line:84% usually it reduces the directionality of the structure 00:36:07.910 --> 00:36:09.042 align:middle line:90% there. 00:36:09.042 --> 00:36:10.750 align:middle line:84% This also contributes to actually reduced 00:36:10.750 --> 00:36:14.630 align:middle line:90% stiffness of chemical bonds OK. 00:36:14.630 --> 00:36:18.758 align:middle line:84% And on top of that, because the local structure 00:36:18.758 --> 00:36:20.800 align:middle line:84% is essentially inhomogeneous at the atomic scale. 00:36:20.800 --> 00:36:22.760 align:middle line:84% If you look at one region of amorphous metal, 00:36:22.760 --> 00:36:25.177 align:middle line:84% atomically, it's going to be different from another region 00:36:25.177 --> 00:36:26.560 align:middle line:90% just because it's amorphous. 00:36:26.560 --> 00:36:28.640 align:middle line:84% So what that means is that there are always 00:36:28.640 --> 00:36:33.420 align:middle line:84% some microscopic region that tend to have less stiffness. 00:36:33.420 --> 00:36:34.800 align:middle line:90% They are softer. 00:36:34.800 --> 00:36:38.240 align:middle line:84% So then when you try to essentially induce deformation 00:36:38.240 --> 00:36:41.640 align:middle line:84% in the material, those softer regions 00:36:41.640 --> 00:36:43.640 align:middle line:84% will then disproportionately contribute 00:36:43.640 --> 00:36:47.480 align:middle line:84% to a large deformation compared to other more stiff regions. 00:36:47.480 --> 00:36:50.600 align:middle line:84% So overall, essentially the elastic constants 00:36:50.600 --> 00:36:53.380 align:middle line:84% will become more dictated by those softer regions. 00:36:53.380 --> 00:36:56.280 align:middle line:84% And as a result, this will lead to reduce essentially 00:36:56.280 --> 00:36:58.720 align:middle line:90% the elastic modulus. 00:36:58.720 --> 00:37:03.000 align:middle line:84% So it's a combined effect coming from the lower packing density, 00:37:03.000 --> 00:37:04.878 align:middle line:84% coming from the structure inhomogeneity, 00:37:04.878 --> 00:37:06.920 align:middle line:84% and also coming from the lack of structural order 00:37:06.920 --> 00:37:09.220 align:middle line:84% which reduces stiffness of the chemical bonds. 00:37:09.220 --> 00:37:13.108 align:middle line:90% 00:37:13.108 --> 00:37:15.480 align:middle line:84% So that's for elastic deformation. 00:37:15.480 --> 00:37:17.700 align:middle line:84% Now for plastic deformation, we talk 00:37:17.700 --> 00:37:20.060 align:middle line:84% about essentially plastic deformation 00:37:20.060 --> 00:37:22.500 align:middle line:84% that essentially in this case always 00:37:22.500 --> 00:37:26.160 align:middle line:84% involves generation or redistribution of free volume. 00:37:26.160 --> 00:37:28.420 align:middle line:84% So what I'm showing on this slide here 00:37:28.420 --> 00:37:30.340 align:middle line:84% is actually the microscopic models 00:37:30.340 --> 00:37:32.620 align:middle line:84% where plastic deformation can actually take place 00:37:32.620 --> 00:37:34.460 align:middle line:90% in a bulk metallic glass. 00:37:34.460 --> 00:37:37.180 align:middle line:84% There are in general two kind of ways 00:37:37.180 --> 00:37:40.140 align:middle line:84% to actually introduce plastic deformation. 00:37:40.140 --> 00:37:42.580 align:middle line:84% One is called diffusive atomic jump. 00:37:42.580 --> 00:37:46.920 align:middle line:84% This is a smaller scale deformation there. 00:37:46.920 --> 00:37:50.060 align:middle line:84% What we're looking at here is one atom 00:37:50.060 --> 00:37:54.380 align:middle line:84% may have two neighboring sites where you can locate it. 00:37:54.380 --> 00:37:57.700 align:middle line:84% If there's no applied stress, then the two neighboring sites 00:37:57.700 --> 00:38:00.380 align:middle line:84% may be more or less energetically equivalent. 00:38:00.380 --> 00:38:03.820 align:middle line:84% But once you start to apply a shear stress, 00:38:03.820 --> 00:38:06.860 align:middle line:84% you will energetically favor one side over the other. 00:38:06.860 --> 00:38:08.992 align:middle line:84% So then the system will then hop to one side 00:38:08.992 --> 00:38:10.700 align:middle line:84% where it can actually introduce this kind 00:38:10.700 --> 00:38:11.860 align:middle line:90% of plastic deformation. 00:38:11.860 --> 00:38:14.180 align:middle line:84% So essentially it leads to this directional diffusive 00:38:14.180 --> 00:38:19.750 align:middle line:84% flow of atoms that eventually lead to a plastic deformation. 00:38:19.750 --> 00:38:24.110 align:middle line:84% So that's one mechanism where this kind of plastic deformation 00:38:24.110 --> 00:38:25.110 align:middle line:90% can take place. 00:38:25.110 --> 00:38:29.170 align:middle line:84% Now the other one, which is probably the more important one, 00:38:29.170 --> 00:38:32.230 align:middle line:84% a deformation takes place through what's called a shear 00:38:32.230 --> 00:38:34.470 align:middle line:90% transformation zone, STZ. 00:38:34.470 --> 00:38:38.630 align:middle line:90% 00:38:38.630 --> 00:38:42.230 align:middle line:84% Now simplistically, you can think of STZ 00:38:42.230 --> 00:38:45.070 align:middle line:84% as a local atomic arrangement where 00:38:45.070 --> 00:38:50.070 align:middle line:84% you have two clusters of atoms in contact with each other. 00:38:50.070 --> 00:38:51.830 align:middle line:84% The number of atoms involved in an STZ 00:38:51.830 --> 00:38:54.770 align:middle line:84% can really vary, maybe a few tens of atoms, 00:38:54.770 --> 00:38:56.970 align:middle line:84% maybe to a few hundred or thousands of atoms. 00:38:56.970 --> 00:38:59.690 align:middle line:84% So when they come into contact with each other, 00:38:59.690 --> 00:39:01.370 align:middle line:90% this is initial configuration. 00:39:01.370 --> 00:39:04.270 align:middle line:84% There's an interface between these two clusters atoms. 00:39:04.270 --> 00:39:08.950 align:middle line:84% When you apply shear stress, at some point 00:39:08.950 --> 00:39:11.750 align:middle line:84% this atomic cluster group can essentially 00:39:11.750 --> 00:39:16.600 align:middle line:84% hop one interatomic spacing with respect to each other. 00:39:16.600 --> 00:39:19.880 align:middle line:84% So when that happens, essentially introducing 00:39:19.880 --> 00:39:22.800 align:middle line:84% a shear deformation that gives rise 00:39:22.800 --> 00:39:26.200 align:middle line:84% to essentially a one atomic spacing, horizontal one 00:39:26.200 --> 00:39:27.040 align:middle line:90% atomic spacing. 00:39:27.040 --> 00:39:32.080 align:middle line:90% 00:39:32.080 --> 00:39:34.120 align:middle line:84% So then this process continues until you 00:39:34.120 --> 00:39:36.360 align:middle line:90% get macroscopic deformation. 00:39:36.360 --> 00:39:37.960 align:middle line:84% So one thing I want to mention here, 00:39:37.960 --> 00:39:40.960 align:middle line:84% this shear transformation zone is different from dislocations 00:39:40.960 --> 00:39:43.120 align:middle line:90% in crystalline metal. 00:39:43.120 --> 00:39:46.600 align:middle line:84% In a crystalline metal, you can go to a TEM. 00:39:46.600 --> 00:39:48.820 align:middle line:84% You can actually do atomic scale image. 00:39:48.820 --> 00:39:50.360 align:middle line:90% You can precisely pinpoint. 00:39:50.360 --> 00:39:51.620 align:middle line:90% We get one dislocation here. 00:39:51.620 --> 00:39:53.100 align:middle line:84% We get another distribution here. 00:39:53.100 --> 00:39:56.340 align:middle line:84% You know a priori whether it's dislocation states. 00:39:56.340 --> 00:39:58.720 align:middle line:84% They have very clear structure signature that 00:39:58.720 --> 00:40:00.720 align:middle line:90% tell you there's dislocation. 00:40:00.720 --> 00:40:03.840 align:middle line:90% STZ is statistical. 00:40:03.840 --> 00:40:06.260 align:middle line:84% When you apply a shear stress on a metallic glass, 00:40:06.260 --> 00:40:09.560 align:middle line:84% you actually don't know a priori where the shear transformation 00:40:09.560 --> 00:40:11.480 align:middle line:90% is going to take place. 00:40:11.480 --> 00:40:14.420 align:middle line:84% Even if you go to a TEM, you are able to look at atomic scale 00:40:14.420 --> 00:40:16.380 align:middle line:84% image, you will not be able to predict 00:40:16.380 --> 00:40:18.260 align:middle line:84% where is the regime where the deformation is 00:40:18.260 --> 00:40:19.180 align:middle line:90% going to take place. 00:40:19.180 --> 00:40:21.980 align:middle line:90% It's statistical. 00:40:21.980 --> 00:40:26.760 align:middle line:84% So you cannot consider STZ as a structural defect. 00:40:26.760 --> 00:40:30.380 align:middle line:90% It's not a structural defect. 00:40:30.380 --> 00:40:33.740 align:middle line:84% It's something we look at after the plastic deformation takes 00:40:33.740 --> 00:40:34.620 align:middle line:90% place. 00:40:34.620 --> 00:40:37.660 align:middle line:84% Then we know these local regions where you actually 00:40:37.660 --> 00:40:41.300 align:middle line:84% have the atomic transformation is where you correspond to STZs. 00:40:41.300 --> 00:40:43.000 align:middle line:90% So it after the fact. 00:40:43.000 --> 00:40:48.600 align:middle line:90% 00:40:48.600 --> 00:40:49.810 align:middle line:90% Yes? 00:40:49.810 --> 00:40:51.680 align:middle line:84% AUDIENCE: When you're looking at it? 00:40:51.680 --> 00:40:53.680 align:middle line:84% JUEJUN HU: It's somewhat similar to dislocation, 00:40:53.680 --> 00:40:54.430 align:middle line:90% if you look at it. 00:40:54.430 --> 00:40:56.560 align:middle line:84% It's like edge degradation and moving around. 00:40:56.560 --> 00:40:57.180 align:middle line:90% But anyway. 00:40:57.180 --> 00:40:59.700 align:middle line:84% AUDIENCE: You would see evidence that even if it's 00:40:59.700 --> 00:41:06.740 align:middle line:84% like moving one atomic spacing, but since both are shearing 00:41:06.740 --> 00:41:09.087 align:middle line:90% or jumping one small space? 00:41:09.087 --> 00:41:11.420 align:middle line:84% JUEJUN HU: Yeah, there are a few ways you can tell this. 00:41:11.420 --> 00:41:13.990 align:middle line:84% I mean one way, suppose you were able to look at atomic scale 00:41:13.990 --> 00:41:14.530 align:middle line:90% image. 00:41:14.530 --> 00:41:16.700 align:middle line:84% You can do essentially time dependent imaging. 00:41:16.700 --> 00:41:18.450 align:middle line:84% You can see that initially it's like this. 00:41:18.450 --> 00:41:19.370 align:middle line:90% It becomes like this. 00:41:19.370 --> 00:41:21.310 align:middle line:84% You know that there's actually a shear transformation. 00:41:21.310 --> 00:41:22.530 align:middle line:90% That's one way to look at it. 00:41:22.530 --> 00:41:24.447 align:middle line:84% The second way to look at it, you can actually 00:41:24.447 --> 00:41:26.482 align:middle line:90% look at the strain. 00:41:26.482 --> 00:41:27.690 align:middle line:90% We're going to talk about it. 00:41:27.690 --> 00:41:30.710 align:middle line:84% So once we actually introduce the atomic displacement, 00:41:30.710 --> 00:41:33.890 align:middle line:84% inevitably you are squeezing the atoms surrounding it. 00:41:33.890 --> 00:41:36.110 align:middle line:84% So this is actually introducing a local strain field. 00:41:36.110 --> 00:41:37.818 align:middle line:84% AUDIENCE: And that strain would be larger 00:41:37.818 --> 00:41:40.510 align:middle line:84% for shear transformation than like a single diffusion? 00:41:40.510 --> 00:41:41.430 align:middle line:84% JUEJUN HU: Oh, yeah, of course, I 00:41:41.430 --> 00:41:43.097 align:middle line:84% mean it's because there's more clusters. 00:41:43.097 --> 00:41:45.710 align:middle line:84% And also you only see the strain where you actually 00:41:45.710 --> 00:41:47.350 align:middle line:90% have essentially deformation. 00:41:47.350 --> 00:41:49.330 align:middle line:84% So now after the deformation takes place, 00:41:49.330 --> 00:41:51.630 align:middle line:84% you can actually do a post-mortem analysis 00:41:51.630 --> 00:41:53.768 align:middle line:90% and tell you where the STZs are. 00:41:53.768 --> 00:41:56.310 align:middle line:84% You just cannot tell it a priori before the deformation takes 00:41:56.310 --> 00:41:57.770 align:middle line:90% place, because it's statistical. 00:41:57.770 --> 00:41:58.270 align:middle line:90% OK? 00:41:58.270 --> 00:41:59.750 align:middle line:84% There may be certain regions that's 00:41:59.750 --> 00:42:02.010 align:middle line:84% more prone to plastic deformation, 00:42:02.010 --> 00:42:04.150 align:middle line:84% but there's no guarantee that those will be places 00:42:04.150 --> 00:42:05.430 align:middle line:90% that actually takes place. 00:42:05.430 --> 00:42:06.610 align:middle line:90% It's statistical. 00:42:06.610 --> 00:42:09.510 align:middle line:90% 00:42:09.510 --> 00:42:10.010 align:middle line:90% OK. 00:42:10.010 --> 00:42:11.427 align:middle line:84% But as I said, this looks somewhat 00:42:11.427 --> 00:42:14.460 align:middle line:84% similar to edge degradation sweeping through. 00:42:14.460 --> 00:42:16.380 align:middle line:84% If your edge degradation is moving across, 00:42:16.380 --> 00:42:18.740 align:middle line:84% then you get this same kind of transformation there. 00:42:18.740 --> 00:42:21.560 align:middle line:90% But this is not dislocation OK. 00:42:21.560 --> 00:42:26.773 align:middle line:84% All right, well, this is just another one 00:42:26.773 --> 00:42:29.440 align:middle line:84% that shows what actually happens when you have shear deformation 00:42:29.440 --> 00:42:30.080 align:middle line:90% zone. 00:42:30.080 --> 00:42:33.280 align:middle line:84% The way to look at it is that you can have two configurations. 00:42:33.280 --> 00:42:35.300 align:middle line:84% Initially, if you look at energy landscape, 00:42:35.300 --> 00:42:39.680 align:middle line:84% they have maybe a more or less comparable depth. 00:42:39.680 --> 00:42:42.580 align:middle line:84% So there's no preference of one configuration over another. 00:42:42.580 --> 00:42:44.380 align:middle line:84% But once you start to apply stress, 00:42:44.380 --> 00:42:46.180 align:middle line:84% you tilt the potential energy landscape, 00:42:46.180 --> 00:42:48.020 align:middle line:84% so that you're introducing directional flow. 00:42:48.020 --> 00:42:49.520 align:middle line:84% Then from one side to the other, you 00:42:49.520 --> 00:42:51.562 align:middle line:84% have [INAUDIBLE] once you can overcome the energy 00:42:51.562 --> 00:42:52.640 align:middle line:90% barrier in between. 00:42:52.640 --> 00:42:57.960 align:middle line:84% So I'm quoting essentially Professor Schuh here, 00:42:57.960 --> 00:42:59.883 align:middle line:90% who used to be in DMSE. 00:42:59.883 --> 00:43:01.800 align:middle line:84% He basically says that the plastic deformation 00:43:01.800 --> 00:43:03.640 align:middle line:84% of metallic glasses on the macroscopic scale 00:43:03.640 --> 00:43:07.760 align:middle line:84% is an accumulated accumulation of local transformations coming 00:43:07.760 --> 00:43:10.750 align:middle line:84% from STZs which eventually lead to macroscopic deformation. 00:43:10.750 --> 00:43:13.450 align:middle line:84% And in the process, it's important to realize 00:43:13.450 --> 00:43:16.180 align:middle line:84% that in either case, you need free volume, which 00:43:16.180 --> 00:43:18.430 align:middle line:84% is quite obvious in the case of diffusive atomic jump. 00:43:18.430 --> 00:43:20.250 align:middle line:84% You need empty sites for it to hop into. 00:43:20.250 --> 00:43:22.990 align:middle line:84% Same thing for this kind of shear transmission zone, 00:43:22.990 --> 00:43:24.730 align:middle line:84% if it's a very close packed structure 00:43:24.730 --> 00:43:26.522 align:middle line:84% such that no free volume, you don't 00:43:26.522 --> 00:43:29.230 align:middle line:84% have the wiggle room to move one cluster with respect to another. 00:43:29.230 --> 00:43:31.810 align:middle line:84% The resistance is going to be immense. 00:43:31.810 --> 00:43:35.010 align:middle line:84% So more free volume always facilitate this kind 00:43:35.010 --> 00:43:36.370 align:middle line:90% of plastic deformation. 00:43:36.370 --> 00:43:38.450 align:middle line:84% And once you introduce plastic deformation, 00:43:38.450 --> 00:43:39.450 align:middle line:84% you can see that you can generate 00:43:39.450 --> 00:43:40.770 align:middle line:90% free volume, for example, here. 00:43:40.770 --> 00:43:41.970 align:middle line:84% You're essentially moving free volume 00:43:41.970 --> 00:43:43.590 align:middle line:84% from this side to the other side. 00:43:43.590 --> 00:43:45.690 align:middle line:84% So there's generation and redistribution 00:43:45.690 --> 00:43:49.050 align:middle line:84% of free volume in the process once the plastic deformation 00:43:49.050 --> 00:43:49.610 align:middle line:90% takes place. 00:43:49.610 --> 00:43:53.130 align:middle line:90% 00:43:53.130 --> 00:43:55.410 align:middle line:84% All right, so now with those concepts 00:43:55.410 --> 00:43:57.610 align:middle line:84% we can now explain why you have shear 00:43:57.610 --> 00:44:00.450 align:middle line:84% deformation by looking at how the shear transformation 00:44:00.450 --> 00:44:03.770 align:middle line:84% zone essentially impact each other during a deformation 00:44:03.770 --> 00:44:04.350 align:middle line:90% process. 00:44:04.350 --> 00:44:06.390 align:middle line:90% So let's see what happens. 00:44:06.390 --> 00:44:10.590 align:middle line:84% So what we are doing here, this is a very simplistic model 00:44:10.590 --> 00:44:12.630 align:middle line:90% of a bulk metallic glass. 00:44:12.630 --> 00:44:14.430 align:middle line:84% We have many, many local regions. 00:44:14.430 --> 00:44:16.910 align:middle line:84% Within each region, there could be one STZ 00:44:16.910 --> 00:44:18.490 align:middle line:90% that actually takes place. 00:44:18.490 --> 00:44:24.350 align:middle line:84% So let's suppose when you apply the stress at some point one STZ 00:44:24.350 --> 00:44:27.710 align:middle line:90% pops up in the center. 00:44:27.710 --> 00:44:31.130 align:middle line:84% So when that happens, as I said, the atoms, 00:44:31.130 --> 00:44:34.510 align:middle line:84% because they are moving around, the class of atoms 00:44:34.510 --> 00:44:38.310 align:middle line:84% inevitably tries to squeeze only neighboring atoms there. 00:44:38.310 --> 00:44:41.590 align:middle line:84% So this would then introduce essentially a local stress, 00:44:41.590 --> 00:44:45.310 align:middle line:84% local shear stress, around those STZs. 00:44:45.310 --> 00:44:47.550 align:middle line:84% So those local shear stress essentially 00:44:47.550 --> 00:44:51.230 align:middle line:84% adds onto the existing macroscopic shear stress. 00:44:51.230 --> 00:44:52.950 align:middle line:84% And what that means is now if you 00:44:52.950 --> 00:44:55.390 align:middle line:84% look at the neighboring region here, 00:44:55.390 --> 00:44:58.390 align:middle line:84% the actual effective shear stress those neighboring regions 00:44:58.390 --> 00:45:02.050 align:middle line:84% sees becomes much greater than the global shear stress. 00:45:02.050 --> 00:45:05.150 align:middle line:90% 00:45:05.150 --> 00:45:07.110 align:middle line:84% So now statistically, if you look 00:45:07.110 --> 00:45:09.800 align:middle line:84% at the probability of an STZ popping up 00:45:09.800 --> 00:45:13.080 align:middle line:84% across the entire bulk material, the probability for them 00:45:13.080 --> 00:45:16.240 align:middle line:84% to pop up becomes a lot higher near an existing 00:45:16.240 --> 00:45:18.740 align:middle line:84% STZ compared to somewhere that's far away from it. 00:45:18.740 --> 00:45:22.720 align:middle line:90% 00:45:22.720 --> 00:45:24.920 align:middle line:84% So as a result, it becomes more likely 00:45:24.920 --> 00:45:26.900 align:middle line:84% that you have more STZs right around it. 00:45:26.900 --> 00:45:28.733 align:middle line:84% And once that happens, of course, it further 00:45:28.733 --> 00:45:31.120 align:middle line:84% amplifies the local stress, and therefore, you 00:45:31.120 --> 00:45:35.720 align:middle line:84% become more likely to have more STZs right in the neighborhood. 00:45:35.720 --> 00:45:38.880 align:middle line:84% So in the end, this then lead to essentially the formation 00:45:38.880 --> 00:45:41.540 align:middle line:84% of the shear zone and the catastrophic failure. 00:45:41.540 --> 00:45:45.920 align:middle line:90% 00:45:45.920 --> 00:45:48.040 align:middle line:84% So to some extent, you can think of it 00:45:48.040 --> 00:45:51.440 align:middle line:84% as like STZs, they are talking with each other essentially 00:45:51.440 --> 00:45:54.160 align:middle line:84% through strain or through stress. 00:45:54.160 --> 00:46:00.360 align:middle line:84% So there's a definitive positive correlation between STZs 00:46:00.360 --> 00:46:02.440 align:middle line:90% due to the existence of stress. 00:46:02.440 --> 00:46:03.860 align:middle line:84% Once you have one STZ popping up, 00:46:03.860 --> 00:46:08.610 align:middle line:84% it's more likely to have another STZ in the neighboring area. 00:46:08.610 --> 00:46:11.230 align:middle line:84% So this is actually something that can actually be modeled. 00:46:11.230 --> 00:46:13.410 align:middle line:84% So what I'm showing you here, this 00:46:13.410 --> 00:46:15.050 align:middle line:84% is actually coming from this paper. 00:46:15.050 --> 00:46:17.230 align:middle line:84% The authors basically did a Monte Carlo simulation, 00:46:17.230 --> 00:46:20.330 align:middle line:84% a statistical simulation of the kinetics of plastic deformation 00:46:20.330 --> 00:46:21.570 align:middle line:90% in bulk metallic glasses. 00:46:21.570 --> 00:46:23.650 align:middle line:90% So it's a coarse grained model. 00:46:23.650 --> 00:46:26.610 align:middle line:84% So what they did is they divided up the entire material 00:46:26.610 --> 00:46:28.095 align:middle line:90% into many, many unit cells. 00:46:28.095 --> 00:46:29.970 align:middle line:84% Within each unit cell, there could be one STZ 00:46:29.970 --> 00:46:31.070 align:middle line:90% that actually takes place. 00:46:31.070 --> 00:46:34.970 align:middle line:84% So then they run this statistical simulation. 00:46:34.970 --> 00:46:37.530 align:middle line:84% And in the simulation here then these STZs 00:46:37.530 --> 00:46:39.210 align:middle line:90% can initially randomly pop up. 00:46:39.210 --> 00:46:40.930 align:middle line:90% It can pop up anywhere. 00:46:40.930 --> 00:46:45.130 align:middle line:84% But as soon as one STZ comes up, the shear strain field 00:46:45.130 --> 00:46:47.250 align:middle line:90% essentially is getting modified. 00:46:47.250 --> 00:46:50.730 align:middle line:84% So in the next time step, they then again try to re-simulate. 00:46:50.730 --> 00:46:52.970 align:middle line:84% What's the probability of an STZ to pop up 00:46:52.970 --> 00:46:54.250 align:middle line:90% across the entire material? 00:46:54.250 --> 00:46:56.430 align:middle line:84% Initially it's uniform where there's no STZ. 00:46:56.430 --> 00:46:58.430 align:middle line:84% But once you have one STZ coming up, 00:46:58.430 --> 00:47:01.310 align:middle line:84% the neighboring cells becomes more likely to have STZs. 00:47:01.310 --> 00:47:03.730 align:middle line:84% So as a result, they tend to essentially pop 00:47:03.730 --> 00:47:06.200 align:middle line:84% up right in this region here where we already have STZ. 00:47:06.200 --> 00:47:07.950 align:middle line:84% And this is where eventually you are going 00:47:07.950 --> 00:47:09.690 align:middle line:90% to lead to strain localization. 00:47:09.690 --> 00:47:13.190 align:middle line:90% 00:47:13.190 --> 00:47:16.117 align:middle line:84% Basically it's saying that this kind of strain softening 00:47:16.117 --> 00:47:17.950 align:middle line:84% or strain localization behavior is something 00:47:17.950 --> 00:47:19.650 align:middle line:90% you can predict quantitatively. 00:47:19.650 --> 00:47:21.830 align:middle line:84% It shows up naturally in this kind of a Monte Carlo 00:47:21.830 --> 00:47:22.610 align:middle line:90% simulation. 00:47:22.610 --> 00:47:25.550 align:middle line:90% 00:47:25.550 --> 00:47:27.630 align:middle line:84% So what I'm going to show you here in this plot 00:47:27.630 --> 00:47:30.150 align:middle line:90% is actually just two SEM images. 00:47:30.150 --> 00:47:34.030 align:middle line:84% On the left-hand side, this is basically a metallic glass 00:47:34.030 --> 00:47:34.990 align:middle line:90% sheet. 00:47:34.990 --> 00:47:38.790 align:middle line:84% You bend it until you introduce a large plastic deformation. 00:47:38.790 --> 00:47:40.830 align:middle line:84% Now, unlike if you use a crystalline metal, when 00:47:40.830 --> 00:47:43.670 align:middle line:84% you bend it, you see essentially this curvature. 00:47:43.670 --> 00:47:45.890 align:middle line:84% You still see more or less a smooth surface. 00:47:45.890 --> 00:47:47.510 align:middle line:90% It just becomes curved. 00:47:47.510 --> 00:47:50.250 align:middle line:84% For metallic glass, one the other hand, 00:47:50.250 --> 00:47:52.070 align:middle line:84% you see the surface develop this kind 00:47:52.070 --> 00:47:54.550 align:middle line:90% of corrugated microstructure. 00:47:54.550 --> 00:47:57.230 align:middle line:84% At each corrugation, you see this is actually where you 00:47:57.230 --> 00:47:59.123 align:middle line:90% have essentially a shear bend. 00:47:59.123 --> 00:48:00.790 align:middle line:84% So all the shear deformation essentially 00:48:00.790 --> 00:48:04.310 align:middle line:84% gets localized in one of these kind of shear bend here. 00:48:04.310 --> 00:48:07.800 align:middle line:84% So that's why it looks different compared to conventional metal 00:48:07.800 --> 00:48:09.640 align:middle line:90% during plastic deformation. 00:48:09.640 --> 00:48:14.840 align:middle line:84% Now, what you can also imagine is that within this shear event, 00:48:14.840 --> 00:48:18.760 align:middle line:84% the shear deformation is actually enormous, right? 00:48:18.760 --> 00:48:20.800 align:middle line:84% So this very large shear deformation 00:48:20.800 --> 00:48:25.600 align:middle line:84% also corresponds to a significant energy release. 00:48:25.600 --> 00:48:29.400 align:middle line:84% It releases so much energy such that you can actually 00:48:29.400 --> 00:48:31.600 align:middle line:90% melt metal. 00:48:31.600 --> 00:48:33.633 align:middle line:84% So that's what people did on this one here. 00:48:33.633 --> 00:48:35.800 align:middle line:84% So what they did is essentially on the cross-section 00:48:35.800 --> 00:48:39.080 align:middle line:84% of metallic glass, they coat a thin film of tin metal. 00:48:39.080 --> 00:48:40.880 align:middle line:84% Tin has a relatively low melting point. 00:48:40.880 --> 00:48:43.600 align:middle line:84% So when you're actually introducing this deformation, 00:48:43.600 --> 00:48:47.120 align:middle line:84% at the shear zone, there's actually so much heat generation 00:48:47.120 --> 00:48:51.320 align:middle line:84% that the tin metal actually melts into liquid. 00:48:51.320 --> 00:48:53.480 align:middle line:84% And once the tin melts into liquid, due 00:48:53.480 --> 00:48:55.180 align:middle line:84% to the action of surface tension, 00:48:55.180 --> 00:48:58.360 align:middle line:84% this film essentially breaks up into small droplets. 00:48:58.360 --> 00:49:00.540 align:middle line:84% So in the end, instead of a uniform film, 00:49:00.540 --> 00:49:02.720 align:middle line:84% you see these little tin droplets, 00:49:02.720 --> 00:49:05.170 align:middle line:84% which indicates the local temperature exceeds 00:49:05.170 --> 00:49:07.250 align:middle line:90% the melting point of tin. 00:49:07.250 --> 00:49:09.370 align:middle line:84% They use it as a way to map the temperature 00:49:09.370 --> 00:49:13.010 align:middle line:84% distribution during this kind of a plastic deformation process. 00:49:13.010 --> 00:49:15.310 align:middle line:84% But what we can tell, this is a very dramatic process. 00:49:15.310 --> 00:49:17.530 align:middle line:84% It releases lots of local heat right 00:49:17.530 --> 00:49:18.870 align:middle line:90% at those kind of shear zones. 00:49:18.870 --> 00:49:30.770 align:middle line:90% 00:49:30.770 --> 00:49:37.410 align:middle line:84% Now, another thing I also want to mention here, 00:49:37.410 --> 00:49:40.010 align:middle line:84% I've highlighted the fact that any kind of shear plastic 00:49:40.010 --> 00:49:41.970 align:middle line:84% deformation in metallic glass always 00:49:41.970 --> 00:49:45.930 align:middle line:84% involves the generation and redistribution of free volume. 00:49:45.930 --> 00:49:48.330 align:middle line:84% So when you generate free volume, what happens? 00:49:48.330 --> 00:49:50.970 align:middle line:84% If you generate free volume, the volume 00:49:50.970 --> 00:49:52.858 align:middle line:84% becomes bigger, the overall volume. 00:49:52.858 --> 00:49:55.150 align:middle line:84% Because overall volume is basically crystalline volume, 00:49:55.150 --> 00:49:57.025 align:middle line:84% which is a fixed number plus the free volume. 00:49:57.025 --> 00:49:59.570 align:middle line:84% So if you have more free volume, it must expand. 00:49:59.570 --> 00:50:03.190 align:middle line:84% So now if you actually apply compressive stress 00:50:03.190 --> 00:50:05.910 align:middle line:84% on the metallic glass, you are going 00:50:05.910 --> 00:50:10.510 align:middle line:84% to prevent or impede the generation of the free volume. 00:50:10.510 --> 00:50:14.890 align:middle line:84% As a result, this will also impede plastic deformation. 00:50:14.890 --> 00:50:17.670 align:middle line:90% 00:50:17.670 --> 00:50:21.590 align:middle line:84% And vice versa, if you want to facilitate plastic deformation, 00:50:21.590 --> 00:50:23.550 align:middle line:90% you can apply a tensile strain. 00:50:23.550 --> 00:50:25.950 align:middle line:84% Tensile strain, of course facilitates generation 00:50:25.950 --> 00:50:28.350 align:middle line:84% of free volume and therefore, it should also 00:50:28.350 --> 00:50:30.290 align:middle line:90% facilitate plastic deformation. 00:50:30.290 --> 00:50:35.750 align:middle line:90% 00:50:35.750 --> 00:50:37.630 align:middle line:84% So in other words, people call this kind 00:50:37.630 --> 00:50:39.710 align:middle line:84% of shear deformation process in metallic glass 00:50:39.710 --> 00:50:42.290 align:middle line:90% as a dilatational process. 00:50:42.290 --> 00:50:45.550 align:middle line:90% 00:50:45.550 --> 00:50:52.270 align:middle line:84% Essentially it means that the volume expands, dilatation. 00:50:52.270 --> 00:50:54.830 align:middle line:84% There's always volume expansion that 00:50:54.830 --> 00:50:57.410 align:middle line:84% accompanies this kind of shear deformation process. 00:50:57.410 --> 00:51:05.160 align:middle line:90% 00:51:05.160 --> 00:51:06.140 align:middle line:90% Diliational. 00:51:06.140 --> 00:51:13.480 align:middle line:90% 00:51:13.480 --> 00:51:16.640 align:middle line:84% I'm going to use this word as a spelling test for my daughters 00:51:16.640 --> 00:51:18.600 align:middle line:84% to see if they can spell it correctly. 00:51:18.600 --> 00:51:21.760 align:middle line:90% 00:51:21.760 --> 00:51:24.560 align:middle line:84% So now as I mentioned, this should shear dimension also 00:51:24.560 --> 00:51:25.640 align:middle line:90% comes pressure dependent. 00:51:25.640 --> 00:51:27.098 align:middle line:84% If you apply compressive stress you 00:51:27.098 --> 00:51:29.100 align:middle line:90% impede this shear deformation. 00:51:29.100 --> 00:51:31.280 align:middle line:84% So that's why people also consider it 00:51:31.280 --> 00:51:33.180 align:middle line:90% as a frictional process. 00:51:33.180 --> 00:51:34.640 align:middle line:84% You apply stress, you essentially 00:51:34.640 --> 00:51:38.200 align:middle line:90% impede the deformation. 00:51:38.200 --> 00:51:41.200 align:middle line:84% On a phenomenological level, it appears like friction. 00:51:41.200 --> 00:51:42.218 align:middle line:90% OK? 00:51:42.218 --> 00:51:43.760 align:middle line:84% I just want to mention that this kind 00:51:43.760 --> 00:51:46.440 align:middle line:84% of dilatational or frictional process 00:51:46.440 --> 00:51:49.560 align:middle line:84% occurs not only in atomic solids. 00:51:49.560 --> 00:51:51.640 align:middle line:84% It's actually a pretty general phenomena 00:51:51.640 --> 00:51:53.320 align:middle line:84% that's involving deformation of any kind 00:51:53.320 --> 00:51:56.880 align:middle line:84% of amorphous collections of particles. 00:51:56.880 --> 00:51:59.920 align:middle line:84% Where the particles does not have to be atoms. 00:51:59.920 --> 00:52:02.850 align:middle line:90% One example is sand. 00:52:02.850 --> 00:52:08.050 align:middle line:84% So the packing of sand is actually an amorphous lattice 00:52:08.050 --> 00:52:11.367 align:middle line:90% or amorphous structure. 00:52:11.367 --> 00:52:13.450 align:middle line:84% On the beach, you probably all have the experience 00:52:13.450 --> 00:52:16.770 align:middle line:84% when you are in the wet beach, if you step on the sand, 00:52:16.770 --> 00:52:18.810 align:middle line:84% there's actually a region of dry sand 00:52:18.810 --> 00:52:20.970 align:middle line:84% that actually appears around your foot. 00:52:20.970 --> 00:52:23.910 align:middle line:84% So what happens there, is when you actually stepping on it, 00:52:23.910 --> 00:52:27.610 align:middle line:84% you are trying to introduce shear deformation. 00:52:27.610 --> 00:52:29.890 align:middle line:84% When you introduce shear deformation, 00:52:29.890 --> 00:52:31.890 align:middle line:90% the volume must expand. 00:52:31.890 --> 00:52:36.330 align:middle line:84% So when you actually try to generate free volume, 00:52:36.330 --> 00:52:39.770 align:middle line:84% the sand essentially squeezes out the water in between 00:52:39.770 --> 00:52:42.770 align:middle line:84% to accommodate those kind of dilatational processes. 00:52:42.770 --> 00:52:45.690 align:middle line:84% And that's why the sand around your foot 00:52:45.690 --> 00:52:47.730 align:middle line:84% essentially becomes dry, basically because 00:52:47.730 --> 00:52:48.870 align:middle line:90% of the rotational process. 00:52:48.870 --> 00:52:50.730 align:middle line:84% The sand is trying to occupy more volume 00:52:50.730 --> 00:52:52.310 align:middle line:90% during this deformation process. 00:52:52.310 --> 00:52:58.750 align:middle line:90% 00:52:58.750 --> 00:53:00.310 align:middle line:84% So there's actually a lot of studies 00:53:00.310 --> 00:53:02.353 align:middle line:84% in the community of like colloidal solids, 00:53:02.353 --> 00:53:04.270 align:middle line:84% where they essentially use colloidal particles 00:53:04.270 --> 00:53:06.070 align:middle line:84% to essentially study the behavior 00:53:06.070 --> 00:53:07.810 align:middle line:90% of actual atomic solids. 00:53:07.810 --> 00:53:09.390 align:middle line:84% And many of this kind of behavior 00:53:09.390 --> 00:53:14.710 align:middle line:84% is quite analogous in those kind of systems as well. 00:53:14.710 --> 00:53:15.210 align:middle line:90% All right. 00:53:15.210 --> 00:53:18.310 align:middle line:84% So one immediate consequence of this, 00:53:18.310 --> 00:53:21.550 align:middle line:84% it has to do with the angle where 00:53:21.550 --> 00:53:24.890 align:middle line:84% a beam breaks during compressive or during tensile test. 00:53:24.890 --> 00:53:27.390 align:middle line:84% So if it's a crystalline metal, when 00:53:27.390 --> 00:53:30.010 align:middle line:84% you apply essentially a tensile test or compressive test, 00:53:30.010 --> 00:53:31.950 align:middle line:90% we know that they tend to break. 00:53:31.950 --> 00:53:34.390 align:middle line:84% The fracture surface, tends to form a 45 degree 00:53:34.390 --> 00:53:37.410 align:middle line:84% angle along the axis where you apply the uniaxial strain. 00:53:37.410 --> 00:53:40.830 align:middle line:84% The reason it's 45 degrees is because 45 degrees is where you 00:53:40.830 --> 00:53:42.790 align:middle line:90% have the maximum shear stress. 00:53:42.790 --> 00:53:44.790 align:middle line:84% So if the material failed by shear stress, 00:53:44.790 --> 00:53:50.030 align:middle line:84% the angle it breaks is at 45 degrees. 00:53:50.030 --> 00:53:52.070 align:middle line:84% For amorphous metal, on the other hand, 00:53:52.070 --> 00:53:56.590 align:middle line:84% this angle is not 45 degrees and it depends on the direction, 00:53:56.590 --> 00:54:00.870 align:middle line:84% whether you apply compressive or you or tensile strain. 00:54:00.870 --> 00:54:04.640 align:middle line:84% If it's tensile strain, then this angle 00:54:04.640 --> 00:54:06.538 align:middle line:84% tend to be larger than 45 degrees. 00:54:06.538 --> 00:54:08.080 align:middle line:84% So in other words, it tends to break, 00:54:08.080 --> 00:54:12.200 align:middle line:84% this fracture plane, tends to rotate. 00:54:12.200 --> 00:54:14.400 align:middle line:84% So it's surface normal is getting closer 00:54:14.400 --> 00:54:17.868 align:middle line:84% to the axis of the tensile stress. 00:54:17.868 --> 00:54:19.160 align:middle line:90% Now that makes intuitive sense. 00:54:19.160 --> 00:54:21.800 align:middle line:84% Because if you try to rotate so that x is more 00:54:21.800 --> 00:54:24.880 align:middle line:84% aligned with tensile strain, you have more tensile strain 00:54:24.880 --> 00:54:28.040 align:middle line:84% contribution at the surface where it fractures. 00:54:28.040 --> 00:54:30.160 align:middle line:84% We have mentioned that this tensile stress 00:54:30.160 --> 00:54:32.800 align:middle line:84% is going to promote the formation of free volume 00:54:32.800 --> 00:54:35.880 align:middle line:84% and therefore promote the plastic deformation. 00:54:35.880 --> 00:54:38.440 align:middle line:84% So rotating this plane towards this direction 00:54:38.440 --> 00:54:40.900 align:middle line:84% essentially facilitates that kind of process. 00:54:40.900 --> 00:54:44.560 align:middle line:84% It increases the contribution of tensile stress. 00:54:44.560 --> 00:54:47.640 align:middle line:84% Now vice versa, if it's compressive stress, 00:54:47.640 --> 00:54:51.240 align:middle line:84% compressive stress inhibits the rotational process 00:54:51.240 --> 00:54:52.840 align:middle line:90% of deformation. 00:54:52.840 --> 00:54:55.582 align:middle line:84% So in order to introduce fracture, 00:54:55.582 --> 00:54:57.290 align:middle line:84% the system will try to essentially rotate 00:54:57.290 --> 00:54:59.490 align:middle line:84% towards this direction, because the more you rotate 00:54:59.490 --> 00:55:02.250 align:middle line:84% towards this direction, the compressive stress contribution 00:55:02.250 --> 00:55:04.010 align:middle line:90% is getting smaller on the plane. 00:55:04.010 --> 00:55:06.170 align:middle line:84% It essentially it goes by like cosine. 00:55:06.170 --> 00:55:09.610 align:middle line:84% So if it's here, you have full contribution compressive stress. 00:55:09.610 --> 00:55:12.410 align:middle line:84% If you start to rotate, the compressive stress component 00:55:12.410 --> 00:55:14.310 align:middle line:84% on that plane, essentially decreases. 00:55:14.310 --> 00:55:19.130 align:middle line:90% 00:55:19.130 --> 00:55:21.800 align:middle line:90% Does that make sense? 00:55:21.800 --> 00:55:24.050 align:middle line:90% OK, we can look at it. 00:55:24.050 --> 00:55:26.610 align:middle line:84% AUDIENCE: I guess my first question is 00:55:26.610 --> 00:55:29.130 align:middle line:90% so you have a thing-- 00:55:29.130 --> 00:55:30.770 align:middle line:84% JUEJUN HU: Essentially you have a rod. 00:55:30.770 --> 00:55:32.690 align:middle line:84% You try to break it by, for example, applying 00:55:32.690 --> 00:55:35.690 align:middle line:90% compressive stress on two ends. 00:55:35.690 --> 00:55:40.088 align:middle line:84% So if it fails by shear stress, if it's a crystalline material, 00:55:40.088 --> 00:55:41.630 align:middle line:84% don't worry about amorphous material. 00:55:41.630 --> 00:55:43.950 align:middle line:84% Then what happens is it's going to break at 45 degrees. 00:55:43.950 --> 00:55:46.690 align:middle line:84% This [INAUDIBLE] is going to be 45 degrees. 00:55:46.690 --> 00:55:50.930 align:middle line:84% Because the 45 degrees is where you have maximum shear stress. 00:55:50.930 --> 00:55:52.350 align:middle line:90% That's mechanics. 00:55:52.350 --> 00:55:54.550 align:middle line:84% That's really not within the scope of this class. 00:55:54.550 --> 00:55:55.050 align:middle line:90% OK? 00:55:55.050 --> 00:55:57.780 align:middle line:84% Go back to talk to Professor Chiang. 00:55:57.780 --> 00:55:58.880 align:middle line:90% That's his problem. 00:55:58.880 --> 00:56:00.420 align:middle line:90% OK? 00:56:00.420 --> 00:56:02.560 align:middle line:84% So that's what happens to crystalline metal. 00:56:02.560 --> 00:56:04.500 align:middle line:84% Now for amorphous metal, as I said, 00:56:04.500 --> 00:56:06.860 align:middle line:84% you want to avoid compressive strain 00:56:06.860 --> 00:56:09.720 align:middle line:84% because during deformation you need to generate free volume. 00:56:09.720 --> 00:56:11.300 align:middle line:90% You need to expand. 00:56:11.300 --> 00:56:13.740 align:middle line:84% So you try to avoid this compressive stress. 00:56:13.740 --> 00:56:17.060 align:middle line:84% So if you have a plane that's vertical, for example, if it's 00:56:17.060 --> 00:56:19.380 align:middle line:84% vertical you have essentially full compressive stress 00:56:19.380 --> 00:56:21.885 align:middle line:90% exerting on it. 00:56:21.885 --> 00:56:23.260 align:middle line:84% On the other extreme, if you have 00:56:23.260 --> 00:56:25.220 align:middle line:84% a flat plane like this, horizontal, 00:56:25.220 --> 00:56:28.437 align:middle line:84% that's basically no compressive stress. 00:56:28.437 --> 00:56:30.020 align:middle line:84% Because compressive stress essentially 00:56:30.020 --> 00:56:33.420 align:middle line:84% goes by essentially cosine theta. 00:56:33.420 --> 00:56:35.540 align:middle line:84% It's basically the component that 00:56:35.540 --> 00:56:38.820 align:middle line:84% exerted on the plane of the compressive stress scales 00:56:38.820 --> 00:56:41.900 align:middle line:90% by cosine theta. 00:56:41.900 --> 00:56:44.120 align:middle line:84% So instead of breaking at 45 degrees, 00:56:44.120 --> 00:56:48.052 align:middle line:84% the system will try to break at this smaller angle here. 00:56:48.052 --> 00:56:50.260 align:middle line:84% At the smaller angle, you have a smaller contribution 00:56:50.260 --> 00:56:52.940 align:middle line:84% of compressive strength hitting the surface. 00:56:52.940 --> 00:56:57.040 align:middle line:84% So therefore, it will have less impedance 00:56:57.040 --> 00:57:00.000 align:middle line:90% on the plastic deformation. 00:57:00.000 --> 00:57:01.500 align:middle line:90% Yeah. 00:57:01.500 --> 00:57:02.440 align:middle line:90% And then vice versa. 00:57:02.440 --> 00:57:05.810 align:middle line:84% If it's tensile it will try to maximize that tensile stress 00:57:05.810 --> 00:57:07.060 align:middle line:90% that's exerted on the surface. 00:57:07.060 --> 00:57:09.600 align:middle line:90% That's why it rotates this way. 00:57:09.600 --> 00:57:11.920 align:middle line:84% So that's why you see this asymmetric behavior 00:57:11.920 --> 00:57:15.360 align:middle line:84% of the fracture angle with respect 00:57:15.360 --> 00:57:16.800 align:middle line:90% to the direction of the stress. 00:57:16.800 --> 00:57:21.534 align:middle line:90% 00:57:21.534 --> 00:57:24.160 align:middle line:84% And I just want to highlight that this is actually 00:57:24.160 --> 00:57:26.600 align:middle line:84% universally observed in pretty much all kind 00:57:26.600 --> 00:57:27.677 align:middle line:90% of metallic glasses. 00:57:27.677 --> 00:57:29.760 align:middle line:84% So in this table, I'm just summarizing essentially 00:57:29.760 --> 00:57:35.248 align:middle line:84% the fracture surface angle for tensile and compressive test. 00:57:35.248 --> 00:57:37.040 align:middle line:84% You can clearly see that for tensile tests, 00:57:37.040 --> 00:57:40.000 align:middle line:84% the [INAUDIBLE] becomes bigger at 45 degrees. 00:57:40.000 --> 00:57:42.320 align:middle line:84% Compressive test, they pretty much all become smaller 00:57:42.320 --> 00:57:45.550 align:middle line:90% than 45 degrees. 00:57:45.550 --> 00:57:47.840 align:middle line:84% Now another immediate consequence 00:57:47.840 --> 00:57:49.360 align:middle line:84% of this kind of asymmetric behavior 00:57:49.360 --> 00:57:52.930 align:middle line:84% between tensile compression is that the strength is also 00:57:52.930 --> 00:57:54.690 align:middle line:90% different for the material. 00:57:54.690 --> 00:57:58.450 align:middle line:84% We reflect with tension and with respect to compression. 00:57:58.450 --> 00:58:01.210 align:middle line:84% For compression, you tend to have a considerably higher 00:58:01.210 --> 00:58:03.737 align:middle line:90% strength, which makes sense. 00:58:03.737 --> 00:58:05.570 align:middle line:84% Compression, essentially, you are preventing 00:58:05.570 --> 00:58:07.110 align:middle line:90% the formation of free volume. 00:58:07.110 --> 00:58:09.650 align:middle line:84% Therefore, you're inhibiting this plastic flow. 00:58:09.650 --> 00:58:13.450 align:middle line:84% As a result, you should have higher strength. 00:58:13.450 --> 00:58:15.730 align:middle line:84% I want to mention that this behavior is not unique 00:58:15.730 --> 00:58:17.490 align:middle line:90% just to metallic glass. 00:58:17.490 --> 00:58:20.010 align:middle line:84% For inorganic network glasses like silica, 00:58:20.010 --> 00:58:22.570 align:middle line:84% you also see that they tend to be a lot stronger 00:58:22.570 --> 00:58:24.930 align:middle line:84% under compression compared to compression. 00:58:24.930 --> 00:58:27.985 align:middle line:84% But the microscopic mechanism is completely different. 00:58:27.985 --> 00:58:30.610 align:middle line:84% For metallic glass, it has to do with generation of free volume 00:58:30.610 --> 00:58:32.370 align:middle line:90% to the rotational process. 00:58:32.370 --> 00:58:35.650 align:middle line:84% For inorganic network glasses, the mechanism that fails 00:58:35.650 --> 00:58:38.250 align:middle line:84% is through essentially opening of the cracks. 00:58:38.250 --> 00:58:40.130 align:middle line:84% If you do compression, this usually 00:58:40.130 --> 00:58:42.130 align:middle line:90% inhibits the correct opening. 00:58:42.130 --> 00:58:44.550 align:middle line:84% Versus tensile, this promote correct opening. 00:58:44.550 --> 00:58:47.890 align:middle line:84% So that's why for inorganic network glasses like silica, 00:58:47.890 --> 00:58:51.250 align:middle line:84% it's also stronger under compression than under tension. 00:58:51.250 --> 00:58:54.060 align:middle line:84% But the microscopic mechanism is different. 00:58:54.060 --> 00:58:55.800 align:middle line:90% OK? 00:58:55.800 --> 00:58:58.100 align:middle line:84% So let me summarize what I talked about in this lecture 00:58:58.100 --> 00:58:59.180 align:middle line:90% here. 00:58:59.180 --> 00:59:01.660 align:middle line:84% We have essentially discussed about the structural model 00:59:01.660 --> 00:59:03.060 align:middle line:90% for metallic glasses. 00:59:03.060 --> 00:59:04.940 align:middle line:84% The key takeaway message for that 00:59:04.940 --> 00:59:08.140 align:middle line:84% is that this is a topological model. 00:59:08.140 --> 00:59:09.620 align:middle line:84% And the model essentially assumes 00:59:09.620 --> 00:59:12.380 align:middle line:84% that we want to achieve close packing of hard spheres. 00:59:12.380 --> 00:59:15.060 align:middle line:84% How do you engineer the radius as well as the atomic fraction 00:59:15.060 --> 00:59:16.660 align:middle line:84% to maximize packing density, which 00:59:16.660 --> 00:59:20.300 align:middle line:84% then allows you to lower the overall Gibbs free energy coming 00:59:20.300 --> 00:59:21.450 align:middle line:90% from the metallic bonds? 00:59:21.450 --> 00:59:23.200 align:middle line:84% That will stabilize the amorphous network. 00:59:23.200 --> 00:59:25.300 align:middle line:84% That's the whole assumption there. 00:59:25.300 --> 00:59:28.075 align:middle line:84% And then this kind of amorphous packing and the lack 00:59:28.075 --> 00:59:29.700 align:middle line:84% of structural defects, it will indicate 00:59:29.700 --> 00:59:32.440 align:middle line:84% many of the mechanical behavior in amorphous metal here, 00:59:32.440 --> 00:59:36.940 align:middle line:84% such as large elastic limit, lower elastic moduli, and we 00:59:36.940 --> 00:59:40.380 align:middle line:84% also discussed about the plastic deformation mechanisms 00:59:40.380 --> 00:59:44.260 align:middle line:84% and the different kind of plastic deformation regimes. 00:59:44.260 --> 00:59:48.380 align:middle line:84% I guess the key takeaway message is that the atomic scale 00:59:48.380 --> 00:59:50.460 align:middle line:84% deformation of bulk metallic glass 00:59:50.460 --> 00:59:52.880 align:middle line:84% takes place through this STZs, sheer transformation 00:59:52.880 --> 00:59:54.400 align:middle line:84% zones, and the sheer transformation 00:59:54.400 --> 00:59:56.040 align:middle line:84% zones they are not structural defects, 00:59:56.040 --> 00:59:57.707 align:middle line:84% but they can communicate with each other 00:59:57.707 --> 00:59:59.200 align:middle line:84% through stress, which is eventually 00:59:59.200 --> 01:00:03.160 align:middle line:84% lead to this kind of stress, shear stress localization. 01:00:03.160 --> 01:00:03.760 align:middle line:90% All right. 01:00:03.760 --> 01:00:07.260 align:middle line:84% So I'm going to stop here for this lecture. 01:00:07.260 --> 01:00:09.410 align:middle line:90% Any more questions? 01:00:09.410 --> 01:00:51.000 align:middle line:90%