1 00:00:09,802 --> 00:00:11,260 ALEXIS GERVAIX: Hello everyone, and 2 00:00:11,260 --> 00:00:13,500 welcome to this little video presenting 3 00:00:13,500 --> 00:00:15,310 you my project on Mathematica. 4 00:00:15,310 --> 00:00:16,090 My name is Alex. 5 00:00:16,090 --> 00:00:18,610 And I'm currently studying material science 6 00:00:18,610 --> 00:00:20,860 in EPFL in Switzerland. 7 00:00:20,860 --> 00:00:23,200 And we had this personal challenge 8 00:00:23,200 --> 00:00:26,050 to do something you wanted with Mathematica. 9 00:00:26,050 --> 00:00:29,200 So I took an interest into crystallography, 10 00:00:29,200 --> 00:00:33,430 because this is a quite essential field of material 11 00:00:33,430 --> 00:00:35,560 science. 12 00:00:35,560 --> 00:00:37,160 Well, actually, it was on the request 13 00:00:37,160 --> 00:00:42,910 of my girlfriend, who has quite trouble to see things in 3D 14 00:00:42,910 --> 00:00:44,380 that I did this. 15 00:00:44,380 --> 00:00:46,930 And my idea was to create a tool that 16 00:00:46,930 --> 00:00:49,720 could be used by anyone that doesn't especially 17 00:00:49,720 --> 00:00:54,070 know about Mathematica, and that, without coding anything, 18 00:00:54,070 --> 00:00:57,710 he could create a couple of structures, 19 00:00:57,710 --> 00:00:59,960 have a look at the-- 20 00:00:59,960 --> 00:01:04,000 have an interactive part with it, 21 00:01:04,000 --> 00:01:09,090 and choose the atom, et cetera, and visualize more easily 22 00:01:09,090 --> 00:01:11,200 these structures. 23 00:01:11,200 --> 00:01:16,790 So let's have a look first at a bit of theory, 24 00:01:16,790 --> 00:01:18,490 and first with the Bravais lattice. 25 00:01:18,490 --> 00:01:21,700 So Bravais lattice is one of the fundamentals 26 00:01:21,700 --> 00:01:23,820 of crystallography. 27 00:01:23,820 --> 00:01:27,280 It defines the different structure 28 00:01:27,280 --> 00:01:31,130 in which the atom can organize themselves. 29 00:01:31,130 --> 00:01:35,860 So there is 14 of them, where we will 30 00:01:35,860 --> 00:01:40,310 vary the axes, the primitive cells, which are A, B, 31 00:01:40,310 --> 00:01:43,330 and C, the different angle. 32 00:01:43,330 --> 00:01:46,120 And these are the different axes. 33 00:01:46,120 --> 00:01:49,340 And these axes can change their length, all the angle, 34 00:01:49,340 --> 00:01:51,040 as you can see here. 35 00:01:51,040 --> 00:01:54,130 And there is also a place where you 36 00:01:54,130 --> 00:01:55,835 will have more atoms in the middle, 37 00:01:55,835 --> 00:01:59,830 or in the same-- in the faces. 38 00:01:59,830 --> 00:02:03,800 So in my program, I will focus on the simple cubic, 39 00:02:03,800 --> 00:02:07,100 the face-centered cubic, and the body-centered cubic, which 40 00:02:07,100 --> 00:02:12,560 are some of the most, I wouldn't say basic, but some of the ones 41 00:02:12,560 --> 00:02:16,310 you will encounter more often in solids. 42 00:02:16,310 --> 00:02:19,160 There is also [INAUDIBLE] compact 43 00:02:19,160 --> 00:02:24,660 that is quite often represented, but it was quite difficult 44 00:02:24,660 --> 00:02:25,160 implement. 45 00:02:25,160 --> 00:02:27,450 So it could be nice to do it in the future, 46 00:02:27,450 --> 00:02:29,892 but for now, it's not there. 47 00:02:29,892 --> 00:02:34,370 And I also had a look at interstitial sites. 48 00:02:34,370 --> 00:02:38,840 So interstitial sites are atoms that 49 00:02:38,840 --> 00:02:45,910 would come to put themselves in some void area of your lattice. 50 00:02:45,910 --> 00:02:52,090 So here is the FCC lattice with an atom on each summit 51 00:02:52,090 --> 00:02:54,760 and one in the middle of the faces. 52 00:02:54,760 --> 00:03:00,030 And we have in pink an octahedral sets. 53 00:03:00,030 --> 00:03:04,640 So it's an octahedron of void place. 54 00:03:04,640 --> 00:03:08,590 And in the center, you have then the possibility to put an atom. 55 00:03:08,590 --> 00:03:10,210 So this is interesting when you are 56 00:03:10,210 --> 00:03:13,090 looking for alloys in metallurgy, 57 00:03:13,090 --> 00:03:16,630 for example, because it gives a lot of possibilities 58 00:03:16,630 --> 00:03:21,330 to put new atoms in your metal. 59 00:03:21,330 --> 00:03:25,150 And so there are two categories, as I mentioned, 60 00:03:25,150 --> 00:03:29,420 the octahedron and the tetrahedron. 61 00:03:29,420 --> 00:03:31,630 And for each of the three structures 62 00:03:31,630 --> 00:03:37,918 that I have been picking, there is a different number 63 00:03:37,918 --> 00:03:40,850 of octahedron. 64 00:03:40,850 --> 00:03:43,490 For example, for cubic simple, there is only one, 65 00:03:43,490 --> 00:03:45,550 so in the middle. 66 00:03:45,550 --> 00:03:48,350 But for BCC, as we can see here, there 67 00:03:48,350 --> 00:03:54,860 is a lot of tetrahedraces, which are here on the faces. 68 00:03:54,860 --> 00:03:57,540 So yeah, well, this is a 2D graph. 69 00:03:57,540 --> 00:04:02,430 And it's not always easy to really see how things are done. 70 00:04:02,430 --> 00:04:04,880 And I remember having a really hard time 71 00:04:04,880 --> 00:04:08,750 to find where the tetrahedron sites were for the BBC. 72 00:04:08,750 --> 00:04:11,740 So this is why I really wanted also 73 00:04:11,740 --> 00:04:17,490 to put in my 3D graph the interstitials. 74 00:04:17,490 --> 00:04:20,450 And I hope it will be useful for you as well 75 00:04:20,450 --> 00:04:22,550 if you use my program. 76 00:04:22,550 --> 00:04:27,500 So yeah, so about crystallography in general, 77 00:04:27,500 --> 00:04:32,000 this is a field that gives you a lot of information 78 00:04:32,000 --> 00:04:37,160 about the properties of matter, because when you understand how 79 00:04:37,160 --> 00:04:40,010 the atoms organize themselves, you 80 00:04:40,010 --> 00:04:44,860 can start to understand things like metal transition. 81 00:04:44,860 --> 00:04:47,150 And a more advanced thing, you can 82 00:04:47,150 --> 00:04:52,700 start to look at the growth of monocrystals. 83 00:04:52,700 --> 00:04:55,460 For example, if you're working in semiconductors 84 00:04:55,460 --> 00:04:57,290 and you're trying to do nanowires, 85 00:04:57,290 --> 00:05:01,530 then you need to understand how the-- 86 00:05:01,530 --> 00:05:04,330 what are the different plane, how the atoms organize 87 00:05:04,330 --> 00:05:06,570 in plane, themselves. 88 00:05:06,570 --> 00:05:09,170 And when you're working on aircraft engineering, 89 00:05:09,170 --> 00:05:11,530 you have the turbine that you need to do 90 00:05:11,530 --> 00:05:13,550 in a monocrystal of nickel. 91 00:05:13,550 --> 00:05:15,080 This is very important. 92 00:05:15,080 --> 00:05:16,970 So yeah, there is a lot of application 93 00:05:16,970 --> 00:05:18,620 that you can have from this subject. 94 00:05:18,620 --> 00:05:22,050 And I thought it was an interesting one to observe. 95 00:05:22,050 --> 00:05:23,550 So let's have a look at the program. 96 00:05:23,550 --> 00:05:26,480 So this is some reminder about how it works. 97 00:05:26,480 --> 00:05:28,890 And this is the interactive part. 98 00:05:28,890 --> 00:05:31,850 So my program consists of two cells 99 00:05:31,850 --> 00:05:36,650 that you simply have to click on them and press Shift, Enter. 100 00:05:36,650 --> 00:05:38,900 The first parts are the function that 101 00:05:38,900 --> 00:05:42,590 will define the position of the atoms. 102 00:05:42,590 --> 00:05:47,120 And the second part is the interactive tool, 103 00:05:47,120 --> 00:05:49,910 which we call Manipulate Mathematica, 104 00:05:49,910 --> 00:05:52,110 and gives a lot of possibilities. 105 00:05:52,110 --> 00:05:55,790 So you will see, this is a huge cell with a lot of code. 106 00:05:55,790 --> 00:05:58,320 I know that Mr. Carter doesn't like it at all. 107 00:05:58,320 --> 00:06:02,990 But I had to keep it like that to have my Manipulate. 108 00:06:02,990 --> 00:06:04,520 And let's simply run it. 109 00:06:07,642 --> 00:06:09,410 So it takes a bit of time. 110 00:06:09,410 --> 00:06:11,370 And here we have it. 111 00:06:11,370 --> 00:06:13,290 So this is the panel-- 112 00:06:13,290 --> 00:06:16,580 maybe we should put that away-- 113 00:06:16,580 --> 00:06:21,290 where you have, on the left, the controls, on the right, 114 00:06:21,290 --> 00:06:29,780 a display with a panel of the periodic table, the 3D graphic, 115 00:06:29,780 --> 00:06:34,200 and a little graph that helps you to visualize more easily 116 00:06:34,200 --> 00:06:36,920 the parameters of the lattice. 117 00:06:36,920 --> 00:06:39,625 That helps you when you try to calculate the densities 118 00:06:39,625 --> 00:06:42,590 of these particular structures. 119 00:06:42,590 --> 00:06:45,200 So as you see, we can move it. 120 00:06:45,200 --> 00:06:47,920 There is different type of atom here. 121 00:06:47,920 --> 00:06:54,367 I on purpose put NaCl, which is salt. 122 00:06:54,367 --> 00:06:56,450 And now let's have a look at all the possibilities 123 00:06:56,450 --> 00:06:57,680 we have with this program. 124 00:06:57,680 --> 00:07:03,489 Because the thing is that I want you, when you have a-- 125 00:07:03,489 --> 00:07:05,030 you know already a structure, and you 126 00:07:05,030 --> 00:07:08,590 want to know what it looks like, to be able to create it. 127 00:07:11,870 --> 00:07:15,460 Well, first, let's look at the different options. 128 00:07:15,460 --> 00:07:20,450 So we have these three structures, the BCC, 129 00:07:20,450 --> 00:07:22,640 the cubic simple, and the FCC. 130 00:07:22,640 --> 00:07:24,740 You can change the atom size. 131 00:07:24,740 --> 00:07:25,880 Here you can display-- 132 00:07:25,880 --> 00:07:30,710 you can choose if there is the [INAUDIBLE],, and here, 133 00:07:30,710 --> 00:07:32,630 the choice of element, because I wanted 134 00:07:32,630 --> 00:07:37,550 that you can choose what type of atom you put in your cell. 135 00:07:37,550 --> 00:07:39,050 This is why there is this panel. 136 00:07:39,050 --> 00:07:46,290 So I divided my graph into four parts. 137 00:07:46,290 --> 00:07:51,650 Basically, atom one and atom two are the atoms on the edges. 138 00:07:51,650 --> 00:07:54,560 And in the center are a different division 139 00:07:54,560 --> 00:07:59,450 that helps you to create more complex cells. 140 00:07:59,450 --> 00:08:01,020 So let's have a try. 141 00:08:01,020 --> 00:08:03,580 I would like a body-centered cubic. 142 00:08:03,580 --> 00:08:08,200 And I would like an alloy which is iron and aluminum. 143 00:08:08,200 --> 00:08:12,080 That structures itself into a BCC. 144 00:08:12,080 --> 00:08:18,151 So I will put an atom two there, aluminum. 145 00:08:18,151 --> 00:08:20,860 And here you will see it changing. 146 00:08:20,860 --> 00:08:25,680 So this is normal, because I asked the software 147 00:08:25,680 --> 00:08:30,210 to only update this part when I click on the panel [INAUDIBLE].. 148 00:08:30,210 --> 00:08:32,559 It can be improved, this part, but it 149 00:08:32,559 --> 00:08:35,184 was to have stability during the initialization 150 00:08:35,184 --> 00:08:39,690 of the Manipulate. 151 00:08:39,690 --> 00:08:43,059 And here I have a way to initialize 152 00:08:43,059 --> 00:08:46,870 my body-centered cubic with the iron atom 153 00:08:46,870 --> 00:08:52,390 on the edges and my aluminum atom at the center. 154 00:08:52,390 --> 00:08:55,690 You can, of course, change the atom size. 155 00:08:55,690 --> 00:08:58,930 You can click on the same atom, and this way, 156 00:08:58,930 --> 00:09:02,490 get a little bit bigger. 157 00:09:02,490 --> 00:09:07,130 OK, so there is also FCC that you can do. 158 00:09:07,130 --> 00:09:11,010 There is one alloy that works with this, 159 00:09:11,010 --> 00:09:13,120 which is, if I remember well-- 160 00:09:13,120 --> 00:09:15,342 I wrote it somewhere-- 161 00:09:15,342 --> 00:09:16,900 aluminum and nickel. 162 00:09:16,900 --> 00:09:21,440 So let's circle the aluminum and this nickel here. 163 00:09:26,786 --> 00:09:28,590 And that should be [INAUDIBLE]---- yeah. 164 00:09:28,590 --> 00:09:31,650 And here is the FCC. 165 00:09:31,650 --> 00:09:33,330 And here you can turn and have a look. 166 00:09:33,330 --> 00:09:35,820 You see that there is nothing in the middle. 167 00:09:35,820 --> 00:09:39,450 And for me, it helps me a lot to visualize it like that. 168 00:09:39,450 --> 00:09:46,050 There is also the adapted density calculation graph, 169 00:09:46,050 --> 00:09:52,220 where you see that this diagonal in the middle will-- 170 00:09:52,220 --> 00:09:58,500 no, in the face here, will help you calculate the density. 171 00:09:58,500 --> 00:10:05,450 And you know that this line is a square too of the lattice 172 00:10:05,450 --> 00:10:06,800 parameter. 173 00:10:06,800 --> 00:10:09,150 Now let's have a look about the interstitial 174 00:10:09,150 --> 00:10:13,245 that I took some time to put-- 175 00:10:13,245 --> 00:10:14,990 add on my graph. 176 00:10:14,990 --> 00:10:19,881 And I would like to show you a little example that I had-- 177 00:10:19,881 --> 00:10:26,550 that I forwarded, which is this slide about the magnesium 178 00:10:26,550 --> 00:10:29,370 lead, intermetallic Mg2-Pb. 179 00:10:29,370 --> 00:10:32,070 And they said that this should look like this. 180 00:10:32,070 --> 00:10:35,060 And they are giving us that, so the anion, 181 00:10:35,060 --> 00:10:40,140 the magnesium are on the FCC site in blue. 182 00:10:40,140 --> 00:10:43,590 And the lead is on the octahedral site. 183 00:10:43,590 --> 00:10:47,110 So let's try to put it in my program. 184 00:10:47,110 --> 00:10:48,930 So first, I will say, yes, I would 185 00:10:48,930 --> 00:10:51,500 like to have octahedron interstitial. 186 00:10:51,500 --> 00:10:53,800 I will stay in FCC. 187 00:10:53,800 --> 00:11:02,770 I would put the same atom here, magnesium, and here. 188 00:11:05,770 --> 00:11:09,240 And it's a bit long to update. 189 00:11:09,240 --> 00:11:12,650 My computer is having a hard time. 190 00:11:12,650 --> 00:11:15,960 All right, so we see that it doesn't look like at all 191 00:11:15,960 --> 00:11:18,300 on what's [INAUDIBLE] on here. 192 00:11:18,300 --> 00:11:20,980 This is a bit-- 193 00:11:20,980 --> 00:11:21,480 all right. 194 00:11:21,480 --> 00:11:25,660 OK, and here is where I see that this guy did a mistake here 195 00:11:25,660 --> 00:11:29,100 by putting octahedron in this place, 196 00:11:29,100 --> 00:11:30,870 because this place is tetrahedron, 197 00:11:30,870 --> 00:11:34,830 the other type of interstitial. 198 00:11:34,830 --> 00:11:38,116 So we will remove the octahedral, 199 00:11:38,116 --> 00:11:41,172 put the tetrahedral [INAUDIBLE]. 200 00:11:44,010 --> 00:11:45,480 And here we go. 201 00:11:48,930 --> 00:11:51,320 [INAUDIBLE] 202 00:11:51,320 --> 00:11:56,285 OK-- no, no, OK, I should do things properly. 203 00:11:56,285 --> 00:12:00,564 Interstitial tetrahedral and [INAUDIBLE]---- 204 00:12:03,840 --> 00:12:04,740 now it's better. 205 00:12:04,740 --> 00:12:08,220 And it looks like what we have here. 206 00:12:08,220 --> 00:12:10,550 And I find it better to look like that, 207 00:12:10,550 --> 00:12:16,061 because now that we can change a little bit the size, 208 00:12:16,061 --> 00:12:18,100 it is clear now that there is nothing 209 00:12:18,100 --> 00:12:20,230 in the middle, which, it's not that clear when 210 00:12:20,230 --> 00:12:21,730 you look at this thing. 211 00:12:21,730 --> 00:12:25,570 So yeah, I found that it was one nice application 212 00:12:25,570 --> 00:12:30,740 of this little program, to visualize it more easily. 213 00:12:30,740 --> 00:12:33,530 So here is for now. 214 00:12:33,530 --> 00:12:36,210 I hope you enjoyed this little presentation, 215 00:12:36,210 --> 00:12:38,980 and that it will help you by using this program 216 00:12:38,980 --> 00:12:44,690 to see better in 3D your crystalline structure, 217 00:12:44,690 --> 00:12:47,470 and that will help you to have a better 218 00:12:47,470 --> 00:12:51,610 idea of what you're doing with your crystallography courses. 219 00:12:51,610 --> 00:12:53,880 So thank you for watching.