1 00:00:00,500 --> 00:00:02,380 [SQUEAKING] 2 00:00:02,380 --> 00:00:04,284 [RUSTLING] 3 00:00:04,284 --> 00:00:05,710 [CLICKING] 4 00:00:05,710 --> 00:00:07,210 PROFESSOR: In this goodie bag, we'll 5 00:00:07,210 --> 00:00:09,250 be exploring atomic packing and solids 6 00:00:09,250 --> 00:00:11,197 through the cubic Bravais lattices. 7 00:00:11,197 --> 00:00:13,780 We'll make three ball-and-stick models of different cubic unit 8 00:00:13,780 --> 00:00:14,500 cells. 9 00:00:14,500 --> 00:00:17,860 For this, you will need 31 balls and 44 sticks-- 10 00:00:17,860 --> 00:00:21,970 24 for FCC, 12 for SC, and 8 for BCC. 11 00:00:21,970 --> 00:00:24,610 If you don't have a fancy crystal modeling kit like this, 12 00:00:24,610 --> 00:00:26,837 any ball-and-stick equivalents will work. 13 00:00:26,837 --> 00:00:28,420 A delicious alternative would be using 14 00:00:28,420 --> 00:00:30,550 toothpicks and marshmallows. 15 00:00:30,550 --> 00:00:32,049 The objective of the goodie bag is 16 00:00:32,049 --> 00:00:33,550 to explore the different structures 17 00:00:33,550 --> 00:00:35,290 of crystalline materials. 18 00:00:35,290 --> 00:00:37,210 As you build the models, consider how many 19 00:00:37,210 --> 00:00:41,140 nearest neighbors an atom has in an SC, a BCC, and an FCC 20 00:00:41,140 --> 00:00:41,770 crystal. 21 00:00:41,770 --> 00:00:44,470 So now we're going to construct our Bravais lattices. 22 00:00:44,470 --> 00:00:46,750 We'll start with simple cubing. 23 00:00:46,750 --> 00:00:49,870 Begin by taking 8 balls and connecting them with 24 00:00:49,870 --> 00:00:54,820 sticks such that each ball sits at the corner of a cube. 25 00:00:54,820 --> 00:00:56,560 Then for body-centered cubic, we're 26 00:00:56,560 --> 00:00:59,800 going to start with a single ball in the center of a cube 27 00:00:59,800 --> 00:01:02,850 and connect to 8 other balls at the corners with sticks. 28 00:01:06,130 --> 00:01:07,700 For face-centered cubic, it's going 29 00:01:07,700 --> 00:01:09,560 to be a little more involved. 30 00:01:09,560 --> 00:01:13,300 We'll start with the corner of a cube and form tetrahedra 31 00:01:13,300 --> 00:01:16,790 to other balls, which themselves will form tetrahedra 32 00:01:16,790 --> 00:01:19,100 to another corner of a cube. 33 00:01:19,100 --> 00:01:20,780 If we iterate through this process, 34 00:01:20,780 --> 00:01:24,230 we eventually end up with a full face-centered cubic lattice. 35 00:01:27,440 --> 00:01:29,630 We've now constructed three ball-and-stick models 36 00:01:29,630 --> 00:01:31,610 of cubic Bravais lattices. 37 00:01:31,610 --> 00:01:33,320 The simple cubic lattice has atoms 38 00:01:33,320 --> 00:01:36,290 at each of the 8 corners of the unit cell. 39 00:01:36,290 --> 00:01:38,750 The body-centered cubic lattice has an additional atom 40 00:01:38,750 --> 00:01:41,320 in the body center of the unit cell. 41 00:01:41,320 --> 00:01:43,190 And the face-centered cubic lattice 42 00:01:43,190 --> 00:01:45,710 has an additional atom in each of the 6 face 43 00:01:45,710 --> 00:01:48,260 centers of the unit cell. 44 00:01:48,260 --> 00:01:51,080 Each of these lattices has a different coordination number. 45 00:01:51,080 --> 00:01:53,870 That is, an atom in each lattice has a different number 46 00:01:53,870 --> 00:01:55,910 of nearest neighbors. 47 00:01:55,910 --> 00:01:59,600 If we imagine these atoms as hard spheres 48 00:01:59,600 --> 00:02:01,737 rather than this ball-and-stick model, 49 00:02:01,737 --> 00:02:03,320 we can see that each lattice will also 50 00:02:03,320 --> 00:02:05,840 have a different atomic packing factor. 51 00:02:05,840 --> 00:02:10,430 That is, each lattice will have a different volume of space 52 00:02:10,430 --> 00:02:12,470 occupied in the unit cell. 53 00:02:12,470 --> 00:02:16,010 In general, the coordination number of a lattice 54 00:02:16,010 --> 00:02:18,500 correlates with atomic packing factor, which itself 55 00:02:18,500 --> 00:02:20,150 correlates with stability. 56 00:02:20,150 --> 00:02:23,390 That's why we don't often find simple cubic metallic solids 57 00:02:23,390 --> 00:02:25,060 in nature.