1 00:00:00,030 --> 00:00:02,400 The following content is provided under a creative 2 00:00:02,400 --> 00:00:03,820 commons license. 3 00:00:03,820 --> 00:00:06,850 Your support will help MIT OpenCourseWare continue to 4 00:00:06,850 --> 00:00:10,520 offer high quality educational resources for free. 5 00:00:10,520 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:21,868 --> 00:00:22,620 SAL: Hi. 9 00:00:22,620 --> 00:00:23,250 I'm Sal. 10 00:00:23,250 --> 00:00:25,750 Today we're going to solve problem number two of test 11 00:00:25,750 --> 00:00:28,160 three of fall 2009. 12 00:00:28,160 --> 00:00:30,580 Now before you attempt the problem, there are certain 13 00:00:30,580 --> 00:00:33,870 things that you need to know to solve the problem. 14 00:00:33,870 --> 00:00:38,480 One is mechanical properties of metal and also the 15 00:00:38,480 --> 00:00:41,280 properties of amorphous metals, which are known as 16 00:00:41,280 --> 00:00:44,530 metallic glasses, and how to draw crystal 17 00:00:44,530 --> 00:00:46,430 structures given to you. 18 00:00:46,430 --> 00:00:48,590 The problem reads as follows-- 19 00:00:48,590 --> 00:00:51,760 for a given alloy composition, explain why the yield strength 20 00:00:51,760 --> 00:00:54,750 of the amorphous form, the metallic glass, is greater 21 00:00:54,750 --> 00:00:56,880 than that of the crystal form. 22 00:00:56,880 --> 00:00:59,690 Now in order to answer this question, you want to start 23 00:00:59,690 --> 00:01:03,380 thinking about the mechanical properties that these two raw 24 00:01:03,380 --> 00:01:16,320 materials have. So if I look at a metal, I know that the 25 00:01:16,320 --> 00:01:23,280 way a metal deforms before it reaches classic deformation-- 26 00:01:23,280 --> 00:01:27,960 it deforms the planes sliding past one another-- 27 00:01:27,960 --> 00:01:29,260 so it's known as slip. 28 00:01:29,260 --> 00:01:33,000 So I know that metals-- 29 00:01:33,000 --> 00:01:45,080 they form via slip and slip is facilitated by dislocations 30 00:01:45,080 --> 00:01:47,940 and you should know what a dislocation is by now, which 31 00:01:47,940 --> 00:01:50,650 is just a line imperfection in your crystal. 32 00:01:50,650 --> 00:02:01,640 So slip is facilitated by dislocations. 33 00:02:06,130 --> 00:02:11,530 So I know that my metal has planes that are arranged 34 00:02:11,530 --> 00:02:16,370 because it's a nice crystallographic structure-- 35 00:02:16,370 --> 00:02:17,820 and that the slip-- 36 00:02:17,820 --> 00:02:23,070 when it undergoes deformation, that this is actually assisted 37 00:02:23,070 --> 00:02:25,060 by dislocation. 38 00:02:25,060 --> 00:02:29,880 So having dislocations helps to form our metal. 39 00:02:29,880 --> 00:02:33,420 So now I want to start thinking about what a metallic 40 00:02:33,420 --> 00:02:34,830 glass has-- so the amorphous form. 41 00:02:34,830 --> 00:02:38,790 So if I look at the metallic glass-- 42 00:02:38,790 --> 00:02:41,840 and all I'm doing here is comparing the basic properties 43 00:02:41,840 --> 00:02:42,970 between the two-- 44 00:02:42,970 --> 00:02:49,890 so this is going to get me metallic glass. 45 00:02:49,890 --> 00:02:54,670 I know that for metallic glass, there's 46 00:02:54,670 --> 00:02:59,670 no long range order. 47 00:03:02,220 --> 00:03:05,450 So the fact that there's no long range order means that 48 00:03:05,450 --> 00:03:12,340 these metallic glasses don't form a perfect crystal array. 49 00:03:12,340 --> 00:03:18,490 And that lack leads to metallic glasses having no 50 00:03:18,490 --> 00:03:19,740 dislocations. 51 00:03:23,770 --> 00:03:29,380 So if a metal slip is facilitated by dislocations 52 00:03:29,380 --> 00:03:33,700 and if a metallic glass doesn't have dislocations, 53 00:03:33,700 --> 00:03:37,780 then I would assume, just by comparison between the two, 54 00:03:37,780 --> 00:03:44,270 that the threshold for one of the materials to yield would 55 00:03:44,270 --> 00:03:46,720 be due to the fact that-- 56 00:03:46,720 --> 00:03:47,990 whether or not I have dislocations. 57 00:03:47,990 --> 00:03:53,420 So with this argument, I would say that the metallic glass 58 00:03:53,420 --> 00:03:58,350 has a higher yield strength than my metal 59 00:03:58,350 --> 00:04:01,220 because of this property. 60 00:04:01,220 --> 00:04:02,010 So that-- 61 00:04:02,010 --> 00:04:05,610 if you did that-- if you went ahead and wrote all that out 62 00:04:05,610 --> 00:04:09,340 for your answer in part A, you should be able to get most of 63 00:04:09,340 --> 00:04:11,160 the points for this problem. 64 00:04:11,160 --> 00:04:14,170 Now part B-- 65 00:04:14,170 --> 00:04:17,980 it asks, on each of the following separate drawings of 66 00:04:17,980 --> 00:04:20,240 one face of an FCC unit cell-- 67 00:04:20,240 --> 00:04:23,890 FCC stands for face centered cubic-- 68 00:04:23,890 --> 00:04:27,560 indicate one of each of the following. 69 00:04:27,560 --> 00:04:31,650 So now we're going to move on to part B-- 70 00:04:31,650 --> 00:04:32,800 and part B wants-- 71 00:04:32,800 --> 00:04:34,540 there's three scenarios. 72 00:04:34,540 --> 00:04:35,600 One-- 73 00:04:35,600 --> 00:04:41,350 it wants us to indicate on a face of a crystal, a 74 00:04:41,350 --> 00:04:44,150 substitutional impurity-- 75 00:04:44,150 --> 00:04:55,090 so substitutional impurity. 76 00:04:55,090 --> 00:04:57,120 So if I look at-- 77 00:04:57,120 --> 00:05:00,525 if I draw a face-- 78 00:05:13,550 --> 00:05:14,180 here. 79 00:05:14,180 --> 00:05:15,690 I can-- 80 00:05:15,690 --> 00:05:21,600 so to find out what the definition of a substitutional 81 00:05:21,600 --> 00:05:25,250 impurity is, I know that it's not going to be anything that 82 00:05:25,250 --> 00:05:29,140 can be just embedded in between atoms-- 83 00:05:29,140 --> 00:05:30,410 like an interstitial. 84 00:05:30,410 --> 00:05:32,630 I know that it's going to be a substitutional impurity. 85 00:05:32,630 --> 00:05:36,780 So if this is one of the faces of your crystal-- 86 00:05:36,780 --> 00:05:39,480 and it's FCC, which is face centered, from the face-- the 87 00:05:39,480 --> 00:05:45,230 face is centered on the center of an atom on your face. 88 00:05:45,230 --> 00:05:52,150 Then I would say that if I substitute this out for a 89 00:05:52,150 --> 00:05:59,600 different atom of type B compared to these atoms, then 90 00:05:59,600 --> 00:06:02,910 that's a substitutional impurity because that atom is 91 00:06:02,910 --> 00:06:03,930 not the same as the other. 92 00:06:03,930 --> 00:06:09,390 It's like having silver and gold, for example, in 93 00:06:09,390 --> 00:06:10,610 composition. 94 00:06:10,610 --> 00:06:14,135 And then it also asks for the second part. 95 00:06:14,135 --> 00:06:16,300 So that's number one. 96 00:06:16,300 --> 00:06:24,410 For number two, it wants us to demonstrate a vacancy. 97 00:06:24,410 --> 00:06:30,520 Now a vacancy is simply an atom missing from a normal 98 00:06:30,520 --> 00:06:33,160 lattice site on your crystal array. 99 00:06:33,160 --> 00:06:47,240 So if I draw again another face, then I can leave that 100 00:06:47,240 --> 00:06:50,790 blank and I can go ahead and I can point and I can say that 101 00:06:50,790 --> 00:06:52,350 the vacancy is actually-- 102 00:06:52,350 --> 00:06:53,165 sits right here. 103 00:06:53,165 --> 00:06:54,506 So this is my vacancy. 104 00:06:57,220 --> 00:06:58,540 There's no atom that's there. 105 00:06:58,540 --> 00:06:59,860 It moved out of its place. 106 00:06:59,860 --> 00:07:05,170 So that's another defect that we put in there. 107 00:07:05,170 --> 00:07:11,260 And for three, it asks, an interstitial impurity. 108 00:07:20,880 --> 00:07:24,890 So what's interstitial? 109 00:07:24,890 --> 00:07:31,610 Well, an atom that can fit in between two atoms that are 110 00:07:31,610 --> 00:07:33,750 different than the one that fits. 111 00:07:33,750 --> 00:07:44,980 So if I draw again an FCC face, I notice that there's 112 00:07:44,980 --> 00:07:49,590 certain spots where an atom of a different composition can 113 00:07:49,590 --> 00:07:56,780 fit and I can go ahead and I can just put a-- 114 00:07:56,780 --> 00:08:00,060 that's an atom of different composition and that can very 115 00:08:00,060 --> 00:08:02,070 simply be your interstitial. 116 00:08:02,070 --> 00:08:10,010 So that's your interstitial impurity. 117 00:08:10,010 --> 00:08:14,360 So knowing the definitions, you're able to answer this 118 00:08:14,360 --> 00:08:15,150 problem very simply. 119 00:08:15,150 --> 00:08:18,130 There was no math involved in this and all you needed to 120 00:08:18,130 --> 00:08:21,170 know was knowledge of our mechanical properties of 121 00:08:21,170 --> 00:08:23,800 metals versus amorphous metals, which are known as 122 00:08:23,800 --> 00:08:25,080 metallic glasses. 123 00:08:25,080 --> 00:08:30,340 And knowing that information, you're able to answer a 124 00:08:30,340 --> 00:08:34,090 question like this, which is pretty simple after you finish 125 00:08:34,090 --> 00:08:35,360 and you think about it. 126 00:08:35,360 --> 00:08:37,310 And if you didn't know what FCC was-- 127 00:08:37,310 --> 00:08:40,310 which stands for face centered cubic, you could have probably 128 00:08:40,310 --> 00:08:42,130 lost a lot of points on this problem. 129 00:08:42,130 --> 00:08:44,740 But if you know that, if you know how to draw it, then 130 00:08:44,740 --> 00:08:47,820 you're good to go.