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PROFESSOR: OK, OK,
settle down.

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00:00:24,170 --> 00:00:27,410
It's time to start learning.

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00:00:27,410 --> 00:00:28,210
One announcement.

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00:00:28,210 --> 00:00:31,570
Tomorrow we'll have
the weekly quiz.

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00:00:31,570 --> 00:00:35,530
In lieu of the Tuesday
celebration, we're going to

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00:00:35,530 --> 00:00:39,940
move to Thursday, since the
holiday moved everything,

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00:00:39,940 --> 00:00:41,260
compressed the week.

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00:00:41,260 --> 00:00:44,510
So last day, we were talking
about doping of

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00:00:44,510 --> 00:00:48,790
semiconductors, and I want
to finish up that unit.

17
00:00:48,790 --> 00:00:52,370
Just to refresh your memory,
we looked at how we could

18
00:00:52,370 --> 00:00:55,850
change the behavior of the
semiconductor by introducing

19
00:00:55,850 --> 00:01:00,000
impurity atoms. And when the
behavior of the semiconductor

20
00:01:00,000 --> 00:01:04,300
is dominated by the impurity
atoms, we term

21
00:01:04,300 --> 00:01:05,750
that behavior extrinsic.

22
00:01:05,750 --> 00:01:08,080
In other words, it's not the
behavior of silicon itself,

23
00:01:08,080 --> 00:01:10,880
but it's the behavior of silicon
as determined by the

24
00:01:10,880 --> 00:01:13,750
presence of some dopant atom.

25
00:01:13,750 --> 00:01:16,880
And we looked at the special
case of doping with a

26
00:01:16,880 --> 00:01:18,530
supervalent impurity.

27
00:01:18,530 --> 00:01:21,630
And here's the energy level
diagram for that situation,

28
00:01:21,630 --> 00:01:24,590
where we've got the valence
band down here, we've got

29
00:01:24,590 --> 00:01:27,720
conduction band up here,
separated by an energy gap.

30
00:01:27,720 --> 00:01:31,370
That's all characteristic of
plain vanilla silicon.

31
00:01:31,370 --> 00:01:36,170
But then when we dope with the
supervalent impurity, there is

32
00:01:36,170 --> 00:01:37,800
an extra electron.

33
00:01:37,800 --> 00:01:42,900
And that is put into a donor
level that lies just a tiny

34
00:01:42,900 --> 00:01:45,850
bit below the bottom of
the conduction band.

35
00:01:45,850 --> 00:01:49,750
And then, thanks to thermal
excitation, which gives us an

36
00:01:49,750 --> 00:01:54,810
average energy of about 1/40 of
an electron bolt, we get,

37
00:01:54,810 --> 00:02:00,780
for all intents and purposes,
100% excitation of the

38
00:02:00,780 --> 00:02:04,650
electronics that sit in the
donor level, excitation up

39
00:02:04,650 --> 00:02:06,340
into the conduction band.

40
00:02:06,340 --> 00:02:09,450
And this is what electrical
engineers term ionization.

41
00:02:09,450 --> 00:02:13,310
And I also reminded you last
day that this is the donor

42
00:02:13,310 --> 00:02:20,210
level, and for each donor atom,
there sits a donor level

43
00:02:20,210 --> 00:02:23,570
at the same value of energy,
but these are so far apart

44
00:02:23,570 --> 00:02:27,150
point, owing to the dilution,
the dilute concentration of

45
00:02:27,150 --> 00:02:30,900
the impurity, that we
don't violate the

46
00:02:30,900 --> 00:02:32,610
Pauli Exclusion Principle.

47
00:02:32,610 --> 00:02:35,590
So these are all sitting at the
same level and that's why

48
00:02:35,590 --> 00:02:38,540
they've given temperature
promotes all of them up into

49
00:02:38,540 --> 00:02:41,830
the conduction band, where
they are mobile.

50
00:02:41,830 --> 00:02:48,410
And then, just to complete the
review, we call this n-type

51
00:02:48,410 --> 00:02:52,690
because, thanks to doping, we
generate electrons in the

52
00:02:52,690 --> 00:02:56,230
conduction band, and electrons
are negative.

53
00:02:56,230 --> 00:02:59,220
Supervalent doping
gives us n-type.

54
00:02:59,220 --> 00:03:03,080
Then the total number of
electrons in the conduction

55
00:03:03,080 --> 00:03:06,440
band is the sum of those that
would have been generated by

56
00:03:06,440 --> 00:03:08,530
plain old thermal excitation.

57
00:03:08,530 --> 00:03:11,620
Thermal excitation operates
all the time.

58
00:03:11,620 --> 00:03:17,500
So with thermal excitation,
recall, we promote from the

59
00:03:17,500 --> 00:03:20,160
valence band up into the
conduction band.

60
00:03:20,160 --> 00:03:24,080
So we break one of these bonds,
shoot an electron up

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00:03:24,080 --> 00:03:26,280
here, and leave a hole behind.

62
00:03:26,280 --> 00:03:28,100
So this generates the pair.

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00:03:28,100 --> 00:03:30,870
Hole in the valence band,
and electron in

64
00:03:30,870 --> 00:03:32,320
the conduction band.

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00:03:32,320 --> 00:03:36,410
That's always operative, but
owing to the energies

66
00:03:36,410 --> 00:03:40,650
involved, the band gap is on
the order of one electron

67
00:03:40,650 --> 00:03:46,420
volt, whereas the donor level
sits only about 1/50 of an

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00:03:46,420 --> 00:03:48,470
electron volt below the
conduction band.

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00:03:48,470 --> 00:03:52,820
So we get very, very little
promotion at room temperature.

70
00:03:52,820 --> 00:03:55,680
And in fact, it's something like
10 to the minus 19 is the

71
00:03:55,680 --> 00:03:59,110
fraction of promotion, and if
you say roughly 10 to the

72
00:03:59,110 --> 00:04:01,260
twenty-third per cubic
centimeter, that means you've

73
00:04:01,260 --> 00:04:05,650
got about 10 to the fourth
electrons per cubic centimeter

74
00:04:05,650 --> 00:04:08,680
due to this thermal excitation
from the valence band to the

75
00:04:08,680 --> 00:04:10,120
conduction band.

76
00:04:10,120 --> 00:04:12,880
Normally, when you dope a
semiconductor, you dope it

77
00:04:12,880 --> 00:04:15,080
around parts per
million level.

78
00:04:15,080 --> 00:04:18,110
And parts per million, that's
10 to the minus 6.

79
00:04:18,110 --> 00:04:20,680
If you take 10 to the minus 6
times 10 to the 23, you get

80
00:04:20,680 --> 00:04:21,960
about 10 of the 17.

81
00:04:21,960 --> 00:04:25,600
Now you can see, 10 of the 17
is vastly larger than 10 of

82
00:04:25,600 --> 00:04:26,360
the fourth.

83
00:04:26,360 --> 00:04:29,180
So for all intents and purposes,
once you've doped

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00:04:29,180 --> 00:04:32,780
something, this contribution is
essentially 0, and so the

85
00:04:32,780 --> 00:04:35,140
electron population, the
conduction band, is that

86
00:04:35,140 --> 00:04:38,070
dictated by the impurity atoms,
which is why we say

87
00:04:38,070 --> 00:04:40,130
that this is exhibiting
extrinsic behavior.

88
00:04:40,130 --> 00:04:43,850
The intrinsic properties
are not

89
00:04:43,850 --> 00:04:46,135
visible, they're not palpable.

90
00:04:46,135 --> 00:04:47,610
They're immeasurable.

91
00:04:47,610 --> 00:04:51,180
So intrinsic is substantially
less than extrinsic.

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00:04:51,180 --> 00:04:54,070
Now, the last thing I wanted
to do for you before we say

93
00:04:54,070 --> 00:04:57,030
goodbye to this fascinating
topic, which lays the

94
00:04:57,030 --> 00:04:59,730
groundwork for everything that
we know in the modern

95
00:04:59,730 --> 00:05:04,790
electronic era, parenthetically,
is to look at

96
00:05:04,790 --> 00:05:06,250
the other type of doping.

97
00:05:06,250 --> 00:05:08,810
I've showed you how to make
an n-type semiconductor.

98
00:05:08,810 --> 00:05:11,100
How do we make a p-type
semiconductor?

99
00:05:11,100 --> 00:05:13,930
So in that case, what
we can do is dope

100
00:05:13,930 --> 00:05:15,560
with a subvalent impurity.

101
00:05:20,490 --> 00:05:21,860
What do I mean by subvalent?

102
00:05:21,860 --> 00:05:26,770
Well, the valency of silicon
is 4, so I want

103
00:05:26,770 --> 00:05:28,020
something less than 4.

104
00:05:28,020 --> 00:05:32,770
So a good example is
boron into silicon.

105
00:05:35,290 --> 00:05:39,640
So boron is group 13, or 3, all
right, if you look on your

106
00:05:39,640 --> 00:05:40,600
periodic table.

107
00:05:40,600 --> 00:05:43,190
And silicon is group
14, according

108
00:05:43,190 --> 00:05:45,220
to the IUPAC notation.

109
00:05:45,220 --> 00:05:49,900
So let's go back and take a look
at how that might appear.

110
00:05:49,900 --> 00:05:52,440
So I'm going to draw the
silicon crystal.

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00:05:52,440 --> 00:05:55,380
Remember, this is going into a
single crystal of silicon.

112
00:05:55,380 --> 00:05:59,650
So silicon is sp 3 hybridized,
and we have silicons

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00:05:59,650 --> 00:06:01,660
everywhere in the structure.

114
00:06:01,660 --> 00:06:03,560
So we're going to
put silicons.

115
00:06:03,560 --> 00:06:06,150
And I'm trying to show
sp 3 hybridization.

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00:06:06,150 --> 00:06:10,680
So this is 3 legs each in the
plane, then you've got 109

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00:06:10,680 --> 00:06:11,340
degrees here.

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00:06:11,340 --> 00:06:13,020
So that's silicon, and so on.

119
00:06:13,020 --> 00:06:15,450
I get the three of them
just to complete

120
00:06:15,450 --> 00:06:16,510
enough of the picture.

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00:06:16,510 --> 00:06:18,940
And now what we're going to
do, is introduced boron.

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00:06:18,940 --> 00:06:22,590
And boron goes into the
silicon lattice

123
00:06:22,590 --> 00:06:24,300
and covalently bonds.

124
00:06:24,300 --> 00:06:27,950
It doesn't go sit in some void
space in between the silicons.

125
00:06:27,950 --> 00:06:30,900
It actually sits on
a silicon site and

126
00:06:30,900 --> 00:06:32,990
substitutes for the silicon.

127
00:06:32,990 --> 00:06:34,390
Now, boron is group 13.

128
00:06:34,390 --> 00:06:36,400
It's got 3 valence electrons.

129
00:06:36,400 --> 00:06:40,920
And so it forms bonds
with 3 silicons.

130
00:06:40,920 --> 00:06:44,480
And now there's a fourth silicon
here, and that silicon

131
00:06:44,480 --> 00:06:46,890
has an electron, but
the boron doesn't

132
00:06:46,890 --> 00:06:48,270
have a fourth electron.

133
00:06:48,270 --> 00:06:50,150
Here's where it gets
interesting.

134
00:06:50,150 --> 00:06:54,900
The driving force to complete
the picture here is so great

135
00:06:54,900 --> 00:06:58,840
that the system will actually
pull an electron out of a

136
00:06:58,840 --> 00:07:00,340
silicon-silicon bond--

137
00:07:04,410 --> 00:07:07,420
and so I'm going to use a
different color chalk, and I'm

138
00:07:07,420 --> 00:07:10,370
going to indicate, just for
argument's sake, that we're

139
00:07:10,370 --> 00:07:14,170
going to pull an electron out of
this bond here, break this

140
00:07:14,170 --> 00:07:17,490
bond, and shoot that electron
over to here.

141
00:07:17,490 --> 00:07:21,450
That way, we get r months
around the boron.

142
00:07:21,450 --> 00:07:23,220
It says p3 hybridized.

143
00:07:23,220 --> 00:07:25,100
It just doesn't have that
extra electron.

144
00:07:25,100 --> 00:07:27,510
But now it rips the electron
out of this

145
00:07:27,510 --> 00:07:29,120
silicon-silicon bond.

146
00:07:29,120 --> 00:07:31,640
And what's the consequence
of breaking this bod?

147
00:07:31,640 --> 00:07:34,770
What's the electrical feature
that we've created here?

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00:07:34,770 --> 00:07:35,790
A hole.

149
00:07:35,790 --> 00:07:40,300
So now we've created a hole
somewhere else in the crystal

150
00:07:40,300 --> 00:07:43,400
in order to satisfy the
desire of boron to

151
00:07:43,400 --> 00:07:45,330
get that fourth bond.

152
00:07:45,330 --> 00:07:48,370
And now can you see that for
every boron that I introduced

153
00:07:48,370 --> 00:07:51,060
into the crystal, I'm
going to make a hole

154
00:07:51,060 --> 00:07:53,640
somewhere in the crystal.

155
00:07:53,640 --> 00:07:56,080
And on the energy level
diagram, where

156
00:07:56,080 --> 00:07:58,330
do those holes live?

157
00:07:58,330 --> 00:08:01,080
Those holes live in
the valence band.

158
00:08:01,080 --> 00:08:03,750
So let's go make the energy
level diagram.

159
00:08:03,750 --> 00:08:06,520
So up here we have the
conduction band, and

160
00:08:06,520 --> 00:08:10,220
downstairs, we have the valence
band, as before.

161
00:08:10,220 --> 00:08:12,520
And I'm going to assume that we
got the thermal promotion.

162
00:08:12,520 --> 00:08:16,220
But it's so tiny in comparison
to the amount of boron we're

163
00:08:16,220 --> 00:08:16,760
going to put in.

164
00:08:16,760 --> 00:08:19,150
I'm not going to muddy the
water here and show that

165
00:08:19,150 --> 00:08:21,340
you've got pair formation.

166
00:08:21,340 --> 00:08:24,720
Because the extent of it is so
small, it doesn't make any

167
00:08:24,720 --> 00:08:25,540
difference.

168
00:08:25,540 --> 00:08:26,850
So now what happens?

169
00:08:26,850 --> 00:08:29,010
Now, I know I'm going to
generate holes here, and I've

170
00:08:29,010 --> 00:08:30,980
got to show this energy level.

171
00:08:30,980 --> 00:08:33,090
And this bonding level
is different from

172
00:08:33,090 --> 00:08:34,060
this bonding level.

173
00:08:34,060 --> 00:08:34,810
Agree?

174
00:08:34,810 --> 00:08:38,440
Silicon-silicon bond has
different bond energy from

175
00:08:38,440 --> 00:08:40,460
boron-silicon bond.

176
00:08:40,460 --> 00:08:42,500
So that means the top
of the valence band

177
00:08:42,500 --> 00:08:43,810
is different from--

178
00:08:43,810 --> 00:08:46,920
because this valence band is
silicon-silicon-silicon.

179
00:08:46,920 --> 00:08:52,150
So it turns out that, and this
is not to scale, that the

180
00:08:52,150 --> 00:08:56,330
energy level of this bond is
just a little bit higher.

181
00:08:56,330 --> 00:09:02,170
And this is an energy level that
involves the accepting of

182
00:09:02,170 --> 00:09:05,000
electrons, whereas in
the other case, we

183
00:09:05,000 --> 00:09:06,900
were donating electrons.

184
00:09:06,900 --> 00:09:08,760
Hence, that's called
the donor level.

185
00:09:08,760 --> 00:09:10,780
This is called the
acceptor level.

186
00:09:16,860 --> 00:09:20,530
And it's about 1/50 of an
electron volt above the top of

187
00:09:20,530 --> 00:09:21,670
the valence band.

188
00:09:21,670 --> 00:09:26,020
And so what happens is that in
order to make this bond, we

189
00:09:26,020 --> 00:09:31,630
move something out of the
valence band up into the

190
00:09:31,630 --> 00:09:35,410
acceptor level and
generate a hole.

191
00:09:35,410 --> 00:09:38,930
And so for every boron that
we put in, we have

192
00:09:38,930 --> 00:09:41,080
another broken bond.

193
00:09:41,080 --> 00:09:43,900
And all of these lie at the same
level, but the dilution

194
00:09:43,900 --> 00:09:46,720
is so high, that they're so
far apart, that they don't

195
00:09:46,720 --> 00:09:49,080
violate the polyexplosion
principle.

196
00:09:49,080 --> 00:09:51,410
They're thermally promoted
up, and away we go.

197
00:09:51,410 --> 00:09:55,640
So now, under these
circumstances, the number of

198
00:09:55,640 --> 00:09:57,930
negative charge carriers no
longer equals the number of

199
00:09:57,930 --> 00:10:00,600
positive charge carriers.

200
00:10:00,600 --> 00:10:03,140
Because I've got all these
positive charge carriers.

201
00:10:03,140 --> 00:10:06,990
Thanks to the introduction of
boron, p is greater than n.

202
00:10:06,990 --> 00:10:13,820
So we've made a p-type
semiconductor, by the

203
00:10:13,820 --> 00:10:17,390
introduction of a subvalent
impurity.

204
00:10:17,390 --> 00:10:21,520
And we can redo the entire
central part of last day's

205
00:10:21,520 --> 00:10:24,850
lesson, which was
the Bohr model.

206
00:10:24,850 --> 00:10:26,860
Now, this is the sexiest
part of the Bohr

207
00:10:26,860 --> 00:10:28,450
model I've ever seen.

208
00:10:28,450 --> 00:10:30,750
This is really, really cool.

209
00:10:30,750 --> 00:10:32,840
The hole is mobile!

210
00:10:32,840 --> 00:10:34,620
The hole is mobile!

211
00:10:34,620 --> 00:10:41,980
And the boron is a little bit
shy of protons, right?

212
00:10:41,980 --> 00:10:45,620
It's 3 in a land of 4.

213
00:10:45,620 --> 00:10:47,580
So it's negative.

214
00:10:47,580 --> 00:10:57,000
So I've got a stationary
negative center, and I've got

215
00:10:57,000 --> 00:11:00,340
something positive revolving
around a negative center.

216
00:11:00,340 --> 00:11:03,670
This is an inverse Bohr model!

217
00:11:03,670 --> 00:11:07,140
Because the Bohr model has a
honking big positive center

218
00:11:07,140 --> 00:11:10,340
with a dinky little electron
revolving around.

219
00:11:10,340 --> 00:11:13,660
We've got the immobile negative
center, and the

220
00:11:13,660 --> 00:11:16,810
mobile hole revolving around.

221
00:11:16,810 --> 00:11:19,340
Go through, you get the
same set of quantum--

222
00:11:19,340 --> 00:11:21,600
I mean, there's a whole bunch
of quantum levels in here.

223
00:11:21,600 --> 00:11:22,940
Fantastic!

224
00:11:22,940 --> 00:11:25,200
How far that Bohr model
can take us.

225
00:11:25,200 --> 00:11:28,130
So now you know how to make a
p-type semiconductor, you know

226
00:11:28,130 --> 00:11:30,100
how to make an n-type
semiconductor.

227
00:11:30,100 --> 00:11:34,830
And then what you can do
is put them together.

228
00:11:34,830 --> 00:11:41,190
And you can put, say,
boron-doped silicon opposite

229
00:11:41,190 --> 00:11:44,310
phosphorus-doped silicon.

230
00:11:44,310 --> 00:11:46,050
Be careful here.

231
00:11:46,050 --> 00:11:48,680
The fonts are really critical.

232
00:11:48,680 --> 00:11:51,530
This is uppercase P,
for phosphorus.

233
00:11:51,530 --> 00:11:56,090
This is lowercase p, for
positive doping.

234
00:11:56,090 --> 00:11:58,190
So don't go, oh, P, phosphorus,

235
00:11:58,190 --> 00:11:59,450
that means it's p-type.

236
00:11:59,450 --> 00:12:01,970
No, P gives you extra
electrons.

237
00:12:01,970 --> 00:12:03,360
It's n-type.

238
00:12:03,360 --> 00:12:04,980
So that's what uppercase P.

239
00:12:04,980 --> 00:12:06,720
This is a lowercase p.

240
00:12:06,720 --> 00:12:09,450
This is p-type.

241
00:12:09,450 --> 00:12:11,820
So now I've got p-type,
n-type, and so

242
00:12:11,820 --> 00:12:13,020
what do I have here?

243
00:12:13,020 --> 00:12:17,600
I've got a p-n junction.

244
00:12:17,600 --> 00:12:21,750
And this is the beginning
of solid state devices,

245
00:12:21,750 --> 00:12:25,810
rectification of A/C current,
diodes, you name it.

246
00:12:25,810 --> 00:12:30,960
And it all starts with
this, the chemistry.

247
00:12:30,960 --> 00:12:37,290
This is the birth of the
transistor, and all the modern

248
00:12:37,290 --> 00:12:39,980
electronics that we have
based on that.

249
00:12:39,980 --> 00:12:43,735
Later on, we'll show you how you
get the boron in, and how

250
00:12:43,735 --> 00:12:44,940
you get the phosphorus in.

251
00:12:44,940 --> 00:12:47,130
You don't just come in and
sprinkle it on top, and hope

252
00:12:47,130 --> 00:12:48,920
that it goes to the
lattice site.

253
00:12:48,920 --> 00:12:51,110
There's a lot of processing
involved.

254
00:12:51,110 --> 00:12:51,740
OK.

255
00:12:51,740 --> 00:12:57,670
So this is where I want to
hold for the unit on

256
00:12:57,670 --> 00:13:00,910
semiconductors, and how
it fits into the

257
00:13:00,910 --> 00:13:02,190
grand scheme of things.

258
00:13:02,190 --> 00:13:04,790
So in the books, you'll see--

259
00:13:04,790 --> 00:13:08,020
this is a very crude drawing,
because this is showing n-type

260
00:13:08,020 --> 00:13:14,410
semiconductor with grossly
exaggerated numbers of donor

261
00:13:14,410 --> 00:13:15,540
electronics up here.

262
00:13:15,540 --> 00:13:17,350
There's no mention of
the donor level.

263
00:13:17,350 --> 00:13:19,420
So this is sort of

264
00:13:19,420 --> 00:13:23,390
semiconductivity, sort of pre-3091.

265
00:13:23,390 --> 00:13:27,900
This is extrinsic semiconduction
for idiots, I

266
00:13:27,900 --> 00:13:28,960
guess you'd call it.

267
00:13:28,960 --> 00:13:29,910
And then, same thing here.

268
00:13:29,910 --> 00:13:32,550
You see all of the holes
in the valence band.

269
00:13:32,550 --> 00:13:34,800
We know better, because we know
there's an acceptor level

270
00:13:34,800 --> 00:13:36,340
and there's a donor level.

271
00:13:36,340 --> 00:13:36,990
OK.

272
00:13:36,990 --> 00:13:38,850
So now we're going
to switch gears.

273
00:13:38,850 --> 00:13:41,390
Now here's the big transition,
right now.

274
00:13:41,390 --> 00:13:44,600
If the last two lectures didn't
leave high school

275
00:13:44,600 --> 00:13:47,090
behind, today we leave
high school behind.

276
00:13:47,090 --> 00:13:50,090
So those of you who have been
coasting up until now, thanks

277
00:13:50,090 --> 00:13:53,230
to your very good high
school background,

278
00:13:53,230 --> 00:13:54,390
start paying attention.

279
00:13:54,390 --> 00:13:56,700
Because it's high
school no more.

280
00:13:56,700 --> 00:13:58,790
So just to remind you
where we've come.

281
00:13:58,790 --> 00:14:03,630
We started over here, at the
beginning of the semester.

282
00:14:03,630 --> 00:14:06,980
And the big theme is going to
be, electronic structure

283
00:14:06,980 --> 00:14:09,530
informs bonding, which informs
state of aggregation.

284
00:14:09,530 --> 00:14:12,890
State of aggregation is
solid, liquid, or gas.

285
00:14:12,890 --> 00:14:15,330
So I want to show you how
we get to where we are.

286
00:14:15,330 --> 00:14:17,300
So we did all of these
topics, right?

287
00:14:17,300 --> 00:14:20,980
Bohr, or Sommerfeld quantum
numbers, multielectron.

288
00:14:20,980 --> 00:14:23,110
And then we came to
octet stability.

289
00:14:23,110 --> 00:14:25,430
And with octet stability,
we went a long way.

290
00:14:25,430 --> 00:14:26,980
We got into ionic bonding.

291
00:14:26,980 --> 00:14:32,300
We got into completing
the valence shell.

292
00:14:32,300 --> 00:14:34,270
And in fact, all of this
is a consequence

293
00:14:34,270 --> 00:14:36,060
of the octet stability.

294
00:14:36,060 --> 00:14:37,430
And that led us into
the various

295
00:14:37,430 --> 00:14:38,610
types of primary bonding.

296
00:14:38,610 --> 00:14:40,720
Ionic, covalent, metallic.

297
00:14:40,720 --> 00:14:42,510
And in some instances,
van der Waals.

298
00:14:42,510 --> 00:14:44,940
Solid argon is van
der Waals bond.

299
00:14:44,940 --> 00:14:47,840
It's the only kind of bonding,
so it's the primary bonding.

300
00:14:47,840 --> 00:14:51,980
But in some cases, like HCl,
how do you get liquid HCl?

301
00:14:51,980 --> 00:14:54,290
How do you get solid methane?

302
00:14:54,290 --> 00:14:56,690
So we had invoke secondary
bonding for some of these

303
00:14:56,690 --> 00:14:59,880
covalent molecules, and that
invoked dipole-dipole

304
00:14:59,880 --> 00:15:02,150
interaction, the London
dispersion force, which is the

305
00:15:02,150 --> 00:15:04,710
same as the van der Walls bond,
but I decided to mix

306
00:15:04,710 --> 00:15:07,650
things up, so that both men get
a little bit of attention,

307
00:15:07,650 --> 00:15:09,290
none of them feel slighted.

308
00:15:09,290 --> 00:15:12,700
And finally, hydrogen bonding,
in those special instances.

309
00:15:12,700 --> 00:15:15,480
And that allowed us to then
determine whether something

310
00:15:15,480 --> 00:15:17,700
was a gas, a liquid,
or a solid.

311
00:15:17,700 --> 00:15:19,140
And when it's a solid,
we're happy.

312
00:15:19,140 --> 00:15:21,320
Because this is 3091,
and we're interested

313
00:15:21,320 --> 00:15:23,910
in the solid state.

314
00:15:23,910 --> 00:15:25,280
By the way, what is a solid?

315
00:15:25,280 --> 00:15:27,420
Well, here's an operative
definition.

316
00:15:27,420 --> 00:15:30,210
That which is dimensionally
stable, has a

317
00:15:30,210 --> 00:15:31,620
volume of its own.

318
00:15:31,620 --> 00:15:34,370
It doesn't distort in
a gravity field.

319
00:15:34,370 --> 00:15:35,750
All right?

320
00:15:35,750 --> 00:15:37,880
Liquids will distort.

321
00:15:37,880 --> 00:15:40,490
Fluids, gases will distort.

322
00:15:40,490 --> 00:15:42,870
Now, there's two ways of
classifying solids.

323
00:15:42,870 --> 00:15:43,900
One is bonding type.

324
00:15:43,900 --> 00:15:45,310
That's what we did here.

325
00:15:45,310 --> 00:15:47,860
But the second way of
classifying solids is based on

326
00:15:47,860 --> 00:15:49,355
atomic arrangements.

327
00:15:49,355 --> 00:15:50,150
All right?

328
00:15:50,150 --> 00:15:51,910
So let's look at that.

329
00:15:51,910 --> 00:15:54,550
There's only two types of
atomic arrangement.

330
00:15:54,550 --> 00:15:57,820
Ordered and disordered.

331
00:15:57,820 --> 00:16:00,670
I love these taxonomies
that split everything

332
00:16:00,670 --> 00:16:02,160
into a choice of 2.

333
00:16:02,160 --> 00:16:04,790
That way, you just sort of go
through life and decide, is it

334
00:16:04,790 --> 00:16:05,900
left or is it right?

335
00:16:05,900 --> 00:16:07,650
Is it up or is it down?

336
00:16:07,650 --> 00:16:10,150
Is it ordered or is
it disordered?

337
00:16:10,150 --> 00:16:11,380
So what are the characteristics

338
00:16:11,380 --> 00:16:12,510
or an ordered solid?

339
00:16:12,510 --> 00:16:15,100
It has a regular atomic
arrangement.

340
00:16:15,100 --> 00:16:17,680
That means it's got a
long-range order.

341
00:16:17,680 --> 00:16:21,710
And I'll show you that in an
ordered solid, I know not only

342
00:16:21,710 --> 00:16:24,690
where my next nearest neighbor
is, where my tenth nearest

343
00:16:24,690 --> 00:16:25,100
neighbor is.

344
00:16:25,100 --> 00:16:27,690
I know where my hundred and
fifty second nearest neighbor

345
00:16:27,690 --> 00:16:30,350
is, because it's an
ordered solid.

346
00:16:30,350 --> 00:16:32,720
And we have a simple Anglo-Saxon
word for an

347
00:16:32,720 --> 00:16:33,590
ordered solid.

348
00:16:33,590 --> 00:16:35,710
It's called crystal.

349
00:16:35,710 --> 00:16:38,460
So when I say something is a
metallic crystal, I don't mean

350
00:16:38,460 --> 00:16:41,510
it's something that's got
magical properties, and if I

351
00:16:41,510 --> 00:16:44,600
put it over my head, I get
powerful or something.

352
00:16:44,600 --> 00:16:48,080
It just means I've got atoms
in an atomic regular

353
00:16:48,080 --> 00:16:49,540
arrangement.

354
00:16:49,540 --> 00:16:53,190
Now contrasting to that
is a disordered solid.

355
00:16:53,190 --> 00:16:57,010
And in that case, we have
a random arrangement.

356
00:16:57,010 --> 00:16:59,980
But I put an asterisk here
because, as they say in

357
00:16:59,980 --> 00:17:02,610
California, it's not
totally random.

358
00:17:02,610 --> 00:17:04,460
It's only random
up to a point.

359
00:17:04,460 --> 00:17:06,470
No long-range order.

360
00:17:06,470 --> 00:17:07,930
There may be short-range
order.

361
00:17:07,930 --> 00:17:11,050
In other words, I know what my
next nearest neighbor is, but

362
00:17:11,050 --> 00:17:14,550
I probably don't know where my
tenth nearest neighbor is

363
00:17:14,550 --> 00:17:18,850
Because the coordination shell
is established, but the next

364
00:17:18,850 --> 00:17:21,420
coordination shell, and the
next coordination shell,

365
00:17:21,420 --> 00:17:22,410
they're not established.

366
00:17:22,410 --> 00:17:25,590
And I'm going to show you, with
examples, what that means

367
00:17:25,590 --> 00:17:29,160
So we call those kinds of
disordered solids amorphous

368
00:17:29,160 --> 00:17:32,100
solids, as opposed to the
regular solids, which are

369
00:17:32,100 --> 00:17:33,380
crystalline solids.

370
00:17:33,380 --> 00:17:35,580
And there's a plain Anglo-Saxon
word for a

371
00:17:35,580 --> 00:17:36,790
disordered solid.

372
00:17:36,790 --> 00:17:38,910
It's glass.

373
00:17:38,910 --> 00:17:42,380
Now you might think, well, gee,
doesn't glass mean that

374
00:17:42,380 --> 00:17:45,230
it's transparent in
visible light?

375
00:17:45,230 --> 00:17:47,330
No, no.

376
00:17:47,330 --> 00:17:50,540
Maybe up until now, but I want
everybody who's ever taken

377
00:17:50,540 --> 00:17:54,660
3091 from me to be disabused of
the notion that glass means

378
00:17:54,660 --> 00:17:55,620
transparent.

379
00:17:55,620 --> 00:17:58,260
How do we think about the
question of transparency?

380
00:17:58,260 --> 00:18:02,990
And here I mean transparency
vis-a-vis visible light.

381
00:18:02,990 --> 00:18:04,830
I'm not going to say, what's
transparent to x-rays?

382
00:18:04,830 --> 00:18:06,560
That's pedantry.

383
00:18:06,560 --> 00:18:09,310
So how do we think about
whether something is

384
00:18:09,310 --> 00:18:11,430
transparent to visible light?

385
00:18:11,430 --> 00:18:14,230
We just ask ourselves, is the
band gap greater than 3

386
00:18:14,230 --> 00:18:16,090
electron volts?

387
00:18:16,090 --> 00:18:19,210
The band gap is greater than 3
electron volts, visible light

388
00:18:19,210 --> 00:18:20,185
zooms right through.

389
00:18:20,185 --> 00:18:23,430
It doesn't have enough energy
to excite the electrons, be

390
00:18:23,430 --> 00:18:24,780
absorbed, and re-emit.

391
00:18:24,780 --> 00:18:26,980
So that's what transparency
means.

392
00:18:26,980 --> 00:18:32,130
So I can have the kind of
material that's used in things

393
00:18:32,130 --> 00:18:33,820
like eyeglasses.

394
00:18:33,820 --> 00:18:36,300
It's transparent to visible
light because of

395
00:18:36,300 --> 00:18:37,940
its high band gap.

396
00:18:37,940 --> 00:18:41,390
Diamond, diamond is transparent
to visible light,

397
00:18:41,390 --> 00:18:43,950
and you wouldn't dare insult
diamond by saying

398
00:18:43,950 --> 00:18:45,700
that diamond is glass!

399
00:18:45,700 --> 00:18:48,030
In fact, watch the old gangster
movies from the

400
00:18:48,030 --> 00:18:52,790
1930s, that was the derogatory
term for fake diamonds.

401
00:18:52,790 --> 00:18:55,270
You call them glass.

402
00:18:55,270 --> 00:18:58,340
So how is it that diamond, which
is crystalline, it's

403
00:18:58,340 --> 00:19:01,850
transparent to visible light,
and yet the window glass that

404
00:19:01,850 --> 00:19:04,740
we have is transparent
to visible light?

405
00:19:04,740 --> 00:19:07,800
It has nothing to do with
state of order.

406
00:19:07,800 --> 00:19:09,100
Has everything to
do with this.

407
00:19:09,100 --> 00:19:12,650
In fact, David, if we could
shoot to the document camera,

408
00:19:12,650 --> 00:19:15,700
I'll show you a piece of glass
that's not transparent to

409
00:19:15,700 --> 00:19:17,340
visible light.

410
00:19:17,340 --> 00:19:19,240
How do we zoom in
on this thing?

411
00:19:19,240 --> 00:19:20,890
OK.

412
00:19:20,890 --> 00:19:21,460
Auto focus.

413
00:19:21,460 --> 00:19:23,530
So what I'm showing you is
a piece of obsidian.

414
00:19:28,160 --> 00:19:30,320
It's a naturally occurring
mineral.

415
00:19:30,320 --> 00:19:34,680
It's rich in silica, and it's
turned dark because it's got

416
00:19:34,680 --> 00:19:37,810
some iron impurity, and the iron
absorbs in the visible.

417
00:19:37,810 --> 00:19:41,050
And this is clearly not
transparent to visible light,

418
00:19:41,050 --> 00:19:42,760
and yet, it is a disordered
solid.

419
00:19:42,760 --> 00:19:44,510
This is a glassy solid.

420
00:19:44,510 --> 00:19:48,920
In fact, the white
speckles there

421
00:19:48,920 --> 00:19:51,730
are devitrified obsidian.

422
00:19:51,730 --> 00:19:54,440
It's actually started
to crystallize.

423
00:19:54,440 --> 00:19:58,040
So the crystalline form is the
part that's transparent.

424
00:19:58,040 --> 00:20:00,220
If you could peel off this
crystalline form, you'd

425
00:20:00,220 --> 00:20:01,370
actually end up with
something that's

426
00:20:01,370 --> 00:20:02,430
transparent to visible light.

427
00:20:02,430 --> 00:20:04,920
So here's an example of where
the crystalline form is

428
00:20:04,920 --> 00:20:07,930
transparent to visible light,
and the glassy form is opaque.

429
00:20:07,930 --> 00:20:11,240
So glass has nothing to
do with transparency.

430
00:20:11,240 --> 00:20:15,290
This is how you think about the
question of transparency.

431
00:20:15,290 --> 00:20:15,600
OK.

432
00:20:15,600 --> 00:20:22,950
So let's cut back to the
slides, David, please.

433
00:20:22,950 --> 00:20:27,100
So we're now going to start by
looking at ordered solids.

434
00:20:27,100 --> 00:20:29,900
So we're going to take next
several lessons and talk about

435
00:20:29,900 --> 00:20:33,760
ordered solids, and then after
that, we're going to take a

436
00:20:33,760 --> 00:20:36,150
few more lessons and talk
about distorted solids.

437
00:20:36,150 --> 00:20:38,510
Now first of all, what's
the term crystal?

438
00:20:38,510 --> 00:20:39,310
Where does it come from?

439
00:20:39,310 --> 00:20:42,100
It comes from the Greek word,
crystallus, which is the Greek

440
00:20:42,100 --> 00:20:43,570
word for ice.

441
00:20:43,570 --> 00:20:46,720
That's where we get
the term crystal.

442
00:20:46,720 --> 00:20:48,190
So we're going to start
with a history lesson.

443
00:20:48,190 --> 00:20:49,670
That's how we start everything
in 3091.

444
00:20:49,670 --> 00:20:50,550
A history lesson.

445
00:20:50,550 --> 00:20:54,950
So we go way, way back to
Isaac Newton's time.

446
00:20:54,950 --> 00:20:58,070
The Reformation, Charles, Oliver
Cromwell, all those

447
00:20:58,070 --> 00:20:59,900
exciting times.

448
00:20:59,900 --> 00:21:01,990
In merry old England, there
was Robert Hook.

449
00:21:01,990 --> 00:21:06,120
You know him from Hook's
Law, in mechanics.

450
00:21:06,120 --> 00:21:09,060
So he was doing military
research in 1660.

451
00:21:09,060 --> 00:21:11,320
He was trying to understand what
was the optimal way to

452
00:21:11,320 --> 00:21:13,010
stack cannon balls.

453
00:21:13,010 --> 00:21:15,160
So when you're on a battle
front, you want to figure out

454
00:21:15,160 --> 00:21:18,310
how to keep your material
compactly arranged.

455
00:21:18,310 --> 00:21:21,810
You don't lie them
on the ground.

456
00:21:21,810 --> 00:21:25,690
So from that, he concluded that
crystal that is a regular

457
00:21:25,690 --> 00:21:28,560
array must owe its shape
to the packing

458
00:21:28,560 --> 00:21:30,142
of spherical particles.

459
00:21:30,142 --> 00:21:31,320
So that's what he was thinking,

460
00:21:31,320 --> 00:21:31,980
or trying to imagine.

461
00:21:31,980 --> 00:21:34,410
Remember, Democritus said that
we have these indivisible

462
00:21:34,410 --> 00:21:37,800
particles, but no one had
ever seen them before.

463
00:21:37,800 --> 00:21:40,790
Then in 1669, a Dane by the
name of Steenson who was

464
00:21:40,790 --> 00:21:43,980
working in Italy was looking
at quartz crystals.

465
00:21:43,980 --> 00:21:46,040
And he was studying various
quartz crystals.

466
00:21:46,040 --> 00:21:48,740
By that I mean, quartz crystals
of different sizes.

467
00:21:48,740 --> 00:21:50,900
And what he observed was, didn't
matter what the size of

468
00:21:50,900 --> 00:21:52,050
the crystal was.

469
00:21:52,050 --> 00:21:53,690
They always had the same
angles between

470
00:21:53,690 --> 00:21:55,240
corresponding faces.

471
00:21:55,240 --> 00:21:58,340
So if I give you a big crystal
and a smaller crystal of the

472
00:21:58,340 --> 00:22:01,220
same material, and a smaller
crystal, and they all have the

473
00:22:01,220 --> 00:22:05,770
same shape, Can you imagine that
you might conclude that

474
00:22:05,770 --> 00:22:08,460
that is reflective of something
down at the atomic

475
00:22:08,460 --> 00:22:11,200
level, and if you could get down
to the atomic level, that

476
00:22:11,200 --> 00:22:13,700
spacial arrangement would
hold right now?

477
00:22:13,700 --> 00:22:14,940
Because that's how
it grew, right?

478
00:22:14,940 --> 00:22:18,810
It started from a small number
of atoms and grew, grew, grew.

479
00:22:18,810 --> 00:22:21,470
Why would it start with one
shape, and all of a sudden

480
00:22:21,470 --> 00:22:22,430
change to another shape?

481
00:22:22,430 --> 00:22:23,800
It doesn't make any sense.

482
00:22:23,800 --> 00:22:24,770
At least, not to me.

483
00:22:24,770 --> 00:22:26,780
And certainly not to Steenson.

484
00:22:26,780 --> 00:22:29,840
And then we go to
Holland, 1690.

485
00:22:29,840 --> 00:22:31,610
Christiaan Huygens.

486
00:22:31,610 --> 00:22:35,160
And he was studying
calcite crystals.

487
00:22:35,160 --> 00:22:40,350
And he drew drawings of atomic
packing and bulk shape.

488
00:22:40,350 --> 00:22:41,180
This is 1960.

489
00:22:41,180 --> 00:22:43,010
I'm going ot show you an
image from his book.

490
00:22:43,010 --> 00:22:45,860
This was drawn in 1690.

491
00:22:45,860 --> 00:22:48,260
See, this is stacking of
cannonballs, but he was

492
00:22:48,260 --> 00:22:49,690
looking at a calcite crystal.

493
00:22:49,690 --> 00:22:51,950
Actually, Dave, could we cut
back to the document camera?

494
00:22:51,950 --> 00:22:53,400
We're going to do a
fair bit of this.

495
00:22:53,400 --> 00:22:54,660
I'll show you calcite crystal.

496
00:22:54,660 --> 00:22:55,710
This is what he had
to work with.

497
00:22:55,710 --> 00:22:56,960
It looks like this.

498
00:23:01,370 --> 00:23:04,100
To give you a sense of scale--

499
00:23:04,100 --> 00:23:05,165
what do I have?

500
00:23:05,165 --> 00:23:06,760
Do I have anything
you'd recognize?

501
00:23:06,760 --> 00:23:09,980
OK, here's a soda can to give
you a sense of scale, OK?

502
00:23:09,980 --> 00:23:12,890
This is one honking big
calcite crystal.

503
00:23:12,890 --> 00:23:16,960
I got it as a gift from someone
who watched 3091

504
00:23:16,960 --> 00:23:19,180
lectures on OpenCourseWare.

505
00:23:19,180 --> 00:23:21,680
And he said, if I ever
come to town, can

506
00:23:21,680 --> 00:23:22,600
I attend your lecture?

507
00:23:22,600 --> 00:23:23,280
I said, sure.

508
00:23:23,280 --> 00:23:25,180
And he showed up, he attended
the lecture.

509
00:23:25,180 --> 00:23:29,990
He was a man probably in his
early 40s, and as a pastime he

510
00:23:29,990 --> 00:23:32,180
collects gemstones.

511
00:23:32,180 --> 00:23:35,180
And he gave me this giant
calcite crystal, because the

512
00:23:35,180 --> 00:23:37,040
one I was using before
was so pathetic.

513
00:23:37,040 --> 00:23:38,530
He said, I've got
to give you one.

514
00:23:38,530 --> 00:23:40,920
And then, I thought, jeez,
if I could ever come upon

515
00:23:40,920 --> 00:23:43,180
somebody who's in the
gold business--

516
00:23:43,180 --> 00:23:47,110
and you know, he might give me
a big honking crystal of

517
00:23:47,110 --> 00:23:50,080
face-centered cubic metal
called gold--

518
00:23:50,080 --> 00:23:52,860
which broke $1,000 an ounce
yesterday, but--

519
00:23:52,860 --> 00:23:54,770
anyways, if you're out there,
and you're watching these

520
00:23:54,770 --> 00:23:55,820
lectures, I'm here.

521
00:23:55,820 --> 00:24:01,500
It's 8201, and you can
see any anytime.

522
00:24:01,500 --> 00:24:04,410
My assistant's name is Hillary,
she'll take the call.

523
00:24:04,410 --> 00:24:04,820
All right.

524
00:24:04,820 --> 00:24:09,230
So let's go back
to the slides.

525
00:24:09,230 --> 00:24:10,770
Dave, could we cut to
the slides, please?

526
00:24:10,770 --> 00:24:11,880
Thanks.

527
00:24:11,880 --> 00:24:12,140
All right.

528
00:24:12,140 --> 00:24:12,940
So now--

529
00:24:12,940 --> 00:24:16,030
oh, I'm going to show
you a few others.

530
00:24:16,030 --> 00:24:18,850
Remember, here's the idea, that
we're looking down to the

531
00:24:18,850 --> 00:24:19,690
elemental level.

532
00:24:19,690 --> 00:24:21,965
So if you look on your periodic
table, it says 10,

533
00:24:21,965 --> 00:24:24,560
you see, 10, it's supposed
to be tetragonal.

534
00:24:24,560 --> 00:24:25,930
So here's a crystal of 10.

535
00:24:25,930 --> 00:24:26,940
Dave, cut back, please.

536
00:24:26,940 --> 00:24:29,526
We're going to go back and
forth today a lot.

537
00:24:29,526 --> 00:24:32,170
There's a piece of ten 10.

538
00:24:32,170 --> 00:24:33,610
So you might look at it
and say, gee, that

539
00:24:33,610 --> 00:24:36,380
looks kind of cubic.

540
00:24:36,380 --> 00:24:41,120
But if you look carefully, the
vertical dimension is greater

541
00:24:41,120 --> 00:24:41,930
than the horizontal.

542
00:24:41,930 --> 00:24:44,080
In fact, it's got
a square base.

543
00:24:44,080 --> 00:24:45,870
And then, this is
the tall one.

544
00:24:45,870 --> 00:24:51,000
Which, if we cut back to
the slides, let's see.

545
00:24:51,000 --> 00:24:52,520
And that's what tetragonal
looks like.

546
00:24:52,520 --> 00:24:56,440
And we'll study all of these
in a few minutes.

547
00:24:56,440 --> 00:24:58,990
These are some giant crystals
I didn't dare drag in.

548
00:24:58,990 --> 00:25:01,050
This is sort of human-sized
scale.

549
00:25:01,050 --> 00:25:04,190
This is balsalt, which is a
magnesium iron silicate.

550
00:25:04,190 --> 00:25:07,170
It's on a coast of Iceland.

551
00:25:07,170 --> 00:25:10,180
Dave, let's show them
a few more.

552
00:25:10,180 --> 00:25:12,180
Here's one more, if we go
to the document camera.

553
00:25:12,180 --> 00:25:14,680
This was beryllium aluminum
silicate.

554
00:25:14,680 --> 00:25:16,910
This is a barrel.

555
00:25:16,910 --> 00:25:20,215
And you can see, this has
got a hexagonal habit.

556
00:25:23,400 --> 00:25:26,780
So something's going on at the
atomic level that's different

557
00:25:26,780 --> 00:25:29,360
as we go from one crystal
structure to the other.

558
00:25:29,360 --> 00:25:30,250
What else have I got here?

559
00:25:30,250 --> 00:25:33,320
Here's some calcite, here's
some fluorite.

560
00:25:33,320 --> 00:25:34,410
Look at this one.

561
00:25:34,410 --> 00:25:39,420
This is square pyramidal
but it's ionic.

562
00:25:39,420 --> 00:25:43,190
So don't give me any of
that sp3 d2 stuff.

563
00:25:43,190 --> 00:25:46,740
Because it's not going
to work here.

564
00:25:46,740 --> 00:25:47,850
All right.

565
00:25:47,850 --> 00:25:49,960
Let's go back to the
slides, please.

566
00:25:52,840 --> 00:25:56,570
So then we jump to
1781, to France.

567
00:25:56,570 --> 00:26:01,100
Rene Juste-Hauy was at the
Sorbonne, and he was studying

568
00:26:01,100 --> 00:26:02,900
the cleavage of calcite
crystals.

569
00:26:02,900 --> 00:26:04,890
In other words, he was
taking these things

570
00:26:04,890 --> 00:26:05,670
and breaking them.

571
00:26:05,670 --> 00:26:08,040
So he'd go to work every
day and break things.

572
00:26:08,040 --> 00:26:11,710
And he studied the shards, and
he found that the shards were

573
00:26:11,710 --> 00:26:13,300
all rhombahedral.

574
00:26:13,300 --> 00:26:15,150
the same shape as the
parent crystal.

575
00:26:15,150 --> 00:26:17,070
No matter how small the
shards got, they

576
00:26:17,070 --> 00:26:18,650
always looked like this.

577
00:26:18,650 --> 00:26:20,580
He didn't end up with
cubic shards.

578
00:26:20,580 --> 00:26:22,245
He didn't end up with
long slivers.

579
00:26:22,245 --> 00:26:25,830
He always ended up with
rhombahedral slices.

580
00:26:25,830 --> 00:26:29,960
So the other thing is that he
didn't end up with any voids.

581
00:26:29,960 --> 00:26:32,790
No matter how he cut this thing,
he never got voids.

582
00:26:32,790 --> 00:26:36,740
So he reasoned that this must be
the way things are packing

583
00:26:36,740 --> 00:26:40,330
in three space perfectly.

584
00:26:40,330 --> 00:26:42,100
So then he said, gee.

585
00:26:42,100 --> 00:26:44,540
If they pack perfectly
rhombahedrally--

586
00:26:44,540 --> 00:26:48,370
we all know that we can stack
boxes together perfectly,

587
00:26:48,370 --> 00:26:49,510
cubes together.

588
00:26:49,510 --> 00:26:53,100
So he, being a Frenchman, said,
what's the mathematical

589
00:26:53,100 --> 00:26:54,160
formulation?

590
00:26:54,160 --> 00:26:56,280
They were steeped in
mathematics there.

591
00:26:56,280 --> 00:26:58,320
That wasn't a slur against
the French.

592
00:26:58,320 --> 00:26:59,300
It's a compliment.

593
00:26:59,300 --> 00:27:03,720
He said, what are the
mathematically distinct

594
00:27:03,720 --> 00:27:07,370
shapes, that if we stack them
together in three space they

595
00:27:07,370 --> 00:27:09,800
will fill three space
with no void?

596
00:27:09,800 --> 00:27:11,370
And the answer is seven.

597
00:27:11,370 --> 00:27:13,870
Seven space-filling
volume elements.

598
00:27:13,870 --> 00:27:17,890
By the way, the gabled milk
carton isn't one of them.

599
00:27:17,890 --> 00:27:20,850
And so he called the crystal
system, so I call seven

600
00:27:20,850 --> 00:27:24,050
distinct shades of
milk cartons.

601
00:27:24,050 --> 00:27:26,850
And these are the seven crystal
systems, and they're

602
00:27:26,850 --> 00:27:29,680
described geometrically, and
you'll get a chance to go

603
00:27:29,680 --> 00:27:30,010
through them.

604
00:27:30,010 --> 00:27:30,940
The cube is one of them.

605
00:27:30,940 --> 00:27:31,690
Tetragonal.

606
00:27:31,690 --> 00:27:34,850
Here's the calcite,
rhombahedral.

607
00:27:34,850 --> 00:27:36,725
There's barrel, hexagonal,
and so on.

608
00:27:36,725 --> 00:27:40,510
The seven different ways you
can feel three space.

609
00:27:40,510 --> 00:27:43,680
And this is from the archival
readings of my predecessor,

610
00:27:43,680 --> 00:27:46,080
Professor Witt.

611
00:27:46,080 --> 00:27:47,680
Actually, just to give your
a sense, here's the

612
00:27:47,680 --> 00:27:48,940
two-dimensional analogy.

613
00:27:48,940 --> 00:27:52,190
If I said to you, we're going
to open a company, and we're

614
00:27:52,190 --> 00:27:54,890
going to make bathroom tile, and
we want to make it sort of

615
00:27:54,890 --> 00:27:58,840
an upscale company, you know,
not everybody wants boring old

616
00:27:58,840 --> 00:28:00,160
square tiles.

617
00:28:00,160 --> 00:28:03,910
But definitely, I can cover two
space with square tiles by

618
00:28:03,910 --> 00:28:06,540
putting them side by side,
one on top of the other.

619
00:28:06,540 --> 00:28:08,180
What's another way I can fill?

620
00:28:08,180 --> 00:28:09,800
I can go with rectangular
tiles.

621
00:28:09,800 --> 00:28:12,210
So this dimension is different
from that dimension.

622
00:28:12,210 --> 00:28:12,970
What's another way?

623
00:28:12,970 --> 00:28:17,770
I can use a rhombus, right,
at 60 degrees.

624
00:28:17,770 --> 00:28:22,540
Or I can use just a plain old
parallelepipede at some

625
00:28:22,540 --> 00:28:23,620
arbitrary angle.

626
00:28:23,620 --> 00:28:26,550
And if you go over to the Stata
Center, to the Gehry

627
00:28:26,550 --> 00:28:29,400
building, take a look at
the shape that they

628
00:28:29,400 --> 00:28:31,850
chose as the unit cell.

629
00:28:31,850 --> 00:28:35,870
This is the repeat group, if
you like, or the unit cell,

630
00:28:35,870 --> 00:28:37,770
because that's the one that's
going to be cookie cutter

631
00:28:37,770 --> 00:28:39,660
replicated, side by side.

632
00:28:39,660 --> 00:28:42,470
When you're putting the skin
on a building, you have to

633
00:28:42,470 --> 00:28:44,830
make everything fit with
no holidays, right?

634
00:28:44,830 --> 00:28:46,810
Because you don't want gaps.

635
00:28:46,810 --> 00:28:54,340
what they chose was
this area element.

636
00:28:54,340 --> 00:28:56,680
And all the pieces of stainless
steel are cut to

637
00:28:56,680 --> 00:28:57,670
this shape.

638
00:28:57,670 --> 00:28:59,340
And that's how you
make things fit.

639
00:28:59,340 --> 00:29:02,510
How you take something and make
it fit around a three

640
00:29:02,510 --> 00:29:04,160
dimensional object is tricky.

641
00:29:04,160 --> 00:29:06,270
It's the same thing as the
clothing problem, right?

642
00:29:06,270 --> 00:29:08,510
How do you take a flat piece of
cloth and make it fit the

643
00:29:08,510 --> 00:29:11,100
contour of the human body?

644
00:29:11,100 --> 00:29:13,750
At least, you know, in men's
clothes, you know, we've got

645
00:29:13,750 --> 00:29:14,220
dimensions.

646
00:29:14,220 --> 00:29:18,540
We've got sleeve length, got
waist, chest. We've got all

647
00:29:18,540 --> 00:29:19,110
these numbers.

648
00:29:19,110 --> 00:29:20,890
For a woman, 8.

649
00:29:20,890 --> 00:29:22,920
One number?

650
00:29:22,920 --> 00:29:24,070
One number?

651
00:29:24,070 --> 00:29:27,572
Fashion designers don't
know crystallograpy!

652
00:29:27,572 --> 00:29:29,700
If they knew crystallography,
they'd know how

653
00:29:29,700 --> 00:29:31,480
to specify the shapes!

654
00:29:31,480 --> 00:29:33,860
If you understand this, you can
start your own business

655
00:29:33,860 --> 00:29:34,950
and make clothes that fit.

656
00:29:34,950 --> 00:29:37,310
And I guarantee you, there's
a market out there for

657
00:29:37,310 --> 00:29:39,420
clothes that fit.

658
00:29:39,420 --> 00:29:41,560
What about this one?

659
00:29:41,560 --> 00:29:42,320
Pentagon.

660
00:29:42,320 --> 00:29:44,820
We're going to make pentagonal
bathroom tile.

661
00:29:44,820 --> 00:29:48,560
Well, when we install these,
we're going to have to use two

662
00:29:48,560 --> 00:29:49,170
different colors.

663
00:29:49,170 --> 00:29:51,050
You can see this
up here, right?

664
00:29:51,050 --> 00:29:53,390
This is pentagonal
bathroom tile.

665
00:29:53,390 --> 00:29:53,970
It doesn't fit.

666
00:29:53,970 --> 00:29:55,960
You've got all these
white spots.

667
00:29:55,960 --> 00:29:57,550
So this is not a unit cell.

668
00:29:57,550 --> 00:30:01,900
This is not one of the crystal
systems for two dimensional.

669
00:30:01,900 --> 00:30:02,850
So this one's no good.

670
00:30:02,850 --> 00:30:05,370
We better put an x through it,
in case someone fell asleep,

671
00:30:05,370 --> 00:30:09,100
and wake up, and then tell
me that that's OK.

672
00:30:09,100 --> 00:30:09,540
All right.

673
00:30:09,540 --> 00:30:14,400
So then we move about half
a century forward, to the

674
00:30:14,400 --> 00:30:18,560
turbulent year 1848,
also in France.

675
00:30:18,560 --> 00:30:20,300
Auguste Bravais.

676
00:30:20,300 --> 00:30:21,970
And what Bravais did, is
he said, all right.

677
00:30:21,970 --> 00:30:24,120
This is just filling space.

678
00:30:24,120 --> 00:30:25,320
But where are the atoms?

679
00:30:25,320 --> 00:30:27,310
I haven't told you where
the atoms are, right?

680
00:30:27,310 --> 00:30:29,430
You know, as far as you're
concerned, maybe there's one

681
00:30:29,430 --> 00:30:32,270
atom in each of these boxes.

682
00:30:32,270 --> 00:30:34,890
Or maybe there's atoms at
the corners of the box.

683
00:30:34,890 --> 00:30:36,410
Or maybe there's atoms
at the corner and the

684
00:30:36,410 --> 00:30:37,080
center of the box.

685
00:30:37,080 --> 00:30:38,120
Where are the atoms?

686
00:30:38,120 --> 00:30:40,700
I've simply told you that I
can fill three space with

687
00:30:40,700 --> 00:30:44,350
boxes, or with these rectangular
boxes, and so on.

688
00:30:44,350 --> 00:30:48,470
So he set out mathematically
to prove how many different

689
00:30:48,470 --> 00:30:51,500
arrangements of points
there are in space.

690
00:30:51,500 --> 00:30:53,640
It's sort of like saying, if I
want to tell you where all the

691
00:30:53,640 --> 00:30:55,930
apples are in the orchard, I'm
going to tell you where the

692
00:30:55,930 --> 00:30:57,850
trees are, and I'm going
to tell you where the

693
00:30:57,850 --> 00:30:59,370
apples are on a tree.

694
00:30:59,370 --> 00:31:04,120
So where do the atoms go
inside these boxes?

695
00:31:04,120 --> 00:31:09,130
Turns out there's 14 different
arrangements.

696
00:31:09,130 --> 00:31:10,140
And what do I mean by that?

697
00:31:10,140 --> 00:31:11,190
This is a good example.

698
00:31:11,190 --> 00:31:14,980
So we've already established
that the cube is a

699
00:31:14,980 --> 00:31:16,690
space-filling volume element.

700
00:31:16,690 --> 00:31:18,020
It's one of the seven.

701
00:31:18,020 --> 00:31:18,850
But look.

702
00:31:18,850 --> 00:31:22,660
If I'm one of the atoms at the
corners here, I've got six

703
00:31:22,660 --> 00:31:24,350
nearest neighbors.

704
00:31:24,350 --> 00:31:27,780
This is also a cube, but it's
got atoms at the corners and

705
00:31:27,780 --> 00:31:28,610
an atom in the center.

706
00:31:28,610 --> 00:31:30,130
You might say, well, what's
the big deal?

707
00:31:30,130 --> 00:31:33,220
If you're in the atom in the
center, and you look to the

708
00:31:33,220 --> 00:31:36,020
nearest neighbors, you've got
eight nearest neighbors.

709
00:31:36,020 --> 00:31:38,190
Here you only have six
nearest neighbors.

710
00:31:38,190 --> 00:31:42,900
So this is spatially
differentiated from this.

711
00:31:42,900 --> 00:31:44,340
So what why don't
we keep going?

712
00:31:44,340 --> 00:31:47,410
And by the way, the same
environment of that central

713
00:31:47,410 --> 00:31:50,530
atom that's coded green is the
same environment of any of the

714
00:31:50,530 --> 00:31:51,440
atoms on the corners.

715
00:31:51,440 --> 00:31:53,860
They're all symmetric.

716
00:31:53,860 --> 00:31:57,230
So both are cubes, but they
have different space point

717
00:31:57,230 --> 00:31:58,240
environments.

718
00:31:58,240 --> 00:32:01,070
And here's a third one, where
we put atoms at the corners

719
00:32:01,070 --> 00:32:02,620
and atoms on each
of the faces.

720
00:32:02,620 --> 00:32:05,550
So this atom on the face, you
can see, it's got one, two,

721
00:32:05,550 --> 00:32:08,030
three, four atoms in
the plane, three

722
00:32:08,030 --> 00:32:08,800
behind, three in front.

723
00:32:08,800 --> 00:32:10,210
It's got 12 nearest neighbors.

724
00:32:10,210 --> 00:32:11,910
This has got eight nearest
neighbors, this has got six

725
00:32:11,910 --> 00:32:12,980
nearest neighbors.

726
00:32:12,980 --> 00:32:16,350
So Bravais went through and he
said, let's take those seven

727
00:32:16,350 --> 00:32:20,780
crystal systems. Let's put atoms
in distinguishable ways.

728
00:32:20,780 --> 00:32:24,240
How many distinguishable ways
can we come up with atom

729
00:32:24,240 --> 00:32:24,810
arrangements?

730
00:32:24,810 --> 00:32:26,345
And the answer is 14.

731
00:32:26,345 --> 00:32:29,130
Now, what we're going to do in
3091, is we're just going to

732
00:32:29,130 --> 00:32:31,570
confine our conversation
to the cubics.

733
00:32:31,570 --> 00:32:36,500
Because you use orthogonal
vectors, they're all the same

734
00:32:36,500 --> 00:32:39,010
length, the mathematics
are simple, and the

735
00:32:39,010 --> 00:32:40,120
principles are the same.

736
00:32:40,120 --> 00:32:43,200
And by the way, boatloads
of materials are

737
00:32:43,200 --> 00:32:44,270
in the cubic system.

738
00:32:44,270 --> 00:32:47,400
So it's not as though we just
chose something that's

739
00:32:47,400 --> 00:32:51,070
convenient but irrelevant.

740
00:32:51,070 --> 00:32:54,450
So here are the different
Bravais lattices.

741
00:32:54,450 --> 00:32:56,710
So you can see the cubic,
there's simple cubic,

742
00:32:56,710 --> 00:32:58,700
body-centered cubic,
face-centered cubic.

743
00:32:58,700 --> 00:33:01,250
With tetragonal, there
is simple tetragonal,

744
00:33:01,250 --> 00:33:03,100
body-centered tetragonal.

745
00:33:03,100 --> 00:33:04,490
There's no face-center
tetragonal.

746
00:33:04,490 --> 00:33:07,550
If you try to make face-center
tetragonal it's degenerate,

747
00:33:07,550 --> 00:33:08,980
reverts to one of the
other systems.

748
00:33:08,980 --> 00:33:12,450
So these are the distinguishable
systems. And

749
00:33:12,450 --> 00:33:15,910
everything, including
crystalline proteins--

750
00:33:15,910 --> 00:33:20,180
if the protein crystallizes, it
forms atomic arrangements

751
00:33:20,180 --> 00:33:22,300
in one of these Bravais
lattices.

752
00:33:22,300 --> 00:33:24,770
Everything conforms to one of
these Bravais lattices.

753
00:33:24,770 --> 00:33:27,760
And if it doesn't, it means it
lacks long-range order, in

754
00:33:27,760 --> 00:33:30,620
which case it is a glass.

755
00:33:30,620 --> 00:33:31,870
That's it.

756
00:33:34,100 --> 00:33:35,930
So here's face-centered cubic.

757
00:33:35,930 --> 00:33:39,280
You can see the placement.

758
00:33:39,280 --> 00:33:42,670
But there's something that's
been simplified here.

759
00:33:42,670 --> 00:33:47,540
Right now what you see is a
single atom, designated by a

760
00:33:47,540 --> 00:33:48,470
hard sphere.

761
00:33:48,470 --> 00:33:52,660
But at each of these lattice
points, I can put

762
00:33:52,660 --> 00:33:53,550
more than one atom.

763
00:33:53,550 --> 00:33:55,450
So let me show you what
I mean by that.

764
00:33:55,450 --> 00:34:00,120
What I want to do, is put
different numbers of atom

765
00:34:00,120 --> 00:34:01,930
arrangements at the
lattice point.

766
00:34:01,930 --> 00:34:05,090
So those positions, the
distinguishable positions, are

767
00:34:05,090 --> 00:34:06,450
called lattice points.

768
00:34:06,450 --> 00:34:09,890
And now I want to define
the crystal structure--

769
00:34:09,890 --> 00:34:13,080
the crystal structure is the
complete accounting of atomic

770
00:34:13,080 --> 00:34:14,300
arrangement.

771
00:34:14,300 --> 00:34:20,630
It's the complete description
of atomic arrangement.

772
00:34:23,200 --> 00:34:25,510
And we don't have to go too far,
because we just have to

773
00:34:25,510 --> 00:34:27,920
get the base unit, the unit
cell, and then just

774
00:34:27,920 --> 00:34:28,840
repeat the unit cell.

775
00:34:28,840 --> 00:34:33,020
Complete description of
atomic arrangement.

776
00:34:33,020 --> 00:34:37,540
And so how we going
to go about this?

777
00:34:37,540 --> 00:34:39,250
We're going to start with
a Bravais lattice.

778
00:34:42,504 --> 00:34:44,140
And what is the Bravais
lattice?

779
00:34:44,140 --> 00:34:46,479
The Bravais lattice is simply
a point environment.

780
00:34:51,260 --> 00:34:53,610
And this will mean something to
you in about three minutes,

781
00:34:53,610 --> 00:35:00,490
when I give you the rest
of the description.

782
00:35:00,490 --> 00:35:09,190
So it's a set of points in
space and the basis.

783
00:35:09,190 --> 00:35:10,140
And what is the basis?

784
00:35:10,140 --> 00:35:12,740
The basis is the atom group
at each lattice point.

785
00:35:20,280 --> 00:35:23,260
So what do we mean by that?

786
00:35:23,260 --> 00:35:27,270
Well, let's look at what's
up on the board.

787
00:35:27,270 --> 00:35:29,800
What's up on the board is
face-centered cubic.

788
00:35:29,800 --> 00:35:30,810
So let's do all of these.

789
00:35:30,810 --> 00:35:37,440
So we're going to say that the
Bravais lattice, in this case,

790
00:35:37,440 --> 00:35:39,990
in face-centered cubic, FCC.

791
00:35:39,990 --> 00:35:42,100
That's what this one is,
up on the board.

792
00:35:42,100 --> 00:35:43,870
And we've got dots indicate
the points.

793
00:35:43,870 --> 00:35:45,130
Because really, the points
are nothing.

794
00:35:45,130 --> 00:35:46,080
It's a concept.

795
00:35:46,080 --> 00:35:46,850
See, it's French.

796
00:35:46,850 --> 00:35:48,430
It's a concept, right?

797
00:35:48,430 --> 00:35:49,930
What's this?

798
00:35:49,930 --> 00:35:50,760
See what I'm holding?

799
00:35:50,760 --> 00:35:53,100
I'm holding a Bravais lattice.

800
00:35:53,100 --> 00:35:54,050
It's just a set of points.

801
00:35:54,050 --> 00:35:58,910
It's like a John Cage piece,
you know, a bunch of rests.

802
00:35:58,910 --> 00:36:01,820
So if I go to the piano
and I play rests in

803
00:36:01,820 --> 00:36:05,050
five four time, listen.

804
00:36:05,050 --> 00:36:05,680
Isn't that great?

805
00:36:05,680 --> 00:36:07,040
Man, it's fantastic.

806
00:36:07,040 --> 00:36:09,660
All the different rests,
and different--

807
00:36:09,660 --> 00:36:12,130
So this is a set of
lattice points.

808
00:36:12,130 --> 00:36:14,060
Now I'm going to put
something on them.

809
00:36:14,060 --> 00:36:14,880
You think I'm kidding.

810
00:36:14,880 --> 00:36:15,640
I'm not.

811
00:36:15,640 --> 00:36:15,910
All right.

812
00:36:15,910 --> 00:36:17,160
Now what's the basis?

813
00:36:19,880 --> 00:36:24,455
If I put a single atom, we have
what's up on the slide.

814
00:36:27,600 --> 00:36:29,880
And so that's the representation
of metal.

815
00:36:29,880 --> 00:36:34,280
So for example, gold is FCC,
with a single gold atom at

816
00:36:34,280 --> 00:36:35,300
each lattice point.

817
00:36:35,300 --> 00:36:37,870
Aluminum, copper, platinum.

818
00:36:37,870 --> 00:36:39,540
These are all FCC metals.

819
00:36:39,540 --> 00:36:43,570
So there's a single atom at
Bravais lattice point, and so

820
00:36:43,570 --> 00:36:49,190
the crystal structure
is known as FCC.

821
00:36:49,190 --> 00:36:50,780
It's the same as the
Bravais lattice.

822
00:36:50,780 --> 00:36:53,660
It's called FCC.

823
00:36:53,660 --> 00:36:54,420
OK.

824
00:36:54,420 --> 00:36:59,960
Now, we can also put a molecule
at each lattice site.

825
00:36:59,960 --> 00:37:02,940
So I'm going to put
up the FCC here.

826
00:37:02,940 --> 00:37:03,800
Here's the FCC.

827
00:37:03,800 --> 00:37:06,790
There's the cube, the set of
lattice points, and the

828
00:37:06,790 --> 00:37:08,050
lattice points are--

829
00:37:08,050 --> 00:37:10,220
I'm going to just illustrate
on the front face.

830
00:37:10,220 --> 00:37:13,870
One, two, three, four, and a
fifth atom at the front face.

831
00:37:13,870 --> 00:37:15,080
Now these are the points.

832
00:37:15,080 --> 00:37:18,690
I could either put simple atoms
there, and the central

833
00:37:18,690 --> 00:37:21,900
image there shows what happens
when you have the close-packed

834
00:37:21,900 --> 00:37:24,510
arrangement, the atoms are
so big that they touch.

835
00:37:24,510 --> 00:37:26,940
Or what I could do, at
each lattice point,

836
00:37:26,940 --> 00:37:28,640
I could put a molecule.

837
00:37:28,640 --> 00:37:30,640
So for example, I could
put methane.

838
00:37:30,640 --> 00:37:31,890
I could put CH4.

839
00:37:34,470 --> 00:37:35,260
A methane molecule.

840
00:37:35,260 --> 00:37:40,660
Because when one of you gets
to Jupiter, and you see the

841
00:37:40,660 --> 00:37:44,360
methane ice, and you go, oh.

842
00:37:44,360 --> 00:37:45,250
That's FCC.

843
00:37:45,250 --> 00:37:47,860
Because everybody else on the
mission hasn't taken 3091.

844
00:37:47,860 --> 00:37:49,390
They don't have a clue what
they're looking at.

845
00:37:49,390 --> 00:37:51,500
But you go, that's face-centered
cubic.

846
00:37:51,500 --> 00:37:52,410
And they go, huh?

847
00:37:52,410 --> 00:37:57,560
And this is at each
lattice site.

848
00:37:57,560 --> 00:38:00,290
You see, my point is, now look,
here's the difference.

849
00:38:00,290 --> 00:38:06,970
All five of these, the carbon
and the four hydrogens, sit at

850
00:38:06,970 --> 00:38:08,010
this lattice site.

851
00:38:08,010 --> 00:38:10,260
All five atoms sit at
this lattice site.

852
00:38:10,260 --> 00:38:14,110
It's not that the carbon goes
here, one hydrogen goes over

853
00:38:14,110 --> 00:38:16,760
at one lattice site, one
hydrogen over here.

854
00:38:16,760 --> 00:38:20,960
You don't have the methane
straddling the unit cell.

855
00:38:20,960 --> 00:38:23,360
You have all five atoms
here, five atoms here.

856
00:38:23,360 --> 00:38:27,750
At every lattice point, I
have all five atoms at

857
00:38:27,750 --> 00:38:31,690
each lattice point.

858
00:38:31,690 --> 00:38:34,580
So in that case, we also
have, it's FCC.

859
00:38:34,580 --> 00:38:38,430
So methane ice is face-centered
cubic.

860
00:38:38,430 --> 00:38:39,350
Because it's spherical.

861
00:38:39,350 --> 00:38:43,040
They pack just like gold
atoms. You know, from a

862
00:38:43,040 --> 00:38:46,650
distance, we can model this
as a sphere, as a point.

863
00:38:46,650 --> 00:38:48,352
Or we could put an ion pair.

864
00:38:50,950 --> 00:38:55,720
An example of that is sodium
and chloride, and this is

865
00:38:55,720 --> 00:38:58,350
called rock salt crystal
structure.

866
00:38:58,350 --> 00:38:58,950
Rock salt.

867
00:38:58,950 --> 00:38:59,820
Let's look at that one.

868
00:38:59,820 --> 00:39:03,420
So at each last lattice point,
I'm going to put two ions.

869
00:39:03,420 --> 00:39:05,980
Not one, two.

870
00:39:05,980 --> 00:39:07,980
This is taken from your text.

871
00:39:07,980 --> 00:39:10,880
So you might look at this and
say, well, here's the front.

872
00:39:10,880 --> 00:39:14,340
You might look at this and say,
well, isn't this kind of

873
00:39:14,340 --> 00:39:15,250
like simple cubic?

874
00:39:15,250 --> 00:39:18,190
Because I've got one, two,
three, four, but I've got

875
00:39:18,190 --> 00:39:21,090
different atoms if I
try it that way.

876
00:39:21,090 --> 00:39:22,800
See, this is taken from
a different book.

877
00:39:22,800 --> 00:39:23,930
I did some highlighting on it.

878
00:39:23,930 --> 00:39:25,450
So this is sodium
chloride again.

879
00:39:25,450 --> 00:39:27,440
One, two, three, four, five.

880
00:39:27,440 --> 00:39:30,810
With this lattice site, I put
the chloride atom and the

881
00:39:30,810 --> 00:39:31,670
sodium atom.

882
00:39:31,670 --> 00:39:34,310
The pair of atoms are
associated with

883
00:39:34,310 --> 00:39:36,080
this lattice site.

884
00:39:36,080 --> 00:39:37,930
You might say, yeah, but
this is way over here.

885
00:39:37,930 --> 00:39:39,030
Doesn't matter.

886
00:39:39,030 --> 00:39:42,610
I'm going to anchor all of those
to this lattice site.

887
00:39:42,610 --> 00:39:45,830
To this lattice site, I'm going
to anchor this and the

888
00:39:45,830 --> 00:39:47,170
sodium ion.

889
00:39:47,170 --> 00:39:49,050
So this is not simple cubic.

890
00:39:49,050 --> 00:39:52,150
Because if I try to call this
simple cubic, I have different

891
00:39:52,150 --> 00:39:54,880
atoms at different lattice
sites, and that's a no-no.

892
00:39:54,880 --> 00:39:57,050
Has to be the same.

893
00:39:57,050 --> 00:40:01,330
So if I associate the pair,
chloride ion and sodium ion,

894
00:40:01,330 --> 00:40:04,590
chloride ion and sodium ion,
chloride ion and a sodium ion

895
00:40:04,590 --> 00:40:05,300
not depicted.

896
00:40:05,300 --> 00:40:07,790
It's off the diagram here.

897
00:40:07,790 --> 00:40:11,230
And I put these dots at the
center of each chloride ion.

898
00:40:11,230 --> 00:40:14,810
Can you see that I'm
at the face of FCC?

899
00:40:14,810 --> 00:40:18,990
So that's an FCC Bravais
lattice, but it's got two

900
00:40:18,990 --> 00:40:21,970
atoms, in this case, both ions,
associated with each

901
00:40:21,970 --> 00:40:23,220
lattice point.

902
00:40:24,880 --> 00:40:26,890
I will come to the
dogs in a second.

903
00:40:26,890 --> 00:40:30,420
And now there's a last
one I can do.

904
00:40:30,420 --> 00:40:35,380
And that's got two atoms,
but not an ion pair.

905
00:40:35,380 --> 00:40:36,680
We're going to put
an atom pair.

906
00:40:40,950 --> 00:40:45,440
Got an atom pair, and that
looks like this.

907
00:40:45,440 --> 00:40:50,160
I'm going to put a carbon atom,
one carbon atom, and a

908
00:40:50,160 --> 00:40:51,900
second carbon atom.

909
00:40:51,900 --> 00:40:55,610
And this angle here
is 109 degrees.

910
00:40:55,610 --> 00:40:58,090
And I'm going to put this pair
of carbon atoms together, and

911
00:40:58,090 --> 00:41:01,510
when I do that, and I replicate
that through FCC, I

912
00:41:01,510 --> 00:41:02,970
end up with diamond cubic.

913
00:41:08,110 --> 00:41:12,380
And I'll show you a
three-dimensional example of

914
00:41:12,380 --> 00:41:13,330
that next day.

915
00:41:13,330 --> 00:41:17,490
So just bear in mind that if you
have an ion pair, you end

916
00:41:17,490 --> 00:41:18,290
up with rock salt.

917
00:41:18,290 --> 00:41:21,640
If I show you this pair,
this is due to the sp3

918
00:41:21,640 --> 00:41:22,600
hybridization.

919
00:41:22,600 --> 00:41:27,390
And so examples of this one
are diamond, not graphite,

920
00:41:27,390 --> 00:41:29,970
just diamond, silicon--

921
00:41:29,970 --> 00:41:32,630
so everything that I've shown
you about single crystals, and

922
00:41:32,630 --> 00:41:36,770
intrinsic and extrinsic
semiconduction, is diamond

923
00:41:36,770 --> 00:41:38,490
cubic crystal structure.

924
00:41:38,490 --> 00:41:40,850
But it's not one of the
Bravais lattices.

925
00:41:40,850 --> 00:41:43,790
It's an FCC Bravais
lattice with two

926
00:41:43,790 --> 00:41:46,040
atoms per lattice site.

927
00:41:46,040 --> 00:41:48,850
That's diamond cubic
crystal structure.

928
00:41:48,850 --> 00:41:50,980
But it extends to
two dimensions.

929
00:41:50,980 --> 00:41:52,710
So here's an Escher print.

930
00:41:52,710 --> 00:41:54,520
It's got all these dogs.

931
00:41:54,520 --> 00:41:58,460
In two dimensions, what's the
crystal structure here?

932
00:41:58,460 --> 00:42:01,100
Well, there's no such thing
as body-centered cubic.

933
00:42:01,100 --> 00:42:05,310
There's no third dimension
in two dimensions.

934
00:42:05,310 --> 00:42:10,690
So you've only got simple cubic
or face-centered cubic.

935
00:42:10,690 --> 00:42:11,940
So what do we have here?

936
00:42:15,080 --> 00:42:17,640
Well, you see, you've
got a problem.

937
00:42:17,640 --> 00:42:19,820
Because the black dogs are
facing the opposite direction

938
00:42:19,820 --> 00:42:20,540
of the white dogs.

939
00:42:20,540 --> 00:42:23,200
So you can't go one, two,
three, four, and make

940
00:42:23,200 --> 00:42:23,960
anything that way.

941
00:42:23,960 --> 00:42:29,040
So instead, I put dots on the,
I don't know what you call

942
00:42:29,040 --> 00:42:30,090
this part of the dog.

943
00:42:30,090 --> 00:42:31,250
I don't know.

944
00:42:31,250 --> 00:42:32,340
This part of the dog.

945
00:42:32,340 --> 00:42:33,380
The leg?

946
00:42:33,380 --> 00:42:34,880
Whatever you call this thing.

947
00:42:34,880 --> 00:42:35,070
Yeah.

948
00:42:35,070 --> 00:42:37,430
You put it on the same
spot of the dog--

949
00:42:37,430 --> 00:42:39,940
maybe I should have used his
eye, I know how to call it.

950
00:42:39,940 --> 00:42:40,220
Anyway.

951
00:42:40,220 --> 00:42:41,760
So I put these things
up, right?

952
00:42:41,760 --> 00:42:45,040
And that means that if I
associate the four dogs with

953
00:42:45,040 --> 00:42:48,440
this point, the two dogs facing
the right, and these

954
00:42:48,440 --> 00:42:49,830
two dogs facing the left.

955
00:42:49,830 --> 00:42:51,730
So these four dogs are
associated with

956
00:42:51,730 --> 00:42:52,920
this lattice site.

957
00:42:52,920 --> 00:42:56,090
Then I move up here, and I've
got the same thing.

958
00:42:56,090 --> 00:42:57,560
One, two, three four.

959
00:42:57,560 --> 00:43:00,850
Two dogs facing right,
two dogs facing left.

960
00:43:00,850 --> 00:43:06,040
So that means I've got a simple
cubic bravais lattice,

961
00:43:06,040 --> 00:43:09,650
and the basis is four dogs.

962
00:43:09,650 --> 00:43:11,390
Four dogs as my basis.

963
00:43:11,390 --> 00:43:15,770
And with that combination of a
simple cubic lattice and four

964
00:43:15,770 --> 00:43:18,900
dogs is the basis, I can make
the entire structure.

965
00:43:18,900 --> 00:43:20,100
That's what this is all about.

966
00:43:20,100 --> 00:43:21,880
That's my unit cell, that's
my repeat unit.

967
00:43:25,500 --> 00:43:27,060
So there's simple cubic,
right there.

968
00:43:27,060 --> 00:43:30,300
So instead of a single atom at
each corner, or these are

969
00:43:30,300 --> 00:43:34,340
spheres that are touching,
we got the four dogs.

970
00:43:34,340 --> 00:43:34,980
Here's another one.

971
00:43:34,980 --> 00:43:37,480
Once I got the Escher, I kept
flipping through the book.

972
00:43:37,480 --> 00:43:39,860
I don't know what this thing
is, but it's creepy.

973
00:43:39,860 --> 00:43:40,540
Anyway.

974
00:43:40,540 --> 00:43:42,040
It's wallpaper.

975
00:43:42,040 --> 00:43:44,100
If it's wallpaper,
it's ordered.

976
00:43:44,100 --> 00:43:46,440
If it's ordered, it's a
two-dimensional crystal.

977
00:43:46,440 --> 00:43:49,080
If it's a two-dimensional
crystal, it has to conform to

978
00:43:49,080 --> 00:43:51,520
one of the 14 Bravais
lattices.

979
00:43:51,520 --> 00:43:53,190
So which one is it?

980
00:43:53,190 --> 00:43:57,750
So I looked at this for a while,
and I took this happy

981
00:43:57,750 --> 00:44:00,570
entity here, and I put
a dot in its belly.

982
00:44:00,570 --> 00:44:03,660
So wherever I found one
of these, I put a dot.

983
00:44:03,660 --> 00:44:06,010
and then I connected the dots,
and what do I get?

984
00:44:06,010 --> 00:44:09,230
I got the rhombus.

985
00:44:09,230 --> 00:44:10,990
Now, what's the basis?

986
00:44:10,990 --> 00:44:13,470
That's the Bravais lattice.

987
00:44:13,470 --> 00:44:15,630
What is the basis?

988
00:44:15,630 --> 00:44:18,210
So I went over here and I said,
well, if I start from

989
00:44:18,210 --> 00:44:20,630
this thing and I go all
the way up, I got some

990
00:44:20,630 --> 00:44:22,350
tail, blue tail here.

991
00:44:22,350 --> 00:44:23,900
And this thing way down
here looks like

992
00:44:23,900 --> 00:44:24,920
it's missing a tail.

993
00:44:24,920 --> 00:44:28,350
So if I start from this, go all
the way down to here, and

994
00:44:28,350 --> 00:44:32,560
capture all of this material
in between and associate it

995
00:44:32,560 --> 00:44:36,510
with that lattice point,
that can be my basis.

996
00:44:36,510 --> 00:44:41,580
And then I take that set of
imagery, and I put it on top

997
00:44:41,580 --> 00:44:45,250
of this, where it's centered at
about this thing's navel,

998
00:44:45,250 --> 00:44:46,690
and put it around here.

999
00:44:46,690 --> 00:44:49,170
You can see, the translation
is obvious there, and the

1000
00:44:49,170 --> 00:44:50,730
translation is obvious here.

1001
00:44:50,730 --> 00:44:52,270
There's the wallpaper.

1002
00:44:52,270 --> 00:44:55,300
So it's part of a Bravais
lattice, only in two

1003
00:44:55,300 --> 00:44:57,060
dimensions, you see?

1004
00:44:57,060 --> 00:44:59,170
This is crystallography.

1005
00:44:59,170 --> 00:45:00,180
That's all it is.

1006
00:45:00,180 --> 00:45:02,310
Crystallography.

1007
00:45:02,310 --> 00:45:03,130
All right.

1008
00:45:03,130 --> 00:45:06,240
So the next thing that we have
to do, it's kind of a little

1009
00:45:06,240 --> 00:45:09,310
bit boring, but you need to know
this stuff, because it's

1010
00:45:09,310 --> 00:45:12,290
formative for the next unit.

1011
00:45:12,290 --> 00:45:15,060
It's the characteristics
of cubic lattices.

1012
00:45:15,060 --> 00:45:16,200
Now what do I mean, the
characteristics?

1013
00:45:16,200 --> 00:45:17,880
I mean the geometric
characteristics.

1014
00:45:17,880 --> 00:45:20,270
So there's a table here that
I've taken out of your

1015
00:45:20,270 --> 00:45:21,880
archival reading.

1016
00:45:21,880 --> 00:45:25,290
If you go to the website,
there's a set of notes that

1017
00:45:25,290 --> 00:45:27,880
were written by my predecessor,
Professor Witt.

1018
00:45:27,880 --> 00:45:30,560
And if you go and look
this up, this unit on

1019
00:45:30,560 --> 00:45:32,610
crystallography, there's
this table.

1020
00:45:32,610 --> 00:45:35,780
And it shows such things as
the unit cell volume.

1021
00:45:35,780 --> 00:45:36,610
Well, what's the unit cell?

1022
00:45:36,610 --> 00:45:40,190
The unit cell is this cookie
cutter cube that's the repeat

1023
00:45:40,190 --> 00:45:44,340
unit, and it has a dimension
here called a, which is the

1024
00:45:44,340 --> 00:45:46,985
lattice constant.

1025
00:45:46,985 --> 00:45:49,440
It's the size of the box.

1026
00:45:49,440 --> 00:45:51,440
So what's the volume
of the unit cell

1027
00:45:51,440 --> 00:45:52,750
Well, duh, it's a cubed.

1028
00:45:52,750 --> 00:45:54,100
That's obvious, all right?

1029
00:45:54,100 --> 00:45:56,200
Doesn't matter whether it's
simple cubic, face-centered

1030
00:45:56,200 --> 00:45:57,900
cubic, body centered cubic.

1031
00:45:57,900 --> 00:46:00,740
How many lattice points
per unit cell?

1032
00:46:00,740 --> 00:46:05,385
Well, that's-- how many atoms
do I get per unit cell?

1033
00:46:05,385 --> 00:46:08,120
If you look at this, you
say, well gee, it's--

1034
00:46:08,120 --> 00:46:09,960
you know, if you've got the
simple cubic, you've got them

1035
00:46:09,960 --> 00:46:11,820
at the eight corners, so
it's eight, right?

1036
00:46:11,820 --> 00:46:15,800
Well, no, because each atom on
the corner is inside this

1037
00:46:15,800 --> 00:46:18,950
cell, but it's also inside the
neighboring cell, and it's

1038
00:46:18,950 --> 00:46:21,200
inside each of the eight
neighboring cells.

1039
00:46:21,200 --> 00:46:23,725
So I have eight times
one eighth.

1040
00:46:23,725 --> 00:46:28,000
So the total amount of atom
within the cube is only one.

1041
00:46:28,000 --> 00:46:30,110
That's why you've got to go
through this derivation.

1042
00:46:30,110 --> 00:46:32,540
So here's an example for
face-centered cubic.

1043
00:46:32,540 --> 00:46:35,190
You see the corners, one,
two, three, four?

1044
00:46:35,190 --> 00:46:36,580
There's eight of those.

1045
00:46:36,580 --> 00:46:38,300
Eight times one eighth is one.

1046
00:46:38,300 --> 00:46:40,770
And then you've got these atoms
on the face, and there's

1047
00:46:40,770 --> 00:46:43,130
one, two, three, four,
five, six, right?

1048
00:46:43,130 --> 00:46:44,850
Six faces.

1049
00:46:44,850 --> 00:46:46,870
But each of these atoms
on the face is only

1050
00:46:46,870 --> 00:46:48,170
half inside the cube.

1051
00:46:48,170 --> 00:46:50,420
The other half is in
the other cube.

1052
00:46:50,420 --> 00:46:52,850
So I got six times one half is
three, and that gives me four.

1053
00:46:52,850 --> 00:46:55,270
So that's how you go through,
and figure out

1054
00:46:55,270 --> 00:46:55,990
what's going on.

1055
00:46:55,990 --> 00:46:58,270
And then you can look at things
like nearest neighbor

1056
00:46:58,270 --> 00:47:00,920
distance, and what's the
relationship between the

1057
00:47:00,920 --> 00:47:03,860
radius, if you're looking
at hard sphere packing.

1058
00:47:03,860 --> 00:47:04,650
So here's a good example.

1059
00:47:04,650 --> 00:47:07,240
Here's the hard sphere
packing model.

1060
00:47:07,240 --> 00:47:09,920
So I've got atoms all
the same size, and

1061
00:47:09,920 --> 00:47:12,360
they're packed to touch.

1062
00:47:12,360 --> 00:47:14,830
And they're packed to touch so
that in the end, I end up with

1063
00:47:14,830 --> 00:47:17,000
a face centered cubic
arrangement.

1064
00:47:17,000 --> 00:47:20,370
And so what's the relationship
between the radius and the

1065
00:47:20,370 --> 00:47:21,370
lattice constant?

1066
00:47:21,370 --> 00:47:23,170
And it's just simple
trigonometry, right?

1067
00:47:23,170 --> 00:47:27,500
4r equals 2a squared, and you go
through it, and that's how

1068
00:47:27,500 --> 00:47:30,090
you end up with all
these formulas.

1069
00:47:30,090 --> 00:47:31,880
So that's what going on.

1070
00:47:31,880 --> 00:47:32,220
All right.

1071
00:47:32,220 --> 00:47:36,350
So I think we're going to move
to the last five minutes here.

1072
00:47:36,350 --> 00:47:38,570
So just a couple of comments.

1073
00:47:38,570 --> 00:47:41,340
Today we played music
when you came in.

1074
00:47:41,340 --> 00:47:44,630
It was Burning Down the House.

1075
00:47:44,630 --> 00:47:46,620
An old piece by Talking Heads.

1076
00:47:46,620 --> 00:47:48,280
Why was I playing Burning
Down the House?

1077
00:47:48,280 --> 00:47:50,740
Well, I want you to study
this painting.

1078
00:47:50,740 --> 00:47:54,532
This is a painting by Georges
Braques, from 1908, And it's

1079
00:47:54,532 --> 00:47:57,510
called The Houses at L'estac,
or if I speak Canadian, The

1080
00:47:57,510 --> 00:47:59,042
Houses at L'estac.

1081
00:47:59,042 --> 00:48:01,440
And you see the thing
about these houses?

1082
00:48:01,440 --> 00:48:03,280
You see the ones in the
background have better

1083
00:48:03,280 --> 00:48:05,620
definitions than the ones
in the foreground?

1084
00:48:05,620 --> 00:48:09,550
And the ones in the foreground
are all distorted, and kind of

1085
00:48:09,550 --> 00:48:11,240
falling over?

1086
00:48:11,240 --> 00:48:14,710
Well, when this was exhibited
at the Salon, on the critics

1087
00:48:14,710 --> 00:48:15,590
lambasted it.

1088
00:48:15,590 --> 00:48:18,590
They said, this thing is
absolutely childish.

1089
00:48:18,590 --> 00:48:20,860
And one of the critics
said, this isn't

1090
00:48:20,860 --> 00:48:21,790
a painting of houses.

1091
00:48:21,790 --> 00:48:24,240
This is nothing but
a stack of cubes.

1092
00:48:24,240 --> 00:48:28,550
And from this painting, and that
negative comment, came

1093
00:48:28,550 --> 00:48:30,160
the term cubism.

1094
00:48:30,160 --> 00:48:32,600
And so the entire movement of
cubism comes from this.

1095
00:48:32,600 --> 00:48:34,780
And since we're studying the
properties of cubic crystals,

1096
00:48:34,780 --> 00:48:37,060
I thought the connection
was pretty tight.

1097
00:48:37,060 --> 00:48:40,220
And that's why I chose
that piece.

1098
00:48:40,220 --> 00:48:41,120
Don't go anywhere yet.

1099
00:48:41,120 --> 00:48:43,880
We still have a couple
of minutes.

1100
00:48:43,880 --> 00:48:46,090
It's not better out there
than it is in

1101
00:48:46,090 --> 00:48:47,770
here, I guarantee you.

1102
00:48:47,770 --> 00:48:48,030
All right.

1103
00:48:48,030 --> 00:48:49,730
So now I want to show you
one of the properties.

1104
00:48:49,730 --> 00:48:52,840
Why do we care about atomic
arrangement Suppose some of

1105
00:48:52,840 --> 00:48:54,590
you are interested
in fiberoptics.

1106
00:48:54,590 --> 00:48:56,620
One of the things you have to
do in fiberoptics is make

1107
00:48:56,620 --> 00:48:59,710
junctures, because you can't run
a cable 100 miles without

1108
00:48:59,710 --> 00:49:01,030
making some junctures.

1109
00:49:01,030 --> 00:49:04,340
Well, atomic arrangement
reflects microscopic

1110
00:49:04,340 --> 00:49:04,870
properties.

1111
00:49:04,870 --> 00:49:07,730
And one of the properties that
you can have in a crystal is

1112
00:49:07,730 --> 00:49:10,220
something called birefringence,
depending on

1113
00:49:10,220 --> 00:49:11,470
the atomic arrangement.

1114
00:49:11,470 --> 00:49:13,740
So what happens is if you have
a ray that comes in from the

1115
00:49:13,740 --> 00:49:16,760
left here, it splits into two.

1116
00:49:16,760 --> 00:49:19,340
And that's no good, in
certain instances.

1117
00:49:19,340 --> 00:49:22,110
In other instances, if you want
a beam splitter, you want

1118
00:49:22,110 --> 00:49:23,360
something birefringent.

1119
00:49:25,320 --> 00:49:26,910
So look at all these crystals.

1120
00:49:26,910 --> 00:49:28,470
Quartz is birefringent.

1121
00:49:28,470 --> 00:49:29,130
Ice is.

1122
00:49:29,130 --> 00:49:30,490
You've seen it.

1123
00:49:30,490 --> 00:49:32,310
Calcite is birefringent.

1124
00:49:32,310 --> 00:49:33,260
What do I mean by that?

1125
00:49:33,260 --> 00:49:39,900
Well, Dave, can we cut to
the document camera?

1126
00:49:39,900 --> 00:49:40,070
Right.

1127
00:49:40,070 --> 00:49:43,310
So here's a here's
a crystal of--

1128
00:49:43,310 --> 00:49:44,580
well, this is my handwriting.

1129
00:49:44,580 --> 00:49:45,550
It's beautiful.

1130
00:49:45,550 --> 00:49:47,240
Let's write-- here's more.

1131
00:49:47,240 --> 00:49:48,870
Isn't that beautiful?

1132
00:49:48,870 --> 00:49:50,090
OK, enough about me.

1133
00:49:50,090 --> 00:49:51,085
Now let's--

1134
00:49:51,085 --> 00:49:51,590
All right.

1135
00:49:51,590 --> 00:49:52,840
So this is birefringent.

1136
00:49:55,010 --> 00:49:57,800
But what happens if
we rotate it?

1137
00:49:57,800 --> 00:49:59,870
We can change the degree.

1138
00:49:59,870 --> 00:50:04,070
And if we're really clever, and
we get it onto the optical

1139
00:50:04,070 --> 00:50:07,770
axis, we can actually get these
things to superimpose.

1140
00:50:07,770 --> 00:50:09,210
Here's a piece of cryolite.

1141
00:50:09,210 --> 00:50:12,460
This is the stuff they
make aluminum out of.

1142
00:50:12,460 --> 00:50:13,670
They dissolve aluminum in it.

1143
00:50:13,670 --> 00:50:16,280
And you can see that, see, I
loaned it to somebody, and

1144
00:50:16,280 --> 00:50:17,070
they dropped it.

1145
00:50:17,070 --> 00:50:18,970
And when they dropped
it, they damaged it.

1146
00:50:18,970 --> 00:50:20,470
That's what happens.

1147
00:50:20,470 --> 00:50:22,300
Look, it's all crunched
up there.

1148
00:50:22,300 --> 00:50:25,120
But anyway, I don't want
to get into that.

1149
00:50:25,120 --> 00:50:28,630
But so you can see, if we turn
this and we get it right on

1150
00:50:28,630 --> 00:50:32,010
the optical axis, we can
actually make these things

1151
00:50:32,010 --> 00:50:36,060
line up sometimes.

1152
00:50:36,060 --> 00:50:36,680
Anyway.

1153
00:50:36,680 --> 00:50:40,090
So you can see the property
of birefringence.

1154
00:50:40,090 --> 00:50:41,010
OK.

1155
00:50:41,010 --> 00:50:44,310
Let's go back to documents,
Dave. One more thing.

1156
00:50:47,950 --> 00:50:49,110
Last thing I want to show you.

1157
00:50:49,110 --> 00:50:49,840
You know gold.

1158
00:50:49,840 --> 00:50:50,840
Gold looks like this.

1159
00:50:50,840 --> 00:50:51,770
It's yellow, right?

1160
00:50:51,770 --> 00:50:54,830
Well, depending on how you, you
know, those of you have

1161
00:50:54,830 --> 00:50:57,660
seen certain wedding bands know
that if you want to make

1162
00:50:57,660 --> 00:50:59,240
a white gold, you add
nickel to it.

1163
00:50:59,240 --> 00:51:01,695
And once the nickel content gets
above a certain level,

1164
00:51:01,695 --> 00:51:03,020
the gold looks white.

1165
00:51:03,020 --> 00:51:06,030
In other words, just metallic
reflective.

1166
00:51:06,030 --> 00:51:08,490
In Eastern Europe, it was common
to add high levels of

1167
00:51:08,490 --> 00:51:11,410
copper, in which case, you get a
beautiful rose-colored gold,

1168
00:51:11,410 --> 00:51:12,710
or pink gold.

1169
00:51:12,710 --> 00:51:16,080
I'm going to show you
some blue gold.

1170
00:51:16,080 --> 00:51:17,020
This isn't a joke.

1171
00:51:17,020 --> 00:51:19,360
This is 14 karat.

1172
00:51:19,360 --> 00:51:23,270
It's 40 plus percent
by weight gold, and

1173
00:51:23,270 --> 00:51:24,745
the balance is indium.

1174
00:51:24,745 --> 00:51:28,950
And when you add indium
to gold, you get blue.

1175
00:51:28,950 --> 00:51:30,400
Document camera, please.

1176
00:51:33,520 --> 00:51:35,940
Just so that you remember.

1177
00:51:35,940 --> 00:51:37,160
OK.

1178
00:51:37,160 --> 00:51:37,950
That's gold.

1179
00:51:37,950 --> 00:51:38,950
This is gold foil.

1180
00:51:38,950 --> 00:51:41,200
Rutherford, et cetera,
et cetera.

1181
00:51:41,200 --> 00:51:44,520
You know, this is yellow gold.

1182
00:51:44,520 --> 00:51:45,760
Ho-hum.

1183
00:51:45,760 --> 00:51:46,940
This is white gold.

1184
00:51:46,940 --> 00:51:48,660
Same deal, but with
some nickel.

1185
00:51:48,660 --> 00:51:51,770
Now it's reflecting off
of the yellow gold.

1186
00:51:51,770 --> 00:51:53,314
Boy, there's a lot of
yellow in here.

1187
00:51:53,314 --> 00:51:55,980
Where's that coming from?

1188
00:51:55,980 --> 00:51:58,610
It's hard to tell.

1189
00:51:58,610 --> 00:51:58,870
All right.

1190
00:51:58,870 --> 00:52:00,120
Now Let's look at
some blue gold.

1191
00:52:03,370 --> 00:52:04,620
This is blue.

1192
00:52:08,970 --> 00:52:10,820
So, but it's brittle.

1193
00:52:10,820 --> 00:52:12,380
So you know, what are you going
to do with something

1194
00:52:12,380 --> 00:52:12,810
that's brittle?

1195
00:52:12,810 --> 00:52:13,580
You can't shape it.

1196
00:52:13,580 --> 00:52:14,790
So I have an idea.

1197
00:52:14,790 --> 00:52:16,170
So here's my idea.

1198
00:52:16,170 --> 00:52:17,420
See, what we do is--

1199
00:52:21,920 --> 00:52:23,030
see this?

1200
00:52:23,030 --> 00:52:26,550
We do, instead of this,
we put this.

1201
00:52:26,550 --> 00:52:29,520
We drill a hole in it, we put
hands on it, we sell it for a

1202
00:52:29,520 --> 00:52:31,360
lot of money.

1203
00:52:31,360 --> 00:52:32,560
It's blue gold.

1204
00:52:32,560 --> 00:52:36,180
It's blue karat gold.

1205
00:52:36,180 --> 00:52:39,170
What you can do if you
understand crystallography.

1206
00:52:39,170 --> 00:52:39,840
All right, get out of here.

1207
00:52:39,840 --> 00:52:41,720
I'll see you on Friday.