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03 Drude Theory of Electrons in Metals Sommerfeld Free Electron Theory of Electrons in Metals.srt
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3051 lines (2541 loc) · 85.7 KB
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在我们开始之前,我想对如何
before we get going I want to do a
little bit of philosophizing about how
2
00:00:03,689 --> 00:00:07,740
我们开始的一周开始就是在物理学中学习东西
it is we learn things in in physics at
the beginning of the week we started
3
00:00:07,740 --> 00:00:11,910
用固体振动的玻尔兹曼模型,然后我们决定
with the Boltzmann model of vibrations
in solids and then we decided that
4
00:00:11,910 --> 00:00:15,570
不太正确,因此我们必须使用固体的爱因斯坦模型对其进行改进
wasn't quite right so we had to improve
it with the Einstein model of the solid
5
00:00:15,570 --> 00:00:18,840
那是相当不错的,但是没有正确的低温行为
and that was pretty good but it didn't
get the low-temperature behavior right
6
00:00:18,840 --> 00:00:22,199
所以我们不得不用德拜固体理论对其进行改进,甚至
so we had to improve it with the Debye
theory of solids and that was even
7
00:00:22,199 --> 00:00:25,019
更好,但今年晚些时候我们也将不得不对其进行改进
better but we're going to have to
improve it later on in the year as well
8
00:00:25,019 --> 00:00:28,949
一个完全正确的问题是我们为什么不从中学到正确的东西
and a perfectly valid question is why
didn't we learn the right thing at the
9
00:00:28,949 --> 00:00:32,969
开始,而不必经历所有这些错误的模型,并且
beginning and not have to go through all
of these models which are all wrong and
10
00:00:32,969 --> 00:00:37,530
这不仅仅是因为我喜欢告诉您了解有关所有
it's not just because I like telling you
know history stories about how all of
11
00:00:37,530 --> 00:00:41,160
这是开发出来的,但我们这样做的原因是因为这始终是我们的方式
this was developed but the reason we do
this is because this is always how we
12
00:00:41,160 --> 00:00:43,920
在物理学中学习事物,即使它是
learn things in physics you always learn
the simple model even though it's
13
00:00:43,920 --> 00:00:47,789
首先是错误的,因为这样容易思考,例如
incorrect first because it's a lot
easier to think about so for example you
14
00:00:47,789 --> 00:00:51,149
首先要学习古典力学,这是不对的,因为你知道
learn in classical mechanics first and
it's not really right because you know
15
00:00:51,149 --> 00:00:54,059
有相对论和量子力学,然后将它们叠加
there's special relativity and there's
quantum mechanics and you layer those on
16
00:00:54,059 --> 00:00:58,469
回到顶部,但是您的直觉总是回到简单的模型上
top later but your intuition always
falls back to the simple model it's a
17
00:00:58,469 --> 00:01:01,559
更容易思考,这就是我们这样做的原因,而这正是
lot easier to think about and that's why
we do this and this is exactly what
18
00:01:01,559 --> 00:01:06,380
今天我们要谈论上次开始的金属时要做的
we're going to be doing today when we
talk about metals we started last time
19
00:01:06,380 --> 00:01:13,020
金属和我们用于许多事物的简单原油模型是德鲁伊
metals and the simple crude model we use
for many many things is the druid
20
00:01:13,020 --> 00:01:15,869
电子和金属的图片
apicture
of electrons and metals which is
21
00:01:15,869 --> 00:01:24,530
基本上只是动力学理论。
basically just kinetic theory kinetic
theory for electrons for electrons and
22
00:01:24,530 --> 00:01:32,610
在最后一次结束时,我们导出了dru来传递方程D动量DT
at the end of last time we derived the
dru to transport equation D momentum DT
23
00:01:32,610 --> 00:01:39,840
等于在某些现象学散射上电子减去P上的力
equals the force on the electron minus P
over some phenomenological scattering
24
00:01:39,840 --> 00:01:48,570
时间力是洛伦兹力的时间tau
time tau where the force is Lorentz
force the general force that the
25
00:01:48,570 --> 00:01:52,770
电子的感觉,所以基本上只是牛顿方程,增加了阻力
electron feels so it's basically just
Newton's equation with an added drag
26
00:01:52,770 --> 00:01:57,960
P超过tau的力P代表散射
force P over tau which sort of
represents scattering sort of slows the
27
00:01:57,960 --> 00:02:01,799
现在,对于许多实验,电子都会以某种方式下降,我们将对此感兴趣
electron down in some way now for many
experiments we're going to be interested
28
00:02:01,799 --> 00:02:05,939
在我们实际上正在进行某种稳态实验,您可能会应用
in we are actually doing some sort of
steady state experiment you might apply
29
00:02:05,939 --> 00:02:10,080
稳定的电场,您可能会施加稳定的电流,并且您对此感兴趣
a steady electric field you might apply
a steady current and you're interested
30
00:02:10,080 --> 00:02:15,590
处于稳定状态的结果,因此大大简化了寻找工作
in a steady state result so it's
simplifies things a lot to look for
31
00:02:15,590 --> 00:02:25,189
稳态,所以DP DT等于零,所以我们尝试解决,使GP DT等于
steady states so DP DT equals zero so
let's try to solve that so GP DT equals
32
00:02:25,189 --> 00:02:28,939
零,我们将在右侧施加力,因此我要使用的力
zero we'll put in the force on the right
hand side here so the force I'm going to
33
00:02:28,939 --> 00:02:36,680
用洛伦兹力加V叉B代替,然后我们需要P超过tau
replace that by the Lorentz force plus V
cross B and then we need P over tau over
34
00:02:36,680 --> 00:02:42,139
在这里,但是我要用tau的MV代替P,因为我们有一个速度
here but I'm going to replace P by M V
over tau just because we have a velocity
35
00:02:42,139 --> 00:02:46,970
哦,这里有相同的速度,我们现在要在其中放置另一个速度
here oh there's the same velocity here
we'll put another velocity there now
36
00:02:46,970 --> 00:02:51,260
速度是一个非常好的数量,但实际上不是你所需要的
velocity is a perfectly good quantity
but it's not actually what you are
37
00:02:51,260 --> 00:02:54,620
有可能在实验中进行测量,而您更有可能进行测量
likely to measure in the experiment
which you're much more likely to measure
38
00:02:54,620 --> 00:03:02,030
实验是电流密度电流密度与
an experiment is the current density
current density very closely related to
39
00:03:02,030 --> 00:03:10,750
速度J是电子数或电子密度
velocity J is the number of electron or
the density of electrons density of
40
00:03:10,750 --> 00:03:16,400
电子乘以电子上的电荷至负e乘以电子
electrons times the charge on the
electron goes to minus e times his
41
00:03:16,400 --> 00:03:21,109
速度好,所以电流密度就是你拥有多少电子,但是
velocity okay so the current density is
just how many electrons you have but the
42
00:03:21,109 --> 00:03:26,269
给他们充电,移动速度有多快,所以每次我有速度时
charge they have and how fast they're
moving so every time I have velocity in
43
00:03:26,269 --> 00:03:30,859
该方程式我将插入J并除以N和负E
that equation I'm going to plug in J
instead and divide by an N and a minus E
44
00:03:30,859 --> 00:03:36,979
第一步,我还要将e移到另一边
and one step I'm also going to move e
over to the other side and get this
45
00:03:36,979 --> 00:03:53,840
方程e在整个J交叉B上等于1,然后在N平方的tau时间上等于M
equation e equals one over n e J cross B
and then plus M over N squared tau times
46
00:03:53,840 --> 00:04:05,239
J对一次太多的步骤感到非常高兴,是的,所以我只是我
J is that good happy with that too many
steps at once yeah so I just I just
47
00:04:05,239 --> 00:04:07,819
插入j4v,然后将D移动到另一侧
plugged in j4v
and then move D to the other side and
48
00:04:07,819 --> 00:04:13,069
通过任何驱动器将其划分为我的密钥,好吧,所以这有两个术语
divide it through by any drive to my key
okay good so there's two terms in this
49
00:04:13,069 --> 00:04:15,739
等式,我们称它们为两个不同的东西
equation and we'll call them two
different things
50
00:04:15,739 --> 00:04:23,530
让我们将此称为e并行,我们将其称为e暂停
let's call this e parallel and we'll
call this e halt
51
00:04:23,530 --> 00:04:29,620
我用这个画一个图,所以我们有一块金属
let me draw a diagram with this so we
have is we have a block of metal like
52
00:04:29,620 --> 00:04:35,710
这将使电流像这样的电流流过金属
this we're going to run a current
through the metal like this current
53
00:04:35,710 --> 00:04:40,360
像我们可能会施加磁场
density in content C out like that we
might apply a magnetic field
54
00:04:40,360 --> 00:04:46,300
也许像这样的B垂直于金属,然后我们将有一个平行
maybe perpendicular to the metal like
this B and then we will have a parallel
55
00:04:46,300 --> 00:04:50,680
在这个方向上的电场在那个方向上然后是霍尔垂直
in this direction electric field in that
direction and then a Hall perpendicular
56
00:04:50,680 --> 00:05:00,580
电流和垂直于磁场以及一个大厅,它是
to the current and perpendicular to the
magnetic field as well a hall and it's
57
00:05:00,580 --> 00:05:04,960
之所以称为霍尔电场是因为它是由埃德温·霍尔(Edwin Hall)发现的,
called the hall electric field because
it was discovered by Edwin Hall who is
58
00:05:04,960 --> 00:05:09,370
正是在1879年进行了这类实验,他发现当他
doing exactly these kind of experiments
in 1879 and he discovered that when he
59
00:05:09,370 --> 00:05:13,270
在磁场中使电流流过金属,最终导致
ran a current through a metal in a
magnetic field he ended up with an
60
00:05:13,270 --> 00:05:15,880
垂直于它们两个的电场,您之前可能已经遇到过
electric field perpendicular both of
them you may have run into this before
61
00:05:15,880 --> 00:05:20,110
这是洛伦兹力量的一个非常明显的结果,发生的是你在
it's a pretty clear result of the
Lorentz force what's happening is you're
62
00:05:20,110 --> 00:05:23,980
使电子穿过材料,并且它们试图弯曲,因为
running electrons through the material
and they're trying to curve because of
63
00:05:23,980 --> 00:05:29,410
磁场并建立一个电场,每个人都满意
the magnetic field and that builds up an
electric field good everyone happy with
64
00:05:29,410 --> 00:05:36,310
差不多,所以让我们尝试了解一下这个方程
that more or less okay so let's try to
you know think about this equation a
65
00:05:36,310 --> 00:05:42,780
让我们更简单地考虑一个磁场为零的简单情况
little more closely let's take a simple
case case one magnetic field equals zero
66
00:05:42,780 --> 00:05:48,580
所以在那种情况下,我们只有电场让我绕过另一个
so in that case we just have electric
field let me turn it around the other
67
00:05:48,580 --> 00:05:50,860
将J移到他们旁边的方式
way
move the J to their side so J the
68
00:05:50,860 --> 00:05:58,390
然后,电流在m倍于电场的平方n上被平方
current is then n e squared Tao over m
times the electric field this quantity
69
00:05:58,390 --> 00:06:07,450
这是电导率Sigma电导率这是电导率,因为
here is a conductivity Sigma
conductivity it's a conductivity because
70
00:06:07,450 --> 00:06:12,640
它把电场与电流联系起来
it relates the electric field to the
current now the expression for the
71
00:06:12,640 --> 00:06:16,750
我们在m上推导出e平方的Tao的电导率是Deuter
conductivity that we derived an e
squared Tao over m is the Deuter
72
00:06:16,750 --> 00:06:20,350
电导率是我们将在Drude理论中计算出的电导率
conductivity is the conductivity we
would calculate in the Drude theory we
73
00:06:20,350 --> 00:06:24,729
只是计算了一下,我们对什么是什么应该有一个很容易的直觉
just calculated it and we should have
pretty easy intuition for what's what's
74
00:06:24,729 --> 00:06:31,300
继续讲,电导率具有最高密度的因素,因为
going on here the conductivity has a
factor of density up top because the
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00:06:31,300 --> 00:06:34,240
电子越多,电流就越多
more electrons you have the more current
you're going to get and the more
76
00:06:34,240 --> 00:06:37,840
您将要获得的电导率是tau的系数
conductivity you're going to get it has
a factor of tau up top
77
00:06:37,840 --> 00:06:41,950
因为越长的道越大道意味着更长的散射时间和更长的时间
because longer Tao bigger Tao means
longer scattering time and the longer
78
00:06:41,950 --> 00:06:45,040
散布时间或更少的事情变得更好
scattering time you have or the less
things you have to run into the better
79
00:06:45,040 --> 00:06:48,700
现在你的电导率会变成事实,我正在楼下,看起来有点
your conductivity is going to be now the
fact I'm mass downstairs looks a little
80
00:06:48,700 --> 00:06:53,470
稍微复杂一点,但实际上如果质量等于F等于MA
bit more complicated but actually it
just comes from F equals MA if your mass
81
00:06:53,470 --> 00:06:58,030
对于固定力来说很小,您的加速度必须更大,所以您
is small for a fixed force your
acceleration has to be larger so you
82
00:06:58,030 --> 00:07:02,710
施加一定的固定力,如果电子质量较小,则电子运动得更快
apply out some fixed force the electrons
move faster if their mass were smaller
83
00:07:02,710 --> 00:07:08,650
这就是为什么现在我们可能要问楼下传出大量东西的原因,或者保罗提请德
that's why the mass comes out downstairs
now we might ask or Paul drew de might
84
00:07:08,650 --> 00:07:11,020
问这是一个好答案吗?
ask is this a good answer is this a bad
answer
85
00:07:11,020 --> 00:07:17,320
现在我们实际上不知道,因为它是一个未知数
and right now we actually don't know
because how is some unknown number it's
86
00:07:17,320 --> 00:07:21,550
他不知道如何计算的一些现象,我们只能把
some phenomena he doesn't know how to
calculate it we can just we have to put
87
00:07:21,550 --> 00:07:25,120
从现象学上讲,所以实际上它几乎适合任何东西
it in phenomenologically so really it
would fit pretty much anything at this
88
00:07:25,120 --> 00:07:27,760
点,所以你可能会想到它,你知道排序
point
so you might think of it you know sort
89
00:07:27,760 --> 00:07:31,660
这反过来说明电导率的测量实际上是
of turn this on its head that
measurement of conductivity is actually
90
00:07:31,660 --> 00:07:37,110
参数tau的度量正常,这通常是如何查看的
a measurement of the parameter tau okay
and that's frequently how it's viewed
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00:07:37,110 --> 00:07:43,780
好吧,让我们做一些稍微复杂一些的事
all right let's do a little something a
little bit more complicated case to case
92
00:07:43,780 --> 00:07:48,789
B等于零的两个,我们可能会以多种方式思考
two which is B not equal to zero and
there are various ways we might think
93
00:07:48,789 --> 00:07:53,350
关于B不等于零的一种可能
about B not equal to zero one
possibility of doing this experiment is
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00:07:53,350 --> 00:08:00,070
我们可能想像一下,假设我们知道,所以将其称为假设我们知道一对
we might imagine suppose we know so it's
called its to a suppose we know a couple
95
00:08:00,070 --> 00:08:03,880
假设我们知道电子的密度,当然我们知道
things suppose we know the density of
our electrons of course we know the
96
00:08:03,880 --> 00:08:12,250
电子上的电荷假设我们知道电流并且我们测量我们测量一个
charge on the electron suppose we know
the current and we measure we measure a
97
00:08:12,250 --> 00:08:19,660
然后根据犹大理论停下来,我们知道然后我们得到一个磁场B
halt then according to Judah Theory we
then know then we get a magnetic field B
98
00:08:19,660 --> 00:08:25,479
实际上,这是一种非常常用的测量磁场的方法
and in fact this is a very frequently
used method for measuring magnetic
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00:08:25,479 --> 00:08:34,679
在现场它被称为霍尔传感器,并且您知道它仍然经常在
fields it's known as a hall sensor and
you know it's still used frequently in
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00:08:34,679 --> 00:08:39,218
现在,让我们稍微详细一点
101
00:08:39,219 --> 00:08:46,870
通常在这里,如果您在磁场中有电流,您将会得到一些东西
here generally if you have a current in
a magnetic field you will get something
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00:08:46,870 --> 00:08:54,550
的形式,我们定义此数量rhv cross j注意转订单
of the form we define this quantity
rhv cross j notice that turn the order
103
00:08:54,550 --> 00:08:59,110
J和B在那边的-在这里这只是常用的定义
of J and B over there - over here this
is just a definition of a commonly used
104
00:08:59,110 --> 00:09:03,060
称为霍尔系数的数量
quantity known as the Hall coefficient
105
00:09:05,850 --> 00:09:13,990
所以嗯,你知道你是否知道J是什么,B就是II
so um you know if you know what J is you
know what B is measure II get the Hall
106
00:09:13,990 --> 00:09:25,120
例如,系数如此正确,因此吸引了犹大理论比较
coefficient for example so right so in
drew the theory Judah Theory comparing
107
00:09:25,120 --> 00:09:31,480
这个方程式,所以这是犹大理论中的B霍尔对不起G霍尔
to that equation so this is B Hall sorry
G Hall in Judah Theory comparing to that
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00:09:31,480 --> 00:09:41,110
那里的等式,霍尔系数RH在密度乘以1时得到-e减去
equation over there the hall coefficient
RH is 1 over density times - e the minus
109
00:09:41,110 --> 00:09:45,040
信号来自这样一个事实,即我将这两个顺序颠倒了
sign comes from the fact that I flipped
the order of these two compared to over
110
00:09:45,040 --> 00:09:49,450
那里的霍尔电场
there
so the Hall electric field that you
111
00:09:49,450 --> 00:09:53,890
将测量与霍尔系数成正比,如果你是
would measure would be proportional to
the Hall coefficient here and if you're
112
00:09:53,890 --> 00:09:58,630
试图建立一个霍尔传感器以找到准确的测量方法
trying to build a hall sensor in order
to find accurate ways of measuring
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00:09:58,630 --> 00:10:03,910
使用电子设备或使用电压测量结果产生的磁场
magnetic fields using electronics or
using voltage measurements you really
114
00:10:03,910 --> 00:10:08,290
希望霍尔电压尽可能大,以便
want the hall voltage to be large as
large as possible so that you have a
115
00:10:08,290 --> 00:10:13,090
要测量大电场,以便这样做,您通常会选择一个
large electric field to measure so to do
that what you do is you usually choose a
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00:10:13,090 --> 00:10:22,950
密度较小的材料,所以使用时要用较小的密度来变大
material with a small density so use use
use small density to get big to get big
117
00:10:22,950 --> 00:10:31,090
大e和典型的霍尔传感器由半导体和其他材料制成
big e and typical Hall sensors are built
with semiconductors and other materials
118
00:10:31,090 --> 00:10:36,430
电子密度很小,我们稍后将介绍半导体
that have a small electron density and
we'll come to semiconductors later on in
119
00:10:36,430 --> 00:10:41,740
这个词现在让我们开始实验吧,大概是
the term now let's turn this experiment
now on its head probably the way that
120
00:10:41,740 --> 00:10:49,270
保罗·德鲁(Paul Drude)对他的案子有一个想法,他可能不知道有什么问题,
Paul Drude a thought about it in his
case he probably knew no the dent up and
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00:10:49,270 --> 00:10:52,870
因此,在他的情况下,他可能知道磁场,电子电荷和
so in his case he probably knew the
magnetic field the electron charge and
122
00:10:52,870 --> 00:11:02,260
当前测得的霍尔数和得到的结果
the current measured measure Hall and
what you get
123
00:11:02,260 --> 00:11:07,970
你得到的是样品中电子的密度,因为他当然
what you get is the density of electrons
in your sample because of course he
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00:11:07,970 --> 00:11:12,590
不太了解他材料中的电子密度,所以让我们尝试一下
didn't know the density of electrons in
his materials well so let's try this
125
00:11:12,590 --> 00:11:16,760
假设我们针对多种不同的材料执行此操作,因此我们将采用
suppose we do this for a bunch of
different materials so we'll take a
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00:11:16,760 --> 00:11:23,200
一堆金属,例如锂钠,钾,铜,铜
bunch of metals like lithium sodium
potassium copper are sort of typical
127
00:11:23,200 --> 00:11:29,240
好的金属,保罗·犹大会注意到的第一件事是
good metals and the first thing that
Paul Judah would have noticed is that
128
00:11:29,240 --> 00:11:35,360
对于所有这些金属,相对湿度均小于零,这是他所预测的
for all of these metals RH is less than
zero which is what he predicted by his
129
00:11:35,360 --> 00:11:40,010
公式在这里,所以很多东西都很好,然后他可以实际输入
formula over here so that much is good
and then he can actually put in you know
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00:11:40,010 --> 00:11:45,830
测量e霍尔的幅度并尝试提取电子的密度。
measure the magnitude of e Hall and try
to extract the density of electrons and
131
00:11:45,830 --> 00:11:51,770
他得到的是每个原子约0.8个电子,这里约1.2
what he would have gotten was about 0.8
electrons per atom here about 1.2
132
00:11:51,770 --> 00:11:56,000
每个原子电子约1.1个电子/原子1.5个电子/个
electrons per atom here about 1.1
electrons per atom 1.5 electrons per
133
00:11:56,000 --> 00:12:00,560
原子似乎是个合理的数字,您知道想知道几个电子
atom seems like reasonable numbers a
couple of electrons you know wondering
134
00:12:00,560 --> 00:12:05,060
每个原子或多或少有一个电子,这是一个好答案吗?
one electron per atom more or less is
this a good answer is this a bad answer
135
00:12:05,060 --> 00:12:09,200
好吧,如果你考虑一秒钟,你会记得你的周期表
well if you think about it for a second
you'll remember your periodic table
136
00:12:09,200 --> 00:12:13,940
铜是元素周期表中的第29个元素,因此它具有29个质子
copper is the twenty-ninth element on
the periodic table so it has 29 protons
137
00:12:13,940 --> 00:12:18,890
和29个电子,我们测得每个原子1.5个电子
and 29 electrons and we measured 1.5
electrons per atom
138
00:12:18,890 --> 00:12:24,590
其他27.5到哪里去了,所以这可能有点令人费解
where'd the other 27.5 go so this might
have been a little bit puzzling to to
139
00:12:24,590 --> 00:12:29,000
犹大,但实际上我们现在对原子结构有所了解
Judah but actually now that we know a
little bit about the atomic structure we
140
00:12:29,000 --> 00:12:31,670
了解原子的壳结构,我们对化学有一点了解
know about the shell structure of atoms
we know a little bit about chemical
141
00:12:31,670 --> 00:12:34,250
键合,我们甚至会在稍后的内容中谈论化学键合
bonding we'll even talk a little bit
about chemical bonding later on in the
142
00:12:34,250 --> 00:12:39,650
一年,我们知道实际上一个原子中的许多电子实际上在
year and we know that in fact many of
the electrons in an atom are actually in
143
00:12:39,650 --> 00:12:44,630
这些核心轨道电子非常靠近原子核的轨道
orbitals very close to the to the
nucleus these core orbital electrons are
144
00:12:44,630 --> 00:12:53,570
基本上卡住了,所以核心轨道上的littlez电子或明显的电子
basically stuck so core orbitals
littlez electrons or overt electrons
145
00:12:53,570 --> 00:13:06,230
不要移动唯一能移动外壳电子的电子,也就是
don't move the only ones that do move
outer shell electrons also known as
146
00:13:06,230 --> 00:13:09,220
价电子
valence electrons
147
00:13:10,070 --> 00:13:16,020
移动,因此在固体中运行的电子是
move so the electrons that are running
around in the in the solid are the
148
00:13:16,020 --> 00:13:22,590
所谓的价电子,您知道化学作用,实际上我们知道
so-called valence electrons and you know
do from chemistry we actually know how
149
00:13:22,590 --> 00:13:27,270
这些材料具有许多价电子,实际上所有这四个
many valence electrons these materials
have and in fact all these four
150
00:13:27,270 --> 00:13:33,210
材料的化合价为1,意味着在最外层壳中只有一个电子
materials have valence one meaning only
one electron in the outermost shell so
151
00:13:33,210 --> 00:13:36,660
如果我们假设只有最外面的电子移动最外面的电子
if we assume only the outermost
electrons move the ones in the outermost
152
00:13:36,660 --> 00:13:40,770
壳,我们应该预测每个原子一个电子
shell
we should predict one electron per atom
153
00:13:40,770 --> 00:13:44,760
实际上,您知道与测得的结果相当一致
and that's actually you know in fairly
good agreement with what is measured
154
00:13:44,760 --> 00:13:50,400
从实验上来说,这对于juda理论非常有用
experimentally so that's pretty good for
for juda theory we get roughly one
155
00:13:50,400 --> 00:13:57,570
每个原子移动的电子,所以我们可能会为成功感到鼓舞
electron per atom moving around so we
might you know emboldened by our success
156
00:13:57,570 --> 00:14:02,780
我们可能会尝试其他一些材料,所以让我们尝试一些价
we might try some other materials so
let's try some with valence to valence
157
00:14:02,780 --> 00:14:07,920
等于2我们有像铍这样的材料我们有镁
equals two we have materials like
beryllium we have magnesium
158
00:14:07,920 --> 00:14:13,500
他们两个都有价,突然之间我们遇到了一个大问题
both of them have valence two and all of
a sudden we have a big problem the big
159
00:14:13,500 --> 00:14:19,830
问题是它的相对湿度霍尔系数现在大于零,这是
problem is it RH the Hall coefficient is
now greater than zero and this is
160
00:14:19,830 --> 00:14:24,060
从这张犹大计算机的图片中完全令人困惑的是,应该
completely puzzling from this picture of
Judah computer says that it should be
161
00:14:24,060 --> 00:14:28,020
只是密度乘以负电荷的电子电荷,所以
just the density times the charge of the
electron which is negative and so
162
00:14:28,020 --> 00:14:32,190
在犹大理论中,我们不可能得到霍尔系数
there's no way in Judah Theory we're
going to get a Hall coefficient which is
163
00:14:32,190 --> 00:14:36,570
积极,这一定使保罗·德鲁德(Paul Drude)非常困惑,并在当年晚些时候
positive and this must have puzzled Paul
Drude a terribly and later on the year
164
00:14:36,570 --> 00:14:40,560
当我们研究材料的能带结构时会明白为什么
when we study band structure of
materials will understand why this is
165
00:14:40,560 --> 00:14:44,940
但看起来好像发生了两件事之一,可能是
but it kind of looks like one of two
things is going on possibility one is
166
00:14:44,940 --> 00:14:48,780
电子密度由于某种原因变为负数
that the density of electrons has gone
negative for some reason if that makes
167
00:14:48,780 --> 00:14:52,410
任何有意义的可能性二是充电
any sense
possibility two is that the charge
168
00:14:52,410 --> 00:14:56,310