09 Geometry of Solids I Crystal Structure in Real Space.srt

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好吧，让我们开始吧，欢迎回到这是第九次演讲
okay let's uh let's get going welcome
back this is a ninth lecture of the

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浓缩当然是几个视频中的一些快速事项
condensed matter of course a couple of
quick things first of all the the videos

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从他们开始在线上的讲座中可以找到他们
from the lectures they're starting to
appear online you can get to them

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00:00:11,250 --> 00:00:15,929
如果您想尝试一下，它们已从我的网页链接了，请再次观看
they're linked from my web page if you
want to try them out watch them again if

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00:00:15,929 --> 00:00:19,430
您发现它很有用，如果您对该技术有任何疑问，请告诉我
you find it's useful let me know if you
have any trouble with the technology

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到目前为止，它仍在故障排除中，还有留言板
where it's still troubleshooting some
things also the message board so far

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人们没有那么多地使用它，请不要害羞，我保证你会
people haven't used it all that much
please don't be shy I promise you'll

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觉得它很有帮助，所以在这一点上，我们大约是课程的三分之一
find it helpful so at this point we're
about a third the way through the course

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所以值得停下来一秒钟，盘点一下我们在哪里
so it's it's worth sort of stopping for
a second and taking stock of where we

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到目前为止，我们去过的地方和去过的地方，我们一直在寻找
are and where we've been and where we're
going so far we've really been looking

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试图建立某种微观的理解
at trying to build up some sort of
microscopic understanding of the

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材料的宏观特性我们从几个比较粗糙的材料开始
macroscopic properties of materials we
started with a couple of rather crude

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材料的图片，然后我们开始查看更详细的信息
pictures of materials and then we
started looking at more detailed

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材料，但只在一个维度上，所以最终我们希望有一些
materials but only in one dimension so
eventually we'd like to have some

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材料的详细图片，但是在三个维度上，我们将转向
detailed pictures of materials but in
three dimensions so we're going to turn

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我们现在关注三个维度，这实际上使我们的生活
our attention to three dimensions now
and this actually makes our life a

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有点困难，有点复杂，但这是
little bit more difficult a little bit
more complicated but but this is the

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描述真实材料的最终目标，在这一点上值得
eventual objective to describe real
materials and at this point it's worth

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回想我在第一次演讲中说的一件事
thinking back to one of the things that
I said in the very first lecture that

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凝聚态物理世界极为广阔而多样，一旦我们
the world of condensed matter physics is
extremely broad and diverse and once we

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了解原子之间如何相互键合，您知道离子共价
understand how it is that atoms bond to
each other you know an ionic covalent

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氢金属或范德华力键可以开始建立巨大的
hydrogen metallic or Vander Waals bonds
you can start building up an enormous

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各种不同的材料进行研究，因此似乎我们应该进行
variety of different materials to study
and so it seems appropriate that we do a

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某些类型的凝结物质的强制性游览
little bit of an obligatory tour of some
of the types of condensed matter that

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我们实际上并不会专注于此，但是值得一提
we're not actually going to focus on but
that are out there and are worth knowing

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至少它们存在，所以这里只是一些浓缩的例子
that at least that they exist so here
are just a few examples of condensed

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物质物理学这是我们要去的一种凝聚态物理学
matter physics this is the one type of
condensed matter physics we are going to

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研究结晶固体，我还有很多要说的
study the crystalline solids and I'll
have a whole lot more to say about

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后来关于结晶固体的一般概念，是否有些
crystalline solids later on the general
idea of a crystalline solid is it some

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原子的周期性排列，通常是宏观的
sort of periodic arrangement of atoms
and very frequently the macroscopic

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晶体的形态反映了您的基础结构
morphology of the of the crystal
reflects its underlying structure as you

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可以在这张图片中看到这张水晶的特定图片是
can sort of see in this in this picture
this particular picture of crystal is is

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石英二氧化硅在美丽的faul晶体中，您可以看到它
quartz silicon dioxide in a beauty
faul crystal and you can see that its

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结构以某种方式反映了原子如何被组合在一起
structure somehow is reflecting how the
atoms are put together one can also have

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晶体类型稍微复杂一些，而在大多数晶体中
slightly more complicated types of
crystals whereas in most crystals in

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这些晶体原子可以通过离子或共价键结合在一起
these crystals atoms are held together
in ionic or covalent bonds you can have

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 Vander Waals键非常重要的情况，所以在此图中
situations where Vander Waals bonds are
extremely important so in this picture

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这就是所谓的分子晶体，这里发生的是你有很多
this is known as a molecular crystal
what happens here is you have a lot of

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原子聚在一起形成一个分子，它们牢固地结合在分子中
atoms coming together to form a molecule
they're strongly bonded in the molecule

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通过共价键或离子键，然后分子聚在一起形成一个
via covalent or ionic bonds but then the
molecules come together to form a

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晶体在这种情况下分子之间的键非常弱
crystal where the it's very weak bonding
between the molecules in this case

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范德华勒斯（Vander Waals）粘合了这张特殊的照片，描绘了C 60 60碳
Vander Waals bonds this particular
picture is a depiction of C 60 60 carbon

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原子聚在一起形成足球形状，或者如果您位于
atoms coming together to make a soccer
ball shape or if you're on this side of

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海洋，这是一种足球形状，我想在足球的另一面是
the ocean it's a football shape I guess
on the other side of football is a

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无论如何，它们的形状都不同，所以它们聚在一起形成这些C 60分子
different shape anyway so they come
together to make these C 60 molecules

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和C 60分子是非常不活泼的物种，但它们仍然可以结合
and the C 60 molecules they're very
inactive species but they can still bond

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可以通过范德华力结合在一起形成晶体
together forming to form a crystal via
Vander Waals bonding one can have

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情况有些不那么井井有条的情况
situations where you have a something
where it's not so organized a little bit

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更无序的是无定形固体
more disordered this is what's known as
an amorphous solid the word amorphous

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来自希腊语，没有形式，显然该对象具有某种形式
comes from Greek meaning without form
obviously the object has form of some

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排序，但它是无序形式，这是二氧化硅的另一种描述，但
sort but it's a disordered form this is
another depiction of silicon dioxide but

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是无定形二氧化硅，这里的微观结构是蓝色
it's amorphis silicon dioxide the
microscopic structure here the blue

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物体应该是硅，红色物体是氧气
objects are supposed to be silicon and
the and the red objects are oxygen every

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硅与四个氧键合每个氧与两个硅键合
silicon is bonded to four oxygen every
oxygen is bonded to two silicon's and

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通常我们熟悉这种无定形二氧化硅作为窗口
generally we are familiar with this
silicon dioxide amorphous as window

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玻璃具有与其晶体表弟石英相同的许多特性，但它
glass has a lot of the same properties
as its crystalline cousin quartz but it

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是一种略有不同的材料，我们也可以具有无序的结构，例如
is a slightly different material we can
also have disordered structures such as

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这里的液体和液体之间原子之间的吸引力
liquids there here and in liquids
there's attraction between atoms or

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分子，但是将其保持在永久配置中并不是那么牢固
molecules but it's not so strong to keep
it held in a permanent configuration the

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原子仍然可以有足够的热能来回移动，这使得
the atoms can still have enough thermal
energy to move around and that gives the

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流动它可以流动的属性，您可能会遇到一些情况
liquid its property that it can flow you
can have situations where you

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具有一定流动性和一定结晶度的部分顺序
a partial order with a some amount of
flowing in some amount of crystallinity

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或剩余的订单数量，因此这张图片被称为
or some amount of order that remains so
this picture is known as what's known as

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液晶剩下的顺序是所有这些分子
a liquid crystal the order that remains
is that all of these molecules these

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看起来像鱼雷或Orzo的东西都保持了方向
things that look like torpedoes or orzo
are they all retain their orientation

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它们都朝着相同的方向倾斜，并且都排成一排，但是
they're all angled to the same direction
and they all line up in stacks but

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在每个堆栈中它们都是无序的，它们实际上可以在堆栈中流动
within each stack they're disordered and
they can actually flow within the stack

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这就是使它们成为液晶的原因，并且种类繁多
and that's what makes them a liquid
crystal and there's a huge variety of

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液晶取决于您保留的订单类型和类型
liquid crystals depending on what type
of order you retain and what type of

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秩序在混乱和混乱之间被抛弃了一半
order gets thrown away halfway between
the disorder and disorder is also the

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准晶体的想法这个特殊的图片就是所谓的
idea of the quasi crystal this
particular picture is what's known as a

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彭罗斯（Penrose）瓷砖以罗杰·彭罗斯（Roger Penrose）最著名的数学家之一的名字命名
Penrose tile named after Roger Penrose
one of the most famous mathematicians

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在牛津，这里是世界上最著名的数学家之一
here at Oxford one of the most famous
mathematicians in the world actually

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无论如何，这是由两种不同类型的瓷砖组成的，这些蓝色的小蓝
anyway this is made up of two different
types of tiles these little blue blue

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对象和这些绿色的小对象，它们堆叠在一起适合
objects and these little green objects
and they stack together they fit

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完美地结合在一起，这是一些非常有序的安排，但实际上
perfectly together and it's some very
ordered arrangement but in fact all the

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通往无限的方式，模式从不重复，它是有序的但不重复
way out to infinity the pattern never
repeats it's a ordered but non repeating

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图案，有些具有这种特性的材料被称为
pattern and there are materials that
have this property that are known as

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准晶体存在时间相当长，引起很大争议
quasi crystals it was very controversial
that they existed for quite some time it

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实际上已经确定它们确实存在，并且获得了诺贝尔奖
has actually been determined that yes
indeed they do exist and the Nobel Prize

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就在几年前被授予奖项的还有聚合物的想法
was awarded for it just a couple years
ago there's also the idea of a polymer

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这是一维长而长的分子DNA， 
which is sort of a one-dimensional long
very long molecule DNA is one that

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您可能很熟悉，但是有很多聚合物，例如聚乙烯
you're probably familiar with but
there's many polymers like polyethylene

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例如，聚合物具有许多其他特性
for example and polymers have a lot of
properties that are unlike other

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我们可能会在一件事中熟悉的材料知道它们的流动性
materials that we might be familiar with
for one thing in you know their fluid

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在那里，就像一碗意大利面，很多这样的串
phase there and sort of like a bowl of
spaghetti a lot of these strands sort of

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全部混合在一起，就其而言，它们具有非常非牛顿的行为
all mixed in together and they have a
very non Newtonian behavior in terms of

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他们的流体动力学，其粘度非常依赖于
their fluid dynamics that their
viscosity depends very strongly on the

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您正在考虑的时间范围，因此如果您从未用过
timescales that you're considering so if
you've never done this experiment with

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玉米淀粉和水，你可以混合一些玉米淀粉和水， 
cornstarch and water you can sort of mix
up a goop of cornstarch and water that

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会像液体一样倒，您可以像液体一样将手放在其中，但是如果您碰到
will pour like a fluid you can put your
hands in it like a fluid but if you hit

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用锤子敲它会破裂，这真令人印象深刻，您知道问题是
it with a hammer it will crack it's
really impressive you know the issue is

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那些长的绳子需要一些时间才能纠缠，所以如果您尝试
that that the the long strands they take
some time to unentangled so if you try

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快速移动它们，他们会感觉很扎实，但是如果您给他们一些时间
to move them very quickly they'll feel
like a solid but if you give them time

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放松一下，他们会彼此经过的，所以这只是一个
to relax they'll
past each other okay so that's just a

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非常简短地浏览了凝聚态中的一些主题，我们可以
very brief tour through some of the
topics in condensed matter that we could

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学习他们中的大多数，我们主要是不会学习的
study most of them we're not going to
study mainly we're gonna guess um ice is

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冰是一种晶体，是真正的晶体，它是晶体的顺序。大多数形式的冰
ice is a crystal a genuine crystal it's
an order of crystal most forms of ice

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大约有20种冰，其中大多数实际上是熟悉的
there's like 20 forms of ice most of
them are actually the ones were familiar

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通常是结晶固体，它是有序的，但实际上
with is is generally a crystalline solid
it's all it's ordered but they actually

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哦好吧，你的观点是，冰有点不同，因为
oh well okay there's you make a point
ice is a little bit different because

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氢原子上的氢原子有一些重排
there's some slight rearrangement of the
of the oxygen hydrogen atoms on a

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在微观层面上，它并非一直都是完美的周期性，而是
microscopic level it makes it not
perfectly periodic all the time but uh

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但这主要是水晶，我们可以讨论一下微妙之处
but it's it's mainly a crystal we can we
can discuss the the the slight subtlety

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与冰有关，使其略有不同是的，可以
associated with ice that makes it
slightly different yes okay

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我们主要要研究的是晶体结构，结晶固体和
mainly what we're going to study is
crystal structure crystalline solids and

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在我们出发之前，我先道歉一些，首先道歉的是
here before we get going I have a couple
of apologies the first apology is that

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我将不得不使用很多PowerPoint幻灯片，而且我知道PowerPoint 
I'm going to have to use a lot of
PowerPoint slides and I know PowerPoint

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幻灯片很烦人，很难从PowerPoint幻灯片中学习，但是
slides are annoying it's difficult to
learn from PowerPoint slides but

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不幸的是，我无法绘制出我要发布的所有幻灯片
unfortunately I can't draw this all the
slides that I post are going to be on

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网页中的大多数以一种或另一种形式出现在书中
the web page most of them are in the
book in one one form or another

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希望不是贝丝，而且讲座也将在网上进行
hopefully that wasn't Beth and the
lectures will be on online as well

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希望这会给您足够的信息，以便能够学习
hopefully that will give you enough
information to be able to learn the

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材料，这是第二个道歉
material
so that's the first apology the second

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道歉在本讲课中尤其如此，我们将在下一讲中
apology is particularly in this lecture
and the next lecture we're going to have

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遭受很多定义的困扰，这有点乏味，但是
to suffer through a lot of definitions
and that's a little bit tedious but

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不幸的是，我们需要一种语言才能描述
unfortunately we need to have a language
in order to be able to describe the

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我们正在谈论的事情，我们需要能够说出我们在这张照片中是什么
things we're talking about we need to be
able to say what is this picture we're

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看原子坐在哪里，我们需要一些词汇来
looking at where are the atoms sitting
we need some sort of vocabulary in order

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交流，所以我们将不得不忍受和遭受
to communicate so that's we're gonna
have to just bear with that and suffer

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直到我们了解所有单词是什么，然后我们才能开始
until we until we understand what all
the words are and then we can start

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再次向物理学进发第三道歉的第二个道理是
moving on with the physics again the
second of the third apology is that

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不幸的是，并不是所有的书都对术语的正确定义达成一致
unfortunately not all books agree on
what the proper definitions of terms are

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00:08:47,760 --> 00:08:52,110
因此，您会发现有些书叫狗猫，有些书叫猫， 
so you will find some books that call a
dog a cat and some that call it cat and

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00:08:52,110 --> 00:08:57,839
猴子，所以有点混乱我所用的术语是
a monkey so it's kind of a mess
the terms that I use are the ones that

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00:08:57,839 --> 00:09:01,200
是公认的牛津大学，它们实际上可能是最常用的
are generally accepted Oxford they're
actually probably the most commonly used

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00:09:01,200 --> 00:09:05,430
对于某些事物的术语，我将尝试指出存在某些情况的情况
terms for for certain things I will try
to point out cases where there is some

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00:09:05,430 --> 00:09:09,360
关于术语的含义或应使用的术语存在分歧，只是
disagreement as to what the terms mean
or what terms should be used but just be

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00:09:09,360 --> 00:09:13,350
警告您如果再看其他书，那么内部也有一些警告
warned if you look in other books then
and there's also caveats within within

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00:09:13,350 --> 00:09:18,570
我的教科书中有哪些术语存在争议，因此请注意
my textbook as so which terms are
controversial so just be warned of that

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00:09:18,570 --> 00:09:22,050
那是我们必须处理的问题之一，所以我们要
that that is one of the issues we have
to deal with okay so we're going to

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00:09:22,050 --> 00:09:32,339
从晶体的周期的第一个定义开始
start with the first definition of the
day a crystal crystal is a periodic

133
00:09:32,339 --> 00:09:49,589
排列周期性排列通常是原子的含义，例如哎呀。 
arrangement periodic arrangement usually
meaning of atoms so for example oops

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00:09:49,589 --> 00:09:54,389
这是一个水晶，所以这是左侧的一个简单水晶，然后您
that's a crystal so this is a simple
crystal over on the left and then you

135
00:09:54,389 --> 00:09:56,579
右边有更复杂的晶体他们可以有很多不同的晶体
have more complicated crystals over on
the right they can have many different

136
00:09:56,579 --> 00:10:00,660
原子的类型原子可以处于非常复杂的排列中，但只要
types of atoms the atoms can be in very
complicated Arrangements but as long as

137
00:10:00,660 --> 00:10:05,910
它是周期性的，是晶体我实际上要去定义一个非常重要的定义
it's periodic is a crystal a very
important definition I'm actually going

138
00:10:05,910 --> 00:10:11,220
给出这个词的几个定义，都等同于一个晶格
to give several definitions of this word
which are all equivalent a lattice so

139
00:10:11,220 --> 00:10:25,019
定义a可能是最有用的，因为它是定义的一组点
definition a may be the most useful is
it's a set of points defined as defined

140
00:10:25,019 --> 00:10:27,410
如
as

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00:10:27,870 --> 00:10:40,920
整数诗篇总和um这是另一个词原始格
integer Psalms sums um
here's another word primitive lattice

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00:10:40,920 --> 00:10:51,150
向量点阵向量好吧，现在这是一个案例，我将解释什么原始
vectors lattice vectors okay now here's
a case I'll explain what primitive

143
00:10:51,150 --> 00:10:54,089
晶格向量在瞬间，但是在这种情况下，有一个词
lattice vectors are in a second but
here's a case where there's a word that

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00:10:54,089 --> 00:10:58,440
人们不同意原始语言，有时人们完全放弃这个词，他们
people disagree on primitive sometimes
people drop the word altogether and they

145
00:10:58,440 --> 00:11:06,120
不要说有时候它的原理原理格子有时会被替换
don't say it sometimes it's principle
principle lattice is sometimes replaced

146
00:11:06,120 --> 00:11:13,560
通过翻译，有时被单词基础代替
by translation and it's sometimes
replaced by the word basis that's a

147
00:11:13,560 --> 00:11:16,920
特别不方便，因为我们完全使用词基这个词
particularly inconvenient because we use
the word basis for something completely

148
00:11:16,920 --> 00:11:20,910
不同，使一个真正的混乱向量总是向量，另一个
different so that makes a real mess
vectors is always vector and the other

149
00:11:20,910 --> 00:11:25,140
事实是，有些书会称其为brav而不是格子
thing is that some some books will call
lattice brav a lattice instead of

150
00:11:25,140 --> 00:11:29,430
保留真正意义上的晶体的晶格，从而使晶格完整
lattice reserving lattice for really
meaning crystal so that makes a complete

151
00:11:29,430 --> 00:11:32,390
一些人称其为晶格，而Bravo的晶格为晶格
mass some people call a crystal lattice
and the lattice of Bravo a lattice

152
00:11:32,390 --> 00:11:37,740
请忽略那只是我的意思，这使所有事情都令人困惑
please ignore that that's just I mean it
makes everything incredibly confusing

153
00:11:37,740 --> 00:11:41,790
无论如何，这是一套很好的定义，我们将在牛津考试中使用
anyway this is a good set of definitions
that we will use here at Oxford the exam

154
00:11:41,790 --> 00:11:45,150
委员会同意这些定义，因此希望不会太过
committee agrees with these definitions
so hopefully it won't get too

155
00:11:45,150 --> 00:11:47,880
复杂，我们只需要处理它，因为这就是世界的方式
complicated we just have to deal with it
because that's the way the world is

156
00:11:47,880 --> 00:11:52,709
好吧，让我们让我实际定义这些晶体的例子
okay so let's let me actually define
give examples of what these crystals

157
00:11:52,709 --> 00:11:56,580
这些晶格是什么，所以我们在一维中进行了此操作，您有一排点
what these lattices are so we did this
in 1d you have a bunch of points lined

158
00:11:56,580 --> 00:12:06,060
在1d内它们之间的距离为a，这样我们就可以写出
up in 1d with a distance a between them
so then we can write the positions are

159
00:12:06,060 --> 00:12:13,589
点阵中n的整数倍，aa是a，这里是
of the points in the lattice as n an
integer times a a is the a here is the

160
00:12:13,589 --> 00:12:19,860
原始晶格因子prim lat BEC实际上我会经常称其为plv 
primitive lattice factor prim lat BEC
actually I'll frequently call that plv

161
00:12:19,860 --> 00:12:26,970
原始晶格向量，然后n是整数，所以这是我们
primitive lattice vector and then n is
an integer so this is something we've

162
00:12:26,970 --> 00:12:30,089
在我们有整数倍原始格之前看到
seen before
we have integer times primitive lattice

163
00:12:30,089 --> 00:12:35,190
因素给了我们点阵的点对不起，我在二维中赢了一点
factor it gives us the points in the
lattice sorry I won in 2d a little bit

164
00:12:35,190 --> 00:12:41,400
比较复杂，所以晶格点最后的向量是整数
more complicated so the lattice points
the last vectors here are integer

165
00:12:41,400 --> 00:12:45,590
基本格向量a 1加一个整数，2有时是另一个
a primitive lattice vector a 1 plus an
integer and 2 sometimes another

166
00:12:45,590 --> 00:12:53,060
原始晶格矢量a 1 A是PL v的原始晶格矢量
primitive lattice vector a 1 the A's are
the primitive lattice vectors the PL v's

167
00:12:53,060 --> 00:13:01,140
 A应该是a应该是非共线的非共线的，所以我们有
the A's should be a should be non
collinear non collinear so that we have

168
00:13:01,140 --> 00:13:06,270
真正是二维的，末端是整数，我们
something that's really two-dimensional
and the ends are integers and our

169
00:13:06,270 --> 00:13:12,990
整数元素一些整数可以，所以让我们展示一个这样的例子
integers element some integers
okay so let's show an example of this so

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00:13:12,990 --> 00:13:17,940
这里我们有一个晶格，我们可以1和2是原始晶格
here we have a lattice and we can a 1
and a 2 are the primitive lattice

171
00:13:17,940 --> 00:13:22,020
向量，如果我们认为中心点是每个点零
vectors if we think of this point in the
center as being the point zero every

172
00:13:22,020 --> 00:13:27,000
该晶格中的点是一个整数，该整数是1加上一个的整数
point in this lattice is an integer
that's an integer times a 1 plus an

173
00:13:27,000 --> 00:13:33,420
整数乘以2，例如，这里的点是1加1等于2，然后
integer times a 2 for example this point
here is to a 1 plus 1 a 2 okay and

174
00:13:33,420 --> 00:13:42,570
通常，我们会在方括号中将R等于n 1逗号n 2表示为
frequently we will notate R equals n 1
comma n 2 in square brackets to indicate

175
00:13:42,570 --> 00:13:48,810
 n 1乘以1加n 2乘以2就像这里所示2逗号1到
n 1 times a 1 plus n 2 times a 2 like
it's indicated up here 2 comma 1 to

176
00:13:48,810 --> 00:13:54,810
如果现在将此点视为原点，请指出这一点
indicate this point if this point here
is taken to be the origin now I should

177
00:13:54,810 --> 00:13:59,400
还评论说这种符号经常被滥用，有时人们
also comment that this notation is
frequently abused that sometimes people

178
00:13:59,400 --> 00:14:05,280
会说点1/2逗号0或类似的意思是一个点
will say the point 1/2 comma 0 or
something like that to mean a point

179
00:14:05,280 --> 00:14:09,570
这不是晶格点晶格点之间的点
which is not a lattice point the point
which is in between lattice points so if

180
00:14:09,570 --> 00:14:13,260
您想在此处指定此点，您会说走距离的一半
you want to specify this point here you
would say go a half the distance of the

181
00:14:13,260 --> 00:14:17,010
原始晶格矢量a 1更重要的是它们是正方形
primitive lattice vector a 1 the more
important thing is that they're square

182
00:14:17,010 --> 00:14:23,060
方括号表示空间中的一个点，如果此处为整数系数，则表示
brackets mean a point in space and if
integers coefficients here then you mean

183
00:14:23,060 --> 00:14:27,150
一个晶格点，如果它不是整数系数，那么它不是晶格
a lattice point if it's not integer
coefficient then it's not a lattice

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00:14:27,150 --> 00:14:34,200
到目前为止，还可以，很好，很简单，我们可以做同样的事情
point okay so far so good all right so
far pretty easy we can do the same thing

185
00:14:34,200 --> 00:14:49,430
在3d 3d中，我们将R等于N 1 a 1加n 2 a 2加n 3 a 3，而A等于
in 3d 3d we would write R equals N 1 a 1
plus n 2 a 2 plus n 3 a 3 and the A's

186
00:14:49,430 --> 00:14:52,230
应该是非共面的
should be non coplanar
non

187
00:14:52,230 --> 00:14:57,270
共面的，所以我们谈论的是三维的
coplanar so that we're talking about it
something that's three-dimensional and

188
00:14:57,270 --> 00:15:09,060
我们可以将其记为R，因为R等于方括号，而一，二和三等于那个
we can notate it as R equals brackets
and one and two and three like that one

189
00:15:09,060 --> 00:15:13,560
您应该知道的是原始晶格的选择
thing that you should be aware of is
that the choice of primitive lattice

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00:15:13,560 --> 00:15:24,830
 POV的向量原始格向量不是唯一的，因此您可以选择
vectors of POVs primitive lattice
vectors is not unique so you can choose

191
00:15:24,830 --> 00:15:29,160
不同的原始晶格矢量集，它们完全可以
different sets of primitive lattice
vectors and they're perfectly okay for

192
00:15:29,160 --> 00:15:32,670
例如，您可以选择这两件事作为原始晶格矢量
example you could choose these two
things as primitive lattice vectors you

193
00:15:32,670 --> 00:15:34,680
可以选择这两件事作为原始晶格矢量
could choose these two things as
primitive lattice vectors you could

194
00:15:34,680 --> 00:15:37,620
选择这两件事作为原始晶格向量，重要的是
choose these two things as primitive
lattice vectors the important thing is

195
00:15:37,620 --> 00:15:42,900
晶格上的任何点都应表示为整数
that any point on the lattice should be
expressible as an integer some of the

196
00:15:42,900 --> 00:15:49,560
原始晶格向量还可以，到目前为止一切都很好，首先有机会获胜
primitive lattice vectors okay so far so
good all right first chance to win

197
00:15:49,560 --> 00:15:54,300
神话般的奖赏是这些原始晶格矢量，好吧，谁是第一个
fabulous prizes are these primitive
lattice vectors okay who is the first

198
00:15:54,300 --> 00:15:57,060
有人说我听说还可以，不，不，你不是别人吗？ 
one to say I heard it's okay no no you
weren't someone someone someone else

199
00:15:57,060 --> 00:16:06,990
在这里，你还好，你们这样的骗子，好吧，所以我有些声音
over here it was you okay you guys such
liars so all right so I was some voice

200
00:16:06,990 --> 00:16:09,570
在这里我听到了，但是我不知道是谁把它给你的
over here I heard it over here but I
don't know who gave it to you all right

201
00:16:09,570 --> 00:16:12,690
再有一个机会好吧，是的，这些是原始晶格向量
one more chance okay yes these are
primitive lattice vectors it's its

202
00:16:12,690 --> 00:16:17,310
晶格矢量，因为您可以通过某种方式到达晶格中的任何点
lattice vectors because you can get to
any point in the lattice by some sort of

203
00:16:17,310 --> 00:16:21,930
整数一些原始晶格向量，好吧，这些
integer some of those primitive lattice
vectors okay how about these so these

204
00:16:21,930 --> 00:16:29,730
原始晶格向量不，它们不是，所以不是，因为如果添加它们
primitive lattice vectors no they're not
so they're not because if you add them

205
00:16:29,730 --> 00:16:34,560
以所有整数组合在一起，他们会错过所有其他晶格点
together in all integer combinations
they miss every other lattice point okay

206
00:16:34,560 --> 00:16:38,310
如果我拿走了一半，它们将是这个晶格的原始晶格矢量。 
they would be primitive lattice vectors
for this lattice if I took away half the

207
00:16:38,310 --> 00:16:44,220
晶格点，那么你就拥有杰出的廖的向量，好吧，大家
lattice points then you have preeminence
Liao's vectors okay all right everyone

208
00:16:44,220 --> 00:16:51,480
总是错过每年一个可以的状态，所以第二个定义晶格
always misses that one okay every year
okay so a second definition of a lattice

209
00:16:51,480 --> 00:16:59,960
晶格的等价定义的晶格种类这是B是它是a 
a lattice sort of equivalent definition
of a lattice this is B is that it is a

210
00:16:59,960 --> 00:17:03,470
还可以
okay addition

211
00:17:03,620 --> 00:17:15,640
哦，让我们看看，也许它会改变它是一组向量
oh let's see uh maybe change it it's a
set of vectors set of vectors such that

212
00:17:16,990 --> 00:17:26,140
两个中的两个相加得到第三个
addition of two of two gives a third

213
00:17:28,569 --> 00:17:34,100
好的，这实际上很容易看出，这等同于
okay and this actually it's pretty easy
to see that this is equivalent to the

214
00:17:34,100 --> 00:17:38,809
如果您对两个都是整数的n1个逗号N有一个先前的定义，则为
prior definition if you have n1 comma N
to both of those being integers so it's

215
00:17:38,809 --> 00:17:43,040
晶格的元素，然后将它们添加到n 3逗号n中
an element of the lattice and you add it
to n 3 comma n for both of those being

216
00:17:43,040 --> 00:17:46,940
整数，所以它是ibadis的元素，得到n 5和6，然后是
integer so it's an element of ibadis you
get n 5 and 6 and those are then

217
00:17:46,940 --> 00:17:52,360
那里的整数也代表晶格的元素以及第三个定义
integers also in there for an element of
the lattice as well a third definition

218
00:17:52,360 --> 00:18:11,980
看到的是，从观看到观看，格子看起来都一样
see is that a lattice looks the same
looks the same from viewed from viewed

219
00:18:11,980 --> 00:18:27,770
从任何晶格角度来看都可以，例如，如果我坐在这里
from any lattice point okay so for
example if I sit myself here so this

220
00:18:27,770 --> 00:18:31,640
如果我坐在这里，然后观察环境，现在的事情就成了格子
thing is now is a lattice if I sit
myself here and I view the environment

221
00:18:31,640 --> 00:18:35,150
我周围我说好吧，我左边有一个点，这个距离有一个
around me I say okay there's a there's a
point to my left this distance has a

222
00:18:35,150 --> 00:18:39,650
指向右边的距离与指向上点的距离相同右上左下右下
point to the right the same distance as
a point up right up left down right down

223
00:18:39,650 --> 00:18:43,220
左边，我可以测量距离，我可以测量角度，如果我坐下
the left and I can measure the distances
I can measure the angles and if I sit

224
00:18:43,220 --> 00:18:47,330
这里的另一个晶格点具有完全相同的环境
here another lattice point over here it
has exactly the same environment to

225
00:18:47,330 --> 00:18:50,270
指向右指向左指向右上右上左下右
point to the right to point to the left
point to the up right up left down right

226
00:18:50,270 --> 00:18:53,929
左下完全相同的距离完全相同的晶格
down left exactly the same distance is
exactly the same lattice it's exactly

227
00:18:53,929 --> 00:18:57,470
如果对于这些点中的每一个都是对的，则每个角度相同
the same angles if every if this is true
for every one of these points then what

228
00:18:57,470 --> 00:19:05,929
你有一个格子好吧，例如，这个格子知道谁是谁
you have is a lattice okay so for
example is this a lattice know who's who

229
00:19:05,929 --> 00:19:11,350
我听说那是谁在那边，但是那是你哦，好吧，好吧
that I heard that it's over here who is
it but it was a you oh okay all right

230
00:19:11,350 --> 00:19:16,010
争取一切都好吧，所以我必须放弃其中一些，我已经像六个
fight for all right okay so um I have to
give up some of these I have like six

231
00:19:16,010 --> 00:19:19,710
好的，这不是格子， 
over here all right
so okay this is not a lattice and

232
00:19:19,710 --> 00:19:24,240
有几种方法可以查看为什么它不是晶格，所以首先
there's several ways to see why it's not
a lattice so first of all from the first

233
00:19:24,240 --> 00:19:28,379
定义是原始格向量，我们可以将它们加起来
definition are they're primitive lattice
vectors which we can add up in all

234
00:19:28,379 --> 00:19:32,039
整数组合，它们将恰好给出这些点，并且仅给出这些点
integer combinations which would give
exactly these points and only these

235
00:19:32,039 --> 00:19:36,059
指出当某些与整数系数在一起时不是，但是
points when some together with integer
coefficients well they're aren't but it

236
00:19:36,059 --> 00:19:39,539
可能不太明显，以至于您可以尝试提出两个
may not be so obvious to see that that's
true that you can try coming up with two

237
00:19:39,539 --> 00:19:42,000
您想要的原始晶格矢量，看看我们是否可以提出
primitive lattice vectors that you want
to may to and seeing if we can come up

238
00:19:42,000 --> 00:19:45,210
这些点，只有这些点，你做不到，但是要容易得多
with these points and only these points
you can't do it but it's much easier to

239
00:19:45,210 --> 00:19:48,139
使用其他一些这样的定义
use some of the other definitions like
this one

240
00:19:48,139 --> 00:19:52,860
如果我们认为这里的这一点为零，我们应该有
we should have if we sort of think of
this point here as being zero then we

241
00:19:52,860 --> 00:19:56,190
对它们求和时，在此晶格矢量中具有此晶格因子
have this lattice factor here in this
lattice vector here when you sum them

242
00:19:56,190 --> 00:19:59,220
他们在一起应该给出第三个晶格向量，但是如果将这两个相加
together they should give a third
lattice vector but if you sum these two

243
00:19:59,220 --> 00:20:02,639
在一起，您会在此六角形的中间得到一个点，但它不在那里
together you get a point in the middle
of this hexagon and it's not there

244
00:20:02,639 --> 00:20:05,669
这不是我们集合中的要点之一，所以这不是晶格，因为您
that's not one of the points in our set
so this is not a lattice because you

245
00:20:05,669 --> 00:20:09,750
不能将两件事加在一起，总是得到第三点，第三个定义是
can't sum two things together and always
get a third the third definition is that

246
00:20:09,750 --> 00:20:13,200
如果我们所有的环境都应该是
the environment of our if the
environment of all points should be the

247
00:20:13,200 --> 00:20:16,889
和我们的环境不一样，因为公关的环境
same and the environment of our is not
the same as the environment of P R has a

248
00:20:16,889 --> 00:20:21,809
有一个指向南方的点，而P指向它的南方而不是它的南方
has another point to it South whereas P
has a point not to its South but to its

249
00:20:21,809 --> 00:20:28,649
北，所以等价点P和Q中的P n R等价，所以即使在
North so P n R in equivalent points P
and Q are equivalent okay so even among

250
00:20:28,649 --> 00:20:31,559
专业文学界人士将这个东西称为六角形
the professional literature people will
refer to this thing is the hexagonal

251
00:20:31,559 --> 00:20:34,799
格子，这是错误的，它不是格子，您不应该将其称为
lattice and that's just wrong it's not a
lattice you shouldn't call it the

252
00:20:34,799 --> 00:20:39,690
六角形的格子，尽管人们总是这样做，但我对此有所警惕
hexagonal lattice although people always
do so be warned about that I know this

253
00:20:39,690 --> 00:20:43,350
令人震惊的是，您知道给人所有这些警告，而人们却说这些
is horrible to be you know giving you
all these caveats that people say these

254
00:20:43,350 --> 00:20:50,909
事情总是出错，但是确实如此，所以让我们继续吧
things wrong all the time but it's just
true they do okay so let's go on fact

255
00:20:50,909 --> 00:21:04,879
任何周期性结构都是
any periodic structure is a lattice of

256
00:21:05,629 --> 00:21:17,700
重复的图案好吧，任何周期性的，这仅仅是事实，任何周期性的结构都是
repeating motifs okay any periodic this
is just a fact any periodic structure is

257
00:21:17,700 --> 00:21:21,659
重复图案的格子，所以这是我在书中的同一幅画
a lattice of repeating motifs so here's
my business same picture in the book I

258
00:21:21,659 --> 00:21:25,769
就像这些东西一样，它们就是犰狳，所以你有这个
just like these these things they're
armadillos I guess so this you have this

259
00:21:25,769 --> 00:21:31,230
犰狳的周期性结构，实际上，如果在这里取一个格子
periodic structure of armadillos and in
fact if you take a lattice here the

260
00:21:31,230 --> 00:21:33,960
试图由一堆三角形组成，这是一个
trying
made up of a bunch of triangles it's a

261
00:21:33,960 --> 00:21:37,800
漂亮的格子，您用犰狳替换了所有这些点
nice lattice and you replaced each of
these points with an armadillo you get

262
00:21:37,800 --> 00:21:42,840
整个周期结构，所以我将其绘制为晶格乘以重复
the whole periodic structure so I've
drawn it as lattice times the repeating

263
00:21:42,840 --> 00:21:46,710
这是犰狳的结构，这当然是一个
structure which is the armadillo well
what about this this is certainly a

264
00:21:46,710 --> 00:21:52,040
周期性结构，所以我们可以看到这东西实际上是
periodic structure so can we see how
this thing is actually a lattice of

265
00:21:52,040 --> 00:21:57,780
重复图案，好吧，我声称这是一个三角形的格子
repeating motifs okay I claim that it's
a triangular lattice this triangular

266
00:21:57,780 --> 00:22:01,950
带有蓝色圆点的晶格乘以这个重复的图案，而事实并非如此
lattice with blue dots times this
repeating motif and that might not be so

267
00:22:01,950 --> 00:22:04,980
显而易见，但让我们看看是否可以使其变得明显，所以首先我要做什么
obvious to see but let's see if we can
make it obvious so first what I'm going

268
00:22:04,980 --> 00:22:11,970
要做的是，我将在每个垂直边缘的中间放置一个大红点
to do is I'm going to put a big red dot
in the middle of each vertical edge okay

269
00:22:11,970 --> 00:22:16,140
所以这是一个大红点这里是大红点，现在看起来有点
so here's a big red dot here are big red
dots and now it's looking a little bit

270
00:22:16,140 --> 00:22:20,160
首先，这些大红色点很可能明显形成了
more likely that first of all these big
red dots are clearly forming a

271
00:22:20,160 --> 00:22:24,630
像这个三角形格子一样，现在让我们
triangular lattice just like this
triangle lattice down here now let's

272
00:22:24,630 --> 00:22:29,190
通过在其周围放置绿色菱形使其更明显
make it a little bit more obvious by
putting a green diamond around this

273
00:22:29,190 --> 00:22:33,330
重复的主题，您可以看到，实际上，如果我将这些绿色堆叠在一起
repeating motif and you can see that in
fact if I stack together these green

274
00:22:33,330 --> 00:22:37,470
钻石中的每一个都集中在这些大红色点上，它将重建
diamonds each one of them centered on
these big red dots it will reconstruct

275
00:22:37,470 --> 00:22:42,840
整个蜂窝这个东西，人们称之为六角形格子， 
the entire honeycombs this thing that
people call the hexagonal lattice that

276
00:22:42,840 --> 00:22:47,220
不是格子，所以应该叫做蜂窝，我想是
isn't a lattice so it should be called
the honeycomb I guess all right is that

277
00:22:47,220 --> 00:22:52,860
显然还可以，很好，到目前为止，很好，使我们进入了另一个非常有用的状态
that clear okay good good so far so good
so that brings us to another very useful

278
00:22:52,860 --> 00:23:01,260
定义是单位晶胞单位晶胞等于它的空间区域
definition which is a unit cell unit
cell equals a region of space it

279
00:23:01,260 --> 00:23:11,510
基本上，这是重复的图案，是空间与空间之间的区域
basically it's the repeating motif it's
the region of space from space which

280
00:23:12,170 --> 00:23:16,520
当重复
when repeated

281
00:23:18,750 --> 00:23:23,480
并堆叠在一起
and stacked and stacked together

282
00:23:26,659 --> 00:23:32,039
有时我们使用平铺一词来表示重复，平铺是指重复， 
sometimes we use the word tiled meaning
repeated tiled means repeated and

283
00:23:32,039 --> 00:23:48,510
堆叠在一起重建了我们使用的这个完整的完整周期结构
stacked together reconstructs the full
full periodic structure we use this term

284
00:23:48,510 --> 00:23:52,559
以前在一维的晶胞现在我们可以
unit cell
previously in one dimension now we can

285
00:23:52,559 --> 00:23:58,049
只需在一般尺寸上使用它，这样绿色的钻石就会成为单位
just use it in general dimensions so
this green diamond would be the unit

286
00:23:58,049 --> 00:24:02,880
这个重复结构的单元格好，让我们看看是否可以做另外一个
cell for this repeating structure okay
and let's see if we can do another one

287
00:24:02,880 --> 00:24:08,210
这是我们的犰狳，所以我们有一个单元格，其中包含一个犰狳
here's our armadillos again so we have a
unit cell which contains one armadillo

288
00:24:08,210 --> 00:24:12,120
我们可以将它们堆叠在一起对于晶胞重要的是
we can stack them together what's
important about unit cells is they have

289
00:24:12,120 --> 00:24:15,179
没有空间堆叠在一起，它们应该像浴室瓷砖一样
to stack together with no space they
should be like bathroom tiles they

290
00:24:15,179 --> 00:24:20,070
应该完全放在一起，彼此之间没有空格。 
should fit together exactly with no
space between them another definition

291
00:24:20,070 --> 00:24:24,380
这是一个有用的原始单元格
which is useful is a primitive unit cell

292
00:24:25,159 --> 00:24:37,309
晶胞等于包含
unit cell equals a unit cell containing

293
00:24:38,000 --> 00:24:51,809
正好一个晶格点正好一个晶格点
exactly one lattice point exactly one
lattice point so for example in this

294
00:24:51,809 --> 00:24:56,159
图片，这将是一个基本单位晶胞，因为它包含一个大红点
picture this would be a primitive unit
cell because it contains one big red dot

295
00:24:56,159 --> 00:24:59,970
那是晶格点，好吧，所以我们在这里看不到晶格点
and that's the lattice point and okay so
we can't see the lattice points in here

296
00:24:59,970 --> 00:25:03,809
但是，如果您还记得它们的位置以及那些蓝色图片， 
but if you remember where they were and
those those blue pictures the the

297
00:25:03,809 --> 00:25:07,260
犰狳位于晶格点的顶部，因此每个晶胞都包含
armadillo is sitting on top of the
lattice point so each unit cell contains

298
00:25:07,260 --> 00:25:13,080
我猜这恰好是一个晶格点这是另一种情况
exactly one lattice point I guess here's
here's another case here's a nice

299
00:25:13,080 --> 00:25:17,820
晶格中有一个原始的晶胞，因为如果不能，我将全部
lattice there's a primitive unit cell
because it's if you can't I'll hole all

300
00:25:17,820 --> 00:25:22,230
您将它们放在一起的所有空间都平铺在一起，每个单元格包含
space with it you put them together tile
all spaced and each unit cell contains

301
00:25:22,230 --> 00:25:27,590
一个晶格点，但是如果原始晶胞会被警告
one lattice point however one should be
warned if the primitive unit cell

302
00:25:27,590 --> 00:25:30,830
基本单位单元
primitive unit cell

303
00:25:32,120 --> 00:25:42,660
单元格不是唯一的，您要使用的内容有不同的选择
cell is not unique you have different
choices as to what you want to use for

304
00:25:42,660 --> 00:25:47,220
例如，您的原始晶胞是这样写的，您知道四个
your primitive unit cell for example
here's the lattice written you know four

305
00:25:47,220 --> 00:25:51,090
不同的时间，您可以选择原始单位晶胞为任意形状
different times and you can choose
primitive unit cells to be any shape so

306
00:25:51,090 --> 00:25:53,880
您可以选择他们，这个形状，这个形状，这个形状，只要
you can choose them this shape this
shape this shape this shape as long as

307
00:25:53,880 --> 00:25:58,860
它们可以放在一起并平铺所有空间，您拥有一个非常漂亮的原始单位像元
they fit together and tile all of space
you have a very nice primitive unit cell

308
00:25:58,860 --> 00:26:03,960
好吧，其中一些比其他更方便
okay some of them are more convenient
than others one should be warned that

309
00:26:03,960 --> 00:26:08,970
像这样的东西也是一个很好的原始晶胞，这有点
something like this is also a good
primitive unit cell and that's a little

310
00:26:08,970 --> 00:26:12,750
不太明显，它仅包含一个晶格点，但您必须考虑
less obvious that that contains exactly
one lattice point but you have to think

311
00:26:12,750 --> 00:26:16,320
关于像这个家伙一样被部分封闭在单元格中的东西
about the the things that are partially
enclosed in the unit cell like this guy

312
00:26:16,320 --> 00:26:21,750
因为仅计为整个圆的theta的theta，而这个计为
as only counting as theta of this the of
the full circle and this one counts as

313
00:26:21,750 --> 00:26:24,540
整个圆的theta是pi减去的圆的theta是
theta of the full circle this one is pi
minus theta of the full circle this is

314
00:26:24,540 --> 00:26:28,650
 PI减去完整theta整个圆，如果您收集了所有这些
PI minus full theta the full circle and
if you collect all those pieces of the

315
00:26:28,650 --> 00:26:32,340
将它们放在一起的晶格点，您将获得完整的两个pi，所以
the lattice point you put them together
you'll get the full two pi okay so it's

316
00:26:32,340 --> 00:26:36,540
一个晶格点，但它分成四个部分，好吧，这是一个晶格
one lattice point but it's broken up
into four pieces okay it's one lattice

317
00:26:36,540 --> 00:26:40,470
点分为四部分，也许这是一个很好的原始单元
point broken into four pieces maybe this
one this is also a good primitive unit

318
00:26:40,470 --> 00:26:44,790
单元格，这是一个晶格点，更明显地分为两部分
cell this is a lattice point more
obviously broken into two pieces you

319
00:26:44,790 --> 00:26:48,390
将它们组装在一起，您会得到一个晶格点，而这是一个
assemble them together you get the one
lattice point back and this one is a is

320
00:26:48,390 --> 00:26:52,470
一个更简单的晶胞，可能更容易看到它包含
a simpler unit cell which is maybe
easier to see that that contains exactly

321
00:26:52,470 --> 00:26:57,630
一个格子点另一个定义，我知道我们有很多
one one lattice point
another definition I know we have a lot

322
00:26:57,630 --> 00:27:08,880
这些常规单位单元中的“我等于1”等于
of these conventional unit cell
I mean it's l equals conventional is

323
00:27:08,880 --> 00:27:20,419
方便的单位晶格非原始单位晶格非原始单位晶格
convenient a unit cell a non primitive
unit cell non primitive unit cell that

324
00:27:20,419 --> 00:27:36,409
很方便，通常意味着通常会遇到正交轴
is convenient which usually means
usually meeting orthogonal axes

325
00:27:36,409 --> 00:27:48,090
正交正交轴就这么认为，例如，在这里，我们有一个
orthogonal orthogonal axes right think
so so for example here we have a

326
00:27:48,090 --> 00:27:55,830
三角形晶格和具有正交轴的常规单位晶胞
triangular lattice and a conventional
unit cell here with orthogonal axes

327
00:27:55,830 --> 00:27:59,510
而不是原始的晶胞，所以其中可以有多少个晶格点
rather than primitive unit cell so how
many lattice points are in that can

328
00:27:59,510 --> 00:28:03,630
那里有人吗有人回来吗好吧，是的，我相信
someone up there who is it someone way
back there all right oh yeah I believe

329
00:28:03,630 --> 00:28:10,380
你可以看起来诚实吗，是的，好的
you
could you look honest okay so yes okay

330
00:28:10,380 --> 00:28:20,100
另一个另外一个定义啊，先生，这是葡萄酒商Seitz牢房里的大Nur Seitz 
another another definition ah sir over
here a vintner Seitz cell big nur Seitz

331
00:28:20,100 --> 00:28:26,580
如果您还没有碰到细胞大神经元，他就是一位非常重要的物理学家
cell big nur was a very important
physicist if you haven't run into his

332
00:28:26,580 --> 00:28:35,450
塞兹（Seitz）的名字已经不那么重要了，但在该地区也很重要
name already Seitz was less important
but also important the region the region

333
00:28:35,450 --> 00:28:42,230
围绕晶格点
around a lattice point

334
00:28:44,760 --> 00:29:06,370
更接近那个格子点，然后再指向其他任何点，所以你就是你
closer to that lattice point that point
then to any other okay so you're you

335
00:29:06,370 --> 00:29:09,880
有很多格子点，您想找到一个周围的原因
have a whole bunch of lattice points you
would like to find the reason around one

336
00:29:09,880 --> 00:29:13,060
比任何其他晶格更靠近该晶格点的晶格点
lattice point that is closer to that
lattice point than to any other lattice

337
00:29:13,060 --> 00:29:18,400
点，有一种方法可以做到这一点，那就是Vigna网站建设Vigenere 
point and there's a way to do this which
is the Vigna sites construction Vigenere

338
00:29:18,400 --> 00:29:26,830
网站，您如何找到该区域施工说明，我将
sites how you find that region
construction instruction which I will

339
00:29:26,830 --> 00:29:30,640
解释这种结构，描述它比写出来要容易，但是
explain this construction it's easier to
describe it than to write it out but

340
00:29:30,640 --> 00:29:43,210
我将使用垂直的垂直二等分线写下来，让我们看看
I'll write down use perpendicular
perpendicular bisectors so let's see how

341
00:29:43,210 --> 00:29:48,040
我们这样做很好，所以这是格子，我标记了其中的点之一
we do this okay so here's the lattice
and I've labeled one of the points of

342
00:29:48,040 --> 00:29:52,240
我们想找到那个格子的维格护士Seitz细胞
the lattice black we'd like to find the
Vig nurse Seitz cell of that lattice

343
00:29:52,240 --> 00:29:55,960
换句话说，更接近黑色的空间区域是什么
point in other words what is the region
of space which is closer to that black

344
00:29:55,960 --> 00:29:59,560
点阵比任何蓝色点阵都好，我们该怎么办
lattice point than is to any of the the
blue lattice points okay how do we do

345
00:29:59,560 --> 00:30:04,240
好吧，你在这里选择一个相邻的点，然后把
that well you pick a neighboring point
like this one point up here and you put

346
00:30:04,240 --> 00:30:08,380
沿垂直平分线向下，这条红线现在可以了
down a perpendicular bisector this red
line okay now everything on the lower

347
00:30:08,380 --> 00:30:13,000
红线的一侧比蓝点更靠近黑点
side of that red line is closer to the
black point than it is to the blue point

348
00:30:13,000 --> 00:30:19,330
标记了垂直等分线的一个正确定义现在让我们这样做
labeled one right definition of
perpendicular bisector now let's do that

349
00:30:19,330 --> 00:30:23,080
在这一点上还有另一点，现在我们有了这个垂直
with another point over here this point
too and now we have this vertical

350
00:30:23,080 --> 00:30:29,830
垂直等分线和的的左侧的所有内容
perpendicular bisector and everything on
the left hand side of the of the of the

351
00:30:29,830 --> 00:30:34,570
垂直线比蓝点标签更靠近黑点
vertical line is closer to the black
point than it is to the blue point label

352
00:30:34,570 --> 00:30:38,380
两个，而您对三个，四个，五个和六个以及所有
two and you do the same thing for three
and four and five and six and all the

353
00:30:38,380 --> 00:30:42,790
进入您的墙的区域以及我在该区域中的所有内容
way around into you wall offer region
and everything in that region which I've

354
00:30:42,790 --> 00:30:46,690
现在绿色比其他任何一个都更接近黑点
now colored green is closer to the black
point than it is to any of the other

355
00:30:46,690 --> 00:30:50,890
蓝点好吧，那就是清楚它是如何工作的，好吧，那么你就有了
blue points okay is that clear how that
works okay good so then you have this

356
00:30:50,890 --> 00:30:58,889
一个不错的区域，是一个维格纳·塞茨（Vigna Seitz）的牢房
nice region which is a Vigna Seitz cell
turns out that the big nurse sitesell is

357
00:30:58,889 --> 00:31:06,629
首先，他的原始单位细胞框架甚至本身也很好
primitive his primitive unit cell frame
even itself well first of all it

358
00:31:06,629 --> 00:31:10,409
显然只包含一个晶格点，因此非常适合平铺空间
obviously contains only one lattice
point so that's good at tiles space

359
00:31:10,409 --> 00:31:14,009
因为您可以在空间的每个点周围放置一个大型的nur站点单元， 
because you can put a big nur site cell
around every point in space and

360
00:31:14,009 --> 00:31:18,089
显然，空间的每个点都是在vinner视觉单元中
obviously every point of space is the
bigness is in the vinner sight cell of

361
00:31:18,089 --> 00:31:22,499
 Vigna中的某个晶格点，无论最后一个点与您最接近
some lattice point whichever last points
is closest to you you're in that Vigna

362
00:31:22,499 --> 00:31:26,249
视单元等等，在瓷砖空间，您可以关闭这一晶格点， 
sight cell and so at tile space and you
can close this one lattice point and

363
00:31:26,249 --> 00:31:30,659
这些中的每一个都具有相同的形状，所以它是一个很好的原始单元格
each one of these has the same shape so
it's a nice primitive unit cell okay

364
00:31:30,659 --> 00:31:36,419
好，每个人到目前为止都开心，好吧，嗯，我要说的，我想这是
good everyone happy so far okay now um
I'm gonna this I think I think this is

365
00:31:36,419 --> 00:31:39,899
不在课程提纲上，所以您真的不需要学习它，但是它很酷
not on the syllabus so you don't really
need to learn it but it's pretty cool

366
00:31:39,899 --> 00:31:45,389
我卖的是borin吗？我可以正确地拼写胸罩吗？Noi Voronoi cell Voronoi 
known as a borin do I sell to spell it
right bra Noi Voronoi cell Voronoi

367
00:31:45,389 --> 00:31:59,059
 Voronoi细胞是非晶格的大护士位点细胞
Voronoi cell which is a big nurse site
cell for a non lattice for a non lattice

368
00:32:00,259 --> 00:32:09,899
点集的集合，因此，假设您在一个点中说了一堆点
collection of points points so imagine
you just have a bunch of points say in a

369
00:32:09,899 --> 00:32:14,909
平面，并且您将区域隔离到比这些点更靠近点之一的区域
plane and you wall off the region which
is closer to one of the points than to

370
00:32:14,909 --> 00:32:19,529
其他任何点Voronoi细胞的概念不仅在
any other other points this concept of a
Voronoi cell shows up not only in

371
00:32:19,529 --> 00:32:24,029
物理在化学生物学中流行
physics it shows up in chemistry biology
epidemiology it shows up very heavily in

372
00:32:24,029 --> 00:32:28,499
计算机图形显示在整个地方，包括比萨饼
computer graphics it shows up in just
all over the place including pizza

373
00:32:28,499 --> 00:32:32,639
外送，所以我将向您解释为什么这对披萨外送很重要
delivery so I'm going to explain to you
why it's important for pizza delivery

374
00:32:32,639 --> 00:32:37,259
您会发现为什么Voronoi单元是如此令人难以置信
and you will you'll realize why the
Voronoi cell is such an incredible thing

375
00:32:37,259 --> 00:32:41,219
好吧，这就是这个程序，您可以单击它，知道它已链接到
so okay so this is this program you can
click you know it's linked to on my

376
00:32:41,219 --> 00:32:47,249
网站，所以想象一下这张空白纸是牛津的地图，您一无所知
website so imagine this blank sheet here
is a map of Oxford you know nothing's

377
00:32:47,249 --> 00:32:51,749
上面写着，您还拥有两家披萨店，其中一家在北部
written on it yet and you own two pizza
shops okay and one of them's in North

378
00:32:51,749 --> 00:32:55,409
牛津，我们把它放在这里，其中一个在卡利外面，在这里，所以
Oxford we'll put it here and one of them
is out in Cali it's over here so that

379
00:32:55,409 --> 00:33:00,209
蓝线是这两个之间的垂直等分线
blue line is the perpendicular bisector
between those two okay now if someone

380
00:33:00,209 --> 00:33:03,329
打电话给你，说如果他们在这个地区附近，我要披萨
calls you up and says I want a pizza if
they're in this region they're closer to

381
00:33:03,329 --> 00:33:06,779
这个红点，所以您在北牛津有个送货员，而如果
this red point so you have the guy in
North Oxford a deliverer whereas if it's

382
00:33:06,779 --> 00:33:10,559
如果这个地区的情况很好
in if
it's down in this region well it's

383
00:33:10,559 --> 00:33:13,710
接近这一点，所以您现在可以让那个家伙完成任务， 
closer to this point so you have that
guy deliver now you're making a lot of

384
00:33:13,710 --> 00:33:17,100
钱，所以您又买了几个披萨店，所以又放了几个
money so you buy a couple more pizza
shops so it's put in a couple more one

385
00:33:17,100 --> 00:33:21,690
两个三个好吧，您有一堆披萨店，现在是Voronoi 
two three okay you have a bunch of pizza
shops and now these are the Voronoi

386
00:33:21,690 --> 00:33:26,039
每个红色点的单元格，所以这个区域在这里
cells of each of these red points so
this region here everything inside this

387
00:33:26,039 --> 00:33:31,080
这里的区域最接近这个红色点，即它的Voronoi单元格，因此，如果有人
region here is closest to this red point
that's its Voronoi cell so if someone

388
00:33:31,080 --> 00:33:35,850
呼叫此区域内最靠近他们的那个人为其服务，并且
calls within this region its serviced by
this this guy who's closest to them and

389
00:33:35,850 --> 00:33:39,360
依此类推，依此类推，您可以继续进行下去，并添加点和
so forth and so on you can keep going on
and on and on and adding points and

390
00:33:39,360 --> 00:33:44,340
这些单元格表明它的单元格始终围在
these cells indicate that it cells
always wall off the area which is

391
00:33:44,340 --> 00:33:47,429
最接近那个红点，您可以猜测会有一个
closest to that red point and you can
kind of guess that there's going to be a

392
00:33:47,429 --> 00:33:51,799
 Voronoi细胞概念在数百万种不同的应用中有数百万个应用
millions of applications of the idea of
the Voronoi cell in lots of different

393
00:33:51,799 --> 00:33:57,210
科学领域，包括披萨外送，这应该是一门科学
areas of science including pizza
delivery which should be a science by

394
00:33:57,210 --> 00:34:05,730
现在好吧，这就是我们要说的关于Voronoi细胞的全部内容，所以接下来
now okay all right so that's all we have
to say about Voronoi cells so next the

395
00:34:05,730 --> 00:34:10,379
词基，不应与我们在使用词基时混淆
word basis this should not be confused
with the word basis that we had when we

396
00:34:10,379 --> 00:34:14,250
谈到原始格向量，有人称它们为原始
talked about primitive lattice vectors
and some people call them primitive

397
00:34:14,250 --> 00:34:17,790
基向量不是这个，这就是为什么我们在我们不使用单词base的原因
basis vectors that's not this this is
why we do not use the word basis when we

398
00:34:17,790 --> 00:34:20,580
谈论原始格向量，我们不称它们为原始基向量
talk about primitive lattice vectors we
don't call them primitive basis vectors

399
00:34:20,580 --> 00:34:26,280
因为我们在此使用鸟形基准，对此混淆表示抱歉，所以基准是
because we use the bird basis here sorry
about that confusion okay so a basis is

400
00:34:26,280 --> 00:34:40,770
相对于单元格中单元格中对象的描述
a description of objects in the unit
cell in unit cell with respect with

401
00:34:40,770 --> 00:34:54,589
尊重RESP ECG尊重我们的参考晶格点
respect RESP ECG respect to our
reference lattice point

402
00:34:57,300 --> 00:35:04,570
好吧，例如，哎呀，好吧，所以在这里我们有一个周期结构
okay so for example oops okay there so
here we have a periodic structure I've

403
00:35:04,570 --> 00:35:08,080
将晶格作为参考晶格点，我在每个晶格中将其绘制为蓝色
put the lattice the reference lattice
point I've drawn it blue in each of

404
00:35:08,080 --> 00:35:11,440
这些单元格，然后您必须描述单元中的所有内容
these unit cells and then you'd have to
describe everything that's in the unit

405
00:35:11,440 --> 00:35:15,190
单元格指向那个晶格点，所以您会说有一个犰狳
cell reference to that one lattice point
so you would say there is an armadillo

406
00:35:15,190 --> 00:35:18,790
坐在你的蓝点上面好吧，也许那不是那么有用，让我去做
sitting on top of your blue dot okay
maybe that's not so so useful let me do

407
00:35:18,790 --> 00:35:24,370
一个更注重物理的晶体，所以这里是一个由两个晶体组成的晶体
a more more physics oriented one so
here's a crystal here made up of two

408
00:35:24,370 --> 00:35:29,350
不同类型的原子，大的浅灰色原子和小的深灰色原子
different types of atoms the large light
gray atom and the small dark gray atom

409
00:35:29,350 --> 00:35:34,480
好吧，参考点的黑点给了我
okay the black points of reference
points that give me the corners of the

410
00:35:34,480 --> 00:35:37,840
单位单元，所以这里是单位单元，这里只是炸了一点，所以
unit cell so here's a unit cell and here
it's just been blown up a little bit so

411
00:35:37,840 --> 00:35:41,080
您会看到更好的一点，所以在这里，我们在下一个单位单元中有一个单位单元， 
you can see a little bit better so here
we have a unit cell next unit cell and

412
00:35:41,080 --> 00:35:43,900
如果您将单位单元堆叠在一起，您将重建整个整体
if you stack the unit cells together you
would reconstruct the whole the whole

413
00:35:43,900 --> 00:35:50,560
水晶现在的基础是我们应该列出该单元中的所有对象
crystal now a basis is that we should
list off all of the objects in the unit

414
00:35:50,560 --> 00:35:55,540
参照参考晶格点的单元格，我们称其为零零
cell referenced to the reference lattice
point which we call coordinate zero zero

415
00:35:55,540 --> 00:36:00,880
所以我们说，例如，在位置a上方有一个很大的浅灰色原子
so we would say for example there's a
large light gray atom at position a over

416
00:36:00,880 --> 00:36:05,620
 2a到这里关于这个点零零然后有小
2a over to here with respect to this
point zero zero then there are small

417
00:36:05,620 --> 00:36:10,360
位置2的深灰色原子a over 4 over 4 3 over 4 over 4 3 3 over 4 3 over 4 
dark gray atoms at position two a over 4
over 4 3 over 4 over 4 3 over 4 3 over 4

418
00:36:10,360 --> 00:36:15,280
还有4分以上4分3分4分所以一旦我给你所有这些清单
and a over 4 over 4 so 3 over 4 so once
I've given you all of this list of where

419
00:36:15,280 --> 00:36:19,230
所有对象都在单元格中什么是对象及其对象
all the objects are in the unit cell
what the objects are and what their

420
00:36:19,230 --> 00:36:23,320
相对矢量相对于参考晶格点I然后给出
relative vector is with respect to the
reference lattice point I then giving

421
00:36:23,320 --> 00:36:27,220
你的晶体基础很清楚，所以如果我告诉你晶格，我
you a basis for the crystal is that
clear so if I tell you the lattice and I

422
00:36:27,220 --> 00:36:30,490
告诉你我告诉过你整个晶体的基础，所以这是我们使用的语言
tell you the basis I've told you the
whole crystal so this is the language we

423
00:36:30,490 --> 00:36:36,760
现在需要描述整个晶体有时很有用，所以
need in order to describe the whole
crystal now sometimes it is useful ok so

424
00:36:36,760 --> 00:36:41,260
在这里，使参考晶格与某些原子重合非常有用
here it's useful to take the reference
lattice to be coincident with some atoms

425
00:36:41,260 --> 00:36:46,420
所以这是由红色和蓝色物体，红色和蓝色原子组成的晶体
so here's here's a crystal made up of
red and blue objects red and blue atoms

426
00:36:46,420 --> 00:36:49,750
你知道你可以拿一个像这样的晶胞，它包含一个红色原子
you know you can take a unit cell that
looks like this it contains one red atom

427
00:36:49,750 --> 00:36:55,330
在一个蓝色原子中，但是人们做得更多的是，他们将晶胞与
in one blue atom but what people do more
often is they put the unit cell with

428
00:36:55,330 --> 00:37:00,310
红色原子的角，否则他们可能会选择蓝色，但在这种情况下，我们
corners on the red atom or they could
have chosen blue but in this case we're

429
00:37:00,310 --> 00:37:04,540
要选择选择红色，然后我们会说我们的依据是红色原子在
gonna choose choose red then we would
say our basis is the red atom is at the

430
00:37:04,540 --> 00:37:08,660
零晶胞的零位置，蓝色原子是
zero zero position
of the unit cell and the blue atom is a

431
00:37:08,660 --> 00:37:13,789
与红色原子在a1方向上相距一半，因此它的位置为1/2 
distance one-half in the a1 direction
from the red atom so it's a position 1/2

432
00:37:13,789 --> 00:37:19,039
现在请注意逗号为零，请务必注意不要过度计数红色原子
comma zero now note it's really
important not to over count the red atom

433
00:37:19,039 --> 00:37:23,059
所以你不要说零为零的红色原子，而1为另一个红色原子
so you don't say that there's a red atom
at zero zero and another red atom at 1

434
00:37:23,059 --> 00:37:27,950
在1 1处将另一个红色原子清零在0 1处将要计数的另一个红色原子
zero another red atom at 1 1 another red
atom at at 0 1 that would be counting

435
00:37:27,950 --> 00:37:31,220
四个红色原子，并且在该晶胞中只有一个红色原子被分割
four red atoms and there's only one red
atom in that unit cell it's divided up

436
00:37:31,220 --> 00:37:35,119
分为四个部分，但是如果您只需要列出它一次为零零然后
into four pieces but if you only have to
list it once it's at zero zero and then

437
00:37:35,119 --> 00:37:39,349
这意味着如果它为零零，那么所有其他部分也都是
it's implied that if it's at zero zero
it's also at all the other pieces it's

438
00:37:39,349 --> 00:37:43,759
其他你知道它是四分之一的方式，如果它是它的一部分
other you know it's quarters the way
it's divided up if it's one piece of it

439
00:37:43,759 --> 00:37:46,700
只是这里的其他部分会在那里，所以您不会超出列表
just here the other pieces of it are
going to be there so you don't over list

440
00:37:46,700 --> 00:37:51,499
这是一个清晰的清单，它只是人们经常做出的事情
it is that clear list it just once it's
something people frequently make

441
00:37:51,499 --> 00:37:57,069
好的错误，所以现在我们可以继续进行我们最终要建立的
mistakes on alright so now we can move
on to what we're finally building up to

442
00:37:57,069 --> 00:38:06,559
 3d晶格所以这是3d晶格最重要的说法
3d lattices 3d lattices so this is an
important statement may be the most

443
00:38:06,559 --> 00:38:19,220
重要的声明，我将整天不让您知道
important statement I will make all day
you will not need to know to know by the

444
00:38:19,220 --> 00:38:27,319
您无需了解3D网格中的考试委员会的法令
decrees of the exam committee you will
not need to know about lattices in 3d in

445
00:38:27,319 --> 00:38:44,539
轴与轴不正交的3d原因何在？ 
3d where axes axes are not not
orthogonal why well because then you

446
00:38:44,539 --> 00:38:48,079
明年没有什么要学习的，不，我的意思是，这只是
wouldn't have anything to learn next
year no I mean the reason is it's just

447
00:38:48,079 --> 00:38:50,989
因为它在代数上变得更加复杂，而且这仅仅是
because it gets a lot algebraically more
complicated and it was sort of just

448
00:38:50,989 --> 00:38:56,299
考试委员会同意，第三年我们可以使用所有3D晶格
agreed upon by the exam committee that
in third year we can all the 3d lattices

449
00:38:56,299 --> 00:39:00,140
只是为了防止我们陷入各种代数的
just to prevent us from getting just
knee-deep in all sorts of algebra of

450
00:39:00,140 --> 00:39:04,970
我们只需要在三个维度上保持正交轴的角度， 
angles we're just going to stick with
orthogonal axes in three dimensions and

451
00:39:04,970 --> 00:39:10,130
据我所知，该规则从未被打破，所以我
and I think that that rule has never
been broken as far as I know so I've

452
00:39:10,130 --> 00:39:14,329
有人告诉我这是一条艰难而快速的规则，所以您可以坚持下去，我希望它能继续存在
been told this is a hard and fast rule
so you can stick with it I hope it stays

453
00:39:14,329 --> 00:39:23,820
是的，所以3D立方晶格中最简单的晶格我们通俗地称为
true so the simplest lattice in 3d
cubic lattice we colloquially call it a

454
00:39:23,820 --> 00:39:28,110
立方晶格，但它可能更恰当地称为简单立方简单
cubic lattice but it's probably more
properly called simple cubic simple

455
00:39:28,110 --> 00:39:41,430
三次或原始三次或三次-P表示原始，您可能知道
cubic or primitive cubic or cubic - P
for primitive and you probably know what

456
00:39:41,430 --> 00:39:47,910
这个单元格看起来像这个单元格
this looks like it looks kind of like
this this unit cell for this unit cell

457
00:39:47,910 --> 00:39:57,030
等于一个立方体单位晶胞等于一个立方体，看起来像这样有多少原子
equals a cube unit cell equals a cube
and it looks like this how many atoms

458
00:39:57,030 --> 00:40:02,250
在那个单元格中有多少个最后点1好的，我想每个人都
are in that how many last points are in
that unit cell 1 ok I'd everyone's

459
00:40:02,250 --> 00:40:06,330
大喊大叫，所以我不知道如何让这种巧克力让我自己开心
yelling out so I don't know how to give
this chocolate all happy to myself all

460
00:40:06,330 --> 00:40:10,800
对，是的，这是一个一格点
right
so yes it's one one lattice point in

461
00:40:10,800 --> 00:40:15,180
在那个晶胞中，这是一个原始晶胞，是它的1/8倍
that in that unit cell so that's a
primitive unit cell and it's 1/8 times

462
00:40:15,180 --> 00:40:20,910
所有八个角中的每个角在单位单元格内可写为1/8 
all of the eight corners each corner is
1/8 inside the unit cell we can write

463
00:40:20,910 --> 00:40:28,650
以更合适的方式降低晶格点，使我们等于UV W乘以
down the lattice points in more proper
way that our equals UV W times the

464
00:40:28,650 --> 00:40:41,070
网格边缘长度ay，其中UV和w UV W都是整数，现在我们可以
lattice the edge length ay where UV and
w UV W are all integers okay now we were

465
00:40:41,070 --> 00:40:44,280
在一开始就告诉我们应该能够将晶格点写为
told at the beginning that we should be
able to write the lattice points as

466
00:40:44,280 --> 00:40:49,560
基本晶格矢量的整数和，因此我们可以选择一个等于a 
integer sums of primitive lattice
vectors so we can choose a one equals a

467
00:40:49,560 --> 00:41:01,410
 1 0 0 a 2等于0 1 0和a 3等于1 0 0 1 
times 1 0 0 a 2 equals a 0 1 0 and a 3
equals a 1 0 0 1 and these are the

468
00:41:01,410 --> 00:41:07,260
原始晶格向量P LVS好的
primitive lattice vectors P LVS okay
good

469
00:41:07,260 --> 00:41:12,660
还有一个词很有用，那就是协调的想法
there is yet another word it's useful to
know is the idea of a coordination

470
00:41:12,660 --> 00:41:25,500
数字通常称为Z的数字，它是最接近的数字
number number number which is usually
called Z which is the number of nearest

471
00:41:25,500 --> 00:41:28,040
邻居
neighbors

472
00:41:32,170 --> 00:41:38,180
那么这个立方晶格的协调数是多少？有人说六个
so what's the coordination number of
this cubic lattice someone said six who

473
00:41:38,180 --> 00:41:43,430
是第一个说六个在这里的人哦，好吧，我相信你，我相信你
is the first person to say six it's over
here oh okay I trust you I believe you

474
00:41:43,430 --> 00:41:51,589
是这四种啤酒中的一种，它仍然味道很好，是很好的巧克力，所以
one of these four beers yeah it still
tastes good it's good chocolate so

475
00:41:51,589 --> 00:41:55,279
其实你知道那个活着最古老的人类寿命基因的女人
actually you know the woman who lived
the oldest recorded human lifespan gene

476
00:41:55,279 --> 00:41:58,219
盾牌同志一百二十四岁半她吃了一公斤
comrade shield one hundred twenty four
and a half years old she ate a kilogram

477
00:41:58,219 --> 00:42:04,369
一周有两杯巧克力，维基百科上有两杯，所以好吧，实际上
of chocolate a week it's two it's on
Wikipedia so all right so actually the

478
00:42:04,369 --> 00:42:09,440
简单立方简单立方晶格虽然它是
simple cubic simple cubic lattice
although it's um this is what it would

479
00:42:09,440 --> 00:42:12,589
如果您将原子放在每个晶格点的位置上， 
look like if you put atoms on the
position of each of the lattice points

480
00:42:12,589 --> 00:42:17,690
虽然这是一个非常简单的格子来描述它，但它显然是一个立方体
it's a a cube obviously although this is
a very simple lattice to describe it's

481
00:42:17,690 --> 00:42:23,539
实际上所有材料上所有原子的性质都极为不同寻常
actually extremely unusual in nature of
all the materials all the atoms on the

482
00:42:23,539 --> 00:42:29,329
元素周期表只有一个元素实际上需要一个简单的三次方
periodic table only one only one element
actually takes a simple cubic

483
00:42:29,329 --> 00:42:34,900
元素是po，还有一个发现discovered的人
arrangement the element is polonium and
for one more who discovered polonium

484
00:42:34,900 --> 00:42:41,680
有人相信这是你的好，那是他的，是玛丽居里
some one over here was believed you okay
it was his it was Mary Curie and

485
00:42:41,680 --> 00:42:47,180
 lon以她的祖国波兰而得名
polonium was named after her home
country of Poland have to mention that

486
00:42:47,180 --> 00:42:53,809
因为居里夫人是我的英雄之一，所以原因之所以
because Mary Curie is one of my heroes
all right so the reason the reason why

487
00:42:53,809 --> 00:42:57,739
这是如此不寻常，您必须考虑一下堆叠到第二秒
this is so unusual you have to sort of
think about stacking to that second

488
00:42:57,739 --> 00:43:00,380
球，如果您尝试将网球像放在盒子一样的东西中
spheres if you ever try to put like
tennis balls in a box or something

489
00:43:00,380 --> 00:43:04,160
您会意识到他们真的不喜欢保持他们真正想要的位置
you'll realize they really don't like to
stay in this position they really want

490
00:43:04,160 --> 00:43:08,239
填补中间的那个洞，在那个洞里有很多额外的空间
to fill that hole in the middle there's
a lot of extra space in that hole in the

491
00:43:08,239 --> 00:43:11,960
中间的人会掉进那个额外的洞，另一种思考的方式是
middle and someone will fall into that
extra hole another way to think about is

492
00:43:11,960 --> 00:43:15,440
是你知道有一种结合力想要真正获得这些原子
is that you know there's a bonding force
that wants to get these atoms really

493
00:43:15,440 --> 00:43:19,249
彼此接近或相当接近，您认为很难
close to each other or fairly close to
each other you sort of think of as hard

494
00:43:19,249 --> 00:43:23,809
试图吸引彼此的球，这不是真的想要
spheres that are trying to attract each
other that it's not really gonna like to

495
00:43:23,809 --> 00:43:26,660
在中间留下一个很大的大洞，这是要填补的东西
leave that great big hole in the middle
something's going to want to fill that

496
00:43:26,660 --> 00:43:32,749
孔，这就是为什么简单的立方晶格在纯净中非常不寻常的原因
hole so that's why the simple cubic
lattice is is very unusual among pure

497
00:43:32,749 --> 00:43:36,950
元素，因此我们需要在简单立方晶格上存在一些差异
elements so there's some variance on the
simple cubic lattice that we need to

498
00:43:36,950 --> 00:43:43,210
知道四方格子
know tetragonal lattice

499
00:43:43,569 --> 00:43:57,259
这意味着垂直于边缘的垂直轴的轴相等，因此
which means axes perpendicular axes
perpendicular to edges equal equal so

500
00:43:57,259 --> 00:44:01,039
画一幅画，所以这是简单的立方，在边缘处是四阶
draw a picture of that so here's simple
cubic here's tetr-a g''l to the edges

501
00:44:01,039 --> 00:44:08,410
相等，一条边是不同的，另一条我们需要知道的是正交的
are equal one edge is different and the
other we need to know is orthorhombic

502
00:44:10,690 --> 00:44:23,499
这是垂直于轴线的轴，没有边是相等的，所以我们走了
which is axis perpendicular no edge is
equal okay so there we go

503
00:44:23,499 --> 00:44:28,700
简单正交的所有边长不同，但至少全部正交
simple orthorhombic all edge lengths
different but at least all orthogonal

504
00:44:28,700 --> 00:44:36,349
现在，尽管简单三次在本质上是非常不寻常的，但有些事情
now although simple cubic is a very
unusual in nature there are things that

505
00:44:36,349 --> 00:44:40,519
基于非常普遍的简单三次方，因此您需要了解
are based on simple cubic that are quite
common so you do need to know about the

506
00:44:40,519 --> 00:44:46,309
简单的立方晶格，让我们回到这张图片，这里要记住这一点
simple cubic lattice so let's go back to
this picture here remember this very

507
00:44:46,309 --> 00:44:52,099
如果您要引用多个原子类型，则非常方便
convenient if you have more than one
type of an atom to put the reference

508
00:44:52,099 --> 00:44:56,479
晶格作为晶格点上的参考原子，然后是另一个原子
lattice as the reference atom at the
lattice point and then another atom you

509
00:44:56,479 --> 00:44:59,299
可以引用它，但是您可以通过给出其位置来提供依据
can reference its but you can give a
basis by giving its position with

510
00:44:59,299 --> 00:45:04,160
相对于参考点，参考点格非常重要
respect to the reference the reference
lattice point so a very important

511
00:45:04,160 --> 00:45:10,369
结构就是所谓的氯化铯结构
structure is the so-called caesium
chloride structure named that way

512
00:45:10,369 --> 00:45:15,259
因为氯化铯的材料明显具有这种结构
because the material cesium chloride
takes that structure obviously cesium

513
00:45:15,259 --> 00:45:20,299
氯化物是一种非常离子化的物质铯放弃了它的电子
chloride it's extremely ionic material
cesium gives up it's an electron very

514
00:45:20,299 --> 00:45:23,869
很好，而且氯极具负电性，所以它想
nicely and and chlorine is extremely
electronegative so it wants to take that

515
00:45:23,869 --> 00:45:29,599
电子，所以你得到了很好的离子键，所以铯的定义
electron and so you get a nice ionic
bonding so the definition of cesium

516
00:45:29,599 --> 00:45:37,219
氯化物结构是具有基本立方晶格或豌豆的立方晶格
chloride structure is cubic lattice with
the basis simple cubic lattice or a pea

517
00:45:37,219 --> 00:45:45,039
具有基础的立方原始立方晶格，我们将铯放在
cubic primitive cubic lattice with basis
basis where we put the cesium at

518
00:45:45,039 --> 00:45:53,299
晶格点的位置0 0 0和氯的位置1/2 1/2 1/2 
position 0 0 0 on the lattice point and
the chlorine at position 1/2 1/2 1/2

519
00:45:53,299 --> 00:45:59,539
那是我们在这张照片上的洞的中间，所以这
that's in the middle of the hole
that we had in this picture here so this

520
00:45:59,539 --> 00:46:03,170
氯会填满那个孔，所以我们得到的看起来像
the chlorine is gonna fill that hole so
what we get is something that looks like

521
00:46:03,170 --> 00:46:09,259
这是铯在晶胞和氯的角上
this we get the cesium's on the corner
of the unit cell and the chlorine

522
00:46:09,259 --> 00:46:13,099
坐在晶胞的中央好
sitting in the center of the unit cell
okay

523
00:46:13,099 --> 00:46:18,499
现在您可能会这样认为，铯的角上有铯
now you might think of it this way as
having cesium's on the corners of the

524
00:46:18,499 --> 00:46:21,470
晶胞和在晶胞中心的氯，但这是
unit cell and the chlorine in the center
of unit cell but that's kind of

525
00:46:21,470 --> 00:46:25,519
我们以这种方式选择它是任意的，因为如果您愿意，这是另一张图片
arbitrary that we chose it that way
because if you so here's another picture

526
00:46:25,519 --> 00:46:29,089
具有相同结构的铯为白色，氯和氯为
of the same structure the cesium's are
white and the and the chlorines are

527
00:46:29,089 --> 00:46:33,650
这里是绿色，这是我们刚刚在讨论铯的晶胞
green here so here's the unit cell we
were just discussing the cesium's on the

528
00:46:33,650 --> 00:46:38,930
角落处有clora，中间有氯，但也有可能
clora on the corners and chlorine in the
center but one could just as well have

529
00:46:38,930 --> 00:46:43,730
选择它作为角上有氯和铯的晶胞
chosen this as the unit cell with the
chlorines on the corner and the cesium

530
00:46:43,730 --> 00:46:48,079
在中心，所以我们真正拥有的是两个互锁的简单立方晶格
in the center so what we really have is
two interlocking simple cubic lattices

531
00:46:48,079 --> 00:46:51,650
其中之一是由铯组成的其中之一是由氯组成的
one of them is made up of the cesium's
one of them is made up of the chlorines

532
00:46:51,650 --> 00:46:55,730
好的，这是一个动画，应该显示出来，所以
okay and here's a here's an animation
that's supposed to show that so that's

533
00:46:55,730 --> 00:47:00,230
氯化铯这里是铯，这里又是氯化铯，还有
cesium chloride there's the cesium's
here's cesium chloride again and there's

534
00:47:00,230 --> 00:47:03,380
那里的氯每个都是一个简单的立方晶格，它们有点像
there's the chlorines each of them is a
simple cubic lattice and they're sort of

535
00:47:03,380 --> 00:47:05,630
粘在一起，所以这种结构的铯
stuck together
so this type of structure the cesium

536
00:47:05,630 --> 00:47:12,470
氯化物结构实际上是自然界中很常见的结构
chloride structure is actually quite a
common structure in nature now we can do

537
00:47:12,470 --> 00:47:18,140
还有一些事情要考虑纯铯纯铯
something else which is to consider pure
caesium pure cesium which is a very

538
00:47:18,140 --> 00:47:26,809
相似的结构纯铯结构，所以我们有立方p晶格p 
similar structure pure cesium structure
so we have so it's a cubic p lattice p

539
00:47:26,809 --> 00:47:34,069
格，但我们可能要把它放在括号中，因为我们要
lattice but we may be may I'm gonna put
this in parenthesis because we're gonna

540
00:47:34,069 --> 00:47:39,289
说这是铯的隐居时刻，我们将铯置于零零
say that's a lie-in moment cesium we're
going to put the cesium at zero zero

541
00:47:39,289 --> 00:47:47,329
零，然后再以一半1/2 1/2的另一个铯，那么我们要做的就是
zero and then another cesium at one half
1/2 1/2 okay so all we're going to do is

542
00:47:47,329 --> 00:47:51,049
我们将服用氯化铯，并摆脱
we're going to take that cesium chloride
and we're going to get rid of the

543
00:47:51,049 --> 00:47:56,539
中间的氯，再用另一种铯代替，所以我们可以考虑
chlorine in the middle and replace it
with another cesium okay so we can think

544
00:47:56,539 --> 00:48:00,259
它是简单的三次方，其基础是铯为零零
of it as simple cubic with the basis
where the basis is a cesium at zero zero

545
00:48:00,259 --> 00:48:07,309
零和铯的一半1/2 1/2现在这实际上本身就是一个不同
zero and a cesium at one half 1/2 1/2
now this is actually itself a different

546
00:48:07,309 --> 00:48:09,920
晶格的类型这是我们重要的晶格类型
type of lattice this is
important type of lattice that we're

547
00:48:09,920 --> 00:48:16,640
将要研究的那个叫做体心立方晶格
going to be studying which well it's
known as the body centered cubic lattice

548
00:48:16,640 --> 00:48:27,230
确保我不会错过任何以身体为中心的立方晶格
make sure I don't miss anything body
centered cubic lattice lattice also

549
00:48:27,230 --> 00:48:34,970
被称为立方-我所以这个词居中居然不是听起来像
known as cubic - I so the word body
centered it's not it sounds like

550
00:48:34,970 --> 00:48:38,780
瑜伽之类的东西，但是实际上你知道这个主意是
something out of yoga or something but
it's it's actually you know the idea is

551
00:48:38,780 --> 00:48:43,670
那就是你在那个立方体的中心放了另一个点
that is that you've put a another point
in the center of the body of that cube I

552
00:48:43,670 --> 00:48:48,860
来自德国内心的进入，这一定意味着任何德国学者
is from German inner is entry which must
mean something any German scholar it's

553
00:48:48,860 --> 00:48:52,670
诸如此类的意思是在身体中心或某种形式
something like it means in the center of
the body or something kind of it anyway

554
00:48:52,670 --> 00:48:58,520
所以我要声明所有这些点的所有环境都是
so I'm going to claim that all the
environment of all of these points is

555
00:48:58,520 --> 00:49:03,620
完全一样，所以实际上它本身就是一个格子，让我们看看
exactly the same so this is actually
itself a lattice so let's see how this

556
00:49:03,620 --> 00:49:07,670
这是如何工作的，这是体心立方晶格的晶胞
how this works this is the unit cell of
the body centered cubic lattice

557
00:49:07,670 --> 00:49:15,290
在以人体为中心的立方晶格中有多少个晶格点-是的
how many lattice points are in the body
centered cubic lattice okay it's - this

558
00:49:15,290 --> 00:49:18,410
是体心立方晶格的常规单位晶胞
is a conventional unit cell of the body
centered cubic lattice we take the

559
00:49:18,410 --> 00:49:22,640
常规单位电池再次成为立方体，只是因为它更方便
conventional unit cell to be the cube
again just because it's more convenient

560
00:49:22,640 --> 00:49:27,860
为此，显然在中心有一个，然后我们有一个
to do so there's one in the center
obviously and then we have the one which

561
00:49:27,860 --> 00:49:31,580
在角落里分为八个部分，有一个方便的地方
is divided into eight pieces in the
corners now there's there's a convenient

562
00:49:31,580 --> 00:49:36,920
描述这些三维结构的方法是使用已知的
way to describe these three-dimensional
structures which is to use what's known

563
00:49:36,920 --> 00:49:41,510
作为平面图，平面图是来自某种建筑术语，其中
as a plan view a plan view is it comes
from a sort of architectural term where

564
00:49:41,510 --> 00:49:45,740
您从顶部往下看，然后画出所指示的高度
you look down on the thing from the top
and you draw the heights you indicate

565
00:49:45,740 --> 00:49:48,860
您所看到的所有事物的高度，因此，如果您身处其中，就知道
the heights of all the things that you
see so if you're up in a you know a

566
00:49:48,860 --> 00:49:52,670
直升机，而您正在看不起这个常规的单元格
helicopter and you're looking down on
this conventional unit cell you would

567
00:49:52,670 --> 00:49:55,820
在角落看到四件事，然后在中心看到一件事，然后
see four things in the corners and you
would see one in the center and then you

568
00:49:55,820 --> 00:49:59,360
标记高度，因此将这一高度标记为a超过2，然后降低
label the heights so this one is labeled
with height a over two and then down

569
00:49:59,360 --> 00:50:03,050
在这里它说未标记的点的高度为零，所以这个为零
here it says unlabeled points are at
height zero and a so this one's at zero

570
00:50:03,050 --> 00:50:05,810
一个这个为零，这个一个为零，一个这个坐在这里
and a this one's at zero and a this
one's at zero and a this one sits here

571
00:50:05,810 --> 00:50:11,120
在一个上，这个在一个高处--好的
on a and this one here is at height a /
- okay

572
00:50:11,120 --> 00:50:19,220
如果将原子放到这个以身体为中心的立方结构中，它们将
if you put put atoms together in this
body centered cubic structure they would

573
00:50:19,220 --> 00:50:22,070
看起来更像这样，实际上是
look more like this and and it's
actually it's

574
00:50:22,070 --> 00:50:25,760
显然，它以这种方式填充了更多的晶格孔
it's clearly it's filling up much more
of the holes of the lattice this way

575
00:50:25,760 --> 00:50:29,750
这是更有效的球体填充，并且有很多材料
it's much more efficient sphere packing
and there's quite a few materials that

576
00:50:29,750 --> 00:50:34,490
实际上以这种以人体为中心的形式钠锂铁钾
actually take this body-centered form
sodium lithium iron potassium is many

577
00:50:34,490 --> 00:50:44,810
还有很多，那么协调八号结束了
many many more so what is the
coordination number eight who's over

578
00:50:44,810 --> 00:50:49,340
好的，好的，八点八点，所以如果你想到的话
there okay yeah okay eight it's eight so
if you think of it if you think it

579
00:50:49,340 --> 00:50:52,970
假装你是中间的那个家伙，那么每个人都有八个邻居
pretend you're the guy in the middle
here then you have eight neighbors each

580
00:50:52,970 --> 00:50:57,050
这八个邻居之一是不太明显的是，如果你碰巧是其中之一
one of those eight neighbors what's less
obvious is if you happen to be one of

581
00:50:57,050 --> 00:51:02,020
这些在角落的家伙，你也有八个邻居，好吧，这里的每一点都是
these guys in the corners you also have
eight neighbors okay every point here is

582
00:51:02,020 --> 00:51:08,900
完全相同，也许我会在这里展示，所以这是常规的单元格
identical maybe I'll show it here so
here's the conventional unit cell like

583
00:51:08,900 --> 00:51:13,150
这就是中心点，现在您也可以选择
this and here's the point in the center
now you could just as well have chosen

584
00:51:13,150 --> 00:51:18,320
这个点是一个立方体的中心，然后我们将这个立方体与
this point to be the center of a cube
and then we would have this cube with

585
00:51:18,320 --> 00:51:22,520
这一点在中心还可以，所以请再次记住，这实际上是两个
this point in the center okay so again
remember that this is really two

586
00:51:22,520 --> 00:51:25,910
当我们考虑它时，将简单的立方晶格互锁
interlocking simple cubic lattices when
we were thinking about it is being

587
00:51:25,910 --> 00:51:30,260
氯化铯有两个互锁的简单立方晶格，所以如果
cesium chloride there were two
interlocking simple cubic lattices so if

588
00:51:30,260 --> 00:51:34,220
我们选择该点作为中心，然后黄色的点围绕它
we choose this point as the center then
the yellow ones make the cube around it

589
00:51:34,220 --> 00:51:37,490
如果我们选择一个作为中心，那么红色将围绕它
if we choose this one as a center then
the red ones make the cube around it

590
00:51:37,490 --> 00:51:43,640
无论哪种方式，它总是有八个最近的邻居，好吧，我想的最后一件事
either way it always has eight nearest
neighbors okay the last thing I think

591
00:51:43,640 --> 00:51:46,760
我们有时间我们下次再接，我们将证明这件事是
we're have time we'll pick up next time
and we'll prove that this thing is

592
00:51:46,760 --> 00:51:50,630
实际上是根据我们在开始时给出的晶格定义得出的晶格
actually a lattice by the definitions of
lattice that we gave at the beginning of

593
00:51:50,630 --> 00:51:57,690
好的一天，明天我再见[鼓掌] 
the day all right I'll see you tomorrow
[Applause]