Introduction to Crystal Structure Video Lecture - Civil Engineering (CE)

okay so in this video I'd like to do a
basic introduction to crystal structure
so to start with you know when we heat a
metal up or you may know a heat a metal
up and cool it down we see little little
crystals form sometimes we sketch the
microstructure in a little circle we
might say you've got some some liquid
and then as you cool it down it first
starts to solidify you get little
crystals form and this is something that
we cover in more detail in phase
equilibrium but the concept you might be
familiar with you may have seen this in
I say looking at a jar of honey or
something like that that sits on the
shelf for a number of weeks or months
and you see little crystals of sugar
form in it and what actually happens
initially is some little sucrose
molecules slow down often on a rough
feature a little scratch on the inside
of the container or if if you put a
string into a container of honey the
rough little features on the string will
actually serve as low energy nucleation
sites for sugar crystals to start to
form and so what happens is some little
little crystals little sorry little
molecules of sugar will slow down and
deposit on the string in that example or
in this case with a metal solidifying a
few atoms of a metal will will will come
together and they'll form a metallic
bond and they'll start to form a
crystalline so more and more crystals
will start to or atoms rather will start
to deposit on top of that so if I sketch
just in a cartoon sketch here a little
call out of that crystal what that would
look like is a little collection of
atoms
that's arranging themselves and I'm
doing a very generalized example here
they're starting to to come together and
achieve a lower energy by forming a
metallic bond and they arranged in a
very regular repeating pattern and I'm
trying to illustrate that here just as
this simple orthogonal arrangement of
atoms but that particular repeating
arrangement that regular
repeating arrangement is is what we
refer to as a crystal and often in
material science the word that we use
instead of crystal is grain but really
they're synonymous okay so we know that
atoms in a solid may form in a regular
repeating arrangement as crystals they
don't have two glasses are amorphous and
we'll cover that in another video but if
they do form a crystal there's a regular
repeating arrangement - and if we'd like
to describe that to help us appreciate
the the properties of a crystal for of a
solid for example we'd like a way to
describe the the crystal without having
to describe you know million atoms and
all their positions so could we sort of
take that little arrangement there and
break it down into a small chunk and
sometimes it's useful to think about a
two dimensional analogy so a two
dimensional analogy would be say a wall
that you're coating with we're covering
with tiles in fact this classroom has
these these bricks that are actually in
this case they're I think they're
structural part of the wall but there's
a pattern to them you can see they have
this rectangular shape and if I wanted
to describe the wall I could I could
sketch the entire wall for you but I
could also break it down into the
individual brick you know if I account
for half of the grout line between the
bricks I could actually describe
essentially the wall by describing a
smaller number of bricks and just
defining their dimensions perhaps you
know height and width
maybe I'll call it a and B just for
these purposes and we could call that
little unit well we could call it a you
know a building block and in fact I
don't mean specifically because this is
a brick that I'm calling it building but
it means some-some unit that we're
repeating to form to form the the larger
structure in this case were limited to
this two-dimensional and this example so
we could cover the entire area with
these little rectangles so what we could
look at then is again in the
two-dimensional example what would be
some possible repeating units other than
a rectangle that we could use to
completely cover an area so we'd say it
must completely cover the area you know
with with no voids well we could
certainly use a square you could
translate a square up and down and so on
right and completely cover the area and
100% of the area would be covered right
so it's yes that's possible what about
you know if I took for example a circle
well a circle even if I really tried to
squeeze them in to cover the area as
carefully as I could
there would always be some void space
between the circles you know and I
didn't draw those circles very well but
circles do not have translational
symmetry you can't slide a circle
adjacent to itself and completely cover
this this area so we'd say no
translational symmetry okay what we know
what other shapes could we have well
what about you know I a parallelepiped
or like this and these sides are all
meant to be parallel well certainly yes
you could you could translate that over
as well and completely cover the area so
that would work to cover an area what
about a triangle well a triangle if I
translate it without any rotation the
triangle would not cover the entire area
again there would still be this missing
space this if you will void that's not
filled so triangle on its own doesn't
work so you certainly get the the idea
that we could with there's certain units
that we could use to cover to space
two-dimensional space what about in the
three-dimensional world well in the
three-dimensional world of course sort
of the extension of the square would be
the cube and that could be translated to
fill three dimensional space I could
draw another cube to the right of this
one and so on and up and down and front
and back and fill a volume completely
with cubes there's other there there's
there's other solids that we can use as
well and we'll explore some of these
later today we're really going to focus
on the cube because actually there's
there's a lot of materials many
materials
many materials have cubic symmetry and
that's convenient because the cube is
relatively easy for us to understand as
as humans we're comfortable with an
orthogonal axis system you know X Y and
and Zed we're fairly comfortable with
already so that one works nice so it's
kind of a convenient result of nature
that many materials have cubic symmetry
so if we then say our building block is
going to be a cube there's a few things
that we should describe or be able to
describe about the the building block
here so first of all these repeating
units or building blocks we have another
name for them so instead of calling them
building blocks we call them unit cells
okay so what I've sketched over here
then is a cubic unit cell
and we should be able to describe the
dimensions of the cube so we would need
the cube edge length and of course it's
a cube so each of the dimensions the
linear dimensions is equivalent and
commonly we just refer to them with the
lowercase letter A over here I went
ahead and described another dimension B
for this rectangular two-dimensional
shape and similarly in some volume some
three-dimensional unit cells will have
the height for example if this was
tetr-a g''l it was like a cube that's
elongated a little bit we would have a
height that was different than than the
base dimension and so we'd have a value
of a and B that we have to define and
what we call those are the lattice
parameters
the lattice parameters so we've got only
one lattice parameter in the case of the
cube if it was a rectangle we would have
you can see two lattice parameters
and I should also just for a moment
expand on what this word lattice means
in case it's a if English is perhaps not
your first language you may not have
come across that but lattice the word
lattice essentially describes repeating
framework for example you could have a
lattice in your garden and you could
grow a cool mattes or something on some
climbing vine so in our case here we've
got a lattice you could have a
two-dimensional lattice it would be a
two-dimensional positioning of points so
we could say let's put an atom at each
of these intersections and then what if
we took that into three dimensions well
then we would have the basis for our
unit cell over here so a unit cell is
essentially a small little piece of the
of the lattice that is if we repeat the
unit cell front to back up down left
right we'll build this lattice and
there's positions various different
positions in the unit cell that we could
put atoms so I haven't told you yet
where they're going to go that'll be the
focus of another video but right now
we've just described the the unit cell
the concept of a lattice the lattice
parameters and a little bit later we'll
also look at cases where these angles
are not orthogonal in this case for a
cube of course they're 90 degrees but
later on you'll see some some cases
hexagonal close-packed for example where
one of those angles is 120 degrees so I
think that's a good place to stop for
this initial video thank you