Diamond cubic crystal structure Video Lecture - Civil Engineering (CE)

okay so what am I gonna do here I'm
gonna draw something I don't know like
this hmm
pretty like it's shiny now you know what
it is it's a diamond
okay so diamond we know we is is is 100%
carbon and we certainly know at room
temperature and pressure it seems to
exist it actually is not
thermodynamically stable but we'll get
to that and we know its carbon it's in
fact sp3 hybridized so we've got four
covalent bonds and they're all have the
same behavior you know in two dimensions
we would sketch it like this we'd say
well carbons bonded to four other
carbons and that continues but that is
not you know that that's that's two
dimensions we want to know what this
looks like in three dimensions and so we
have this central carbon atom with four
other carbons coming out of it and a
fourth at four covalent bonds and you
know we can create faces on that if you
will let me draw that for you a little
bigger it and trying to draw a
tetrahedron yeah so tetrahedron is this
four-sided clearly I'm not an artist
four-sided that's and they're supposed
to be all exactly the same shape but
this is a tetrahedron ER ah he drive
tetrahedra so it's got four sides and
you know the positioning of atoms and
would be like got one right in a very
center of that thing get one on each
corner and we've got a covalent bond
two in each so that that's the
arrangement of bonds that we have but
our human minds our human brains
sometimes like than any things a little
bit simpler if we can to visualize I
mean good to say that's the structure of
diamond then that repeats but you can
actually go to a fume when you when you
introduce a few more carbon atoms you
can actually you realize that there's
actually a cubic symmetry to it and
that's nice because we like simple
geometry oh yeah I broke my debt rahiba
I glue it back together ere we go
alright so um and I what I'm trying to
do is I'm going to show you how this
cubic symmetry exists so here's a cube
we're familiar with this we've seen this
face centered cubic we've seen it in the
rock salt crystal structure and so what
it involves is involved in an atom at
each corner all right and I'm drawing
draw here for you depict that there's
1/8 of an atom at each corner this is
the back here now all right so there's
1/8 of an atom at each corner and then
there's atoms in face centered positions
ok front face top face right face but
there's also of course the left face
hidden so I'll dash it in back face and
the bottom face and so that gives us
four atoms in total ok four atoms from
the FCC positions but we need more and
we need to find spaces where we can fit
an atom where it will be touching for
others now this kind of a tetrahedral
coordination this four atoms nearest to
it and I think the easiest way to do
this actually just to show you and then
I'll try to go around and come back to
it and show you different ways to
visualize it to help make it more
concrete if you look at this can of this
region here of this unit cell by this
region I mean towards the bottom okay
bottom half
towards the left hand side and towards
the front right in the middle of that
bottom left front area is a space and I
could actually put an atom there carbon
atom there and then I could draw these
bonds to that left side face the front
sorry the front bottom-left the front
face centered and the bottom face Center
position now because of the perspective
I've drawn this on that it's a little
hard to tell but that is in fact the
same tetrahedral geometry that I
sketched before I could I could try out
this doesn't go too bad but I could show
you the faces um here okay
and don't ask twice there there we go
okay so that is in fact a tetrahedral a
tetrahedral site so it may it may be a
little hard to tell that this is in fact
the same tetrahedron as I had over here
but remember the rotate the angle that
we're looking at is different so this
tetrahedron that I drew up here if you
imagine you when I can rotate to that
over so this atom was in that corner
this one one maybe became that bottom
face you have this ad I'm taking that
face position than this one here taking
my left side face position it is in fact
the same but let me show you some other
ways to visualize that site and then
we're going to go back to create the
finally the entire diamond cubic crystal
structure so what I'd like to do next to
and better to show you where that
tetrahedral site exists because you
might not follow this and admittedly my
artistic abilities are some limited as
hard as I try if I if I cut this thing
in half okay in front to back I'm going
to slice this cube in half that's what
I've done and then I'm going to slice it
in the plane of the page in half again
and finally in this horizontal plane I'm
going to slice in half so what have I
done
I've now sliced it
into eight little will call them sub
cubes okay sub cubes that is there these
little cubes but they're they're smaller
they're within the within the the
original unit cell dot in this top front
right one here for you I've got in the
back so you can kind of see well there's
a cube that's one of these sub cubes
okay and in fact in the very center of
that sub cube is this interstitial site
that I'm talking about so write in a
very center of that front top right
label that so we're clear here this sub
cube is towards the front towards the
top and towards the right okay it's
opposite in the front plane from from
this bottom left front so that's where
that is and then I've draw the direction
of contacting in here and maybe you'll
see this tetrahedral a little bit more
clearly so that is in fact that row he'd
rely could try to make it into it
tetrahedral solid for you by showing the
triangular faces okay so that is there
there you go that's again the
tetrahedral interstitial site so and
I've actually drawn the alternating
corners here on purpose because in fact
for every carbon to be bonded to four
others we can only fill half of these
sub cubes so there's eight sub cubes but
only half that is four of them are
filled a name for a space between other
atoms is interstitial site it's a little
bit unusual to refer to an interstitial
site in diamond because they're all
every atom is carbon but if you start
thinking about this as a space that you
fit an atom between others it will help
you in other crystal structures that
have some similarities to to this so
let's continue on again we've spent a
little time on this and I sketch for you
another yeah unit sell fresh one and
we'll go ahead and identify which ones
have carbon in them and then you'll know
the diamond cubic crystal structure like
the back of your hand so here's a cube
okay - in the back for you there now
this time I'm actually going to go ahead
and I'm gonna cut the sub cubes for you
as we did before so I've got eight
little identical cubes making up the
greater at the larger unit cell and what
I showed you on the previous slide is
I've got in this front bottom left a
carbon in the front top right is a
carbon and then what happens is these
alternating space so they're spaced out
as far apart as they can that they
wouldn't all all four of them would not
occupy the bottom half of the unit cell
or the right side you're going to
alternate so they alternate on top to
bottom left to right here well in the
back of the unit cell you can do the
same thing so that means the back um top
left site will be filled and the back
bottom right so this is sorry the back
top left and the back bottom right will
be filled so they alternate and a
student a few years ago showed me a
little trick that was useful for him and
if you just sort of if you picture those
little sub cubes and what I do for you
is I shade in that expose the free
surfaces of the sub cubes that contain
an occupied tetrahedral site you'll see
the positioning of the tetrahedral sites
perhaps a little bit more clearly so
there you go those are the occupied
territory sites or the positions of
those carbon atoms in amongst all the
other carbon atoms in diamond cubic
until finally what I'll do is I'll just
position the FCC positioned ones for you
okay back in that corner there top front
right side and maybe for simplicity I
want like dot dot and the ones that are
hidden if a completeness so that is
diamond cubic and this tetrahedral
symmetry is a really important one it
comes up in organic molecules it comes
up in many semiconductor devices so
understanding diamond cubic is a really
good foundation for proceeding to other
crystal structures and other structures