see this has like seven carbon wonder
eight carbon here a long chain like this
and the liquid crystal properties
observed between 108 and hundred 47
degrees centigrade in this case 21 and
47 degrees centigrade okay chapter 12 is
about solids and modern materials now we
talked about the properties of solids in
general actually we said that the solids
are made of molecules may be made of
molecules ions or atoms and the solid
state the atoms molecules or the ions
whatever makes the solid only vibrate
make vibration motions but they are not
free to move in the solid and that's why
the solid stays same shape and so on and
we also talked about the Dalton points
of service and so on compared the
physical properties of solid liquid and
gases actually and try to explain them
with the molecular level properties of
the substances made of it now here now
chapter 10 which we have skipped
actually and we left it to you you're
supposed to read it it's about the
gaseous state now chapter 11 we just
finished that's about the more liquid
state right describes the liquid state
properties properties of the liquid now
this chapter 12 is about the solid you
see again these three chapters 10 11 12
simply about the states of matter gas
liquids and solids now let's look at the
solids stage again now there are certain
ways of classifying solids one way
classifying the solids is according to
the bunks that keeps these solid
molecules or whatever solid is made off
the unit's together and according to
this classification based on the bond
actually that means forces that holds up
the molecules or in the solid states are
metallic solids ionic solids covalent
Network solids molecular solids and
polymer polymers these are again solids
and nano materials now let's look at
what are the forces that held the solid
molecules or atoms together in the
metallic solids again as we see here are
held together by sea of collectively
shared electrons what does this means
what is this what are the forces that
keep the solid metals together in a
solid form it's actually might alec bond
remember it's a metallic bond what we
said metallic bond is the attraction
between the electron cloud that moves
freely in the metal and the positively
charged metal ions right this is a
chemical bond actually one type of
chemical bond and it's a very very
strong and in metals actually the force
that keeps the battle together actually
is the metallic bond now ionic solids as
we talked about this also ionic solids
are also held together by the
electrostatic attraction between
positive and negatively charged ions and
what is this ionic bond right actually
it is ionic bonds so in ionic solids
actually we have the ionic bonds and
that ionic bonds keep the ionic solid
together now covalent Network solids
what is it for example example the metal
solids examples are any metals ayran
gold copper whatever nickel and so on
now ionic solids are ionic compounds
such as the sodium chloride cesium
chloride or sodium fluoride and so on
that means in this
our state exists in form of ions
positive and negatively charged ions now
covalent Network solids are joined by an
extensive network of covalent bonds now
one example is diamond now in diamond
actually every carbon atom is bonded to
the other carbon atom by covalent bond
and it expands over all solid diamond
it's a very very strong covalent bonds
and that makes the diamond actually very
very stable very hard so on right so
those are the covalent Network solids
our exam one example is diamond or
graphite or all carbon actually that's
also diamond remember it's also carbon
but graphite is a different form of
carbon again and silicon and silicon
dioxide
all of these are covalent Network solids
that means that the atoms are bonded
together by covalent bonds and this
covalent bonds is the network type that
means it's over all the covers the whole
solid covers the whole solid and they're
very very strong again molecular solids
are discrete molecules has together by
weak forces what are these forces these
are intermolecular forces London forces
right London dispersion forces or
dipole-dipole forces or hydrogen bonding
these are the forces that keep the
molecular solids together as a matter of
fact now if you simply if I ask you
which of these solids will have the
highest mountain point remember again
the mountain point is also determined by
the degree of attractions of the solid
particles or molecules together and in
terms of that highest will be actually
this covalent solids has very very
strong and they are very very high
melting points as a matter of fact next
will be
we ionic solids ionic solids and the
metallic solids remember there are
metals that melts at room temperature 28
degrees 30 degrees actually room
temperature 25 but little about that but
there are metals that melts at 3000
degrees centigrade what is that the
highest melting point for the metals yes
which metal tungsten right remember the
light bulbs inside the light bulb we
have the resistance wire that resistance
wire actually is tungsten and that
tungsten melts over 3000 degrees
centigrade that resistant gets so hot
but still stays together as solid and
you see again in the saw metal cases
depending on the metal the melting
points are variable but the molecular
solids usually have low melting points
because the forces that keeps that
together solid in fact particles
together in the molecular solids are
intermolecular forces intermolecular
forces now polymers again here these are
chains of the atoms long big molecules
and they usually have a unit and
polymerizations of that human unit gives
you polymers and it gives again long
chain of atoms connected by covalent
bonds and the chains can be connected to
other chain by weak forces now weak
forces when we say that's intermolecular
forces again
these molecules have different
properties than small molecules or
metallic or ionic compounds again we
know in polymers you know all over and
we use them every day they're actually
made of long molecules bonded together
chains of atoms bonded together by
covalent bond now none of materials
these are again new type of solids like
10 or 20 years ago in general chemistry
book you will never find mentioning
about this nano materials nano materials
but they are very important now and very
very useful in especially development of
technology different technologies and
what are the nano materials
nanomaterials are crystalline compounds
with the crystals on the order of one to
ten nanometer what does that means
usually the crystals of the crystalline
compound solids are much much bigger
like considering the sodium chloride but
when you have that small these are very
very small crystals you know which are
crystals made of let's say hundred
hundred and twenty molecules and so on
and they have very very different
properties very different properties and
those different properties allow them to
be used you know apply for the
industrial or technological applications
again different applications and again
you see different properties and larger
crystalline materials so these are the
type of solids based on the force of
attraction that keeps them together hold
them together now the solids are also
classified into two according to the
structures or I should probably say the
arrangement of the molecules or the
atoms or the ions make the solids and
that is one is crystalline solid one
type are crystalline solids
the other are called amorphous solids
now crystalline solids are the solids in
which there is a very regular pattern of
arrangement of the units of the solids
very regular pattern what does that mean
that means like the distances between
them all the same and the position with
respect to each other all the same
they're very regular pattern and this
pattern repeats itself as a matter of
fact in the solid and they have a
particular structure in this
three-dimensional structure and those
are called the crystalline solids again
crystalline solids you can you can
determine the structures of those
crystalline sign crystalline solids very
effectively as a matter of fact now the
second is the amorphous solids amorphous
solids on the contrary have no regular
order of the units that makes the solids
they were just you know chaotic order is
present there and we can't really know
exactly the structure of the amorphous
solids because every amorphous solids
will have probably different
arrangements of the atoms or the
molecules or whatever the units made
them examples are for the crystalline
solid copper is a crystalline solids
right any metal Iren crystalline solid
sodium chloride crystalline solid it's
an ionic solid but crystalline solid ice
is a crystalline solid these are all
crystalline solids now what about the
amorphous solids example for the
amorphous solids are rubber and glass is
the amorphous solids as a matter of fact
now what is the difference can we simply
separate one from the other by a very
simple test for example in the lab if
you're given two solids and if they ask
you which one is the amorphous which one
is the crystalline one is amorphous one
crystalline what you have to look at the
melting
points the mountain points of
crystalline solids are sharp that simply
means for example if you take a
crystalline solid and he increases the
temperature of it he'll increase the
temperature and it will be solid until
it reaches to melting point when it
reaches to the melting point if you keep
heating it it will be liquid so actually
there's a sharp melting point at that
one temperature it will melt all if you
keep giving heat to that solid and but
if you have an amorphous solid like a
glass or rubber start heating it it will
simply get softer as you heat it softer
and softer and softer and softer finally
it may be you know liquids you can call
it so that means that the amorphous
solids do not have sharp melting points
like crystalline solids and they have a
range of mountain branch of mountain and
this is actually true for the robber and
true for the glass also - so again
crystalline solids have regular pattern
and they are of more interest to most
chemists actually we will talk about
more crystalline solids not the
amorphous solids because as I said very
difficult to study the amorphous solids
there's no regular pattern regular
structures and so on okay now we said
that the crystalline solids have very
regular pattern in three-dimensions
arrangement of their in terms of
arrangement of their atoms right and it
is sort of a in every crystalline solid
you can find a smallest unit which
repeats itself in the whole crystal
repeats itself in the or crystal that
simply means that all the
structural properties of the crystalline
solid can be obtained from that unit
smallest unit of the solid and that
smallest unit is called the unit cell of
the crystalline solid so the basis of
the repeating pattern is the unit cell
that means this this unit cell repeats
itself to get the crystalline solid the
whole crystalline solid the structure of
the crystalline solid is defined by the
size and shape of this unit cell so
these crystalline solids may be
different shapes and different sizes and
also the locations of the atoms within
the unit cell so the unit cell is the
smallest solids crystalline solid piece
which contains all the structural
properties of the solid what we mean
what I mean by the structural properties
for example the distances between the
atoms or some angles and the size of the
unit cells and positions of the atoms
with respect to each other different
kind of atoms and so on now when we talk
about crystalline solids we also talked
about lattice now letters simply means
the it shows you the arrangement of the
solid units in three dimensions
three dimensions and positions that
define the overall structure of the
crystalline compounds as you see here
are called
the lattice points those are called
lattice points now the lattice points
usually occupied by atoms or molecules
or ions but sometimes there is no atoms
or molecules in the lattice points but
usually they are simply occupied by the
atoms molecules or the ions
as a matter of fact now each lattice
points has an identical environment that
means that the positions of one lattice
point with respect to all the others are
the same now there define it says the
lettuce vectors connected the points and
define the unit cells now let's look at
what we mean here this is again a
three-dimensional lattice do we have a
three-dimensional lattice not really
you're usually the three-dimensional at
it but let's look at what we mean by
three dimensional two dimensional
lattice here you see again these are
called the lattice points and now in
this case they're actually occupied by
atoms occupied by atoms and the unit
cell of this is found by these vectors
see again we have a vector here and
vector there and that angle that means
that the unit cell in this case is this
shape right here that is the unit cell
and and we have the angle here and we
have the distances a and B as a matter
of fact and in this case the unit cell
is again here like this this part is the
unit cells and that is the repeating
unit in fact if you take that and put it
on the top of each other you get the
whole things over here and this is again
the unit cell and unit cell is a little
bit different in hexagonal case and this
is the rhombic unit cells so this is
simply there is a gain very close
relationship between the lattice points
and the positions of the atoms molecules
or the ions that makes the solid
crystalline solids right it simply tells
you information about how the
arrangements of those in the solids now
let's look at the three dimensional
crystals and three dimensional lattices
and in three dimensional lattices
actually we have three dimensional unit
cells unit cells and the unit cells the
these are simply called the primitive
unit cells there are only seven types of
those
seven basic two-dimensional lattices you
see again cubic tetragonal orthorhombic
rhombohedral hexagonal monoclinic and
trackless
these are the special name now if you
just ask me do you you have to remember
these
I guess the cubic is the most important
probably you can remember these but the
others are little bit poor difficult as
a matter of fact now what are these this
is simply a coupe right and then the
actually the a B and C are equal right
and the angles are equal at 90 degrees
and this one is tetragonal tetragonal is
simply a is equal to b but b is not
equal to c all the angles are equal this
is in turkish what or in english yes it
is a square prism right it's a square
prism nothing but just a square prism
now remember these are the lattice
points here right so remember this will
be in three dimension you will have a
lot of those put together side by side
to get the lattice and the crystalline
solid
now this one is orthorhombic they are
not all equal 90 degrees what is this
this is a rectangular prism rectangular
prism now the others actually
rhombohedral there you take the cube and
then press it in one directions you
change the angle here and you get the
rhombohedral now hexagonal is a little
bit different actually the hexagonal
unit cell usually is given in this
fashion
this is the hexagonal prism like this
but the hexagonal unit cell given here
is one third office
this one is one third of this and that
means that okay if you take that there
and you connect this and that and that
here we see again same things is true
here like this each of these prisms is
part of the hexagonal unit cell that
part if you take three of those and put
together you get this this is the
hexagonal prism again now remember you
have the lattice points and also the
atoms or molecules whatever the lattice
crystalline solid is made of that is the
hexagonal prism actually and that is one
third of that is the this unit cell over
here hexagonal unit cell monoclinic
again the a B and C are all different
and angles 90 degrees one of them the
other one is not ninety degrees that
means you take that or two rhombic and
then press it a little bit one side you
get done triclinic is all angles and the
edges are different from one another now
we will these are actually called
primitive unit cells that means that
only the corners are occupied by atoms
or ions or molecules but you can also
have simply atoms or molecules or ions
in the center of these unit cells or
maybe in the center of the faces or
maybe in the center of the edges all of
those are possible and when you have all
those unit cells total number of
ourselves in nature that we find is 32
there are 32 different types of unicel
for crystalline solids in nature and all
of those are derived from these
primitive seven primitive unit cells
seven primitive unit cells now we will
more concentrate on the cubic unit cell
and also three different form of these
cubic unit cell this one is simply
called
primitive cubic unit cells remember this
is just a cube again now this one is we
have the lattice points here and the
atoms and we also have one in the center
here and this may be a lattice point may
not be at it doesn't have to be a legend
but there is a molecule or atom there in
the middle and that is the body centered
cubic unit cell and this one is we have
on the centre of the faces six faces and
this is the face centered unit cell so
we will mostly talk about these three
types of unit cells and in our
calculations and so on we will use these
and these are the unit cells of metals
usually solid metals because the solid
metals can be considered as the same
size Phares right so those metal ions
simply occupy the lattice points and
they simply touch each other as we will
see in later slides this is again motifs
it simply means in those unit lattice
points you may have an atom you may have
an iron ore you may have a molecule
right and those are whatever simply
occupies those lattice points are called
they don't have to be lattice points
actually but they're called they can be
not in the lattice points for example in
this case these are the lattice points
here but the motive or the unit of the
solids is this those two atoms there and
that's what we call motives again but
the ones we will consider are mostly the
atoms or the molecules ions occupies the
lattice points
now metallic structures again metallic
structures easily be understood in terms
of packing of spheres actually packing
of spheres and if we consider three
different structures cubic body-centered
cubic and face centered cubic lattices
and these are the unit cells the metal
atoms Fairs will occupy the corners of
these and if we look at the space
filling type unit cells letters for the
primitive unit cell again simple cubic
unit cell it would look like this what
does that mean that means we have a
sphere actually a metal atom in this
corner that corner that corner eight
corners and all of those four metal
atoms are touching each other they are
simply touching each other and the same
thing is true over here now when you
have a body centered cubic unit cell you
have simply the metal atoms at the
corner here four up four down and one in
the middle of the cube and this is the
unit cell actually for the body centered
cubic structures and face centered wise
we have again at the corners and then we
have in the center of the faces now
let's think about how many metal atoms
actually belongs to one unit cell in a
metal lattice right metal lattice we can
easily find it out here for example in
simple cubic lattice actually this is
going to be the unit cell exactly right
now remember in the previous one here
let's look at there now this is this is
the same as this but
these sphere if you consider one sphere
or metal atom only 1/8 of this metal
atom or this sphere is inside of this
cube now how about the others the others
belongs to the other unit cells the
other cube actually one corner here is
shared in the lattice three-dimensional
lattice is shared by 8 cubes and that
means that any atom on the corner of the
cube in a simple cubic unit cell only
1/8 belongs to that unit cell and 7/8
belongs to the others clear
now if considering that now for example
if you consider the atom metal atom
which in the center of this cube that
belongs all of them belongs to this unit
cell right now but any atom which is in
the center of the faces half belongs to
one unit cell half belongs to the other
unit cell so considering these we can
simply calculate how many metal atoms
will make a unit cell in the letters in
three different lattice structures
simple cubic face a body centered and
face Center if you take the simple cubic
in this case every corner is shared by 8
unit cells that means 1 over 8 belongs
to this since we have eight corners one
over eight times eight one metal atom
makes a unit cell in a simple cubic unit
cell lattice right in a simple cubic
lattice I should say probably that's a
unit cell now if you come over here
again eight of those from the corner one
over eight times eight and that means
one coming from the corner and one
inside over here that makes two atoms
will make a unit cell in a body centered
lattice cubic lattice right in three
dimensions now if you take the face
center in this case one from the corners
again one over eight times eight
but there are six phases and each phase
has one in the center half belongs to
this half belongs to the other six times
one over two three coming from the
phases that means four actually metal
atoms will make a unit cell in phase
centered lattice in phase centered
lattice and these are actually when we
say unit cell actually these are the
unit cells right and when you take those
unit cells put them together you get the
lattice now let's see before we go here
okay
this is a closed packing structure now
in nature when a solid forms it try to
pack the atoms or the molecules or
whatever as close as possible to get the
highest density and occupy the smallest
volume right and now the question here
is if I simply have spares the same size
spheres and if I would like to pack them
closest possible way closer to each
other possible what will be the
structure and actually the structure
will be phase centered lattice or
hexagonal lattice there's only two types
now how can we achieve closest packed
structure close the pack structure with
again take in same size fares that means
that we will try to put maximum number
of spheres in a given volume in a given
volume how can we pack them to get the
met
umhum number of spheres in that given
volume the first layer would be like
this night you will just take the same
size fares and they're all touching each
other this is one roll okay and then the
second row would be we have to put it
here if I'm going to put that closest
like this and they're all touching each
other's now the third would go here I
know this is one layer right now when
you simply put the second layer on the
top same size fears you will simply take
you have to put them in a depression of
three spares in this layer that would be
over here on the top of here or maybe
here if you put there you can't put it
there right and then here here and here
actually you have one here like this and
the other one like that if you put it
there and this is going to be the second
layer you see again and then we'll have
the other layer over here so you have
one layer of spheres closest put
together and then the second layer is
put on the top of that but you have to
use the depressions here
to get the maximum filling or packing I
should say and that means they are a
little bit moved one side from this now
when you put the third layer on there
are two possibilities you can either put
those on the top of these here for
example or you can just put it a little
bit shifted again so the structures
there is called a P a B a B type what
does that means you put one layer second
layer is little off has to be off now
the third layer will be on the top off
the first so it goes like Abe
a B a B type No first layer second layer
third layer and so on or if you put it
that if you put the third layer not on
the top of the first layer it will be
shifted a little bit one way and that's
called ABC ABC ABC type now both of
these pakkun are closest packing that
means by using these two types of
packing you can put the same number of
spheres in a given volume that means
there's no difference what is the
difference the difference is the unit
cells unit cells are different in this
case the unit cells is hexagonal unit
cell exactly no unit cell in this case
it is face centered cubic unit cells
face centered cubic now this structure
is called hexagonal close pack an HCP
hexagonal close packing and this
structure is called cubic close pack and
CCP now the difference the only
difference is the unit cells in terms of
highest packing efficiency both are the
same both are the same same effect what
does that means that means that I will
put the same number of sphere same size
spheres in a given volume by using these
two types of packing off the spheres now
let's see if I can show you here for
example now this one you see you have a
layer of spheres one layer the second
layer put sort of little bit shifted on
the depressions now the third layer
right on the top of that and now the
fourth layer is on the top of the second
layer like this this is the a.b a.b a.b
type structure closest pack structure
and it's called HC
he hexagonal closed back in because the
unit cell is exact hexagon hexagonal
unit cell I should say this one is like
you have first layer second layer is a
little bit sort of shifted put in a
depression the third is also a little
shifted and then the fourth one is on
the top of the first so this goes again
ABC ABC ABC and the unit cell is the
phase centered unit cell and the other
one this is the hexagonal unit cell
remember this is just the one part of
that it is mainly it's simply simply the
one third of this or you can consider
the whole things as the unit cell as a
matter of fact so these are the two
closest packed structures now let's do a
calculation and see if we can find out
what is the packing efficiency in these
cases in close packing structures
now what does that means that simply
means we will try to find out what
fraction of space is filled with the
atoms and what fraction is empty the
whole space right now first let's take
the simple cubic case cubic lattice now
the unit cell remember is cube like this
and we have the metal atoms like
spherical on the top here like this
they're all touching each other so if I
consider the edge of this unit cell that
will be equal to what
edge a is edge of the unit cell actually
this is a cube right will be equal to
what equals to this is our this is our
to our right it's simply to our to our
like this okay now let's remember how
many atoms or spheres will make a unit
cell simple cubic unit cell or how many
atoms belongs to one unit cell in the
lattice in two dimensional structures
one right because remember only one
eight of these are inside of this cube
so one and what is the volume so the
volume occupied here will be equal to
the volume of one sphere right and the
volume of one sphere is four all
three PI R to the Q this is it
now what so this is now how about the
volume of the unit cell let's find out
the volume of the unit cell volume of
the unit cell in this case here to R and
that is going to be equals to 2 R 2 D
cube right that is the volume now the
packing efficiency will be found by
simply 4 over 3 PI R to the cube divided
by 2 R to the cube and if I simply this
is going to be I should probably put
here multiply that by 100 and this will
be percent packing efficiency I should
percent packing efficiency okay now if
you work it out those are just the
numbers you will simply find out that
will be equal to in this case 52 percent
this is simply equals to 52 percent okay
now that simply means if you have a
metal which have simple cubic lattice
and simple cubic unit cell and all of
the atoms are touching each other only
52% of the spain's will be full by these
atoms 48 percent
be empty right now if I take the second
case is the let's say face center face
centered cubic and in this case if I
find out the edge of the unit cell in
terms of the radius of the spheres
remember again the face centered I have
one here like this and I have here here
and here all touching now this is the
edge a this is also a now this part here
ar-ar-ar-ar radius so what I have here
for our right angle triangle relation
here for our two the square will be
equal to 2a squared right and now how
many spheres or atoms make a face
centered unit cell for right four four
spheres or atoms let's see now
that means that volume occupied I can
find out the volume occupied being
equals to 4 times 4 over 3 PI R to the
cube now if I simply find out the value
of I a the edge of the unit in terms of
r then I can find out the volume of the
unit cell and in this case it will be 4
R square and that is 4 R is equal to
square root 2 a and a is equal to 4 R
divided by square root 2 and B
the volume of the unit cell will be
equal to a to the cube and that simply
means for our to the cube and divided by
2 square root to take the clip of that
that will be it
now if I simply take the ratio there
and it would be again as follow 16 PI R
to the cube divided by three and the
whole thing's is divided by 64 R to the
cube that is this one here and divided
by 2 square root 2 and multiply it by
hundreds and this would be equals to 74
percent so if you have a phase centered
lattice that means the phase centered
unit cells in a metal crystalline metal
packing efficiency is much higher than
when you have a simple cubic thing and
actually remember we said that one of
those closed packing structures have the
unit cell phase centered unit cell and
that's why we have the face centered
yourself because the face center unit
cell allows you to pack the same size
fares with a maximum packing efficiency
that means to put the maximum number of
spheres in a given volume now you can
calculate this for the body centered
cubic lattice and body centered cubic
unit just the same fashion let's say
body centered body centered cubic
lattice in that case the number of
spheres is how many to write one coming
from the corners and one coming from the
center because that belongs to the the
whole of them belongs to the unit cell
so two spheres that simply means volume
occupied would be equal to 2 times 4
over 3 PI R to the cube right now how
about the volume of the cube
now that is a little bit more difficult
to see the relationship between the
radius and the edge of the unit cell for
the body-centered unit cell cubic unit
cell you can have this right angle
triangle like this now this is the edge
of the unit cell one edge of the inner
self
now this one is buddy diagonal body
diagonal what does that mean that means
it goes from one side of the cube and
passes comes to right across to this
corner here so that is the body center
which goes through the center of the
cube actually and this one is actually
this part is a face centered face
diagonal this is let's say face diagonal
and this one is the body diagram now in
the body diagonal we have one in the
center like this and we have the other
three cubes our spares are touching each
other so that means that this body
diagonal D is equal to 4 R now this
let's call that B which is the face
diagonal face diagonal square of face
diagonal is equal to 2a squared and from
here I can simply write down this
relationship the square of this body
diagonal which is 4 R square would be
equal to square of this which is a
square plus the square of this which is
equal to that face diagonal 2b squared
and from that you can find out the
relationship between simply R and a
and find out the volume occupied and
volume of the unit cell in this case you
end up with 68% packing efficiency
efficiency is 68% you see again these
simply shows you that the phase centered
cubic unit cell allows you to get the
maximum packing efficiency if you have
that and that's why actually as I said
the unit cell of one of the closest pack
structure is the phase centered cubic
unit cells they Center cubic in yourself
ok any questions