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An engineering structure
made up of several components so there is this handlebar
we have this frame saddle wheel paddle and so on so this is designed for a particular
function and this can be our example of an engineering structure
each of the components are made up of certain material and it is engineers responsibility
to select suitable material for each of these components if we now look at one particular
component this frame for example so the frame is made of a mild steel tube we are now looking
at frame tube in more detail so it is a mild steel tube if we cut this tube and look at
the cross section
then we will see in general a featureless cross section we can polish this and we will
have a nice shining featureless surface
but then if we look at a small region of this featureless surface at higher magnification
using let us say an optical microscope let us magnify
this in an optical microscope which has magnification let us say from fifty times to about thousand
times then we will see a whole new world inside this let me try to draw any schematic of what
we will expect if we see that mild steel tube properly prepared at higher magnification
so we will then start seeing what was featureless before and the magnification of naked eye
at higher magnification it will now start showing certain features
these regions are called grains and the lines are called grain boundaries
these features are coming by looking at the structure through an optical microscope they
are called micro structure so grain boundaries and grains are features
of a micro structure the scale of micro structure is about
let us say microns thats thats where the micrometer comes from so we will talk about grains and
grain boundaries the meaning of these terms will become clear as we go along in the course
and grains and grain boundaries we will discuss in chapter three of this course which deals
with defects in crystalline structure in fact they are not only these grains and grain boundaries
in certain regions there are some dark patches also
which we will call pearlite and these lighter regions which we called grains were the ferrite
and pearlite looked at in detail is again can be seen to be alternate bands of dark
and white region in which the lighter regions are ferrite and the darker regions are cementite
ferrite and cementite are the so called phases in mild steel we will learn about these phases
and in the topic called phase diagram which is our chapter four
now if we wish to look at it in little bit more detail about these grains of ferrite
then we will find out that these grains of ferrite are actually solid solutions to be
more precise interstitial solid solutions interstitial solid solutions solid solution
of carbon in iron we will talk about such a structure such alloy structure solid solution
interstitial solid solution is one kind substitutional is another kind these things will be discussed
in a structure of solids chapter three sorry chapter two finally if we want to go in a
still more detail and look at what this solid solution how the atoms are arranged inside
the solid solution we we have to use technique like x ray diffraction
if we use x ray diffraction it will tell us that this solid solution actually has a structure
of body centred cubic so it has a crystalline structure it has a crystalline structure and
the crystal structure is
body centred cubic b c c we will talk in detail about crystal and crystal structure in our
chapter one
and we will be beginning ah with this chapter in the next video but before we do that
let us ah look at other parts of the course we looked at the micro mechanism of the development
of micro structure involves micro mechanisms such as diffusion and phase transformations
so both of these will be important topics in our course diffusion will be our chapter
five and phase transformation will be chapter six the microstructure which determines properties
and for us the important property in this course which
we are going to talk about is the mechanical property
this topic will come in chapter seven on mechanical behaviour
and finally in chapter eight we will see how ultimately materials fails or breaks that
is fracture and if you are interested in spending more for your bicycle and are not satisfied
with the traditional mild steel frame you can go for lighter but more expensive ah bicycles
made of composite frame so chapter nine the final chapter of this course we will then
talk of composite materials so with this introduction we will now go on
to um a study crystal structure in reasonable detail in from a starting from the next slide
see you
welcome todays topic is crystal geometry in this there are several subtopics which we
will discuss crystals lattice motive seven crystal systems fourteen bravais lattices
and miller indices we will begin with crystal and lattice two related concept but quite
often the distinction is not made clear and then it can get confused so we will spend
some time on a very very clear distinction between crystal and lattice motive is the
linking bridge between crystal and lattice afterwards we will focus mainly on lattice
and see how the lattices can be classified into seven crystal systems and fourteen bravais
lattices and we will end this section with discussion of miller indices of directions
and planes we begin with the definition of crystal what is a crystal so you can pause
here and think about what is your definition or what is your concept of crystal before
i gave my definition we will define crystal as a three three dimensional periodic arrangement
of points of sorry of atoms a three dimensional periodic arrangement of atoms in a space will
be called crystal the related concept ok let me show first a model of ah what we
mean by three dimensional periodic arrangement of atoms so here is here is a unit cell of
sodium chloride so this is unit cell of sodium chloride
the black black atoms you can consider as chlorine the white one says sodium and what
we mean by three dimensional periodic arrangement that these chlorine and sodium atoms are repeating
in each direction at equal distances so for example if we look at along the cube edge
we start with chlorine then after certain distance i find a sodium and then again chlorine
and if i continue in this direction i will keep finding chlorine sodium chlorine sodium
chlorine sodium so on so that is what is meant by periodicity so in this direction i have
periodic arrangement of chlorine and sodium if i go along the face diagonal if i go along
the face diagonal you see we are having chlorine chlorine chlorine again in this direction
if i continue in the crystal i will keep finding chlorine at these equal intervals same thing
is true in all the direction so i have a three dimensional periodic arrangement of sodium
and chlorine atom represented by this unit cell and this is the crystal of sodium chloride
crystal of sodium chloride also known as common salt
we will have we will look at this unit cell and this crystal structure in more detail
as we go along at the moment i am showing you just as an example to begin with
now i come to the related concept of lattice what is a lattice and how is it different
from crystal so a lattice is a three dimensional periodic arrangement of points three dimensional
periodic arrangement of points in a space so the difference between crystal and lattice
is whether the points are being considered or atoms are being considered otherwise both
are periodic arrangement three dimensional periodic arrangement this is the reason for
confusion between these two concepts so let us put that together crystal we said
a three dimensional periodic arrangement of atoms let me write that here lattice a three
dimensional periodic arrangement of points so you can see a crystal will be a physical
object atom is physical object so a crystal will be a physical object it will have physical
properties like weight you can weigh a crystal it will have density you can measure it is
electrical or thermal conductivity
and so on a lattice in contrast is a geometrical concept because it is just a three dimensional
periodic arrangement of points so it will not have any of these physical characteristics
you cannot weigh a lattice you cannot find its density or electrical conductivity and
so on so it has a geometrical concept we will have only so geometrical properties
we will make the distinction clear in more detail as we go along
now what is the relationship between the crystal and lattice both are three dimensional periodic
arrangement and we said crystal is a three d arrangement of atoms and lattice is three
d arrangement of points so the relationship between them is expressed
by an equation crystal is equal to lattice plus motif or basis these are synonyms you
can call it motif or basis so this is a new concept we have now introduced so the linking
bridge between crystal and lattice is a motif so what is a motif is our next topic
so let us define motif or a basis we will define it like an atom sometimes a motif can
be a single atom or a group of atoms
so an atom or a group of atoms associated with each lattice point
is called a motif or a basis of the crystal so every crystal has from our
equation if you see crystal is equal to lattice plus motif so every crystal has a lattice
and it has a motif lattice is only the periodic arrangement of points the motif gives you
the atom which is being repeated or a group of atoms let us make that distinction more
clear so again lattice is a lattice will tell you the periodic arrangement so the underlying
periodicity so lattice gives you
underlying periodicity of crystal motif gives you
atom or group of atom which periodically repeated or if i put it even more simply lattice tells
you how to repeat lattice tells you how to repeat whereas motif
tells you what to repeat so when you have both this information how to repeat the lattice
and what to repeat the motif you get the information of the crystal complete information of the
crystal so let us look at a little bit more concrete
example i have already shown you a three dimensional ah model of the sodium chloride crystal but
it is at the moment a little bit more complicated to analyse so we will take a much simpler
two dimensional example of pattern of hearts and interesting to see a pattern of hearts
so we come here and look at this pattern of hearts so you can see what we are doing here
is repeating the hearts periodically in two dimensional so horizontally hearts are coming
at equal distance vertically also they are going at equal distance so we finally end
up with a two dimensional periodic pattern of heart i want to analysis so this periodic
pattern of heart it is something like our crystal where atoms are repeated instead of
atoms we are now having hearts which are repeating so this represents our crystal or a pattern
now if i want to analysis it this pattern as a lattice and motif just like crystal crystal
is a periodic pattern of atoms now we have a periodic pattern of heart this also can
be analysed as ah lattice plus motif so first let us look at the lattice so i have
now placed a dot in the centre of each of the heart so these dots now represent the
lattice of this pattern so if i remove the heart and only leave only leave the ah these
points this gives me the lattice of the heart pattern but this is not the pattern you can
see but this is associated with the pattern and this is telling me how the heart should
be repeated i should place a one heart at each of these points in identical orientation
to get my full pattern so i need this information that what i want to repeat instead of heart
or instead of a red heart i could have repeated a black heart and would have got a different
pattern or i could have repeated a circle and it still got a different pattern so the
lattice itself does not tell you what pattern you will generate to get the information about
the pattern the real pattern you need to know what is being repeated by this scheme of lattice
and that information is contained in the motif here so this is the motif which is of this
pattern if we put these together if i start associating e one heart with each of the lattice
point i generate the pattern of heart which is the final pattern so this pattern is decomposed
or analyzed in terms of a lattice which tells me how to repeat and a heart which is telling
me what to repeat the same process can be done for three dimensional crystals which
we will do as we progress in this course
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