hello we have defined till now crystal as periodic arrangement of atoms and lattice as periodic set of points in this video we will look at the classification of lattices lattices are periodic set of points and the periodicity can vary in the three directions of a space so the axis and the angles of the crystal can have many different values so it's important to have a system of classification of these lattices two important systems are in common seven crystal systems one of them classifies the crystal into crystal systems seven crystal systems and the another one into fourteen bravais lattices so let us let us look at them here is the list of seven crystal systems we have cubic tetragonal orthorhombic hexagonal trigonal or rhombohedral so there are two alternative names for the same system monoclinic and triclinic each of these systems have a conventional unit cell which we have shown here so in the cubic system you have a unit cell in which all sides are equal a equal b equals c all angles are equal alpha equal beta equal gamma and all these equal angles are equal to 90 degree so basically you have a cube as your unit cell and that unit cell is repeated in space to generate the entire lattice tetragonal lattice tetragonal cube system has a unit cell conventional unit cell which is almost like cube all angles are equal to 90 degree two sides are equal but third side is not equal orthorhombic also all axes are mutually orthogonal all angles are 90 degree but none of the three sides are equal similar relationships are given here for all other systems you do not really have to worry about memorizing all this in one go but gradually you will become familiar and in case if you need a need sometimes and you don't remember you can always look it up in some book but let us try to understand the meaning of the crystal system and bravais lattices so 7 crystal systems we have 14 bravais lattices in each crystal system there are one or more bravais lattices p which stands for primitive or simple is present in all of them so we have seven primitive or simple lattices one each in the seven systems so p stands for primitive or simple and which means lattice points are only at the corners of the unit cell the next type is i or body centered body centered which means lattice points are at corners as well as the body center this bravo lattice is present in cubic tetragonal and orthorhombic so we now have seven plus three ten four more bravais lattices are there f stands for face centered face centered which means lattice points are at corners corners will always have lattice points whether in simple or body centered or face centered corners plus all face centers f is there you have cubic f and you have orthorhombic f so two f lattices are there finally c is called either end centered or it has an alternative name also base centered and centered or base centered here the lattice points are at corners and not on all faces as in face centered but only on one pair one pair of parallel faces the c centered or n centered lattices are there in orthorhombic and in monoclinic so we have now 7 7 p 3 is 10 2 f 12 and 2 c 14. so this constitutes the 14 bravais lattices let us familiarize ourselves little bit more with these bravais lattices so let us look at the three cubic bravais lattices in the cubic system we said we have p we have i and we have f so what do they look like this is my cubic unit cell and when i say cubic p.m or primitive cubic or simple cubic more common name is simple cubic so the bravais lattice name includes the crystal system name as well as either the symbol cubic p or in language we can say simple cubic and the simple cubic lattice will have the simple means the lattice points are only at the corners so only corners are identified as lattice points don't think of these as atoms they are only points i am highlighting them to emphasize that the lattice points are only at the corners let us draw the next one let us draw cubic i this will be body centered cubic both names are synonymous or equivalent so you can say cubic i or you can say body centered cubic here the lattice points will be at the corners as i said corners will always be lattice points but there will be an additional lattice point right in the center of the cube so this will be the body centered cubic lattice and finally let us try to draw the face centered one that's the cube as your lattice points at the corner but to qualify it as cubic f or face centered cubic we have to give additional lattice point at the centers of all the faces so at the center of left and right face at the center of bottom and top face as well as at the center of the front and the back faces so all six faces will be centered so then we will have a cubic f lattice so that is the meaning of these symbols and the location of the lattice point cubic system does not have n centered or as we said can be called base centered also but orthorhombic has so let us look at the example of base centered in an orthorhombic orthorhombic has all three sides are equal but axes are still at 90 degree so that is my unit cell box and the location of lattice points at corners and to make it base centered or end centered i have to center one pair of opposite faces one pair of parallel faces not all faces if i center all faces i get the face centered um lattice but if i center let us say only the bottom and the top faces lattice points additional lattice points only on one pair of spaces then i end up with n centered or base centered orthorhombic lattice its called orthorhombic c because if i choose my axis if i choose my axis x y and z in this way note that in crystallography the a is along the x axis b is along the y axis and c is along the z axis so the face which we have centered is the phase containing a and b this phase is called the c phase capital c phase so when i say orthorhombic c i mean orthorhombic c this means c face is centered of course one can have if i had chosen to center the other faces i can have orthorhombic a orthorhombic a or b also possible however since only one pair of face is centered you can always choose your z axis or the c axis perpendicular to that face and make it orthorhombic c so we have we have seen we have simple where only corners are there corners as lattice point then we had face centered f then we have body centered and we also had a base centered or uncentered so the question can be asked why why don't we have any lattice which we can call edge centered by edge centered we will mean points at the centers of each edge so let us consider edge centered cube so points at corners and at centers of each edge centers of each edge let me construct one unit cell like that again i have my cube i put points at the corners and i also put additional point at the centers of each edges the centers of each edge why is no lattice y is listed like this an edge cubic lattice or an edge-centered orthorhombic lattice the answer to that can be seen by examining the surroundings of the point so let us look at let us look at point a let me call this point a and let me call this point b and let me choose this direction as my x direction so if i move from a and let me call the edge length of the cube as a so if i move from point a in the direction x at a distance a by 2 i find another neighbor this one but if i move from point b in the same direction that is in the x direction the same distance a by 2 i do not find any any additional point so we conclude that points a and b are not equivalent points are not equivalent not translationally equivalent so the set of points do not form a lattice so let us again look at the complete list of bravo lattices which we had so we were we were having cubic p simple cubic cubic i and cubic f we had tetragonal p and tetragonal i we had orthorhombic p orthorhombic i orthorhombic f and orthorhombic c so orthorhombic is quite rich it has all the four varieties we have hexagonal p and that's all we have trigonal p we have monoclinic p and monoclinic c and we have triclinic p so we can see that seven different lattice seven different uh crystal systems are there and in each crystal system like in orthorhombic four possible bravais lattices could have been there p i f and c but only orthorhombic has all four so seven systems four types seven into four twenty eight lattices were possible possible lattices but we have only fourteen but only fourteen bravais lattices so why so many other lattices which were possible but are not there in particular why do not we have cubic c why cubic c is absent from the bravais list of course similar question can be asked for all other empty boxes why is tetragonal f not there why is tetragonal c naught there and so on so all these empty boxes is a question mark and it is this question which we will take up in the next video so this will be our starting point for our next video