 Namaste. Myself, Dr. Mrs. Preeti Sunil Joshi working as assistant professor in Valchan Institute of Technology, Solapur. In this session of crystallography, we are going to learn all about crystal structure. Learning outcomes are, by the end of this session, students will be able to define the terms crystal, space lattice, unit cell. The contents include space lattice, crystal structure, unit cell and crystallography. In the previous session, we have learnt about what is crystalline and what is amorphous. And also one thing we have seen is that, a regular and periodic arrangement of atoms is the most important feature of crystals. The actual arrangement of atoms is called the structure. Suppose the atoms or clusters of atoms in a crystal are represented by points which corresponds to their mean positions, then we obtain a regular distribution of points in space. These points are called lattice points or lattice sites. The three dimensional network of regularly arranged points is known as a space lattice. A point is a dimensional-less and shapeless entity, therefore a lattice is merely an imaginary geometrical framework. The study of crystal structure becomes simpler when it is represented by a space lattice. So we can define space lattice as an array of points in three dimensions in which every point has surroundings identical to that of every other point. A space lattice can be generated by successive translations of an initial point. A very simple operation of repetition consists of repeating the unit without change after translating it a distance T1. So this repetition application of translation of given length and direction T1 to an initial point generates a sequence of periodically spaced points as shown in the figure. Similarly, the repeated application of some other translation which are non-linear means not along the same line T2 to the above row generates a planar array of points which we call it as two dimensional array of points. Students now imagine for three dimensional array of points. Yes, a third translation is non-coplanar that is not in the same plane T3. The second translation applied to a two dimensional array of points is called a space lattice. Thus, space lattices satisfy the condition of periodicity. Hence, the crystal structure that is the arrangement of atoms in the crystal can be understood with reference to the lattice. We also observe that a given point in the lattice is surrounded by a specific number of lattice points which are located at equal distances. This arrangement of points around a given lattice point is called its environment. Thus, the same environment would be found after equal intervals of distance in the same direction but the environment may be different in different directions. The space lattice is the skeleton upon which the crystal structure is built by placing atoms on or near the lattice points. So, in this way space lattice is a mathematical abstraction. The crystal structure is formed only when a group of atoms is identically attached to each lattice point. This group of atoms that is associated with every lattice point is called a basis. Thus, the crystal structure is a combination of space lattice and basis. Here, the figure shows the crystal formation. The basis must be identical in composition, arrangement and orientation such that the crystal appears exactly the same at one point as it does at the other equivalent point. Space lattice and basis together form the crystal structure. In crystals like aluminium, copper, sodium and barium, the basis is a single atom. Then in sodium chloride or potassium chloride, the basis is diatomic whereas in crystals like CaF2, the basis is triatomic. So students, are you getting this concept of basis and crystal formation clear? Okay. Okay. Now, the next important concept is unit cell. Students, now we know that how the crystal structure is formed but if we observe the crystal structure then we can see that a small block is repeated. This smallest volume that carries a full description of the entire lattice is known as a unit cell. Because of the inherent periodicity, the space lattice can be represented by the unit cell. So unit cell can be defined as the smallest geometrical unit which when repeated in space indefinitely generates the space lattice. Now, the next question comes that how to describe this unit cell? So, this unit cell is described by the lattice parameters. The lines which are drawn parallel to the lines of intersection of any three phases of the unit cell which do not lie in the same plane are called crystallographic axes. The three translational vectors A, B and C lie along the crystallographic axes. The intercepts A, B and C define the dimensions of the unit cell and they are also known as primitives. The angle alpha represents the angle between C and B axes, angle gamma between A and B axes and angle beta represents the angle between C and A axes. The volume of a unit cell is given by A multiplied by B into C. Thus the basic lattice parameters are the axial lengths and angles between them. Now, the next question is if we consider the periodicity then how to select the unit cell from space lattice? Unit cells are of two types that is primitive and non-primitive unit cells. Primitive unit cells contain only one lattice point which is made up from the lattice points at each of the corners. Its volume in space contains only one lattice point but keep in mind that it is not necessary that every unit cell should be a primitive cell. Depending on the requirement and symmetry of the lattice we can choose larger cell containing more than one lattice point as a unit cell. Now non-primitive unit cells contain additional lattice points either on the face of the unit cell or within the unit cell and so it has more than one lattice point per unit cell. Most of the unit cells of various lattice contain two or more lattice points and are known as non-primitive cells. Students, now up to this we have seen why the study of crystal is required and how the crystal structure is formed. But again there is a question that how to study these crystal structures? Which technique is used for studying this crystal structure or the different properties of the crystal? So these crystals and their different properties can be studied by different methods and such study of crystals is termed as crystallography. That is the study of the geometric form and other physical properties of crystalline solids by using x-rays, electron beams and neutron beams that constitutes the science of crystallography. Now in the next part we will see the classification of crystals depending upon the lattice parameters. Thank you.