 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 study the different crystal systems and Bravais lattices. Learning outcomes are, by the end of this session, students will be able to identify different crystal systems. The contents include introduction, Bravais lattices and crystal systems. Students, let us recall the definitions, space lattice and unit cell. Yes, space lattice is the three-dimensional network of regularly arranged points and unit cell is the smallest block which when repeated in space indefinitely generates the space lattice. On the basis of lattice parameters i.e. axial lengths A, B and C and the interaxial angles alpha, beta and gamma, the crystals are classified. So, let us now see this classification in detail. Augustine Bravais was a French physicist known for his work in crystallography and best remembered for his work on Bravais lattices. Particularly, his 1848 discovery that there are 14 unique lattices in three-dimensional crystalline systems. Bravais introduced the concept of space lattice in the study of crystal structures. One would expect many lattices which can be generated in three dimensions with different primitive and non-primitive cells. When the discrete points are atoms, ions or polymer strings of solid matter, the Bravais lattice concept is used to formally define a crystalline arrangement. Bravais showed that there are only 14 different ways of arranging identical points in three-dimensional space which satisfies the condition of periodicity so that they are in every way equivalent to their surroundings. These 14 types of arrangements are called the Bravais lattices. There are seven primitive cells and seven non-primitive cells with the 14 types of lattices and on the basis of primitive cells, crystals are grouped into seven systems. They are cubic, rhombohedral, tetragonal, hexagonal, orthorhombic, monoclinic and triclinic. Now, let us now study these seven crystal systems and corresponding Bravais lattices with their features in detail. The first one, cubic crystal. In cubic crystals, the crystal axes are perpendicular to one another. Thus, alpha is equal to beta is equal to gamma is equal to 90 degree. The length of the primitives is the same along the three axes. Thus, the relation between axial lengths is A is equal to B is equal to C. Cubic lattice has three possible types of arrangements that is simple cubic, body-centered and face-centered cubic. Simple cubic has lattice points at all eight corners of the unit cell. Body-centered cube has lattice point at all eight corners and one lattice point at the center of the body. And the face-centered cube has lattice points at all eight corners of the unit cell and one lattice point each at the center of six faces of the cube. In rhombohedral system, which is also known as trigonal system, the angle between each pair of the crystal axes is the same but not equal to 90 degree. The lattice parameters are A is equal to B is equal to C and alpha, beta, gamma all are equal but they are not equal to 90 degree. There is only one way to present a lattice point that is simple trigonal which is having lattice points at all eight corners of the unit cell. In tetragonal system, the crystal axes are perpendicular to one another and the lengths of the edges of unit cell along the two axes are the same but the age along the third axis is different. The lattice parameters are A is equal to B not equal to C but all the angles alpha, beta, gamma are equal to 90 degree. And in tetragonal lattice, there are two possibilities of arrangements that is simple one and body-centered. Simple tetragonal lattice has lattice points at all eight corners of the unit cell. Body-centered tetragonal lattice has points at all eight corners of the unit cell and one lattice point at the center of the body. In hexagonal system, two of the crystal axes are 120 degree apart while the third axis is perpendicular to both of them. The length of the edges of the unit cell is the same along the axes that are 120 degree apart but the age along third axis is different. The lattice parameters are A is equal to B not equal to C and alpha and beta are equal to 90 degree and gamma is equal to 120 degree. Hexagonal lattice has only one possible type of arrangement that is simple. It has lattice points at all twelve corners of the hexagonal unit cell and two lattice points one each at the base and top faces of the hexagonal prism. In orthorhombic system, the crystal axes are perpendicular to one another but the lengths of the edges of the unit cell along the three axes are different. Thus the lattice parameters are A not equal to B not equal to C and alpha, beta, gamma all are equal and they are equal to 90 degree. Orthorhombic lattice has four possible types of arrangements simple having lattice points at all eight corners of the unit cell then base centered which has lattice points at all eight corners of the unit cell and two lattice points one each at the base and top face of the body. Body centered having lattice points at all eight corners and one lattice point at the center of the body and face centered having eight corner points and six lattice points one each at the center of the six faces of the unit cell. In monoclinic system out of the three crystal axes two are not perpendicular to each other but the third is perpendicular to both of them. The lengths of the edges of the unit cell along the three axes are different. Thus the lattice parameters are A not equal to B not equal to C and alpha and gamma they are equal to 90 degree which is not equal to beta. Monoclinic lattice has two possible types of arrangements simple and base centered. Simple monoclinic lattice has lattice points at all eight corners of the unit cell and base centered monoclinic lattice has lattice points at all eight corners of the unit cell and two lattice points one each at the base and top of the unit cell. In dry-clinic system none of the crystal axes is perpendicular to any of the other the lengths of the edges of the unit cell along the three axes are different. The lattice parameters are A not equal to B not equal to C and alpha, beta and gamma all are not equal and they are not equal to 90 degree. Dry-clinic lattice has only one possible type of arrangement which is namely simple which has lattice points at all eight corners of the unit cell. Students now we have seen all the crystal structures in detail now try to solve these questions. Please pause the video and try. I think you are ready with the answers. Yes students please check your answers. Now let us summarize the crystal systems and corresponding lattice parameters. So in total there are seven different types of crystals for which there are fourteen Bravais lattices and of which seven are primitive cells and seven are non-primitive cells. For cubic all the lengths and angles are same and for dry-clinic all angles and lengths are different. Thank you.