MATERIAL SCIENCE AND ENGINEERING ASSIGNMENT Assignment By - Submitted to - Prof. Ranjit Singh MATERIAL SCIENCE ASSIGNMENT CRYSTAL SYSTEM AND CLASSES Before studying about crystal system and classes we should first know what exactly are crystals! As Thomas B. Macaulay has said “Half knowledge is worse than ignorance”. What is a crystal? What are crystal structures? How are they different from other substances? What is a crystal lattice? So let’s talk about these briefly before we discuss our topic! As we all know any solid substance is made up of many small atoms or particles bound together by a force of attraction. What differs crystals from other substances is that Crystals are the solids in which atoms are arranged in some regular repetition pattern in all direction. Here’s a picture of a sodium chloride crystal. As you can see there’s an order and a definite arrangement between all the atoms. When we want to understand what do we mean by the crystal system or structure , we use lattice basically as the framework. A lattice is an ordered array of points describing the arrangement of particles that form a crystal. One important property of a lattice is that a lattice has same surroundings. If I take any two points in the lattice no matter how far they are they should look same from a particular direction. For example , you must have seen those tiles on the pavement they are put next to each other in an ordered way. This idea was proposed by Auguste Bravais that is why they are called Bravais lattice. He said there are seven crystal systems and fourteen crystal structures. Now if I start putting atoms or molecules or ions on the lattice points then I’m building a crystal structure. A lattice point is the position in a crystal where the probability of finding an atom or an ion is highest. In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three- dimensional space in matter. The small particles which constitute these crystals are called Unit Cells. A Unit cell is a geometric pattern which repeats itself through the three dimensional pattern of solid. It generates the crystal lattice when repeated in space indefinitely. Unit cells are arranged like building blocks in crystals. So before going to crystal system and classes we must know that , crystals are first divided into systems then they are divided into classes and then finally classes are divided into forms. CRYSTAL SYSTEM AND CLASSES Major subdivisions include six divisions of system. Each system has some classes and every class has some forms. Due to different symmetries crystals have been classified into classes. There are only 32 possible combinations of symmetry operations, which define 32 crystal classes. The first system is the ISOMETRIC OR CUBIC SYSTEM. The cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. In this system all the three axes which is all the three crystallographic axes are of equal length and angle between them is 90 degree. They are orthogonal to each other and hence they are interchangeable. It has four axes of three fold symmetry. It has five classes. This is a simple cubic lattice. This is how all the unit cells get arranged to form the crystal. The main varieties of these crystals :- 1)Simple cubic 2)Body centred cubic 3)Face centred cubic Next is the TETROGONAL SYSTEM In tetragonal system , the two horizontal axis are equal and perpendicular to each other and both of the axes are perpendicular to the third axis but not equal to it. It can be small or it can be larger than the two horizontal axes. There are two tetragonal lattices: the simple tetragonal (from stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the face-centered or the body-centered cubic lattice). One might suppose stretching face-centered cubic would result in face-centered tetragonal, but the face-centered tetragonal is equivalent to the body-centered tetragonal, BCT (with a smaller lattice spacing). Tetragonal system has total seven number of classes. It looks somewhat like this. The tetragonal unit cell has unique four fold axis symmetry or four fold axis of seven fold inversion. Next is HEXAGONAL SYSTEM. Components of crystals in this system are located by reference to four axes— three of equal length and a fourth axis perpendicular to the plane of the other three. Hexagonal system is again divided into Hexagonal and trigonal divisions and it has total twelve classes. If the atoms or atomic groups in the solid are represented by points and the points are connected by line segments, the resulting lattice will define the edges of an orderly stacking of blocks, or unit cells. The hexagonal unit cell is distinguished by the presence of a single line, called an axis of 6-fold symmetry, about which the cell can be rotated by either 60° or 120° without changing its appearance. In hexagonal system , among the four axes three axes are horizontal and at 60 degree to each other. The fourth axis is vertical and can be shorter or longer in length than the horizontal ones and angle between the horizontal axes and the vertical axis is 90 degree. It has unique six fold axis or inversion of seven classes and the other five classes have unique three fold axis or inversion. Next is ORTHORHOMBIC SYSTEM as you can see in the image. Crystals in this system are referred to have three mutually perpendicular axes that are unequal in length. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base and height, such that a, b, and c are distinct. It has three classes and three axes of two fold symmetry. Next we have MONOCLINIC SYSTEM. 35% of the minerals crystallises in this monoclinic system. Here all the three crystallographic axes are of unequal length. But the angle between a and b axes and b and c axes is 90 degree whereas the angle between a and c axes is not equal to 90 degree. It has three classes and one axis of two fold symmetry. The last one is TRICLINIC SYSTEM. In this system neither the length of the axes are equal nor the angles are 90 degree. This is the system with the minimum amount of symmetry and it does’nt have any axis or plane of symmetry. It has two classes. So this was my brief idea and summary on the different crystal systems and classes. We have been given Isometric and Tetragonal systems to discuss in detail which will be done by my team members. ISOMETRIC (CUBIC) SYSTEM Definition: All those crystals that can be referred to three crystallographic axes, which are- ● essentially equal in length, ● at right angles to each other, and ● mutually interchangeable, are said to belong to the isomeric or cubic system. It has got the following symmetry: (a) Axes of Symmetry: 13 in all, 3 are axes of four-fold symmetry; 4 are axes of three-fold symmetry; 6 are axes of two-fold symmetry. The three axes of four-fold symmetry are chosen as the crystallographic axes. (b) Planes of Symmetry: 9 in all. 3 planes of symmetry are at right angles to each other and are termed the principal (axial) planes; 6 planes of symmetry are diagonal in position and bisect the angles between the principal planes. (c) It has a Centre of symmetry. Forms: Following are the forms that commonly develop in the crystals belonging to Isometric System: i. Cube: A form bounded by six similar square faces, each of which is parallel to two of three crystallographic axes and meets the third axis. Symbol(100). ii. Octahedron: A form bounded by eight similar faces, each of the shape of an equilateral triangle, each meeting the three crystallographic axes at equal distances. Symbol- (111) iii. Dodecahedron: It is a form with twelve similar faces each of which is parallel to one of the three crystallographic axes and meets the other two at equal distances. Symbol(101). iv. Trisoctahedron (hhl): A form of twenty four (24) faces; each face meeting two axes at unit length and to the third at greater than unity. Faces occur in eight groups of three each. v. Trapezohedron (hll): A form of twenty four (24) faces each face meeting one axes at unit length and to the other two at greater than unity. Each face is a trapezium. vi. Tetra-Hexahedron (hol): Twenty four (24) faces; each face is parallel to one axis and meets other two at unequal distance which are simple multiple of each other; faces occur in six groups of four each. vii. Hexaocatahedron (hkl): Forty eight (48) faces; each face meets the three axis at unequal distances. Other Classes: Isometric system comprises five symmetry classes in all. Beside the normal class, following three classes are also represented among the minerals: A. Pyritohedral Class (Pyrite Type): (a) Symmetry: 7 Axes of symmetry, of which, 3 are axial axes of two-fold symmetry, 4 are diagonal axes of two fold symmetry. 3 Planes of symmetry. Centre of symmetry (b) Forms: Pyritohedron and Diploid are two typical forms of this symmetry class.