ASSIGNMENT PRESENTED BY :- SOLOMON JOHN TIRKEY 2020UGCS002 MOHIT RAJ 2020UGCS062 RADHA KUMARI 2020UGCS092 PALLAVI PUSHPAM 2020UGCS122 SUBMITTED TO:- DR. RANJITH PRASAD CRYSTAL STRUCTURE CRYSTALLINE AND NON-CRYSTALLINE MATERIALS . Introduction We see a lot of materials around us on the earth. If we study them , we found few of them having regularity in their structure . These types of materials are crystalline materials or solids. A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances; that is, long-range order exists, such that upon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms. X-ray diffraction photograph [or Laue photograph for a single crystal of magnesium. Crystalline solids have well-defined edges and faces, diffract x-rays, and tend to have sharp melting points. What is meant by Crystallography and why to study the structure of crystalline solids? Crystallography is the experimental science of determining the arrangement of atoms in the crystalline solids. The properties of some materials are directly related to their crystal structures. For example, pure and undeformed magnesium and beryllium, having one crystal structure, are much more brittle (i.e., fracture at lower degrees of deformation) than pure and undeformed metals such as gold and silver that have yet another crystal structure. Furthermore, significant property differences exist between crystalline and non-crystalline materials having the same composition. For example, non-crystalline ceramics and polymers normally are optically transparent; the same materials in crystalline (or semi-crystalline) forms tend to be opaque or, at best, translucent. An important reason to have an understanding of interatomic bonding in solids is that, in some instances, the type of bond allows us to explain a material’s properties. For example, consider carbon, which may exist as both graphite and diamond. Whereas graphite is relatively soft and has a ―Greasy‖ feels to it, diamond is the hardest known material. This dramatic disparity in properties is directly attributable to a type of interatomic bonding found in graphite that does not exist in Diamond. Thus by studying the crystal structure and bonding nature of different materials, we can investigate the reasons for the similar or dissimilar nature of the selected materials in terms of different properties or different parameters. The crystal structure and symmetry of a material play a vital role in determining many of its physical properties, such as cleavage, electronic band structure, and optical transparency, etc. Based on the atomic arrangement in a substance, solids can be broadly classified as either crystalline or non-crystalline. In a crystalline solid, all the atoms are arranged in a periodic manner in all three dimensions whereas in a non-crystalline solid the atomic arrangement is random or non periodic in nature. A crystalline solid can either be a single crystalline or a polycrystalline. In the case of single crystal the entire solid consists of only one crystal and hence, periodic arrangement of atoms continue throughout the entire material. A polycrystalline material is an aggregate of many small crystals separated by well- defined grain boundaries and hence periodic arrangement of atoms is limited to small regions of the material called as grain boundaries as shown in Fig. The noncrystalline substances are also called amorphous substances materials. Single crystalline materials exhibit long range as well as short range periodicities while long range periodicity is absent in case of poly-crystalline materials and non-crystalline materials. Crystallinity : Repeating or periodic array over large atomic distances. 3-D pattern in which each atom is bonded to its nearest neighbors. Crystal structure: the manner in which atoms, ions, or molecules are spatially arranged. Above , in the first and third pictures, we can see how a crystal actually looks , while in the second picture ,we can see the structure of a crystal and a cube which is known as a Unit cell. Unit cell: small repeating entity of the atomic structure. The basic building block of the crystal structure. It defines the entire crystal structure with the atom positions within. • By repeating the pattern of the unit cell over and over in all directions, the entire crystal lattice can be constructed. To define the unit cell parameters or lattice parameters, first we define crystallographic axes. These axes are obtained by the intersection of the three non-coplanar faces of the unit cell. The angle between these faces or crystallographic axes are known as interfacial or interaxial angles. The angles between the axes Y and Z is α, between Z and X is β and between X and Y is γ. The translational vectors or primitives a, b, c of a unit cell along X, Y, Z axes and interaxial angles α, β, γ are called cell parameters. These cell parameters are shown in Fig. The cell parameters determine the actual size and shape of the unit cell. Lattice: 3-D array of points coinciding with atom positions (center of spheres): CRYSTALLINE MATERIALS A crystalline material consists of primarily organized crystal structure. A crystal is: a solid composed of atoms, ions, or molecules arranged in a pattern that is repetitive in three-dimensions. Each crystal structure within a specific crystal system is defined by a unit cell. A unit cell is the smallest repeatable subsection of the crystal. In thinking about crystals, it is often convenient to ignore the actual atoms, ions, or molecules and to focus on the geometry of periodic arrays. The crystal is then represented as a lattice, that is, a three-dimensional array of points (lattice points), each which has identical surroundings. fig:- Lattice points. Each crystal lattice is defined by a crystal system. In three-dimensions, there are seven crystal systems: triclinic, monoclinic, orthorhombic, hexagonal, rhombohedral, tetragonal, and cubic. These collections of systems are called the Bravais lattices. One example of a crystalline material is iron. Iron has a Body Centered Cubic (BCC) unit cell: Fig:- BCC Unit Cell It is grouped in the cubic crystal system. Crystal Systems: Possible Unit Cell Shapes • Goal is to Quantitatively Describe : (a) Shape and Size of the Unit Cell (point symmetry) (b) Location of the Lattice Points (translational symmetry) For (a) to specify the Crystal System and the Lattice Parameters For (b) to define the ―Bravais‖ Lattice Crystal Systems • Unit cells need to be able to ―Stack‖ them to fill all space. • This puts restrictions on Unit Cell Shapes • Cubes Work, Pentagons Don’t! Different types of unit cell are possible, and they are classified based on their level of symmetry. Symmetry Symmetry is a set of mathematical rules that describe the shape of an object. Do you know that there is only ONE object in the geometrical universe with perfect symmetry? It’s a SPHERE. Infinite planes of symmetry pass through its center, infinite rotational axes are present, and no matter how little or much you rotate it on any of its infinite number of axes, it appears the same! Crystal: Space Group By definition crystal is a periodic arrangement of repeating ―motifs‖( e.g. atoms, ions). The symmetry of a periodic pattern of repeated motifs is the total set of symmetry operations allowed by that pattern • Let us apply a rotation of 90 degrees about the center (point) of the pattern which is thought to be indefinitely extended. This pattern will be unchanged as a result of this operation, i.e. the operation maps the pattern onto itself. • Also a linear shift (translation) of this pattern by a certain amount (e.g. by the length of a small square) results in that same pattern again. •The total set of such symmetry operations, applicable to the pattern is the pattern's symmetry, and is mathematically described by a so-called Space Group. The Space Group of a Crystal describes the symmetry of that crystal, and as such it describes an important aspect of that crystal's internal structure. Translational Symmetry A Space Group includes two main types of symmetries (i.e. symmetry operations) (I) The Translational Symmetries, and (II) The Point Symmetries Translations, i.e. executable shifting movements, proceeding along a straight line and on a certain specified distance, such that the operation does not result in any change of the shifted pattern. Typically the translational symmetries are macroscopically not visible because the translation lengths are in the order of Å. Point Symmetries It is a macroscopically visible symmetry operation: after it has been applied to the crystal at least one point remains where it was !! These operations are : •Reflection in a point (inversion) – Center of Symmetry! •Reflection in a plane or Mirror Symmetry ! •Rotation about an imaginary axis –Rotational Symmetry! •Rotation-and- after-it-inversion or Roto-inversion! Center of Symmetry Example: The item consists of two asymmetric faces: then every part of the item can also be found on the opposite side of some point (center of symmetry.) at the same distance. Reflection in a point or inversion. Mirror Symmetry Rotational Symmetry A point around we rotate – symmetry axis Figure looks the same n times in a 360° rotation. n-fold symmetry!! 6 6 / / / % / / / 99 two-fold symmetry Z S N three-fold symmetry four-fold symmetry six-fold symmetry One-fold symmetry = No symmetry!! N-fold