Crystallography Lecture PDF

Crystallography Prepared by: Dr. wafaa soliman For second year chemistry branch  INTRODUCTION All matter (gas, liquid or crystal) is composed of atoms, ions or molecules. 1- A gas adopts both the volume and the shape of its container, molecules move rapidly in spac...

Crystallography Prepared by: Dr. wafaa soliman For second year chemistry branch  INTRODUCTION All matter (gas, liquid or crystal) is composed of atoms, ions or molecules. 1- A gas adopts both the volume and the shape of its container, molecules move rapidly in space, and have a high kinetic energy. The attractive forces between molecules are weak. 2- Liquids have constant volume, but adopts the shape of its container, As the temperature of a gas is lowered, the kinetic energies of the molecules decrease, further cooling converts the gas into a liquid. The attractive forces cause the molecules to “touch” one another, but do not, maintain fixed positions. 3- Crystals retains both its shape and its volume, independent of its container. when the temperature falls below the freezing point, the kinetic energy becomes so small that the molecules become permanently attached to one another. A three- dimensional framework of attractive interactions forms among the molecules and the array becomes solid – it crystallizes a result of these permanent interactions is that the molecules have become regularly ordered. All matter tends to crystallize, if the temperature is sufficiently low, since the ordered crystalline phase is the state of lowest energy. There exist, however, materials, such as glass, which never reach this condition. Molten glass is very viscous, and the atoms of which it is made cannot come into a three-dimensional periodic order rapidly enough as the mass cools. Glasses thus have a higher energy content than the corresponding crystals and can best be considered as a frozen, viscous liquid. They are amorphous or “formless” bodies. Such materials do not produce flat faces or polyhedra since an underlying order is missing. Crystallization or crystallisation is the process by which a solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some of the ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. A crystal is a natural solid substance that has a fixed chemical structure and a specific crystal arrangement. Crystallography is concerned with the laws governing the crystalline state of solid materials, with the arrangement of atoms in crystals, and with their physical and chemical properties, their synthesis and their growth. Crystal Growth Crystals grow from, other things, supersaturated solutions, supercooled melts and vapors. The formation of a crystal may be considered in two steps. 1. Nucleation few atoms come together to form a three dimensional periodic array – the nucleus – which already shows faces, it is only a few unit cells in size. 2. Growth of a Nucleus to a Crystal. As the nucleus attracts further atoms, they take up positions on its faces in accordance with its three-dimensional periodicity. In this way, new lattice planes are formed. - corresponding to the slow growth rate faces become steadily larger, while those corresponding to rapid growth disappear entirely. -crystal growth rates are affected by temperature, pressure, and degree of saturation of the solution. single crystal a single crystal nucleus, or only a few, which can grow separately into single crystals. crystal aggregate If many nuclei are formed simultaneously, they may grow into one another in a random fashion. This disturbance will prevent the development of crystal faces and forms. Instead , polycrystal results. (Polycrystalline material)  Atomic arrangement Crystalline – periodic arrangement of atoms: definite repetitive pattern Non-crystalline or Amorphous – random arrangement of atoms. The periodicity of atoms in crystalline solids can be described by a network of points in space called lattice.  The Crystalline State The outward appearance of a crystal is exceptionally variable, The following are a few properties that are characteristic of crystals: Many crystals have smooth faces, and ideal growth conditions, have regular geometric shapes (shape). If some crystals (e.g. NaCl) are split, the resulting fragments have similar shapes with smooth faces – in the case of NaCl, small cubes. This phenomenon is known as cleavage, and is typical only of crystals. The colors that an observer would see when the crystal is viewed from the given directions. The colors that appear depend on the optical absorption of the crystal in that particular direction. For example, if it absorbs all spectral colors from white light except blue, the crystal will appear blue to the observer. When, as in this case, the absorption differs in the three directions, the crystal is said to exhibit pleochroism. The hardness of this crystal When a crystal is scratched with a steel needle, a deep hollow will be made in it.  Fundamentals of Morphology Morphology is the study of the external boundary of a crystal, built up of crystal faces and edges. In morphology, the words “form” and “habit”. crystal structure (the internal structure) and morphology (the external surfaces) The faces of a crystal are parallel to sets of lattice planes occupied by atoms, while the edges are parallel to lattice lines occupied by atoms. Form The morphology of a crystal is the total collection of faces that characterize a particular crystal. (‫ل الوجه ا لبلورية ل لمع دن‬ ‫)ا لمقصود ب ها مدياكتما ا‬ Habit This term is used to describe the relative sizes of the faces of a crystal. There are three fundamental types of habit: equant, planar or tabular, and prismatic or acicular (needle-shaped). (‫)ا لمقصود ب ها اشكا لو احجام ا الوجه ا لبلورية ل لمع دن‬  Crystal Structure In order to progress from a lattice to a crystal, the points of the lattice must be occupied by atoms, ions or molecules. Because the points are all identical, the collections of objects occupying them must also be identical. This arrangement of atoms within a unit cell is called the basis. Lattice translations reproduce the atoms throughout the entire lattice. lattice + basis = crystal structure The unit cell: The smallest unit in which atoms can be arranged and is called the structural unit. ‫هي اصغر وحده يمكن ان تترتب فيها الذرات و تسمي الوحده البنائية‬ The unit cell have vectors are a, b and c and interaxial angles α β γ Types of unit cell: 1-primitive or simple: atoms are in corners only 2- body centered: atoms are in corners and in center 3- face centered: a toms occur in corners and in the center of each face  The Lattice and Its Properties: A space lattice can be defined as a three dimensional array of points, each of which has identical surroundings. The concept of a lattice will now be developed from a lattice point via the line lattice and the plane lattice, finally to the space lattice. 1-If each atom is represented simply by its center of gravity, what remains is a point called identical points is written as uvw or (uvw). If the periodicity along a line is a, then position of any point along the line can be obtained by a simple translation, ru = ua. 2-Moving from the point 0 along one of the vector to the point 1. By this movement, one point is brought into coincidence with another, and a repetition operation takes place. By means of this operation, called a lattice translation, a line lattice has been generated is written as [uvw] ( some times called vectors and is calculated from tip and base). 3- Two lines moves in two directions on the line lattice the result is the plane lattice or plane net and define a unit mesh. is written as (hkl) = miller indices. Similarly ruv= ua + vb will repeat the point along a 2D plane, where u and v are integers. 4- A space lattice can be defined as a three dimensional array of points, each of which has identical surroundings. A space lattice contains infinitely many lattice planes, lines, and points. According to the arrangement of the vectors a⃗ , b⃗ , and c ,⃗ we may introduce an axial system with the crystallographic axes a, b and c. The position of any atom in the 3D lattice can be described by a vector ruvw= ua + vb + wc, where u, v and w are integers.  Classification of lattice Elements of crystallography 7 systems : The main symmetry a=b=c α=β=γ Space lattice 14 bravais lattice: The location of atoms in the space lattice and the basic unit cell simple cube a Bravais lattice can refer to one of the 14 different types of unit cells that a crystal structure can be made up of. Point groups 32 point group: a point group is defined as a group of point symmetry operations whose operation leaves at least one point unmoved. These point groups of highest symmetry in each crystal system all contain the symmetry elements of one or more point groups of lower symmetry ( sub-groups). Trigonal = rhombohedral 7.1 The Primitive Space Lattices (P-Lattices) Atoms are found only in the corners 7.2 The Centered Lattices 7.2.a. body centered The atoms are located in the corners and the middle of the crystal 7.2.b. face centered Atoms are located in the corners and midpoints of the faces 7.2.c. corner centered Atoms are located in the corners and the middles of the sides The 14 Bravais lattices represent the 14 and only ways in which it is possible to fill space by a three-dimensional periodic array of points.  Point and Space groups Symmetry operations generate a variety of arrangements of lattice points in three dimensions. There are 32 unique ways in which lattice points can be arranged in space. These non-translation elements are called point-groups. A large number of 3D structures are generated when translations [linear translation, translation + reflection (glide plane) and translation + rotation (screw axis)] are applied to the point groups. There are 230 unique shapes which can be generated this way. These are called space groups Relationships Between Point Groups and Space Groups There is a relationship between the point groups of morphology and the space groups of crystal structure. In any crystal, the only crystal forms which can appear are those of its point group, and this may be derived from the space group of its crystal structure. Point Coordinates: Position of any point in a unit cell is given by its coordinates or distances from the x, y and z axes in terms of the lattice vectors a, b and c. Thus the point located at a/2 along x axis, b/3 along y axis and c/2 along z axis, as shown in the figure below, has the Coordinates 1/2 1/3 1/2 To determine a direction of a line in the crystal: Find the coordinates of the two ends of the line and subtract the coordinates (Head – Tail) OR draw a line from the origin parallel to the line and find its projection lengths on x, y and z axis in terms of the unit vectors a, b and c. Convert fractions, if any, in to integers and reduce to lowest term. Enclose in square brackets [uvw] Directions in a crystal:  Plane coordinate = miller indices Planes in a crystal are described by notations called Miller indices. -Miller indices of a plane, indicated by h k l, are given by the reciprocal of the intercepts of the plane on the three axes. -The plane, which intersects X axis at 1 (one lattice parameter) and is parallel to Y and Z axes, has Miller indices ͚ h = 1/1 = 1, k = 1/ = 0, l= l /͚ = 0. It is written as (hkl) = (100). The values (hkl) are called Miller indices, and they are defined as the smallest integral multiples of the reciprocals of the plane intercepts on the axes.  Crystal Planes To find the Miller Indices of a plane, follow these steps: Determine the intercepts of the plane along the crystal axes Take the reciprocals Clear fractions Reduce to lowest terms and enclose in brackets () Ex: Intercepts on a, b, c : ¾, ½, ¼ (h k l) = (4/3, 2, 4) = (2 3 6) Planes can also have negative intercept e.g. 1, -1/2, 1 h k l = 1 -2 1. This is denoted as ( 1 2¯1 ). {100} {110} {111}