Solid State Chemistry PDF

Unit Objectives The Solid Stat Statee 1 After study...

Unit Objectives The Solid Stat Statee 1 After studying this Unit, you will be able to The vast majority of solid substances like high temperature describe general characteristics of superconductors, biocompatible plastics, silicon chips, etc. are destined solid state; to play an ever expanding role in future development of science. distinguish between amorphous and crystalline solids; classify crystalline solids on the We are mostly surrounded by solids and we use them basis of the nature of binding more often than liquids and gases. For different forces; applications we need solids with widely different define crystal lattice and unit cell; properties. These properties depend upon the nature of explain close packing of particles; constituent particles and the binding forces operating describe different types of voids between them. Therefore, study of the structure of solids and close packed structures; is important. The correlation between structure and calculate the packing efficiency of properties helps in discovering new solid materials different types of cubic unit cells; with desired properties like high temperature correlate the density of a superconductors, magnetic materials, biodegradable substance with its unit cell polymers for packaging, biocompliant solids for surgical properties; implants, etc. describe the imperfections in solids and their effect on From our earlier studies, we know that liquids and properties; gases are called fluids because of their ability to flow. correlate the electrical and The fluidity in both of these states is due to the fact that magnetic properties of solids and the molecules are free to move about. On the contrary, their structure. the constituent particles in solids have fixed positions and can only oscillate about their mean positions. This explains the rigidity in solids. In crystalline solids, the constituent particles are arranged in regular patterns. In this Unit, we shall discuss different possible arrangements of particles resulting in several types of structures. The correlation between the nature of interactions within the constituent particles and several properties of solids will also be explored. How these properties get modified due to the structural imperfections or by the presence of impurities in minute amounts would also be discussed. 1.1 General In Class XI you have learnt that matter can exist in three states namely, Characteristics solid, liquid and gas. Under a given set of conditions of temperature and pressure, which of these would be the most stable state of a given of Solid State substance depends upon the net effect of two opposing factors. Intermolecular forces tend to keep the molecules (or atoms or ions) closer, whereas thermal energy tends to keep them apart by making them move faster. At sufficiently low temperature, the thermal energy is low and intermolecular forces bring them so close that they cling to one another and occupy fixed positions. These can still oscillate about their mean positions and the substance exists in solid state. The following are the characteristic properties of the solid state: (i) They have definite mass, volume and shape. (ii) Intermolecular distances are short. (iii) Intermolecular forces are strong. (iv) Their constituent particles (atoms, molecules or ions) have fixed positions and can only oscillate about their mean positions. (v) They are incompressible and rigid. 1.2 Amorphous Solids can be classified as crystalline or amorphous on the basis of the and Crystalline nature of order present in the arrangement of their constituent particles. Solids A crystalline solid usually consists of a large number of small crystals, each of them having a definite characteristic geometrical shape. In a crystal, the arrangement of constituent particles (atoms, molecules or ions) is ordered. It has long range order which means that there is a regular pattern of arrangement of particles which repeats itself periodically over the entire crystal. Sodium chloride and quartz are typical examples of crystalline solids. An amorphous solid (Greek amorphos = no form) consists of particles of irregular shape. The arrangement of constituent particles (atoms, molecules or ions) in such a solid has only short range order. In such an arrangement, a regular and periodically repeating pattern is observed over short distances only. Such portions are scattered and in between the arrangement is disordered. The structures of quartz (crystalline) and quartz glass (amorphous) are shown in Fig. 1.1 (a) and (b) respectively. While the two structures are almost identical, yet in the case of amorphous quartz glass there is no long range order. The structure of amorphous solids is similar to that of liquids. Glass, rubber and plastics are typical examples of amorphous solids. Due to the differences in the arrangement of the constituent Fig. 1.1: Two dimensional structure of particles, the two types of solids differ (a) quartz and (b) quartz glass in their properties. Chemistry 2  Crystalline solids have a sharp melting point. On the other hand, amorphous solids soften over a range of temperature and can be moulded and blown into various shapes. On heating they become crystalline at some temperature. Some glass objects from ancient civilisations are found to become milky in appearance because of some crystallisation. Like B D liquids, amorphous solids have a tendency to flow, though very slowly. Therefore, sometimes these are called pseudo solids or super cooled liquids. Glass panes fixed to windows or doors of old buildings are invariably found to be slightly thicker at the bottom than at the top. This is because the glass flows down very slowly and makes the bottom portion slightly thicker. Crystalline solids are anisotropic in nature, that is, some of their physical properties like electrical resistance or refractive index show different values C A when measured along different directions in the same crystals. This arises from different arrangement of Fig. 1.2: Anisotropy in crystals is due particles in different directions. This is illustrated in to different arrangement of particles along different Fig. 1.2. Since the arrangement of particles is different directions. along different directions, the value of same physical property is found to be different along each direction. Amorphous solids on the other hand are isotropic in nature. It is because there is no long range order in them and arrangement is irregular along all the directions. Therefore, value of any physical property would be same along any direction. These differences are summarised in Table 1.1. Table 1.1: Distinction between Crystalline and Amorphous Solids Property Crystalline solids Amorphous solids Shape Definite characteristic geometrical shape Irregular shape Melting point Melt at a sharp and characteristic Gradually soften over a range of temperature temperature Cleavage When cut with a sharp edged tool, they When cut with a sharp edged tool, they property split into two pieces and the newly cut into two pieces with irregular generated surfaces are plain and surfaces smooth Heat of fusion They have a definite and characteristic They do not have definite heat of fusion heat of fusion Anisotropy Anisotropic in nature Isotropic in nature Nature True solids Pseudo solids or super cooled liquids Order in Long range order Only short range order. arrangement of constituent particles 3 The Solid State  Amorphous solids are useful materials. Glass, rubber and plastics find many applications in our daily lives. Amorphous silicon is one of the best photovoltaic material available for conversion of sunlight into electricity. Intext Questions 1.1 Why are solids rigid? 1.2 Why do solids have a definite volume? 1.3 Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper. 1.4 Why is glass considered a super cooled liquid? 1.5 Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show cleavage property? 1. 3 Classification In Section 1.2, we have learnt about amorphous substances and that of Crystalline they have only short range order. However, most of the solid substances are crystalline in nature. For example, all the metallic elements like iron, Solids copper and silver; non – metallic elements like sulphur, phosphorus and iodine and compounds like sodium chloride, zinc sulphide and naphthalene form crystalline solids. Crystalline solids can be classified on the basis of nature of intermolecular forces operating in them into four categories viz., molecular, ionic, metallic and covalent solids. Let us now learn about these categories. 1.3.1 Molecular Molecules are the constituent particles of molecular solids. These are Solids further sub divided into the following categories: (i) Non polar Molecular Solids: They comprise of either atoms, for example, argon and helium or the molecules formed by non polar covalent bonds for example H2, Cl2 and I2. In these solids, the atoms or molecules are held by weak dispersion forces or London forces about which you have learnt in Class XI. These solids are soft and non-conductors of electricity. They have low melting points and are usually in liquid or gaseous state at room temperature and pressure. (ii) Polar Molecular Solids: The molecules of substances like HCl, SO2, etc. are formed by polar covalent bonds. The molecules in such solids are held together by relatively stronger dipole-dipole interactions. These solids are soft and non-conductors of electricity. Their melting points are higher than those of non polar molecular solids yet most of these are gases or liquids under room temperature and pressure. Solid SO2 and solid NH3 are some examples of such solids. (iii) Hydrogen Bonded Molecular Solids: The molecules of such solids contain polar covalent bonds between H and F, O or N atoms. Strong hydrogen bonding binds molecules of such solids like H2O (ice). They are non-conductors of electricity. Generally they are volatile liquids or soft solids under room temperature and pressure. Chemistry 4 1.3.2 Ionic Solids Ions are the constituent particles of ionic solids. Such solids are formed by the three dimensional arrangements of cations and anions bound by strong coulombic (electrostatic) forces. These solids are hard and brittle in nature. They have high melting and boiling points. Since the ions are not free to move about, they are electrical insulators in the solid state. However, in the molten state or when dissolved in water, the ions become free to move about and they conduct electricity. 1.3.3 Metallic Metals are orderly collection of positive ions surrounded by and held Solids together by a sea of free electrons. These electrons are mobile and are evenly spread out throughout the crystal. Each metal atom contributes one or more electrons towards this sea of mobile electrons. These free and mobile electrons are responsible for high electrical and thermal conductivity of metals. When an electric field is applied, these electrons flow through the network of positive ions. Similarly, when heat is supplied to one portion of a metal, the thermal energy is uniformly spread throughout by free electrons. Another important characteristic of metals is their lustre and colour in certain cases. This is also due to the presence of free electrons in them. Metals are highly malleable and ductile. 1.3.4 Covalent or A wide variety of crystalline solids of non-metals result from the Network formation of covalent bonds between adjacent atoms throughout the Solids crystal. They are also called giant molecules. Covalent bonds are strong and directional in nature, therefore atoms are held very strongly at their positions. Such solids are very hard and brittle. They have extremely high melting points and may even decompose before melting. They are insulators and do not conduct electricity. Diamond (Fig. 1.3) and silicon carbide are typical examples of such solids. Graphite is soft and a conductor of electricity. Its exceptional properties are due to its typical structure (Fig. 1.4). Carbon atoms are arranged in different layers and each atom is covalently bonded to three of its neighbouring atoms in the same layer. The fourth valence electron of each atom is present between different layers and is free to move about. These free electrons make graphite a good conductor of electricity. Different layers can slide one over the other. This makes graphite a soft Fig. 1.3: Network structure Fig. 1.4: Structure of graphite solid and a good solid of diamond lubricant. 5 The Solid State  The different properties of the four types of solids are listed in Table 1.2. Table 1.2: Different Types of Solids Type of Solid Constituent Bonding/ Examples Physical Electrical Melting Particles Attractive Nature Conduc- Point Forces tivity (1) Molecular solids (i) Non polar Molecules Dispersion or Ar, CCl4, Soft Insulator Very low London forces H2, I2, CO2 (ii) Polar Dipole-dipole HCl, SO2 Soft Insulator Low interactions (iii) Hydrogen Hydrogen H2O (ice) Hard Insulator Low bonded bonding (2) Ionic solids Ions Coulombic or NaCl, MgO, Hard but Insulators High electrostatic ZnS, CaF2 brittle in solid state but conductors in molten state and in aqueous solutions (3) Metallic solids Positive Metallic Fe, Cu, Ag, Hard but Conductors Fairly ions in a bonding Mg malleable in solid high sea of and state as delocalised ductile well as in electrons molten state (4) Covalent or Atoms Covalent SiO2 Hard Insulators Very network solids bonding (quartz), high SiC, C (diamond), AlN, C(graphite) Soft Conductor (exception) Intext Questions 1.6 Classify the following solids in different categories based on the nature of intermolecular forces operating in them: Potassium sulphate, tin, benzene, urea, ammonia, water, zinc sulphide, graphite, rubidium, argon, silicon carbide. 1.7 Solid A is a very hard electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it? 1.8 Ionic solids conduct electricity in molten state but not in solid state. Explain. 1.9 What type of solids are electrical conductors, malleable and ductile? Chemistry 6 1.4 Crystal The main characteristic of crystalline Lattices and solids is a regular and repeating pattern of constituent particles. If Unit Cells the three dimensional arrangement of constituent particles in a crystal is represented diagrammatically, in which each particle is depicted as a point, the arrangement is called crystal lattice. Thus, a regular three dimensional arrangement of points in space is called a crystal lattice. Fig. 1.5: A portion of a three A portion of a crystal lattice is shown dimensional cubic lattice in Fig. 1.5. and its unit cell. There are only 14 possible three dimensional lattices. These are called Bravais Lattices (after the French mathematician who first described them). The following are the characteristics of a crystal lattice: (a) Each point in a lattice is called lattice point or lattice site. (b) Each point in a crystal lattice represents one constituent particle which may be an atom, a molecule (group of atoms) or an ion. (c) Lattice points are joined by straight lines to bring out the geometry of the lattice. Unit cell is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice. A unit cell is characterised by: (i) its dimensions along the three edges, a, b and c. These edges may or may not be mutually perpendicular. (ii) angles between the edges, α (between b and c) β (between a and c) and γ (between a and b). Thus, a unit cell is characterised by six parameters, a, b, c, α, β and γ. Fig. 1.6: Illustration of These parameters of a typical unit cell are shown in parameters of a unit cell Fig. 1.6. 1.4.1 Primitive Unit cells can be broadly divided into two categories, primitive and and Centred centred unit cells. Unit Cells (a) Primitive Unit Cells When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell. (b) Centred Unit Cells When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centred unit cells are of three types: (i) Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners. (ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners. 7 The Solid State  (iii) End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners. In all, there are seven types of primitive unit cells (Fig. 1.7). Fig. 1.7: Seven primitive unit cells in crystals Their characteristics along with the centred unit cells they can form have been listed in Table 1.3. Table 1.3: Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells Crystal system Possible Axial distances Axial angles Examples variations or edge lengths Cubic Primitive, a=b=c α = β = γ = 90° NaCl, Zinc blende, Body-centred, Cu Face-centred Tetragonal Primitive, a=b≠c α = β = γ = 90° White tin, SnO2, Body-centred TiO2, CaSO4 Orthorhombic Primitive, a≠b≠c α = β = γ = 90° Rhombic sulphur, Body-centred, KNO3, BaSO4 Face-centred, End-centred Hexagonal Primitive a=b≠c α = β = 90° Graphite, ZnO,CdS, γ = 120° Rhombohedral or Primitive a=b=c α = β = γ ≠ 90° Calcite (CaCO3), HgS Trigonal (cinnabar) Chemistry 8 Monoclinic Primitive, a≠b≠c α = γ = 90° Monoclinic sulphur, End-centred β ≠ 90° Na2SO4.10H2O Triclinic Primitive a≠b≠c α ≠ β ≠ γ ≠ 90° K2Cr2O7, CuSO4. 5H2O, H3BO3 Unit Cells of 14 Types of Bravais Lattices a a a Primitive Body-centred Face-centred (or simple) The three cubic lattices: all sides of same length, angles between faces all 90° Primitive Body-centred The two tetragonal: one side different in length to the other, two angles between faces all 90° Primitive End-centred Body-centred Face-centred The four orthorhombic lattices: unequal sides, angles between faces all 90° More than 90° Less than 90° Primitive End-centred The two monoclinic lattices: unequal sides, two faces have angles different from 90° 9 The Solid State  60 less than 90° a a a a Rhombohedral lattice – Hexagonal lattice – all sides of equal one side different in length, angles on two length to the other faces are less than 90° two, the marked angles on two faces are 60° a b A C Triclinic lattice – B unequal sides a, b, c, c A, B, C are unequal angles with none equal to 90° 1.5 Number of We know that any crystal lattice is made up of a very large number of Atoms in a unit cells and every lattice point is occupied by one constituent particle (atom, molecule or ion). Let us now work out what portion of each particle Unit Cell belongs to a particular unit cell. We shall consider three types of cubic unit cells and for simplicity assume that the constituent particle is an atom. 1.5.1 Primitive Primitive cubic unit cell has atoms only at its corner. Each atom at Cubic Unit a corner is shared between eight adjacent unit cells as shown in Cell Fig. 1.8, four unit cells in the same layer and four unit cells of the 1 th upper (or lower) layer. Therefore, only of an atom (or molecule 8 or ion) actually belongs to a particular unit cell. In Fig. 1.9, a primitive cubic unit cell has been depicted in three different ways. Each small sphere in Fig. 1.9 (a) represents only the centre of the particle occupying that position and not its actual size. Such structures are called open structures. The arrangement of particles is easier to follow in open structures. Fig. 1.9 (b) depicts space-filling representation of the unit cell with actual particle size and Fig. 1.9 (c) shows the actual portions of different atoms present in a cubic unit cell. Fig. 1.8: In a simple cubic unit cell, each corner atom is shared In all, since each cubic unit cell has between 8 unit cells. 8 atoms on its corners, the total number of 1 atoms in one unit cell is 8   1 atom. 8 Fig. 1.9: A primitive cubic unit cell (a) open structure (b) space-filling structure (c) actual portions of atoms belonging to one unit cell. Chemistry 10 1.5.2 Body- A body-centred cubic (bcc) unit cell has an atom at each of its corners Centred and also one atom at its body centre. Fig. 1.10 depicts (a) open Cubic Unit structure (b) space filling model and (c) the unit cell with portions of Cell atoms actually belonging to it. It can be seen that the atom at the (a) (b) (c) Fig. 1.10: A body-centred cubic unit cell (a) open structure (b) space- filling structure (c) actual portions of atoms belonging to one unit cell. body centre wholly belongs to the unit cell in which it is present. Thus in a body-centered cubic (bcc) unit cell: 1 (i) 8 corners × per corner atom  8  1 = 1 atom 8 8 (ii) 1 body centre atom = 1 × 1 = 1 atom ∴ Total number of atoms per unit cell = 2 atoms 1.5.3 Face- A face-centred cubic (fcc) unit cell contains atoms at all the corners and Centred at the centre of all the faces of the cube. It can be seen in Fig. 1.11 that Cubic Unit each atom located at the face-centre is shared between two adjacent Cell 1 unit cells and only of each atom belongs to a unit cell. Fig. 1.12 depicts 2 (a) open structure (b) space-filling model and (c) the unit cell with portions of atoms actually belonging to it. Thus, in a face-centred cubic (fcc) unit cell: 1 (i) 8 corners atoms × atom per unit cell  8  1 = 1 atom 8 8 1 1 (ii) 6 face-centred atoms × atom per unit cell = 6 × = 3 atoms 2 2 ∴ Total number of atoms per unit cell = 4 atoms (a) (b) (b) Fig. 1.11: An atom at face centre of unit cell Fig 1.12: A face-centred cubic unit cell (a) open structure (b) space is shared between filling structure (c) actual portions of atoms belonging to 2 unit cells one unit cell. 11 The Solid State  Intext Questions 1.10 Give the significance of a ‘lattice point’. 1.11 Name the parameters that characterise a unit cell. 1.12 Distinguish between (i) Hexagonal and monoclinic unit cells (ii) Face-centred and end-centred unit cells. 1.13 Explain how much portion of an atom located at (i) corner and (ii) body- centre of a cubic unit cell is part of its neighbouring unit cell. 1.6 Close Packed In solids, the constituent particles are close-packed, leaving the Structures minimum vacant space. Let us consider the constituent particles as identical hard spheres and build up the three dimensional structure in three steps. (a) Close Packing in One Dimension There is only one way of arranging spheres in a one dimensional close packed structure, that is to arrange them in a row and touching each other (Fig. 1.13). In this arrangement, each sphere is in contact with two of its neighbours. The number of nearest neighbours of a particle is called its coordination Fig. 1.13: Close packing of spheres in number. Thus, in one dimensional close packed one dimension arrangement, the coordination number is 2. (b) Close Packing in Two Dimensions Two dimensional close packed structure can be generated by stacking (placing) the rows of close packed spheres. This can be done in two different ways. (i) The second row may be placed in contact with the first one such that the spheres of the second row are exactly above those of the first row. The spheres of the two rows are aligned horizontally as well as vertically. If we call the first row as ‘A’ type row, the second row being exactly the same as the first one, is also of ‘A’ type. Similarly, we may place more rows to obtain AAA type of arrangement as shown in Fig. 1.14 (a). Fig. 1.14: (a) Square close packing (b) hexagonal close packing of spheres in two dimensions Chemistry 12  In this arrangement, each sphere is in contact with four of its neighbours. Thus, the two dimensional coordination number is 4. Also, if the centres of these 4 immediate neighbouring spheres are joined, a square is formed. Hence this packing is called square close packing in two dimensions. (ii) The second row may be placed above the first one in a staggered manner such that its spheres fit in the depressions of the first row. If the arrangement of spheres in the first row is called ‘A’ type, the one in the second row is different and may be called ‘B’ type. When the third row is placed adjacent to the second in staggered manner, its spheres are aligned with those of the first layer. Hence this layer is also of ‘A’ type. The spheres of similarly placed fourth row will be aligned with those of the second row (‘B’ type). Hence this arrangement is of ABAB type. In this arrangement there is less free space and this packing is more efficient than the square close packing. Each sphere is in contact with six of its neighbours and the two dimensional coordination number is 6. The centres of these six spheres are at the corners of a regular hexagon (Fig. 1.14b) hence this packing is called two dimensional hexagonal close- packing. It can be seen in Figure 1.14 (b) that in this layer there are some voids (empty spaces). These are triangular in shape. The triangular voids are of two different types. In one row, the apex of the triangles are pointing upwards and in the next layer downwards. (c) Close Packing in Three Dimensions All real structures are three dimensional structures. They can be obtained by stacking two dimensional layers one above the other. In the last Section, we discussed close packing in two dimensions which can be of two types; square close-packed and hexagonal close-packed. Let us see what types of three dimensional close packing can be obtained from these. (i) Three dimensional close packing from two dimensional square close-packed layers: While placing the second square close-packed layer above the first we follow the same rule that was followed when one row was placed adjacent to the other. The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer. In this arrangement spheres of both the layers are perfectly aligned horizontally as well as vertically as shown in Fig. 1.15. Similarly, we may place more layers one above the other. If the arrangement of spheres in the first layer is called ‘A’ type, all the layers have the same arrangement. Thus this lattice has AAA.... type pattern. The lattice thus generated is the simple cubic lattice, and its unit cell is the primitive cubic unit cell (See Fig. 1.9). (ii) Three dimensional close packing from two dimensional hexagonal close packed layers: Three Fig. 1.15: Simple cubic lattice formed dimensional close packed structure can be generated by A A A.... arrangement by placing layers one over the other. 13 The Solid State  (a) Placing second layer over the first layer Let us take a two dimensional hexagonal close packed layer ‘A’ and place a similar layer above it such that the spheres of the second layer are placed in the depressions of the first layer. Since the spheres of the two layers are aligned differently, let us call the second layer as B. It can be observed from Fig. 1.16 that not all the triangular voids of the first layer are covered by the spheres of the second layer. This gives rise to different arrangements. Wherever a sphere of the second layer is above the void of the first layer (or vice versa) a tetrahedral void is Fig. 1.16: A stack of two layers of close packed spheres and voids generated in them. T = Tetrahedral void; O = Octahedral void formed. These voids are called tetrahedral voids because a tetrahedron is formed when the centres of these four spheres are joined. They have been marked as ‘T’ in Fig. 1.16. One such void has been shown separately in Fig. 1.17. Fig 1.17 Tetrahedral and octahedral voids (a) top view (b) exploded side view and (c) geometrical shape of the void. Chemistry 14  At other places, the triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap. One of them has the apex of the triangle pointing upwards and the other downwards. These voids have been marked as ‘O’ in Fig. 1.16. Such voids are surrounded by six spheres and are called octahedral voids. One such void has been shown separately in Fig. 1.17. The number of these two types of voids depend upon the number of close packed spheres. Let the number of close packed spheres be N, then: The number of octahedral voids generated = N The number of tetrahedral voids generated = 2N (b) Placing third layer over the second layer When third layer is placed over the second, there are two possibilities. (i) Covering Tetrahedral Voids: Tetrahedral voids of the second layer may be covered by the spheres of the third layer. In this case, the spheres of the third layer are exactly aligned with those of the first layer. Thus, the pattern of spheres is repeated in alternate layers. This pattern is often written as ABAB....... pattern. This structure is called hexagonal close packed (hcp) structure (Fig. 1.18). This sort of arrangement of atoms is found in many metals like magnesium and zinc. Fig. 1.18 (a) Hexagonal cubic close-packing exploded view showing stacking of layers of spheres (b) four layers stacked in each case and (c) geometry of packing. Fig. 1.19 A (ii) Covering Octahedral Voids: The (a) ABCABC... third layer may be placed above arrangement of the second layer in a manner such C layers when that its spheres cover the octahedral void is octahedral voids. When placed in covered (b) fragment (b) this manner, the spheres of the of structure formed B third layer are not aligned with by this arrangement those of either the first or the second resulting in cubic closed packed (ccp) A layer. This arrangement is called ‘C’ or face centred cubic type. Only when fourth layer is (fcc) structure. (a) placed, its spheres are aligned with 15 The Solid State  those of the first layer as shown in Figs. 1.18 and 1.19. This pattern of layers is often written as ABCABC........... This structure is called cubic close packed (ccp) or face-centred cubic (fcc) structure. Metals such as copper and silver crystallise in this structure. Both these types of close packing are highly efficient and 74% space in the crystal is filled. In either of them, each sphere is in contact with twelve spheres. Thus, the coordination number is 12 in either of these two structures. 1.6.1 Formula of a Earlier in the section, we have learnt that when particles are close- Compound packed resulting in either ccp or hcp structure, two types of voids are and Number generated. While the number of octahedral voids present in a lattice is of Voids equal to the number of close packed particles, the number of tetrahedral Filled voids generated is twice this number. In ionic solids, the bigger ions (usually anions) form the close packed structure and the smaller ions (usually cations) occupy the voids. If the latter ion is small enough then tetrahedral voids are occupied, if bigger, then octahedral voids. Not all octahedral or tetrahedral voids are occupied. In a given compound, the fraction of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the compound, as can be seen from the following examples. Example 1.1 A compound is formed by two elements X and Y. Atoms of the element Y (as anions) make ccp and those of the element X (as cations) occupy all the octahedral voids. What is the formula of the compound? Solution The ccp lattice is formed by the element Y. The number of octahedral voids generated would be equal to the number of atoms of Y present in it. Since all the octahedral voids are occupied by the atoms of X, their number would also be equal to that of the element Y. Thus, the atoms of elements X and Y are present in equal numbers or 1:1 ratio. Therefore, the formula of the compound is XY. Example 1.2 Atoms of element B form hcp lattice and those of the element A occupy 2/3rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B? Solution The number of tetrahedral voids formed is equal to twice the number of atoms of element B and only 2/3rd of these are occupied by the atoms of element A. Hence the ratio of the number of atoms of A and B is 2 × (2/3):1 or 4:3 and the formula of the compound is A4B3. Locating Tetrahedral and Octahedral Voids We know that close packed structures have both tetrahedral and octahedral voids. Let us take ccp (or fcc) structure and locate these voids in it. (a) Locating Tetrahedral Voids Let us consider a unit cell of ccp or fcc lattice [Fig. 1(a)]. The unit cell is divided into eight small cubes. Chemistry 16  Each small cube has atoms at alternate corners [Fig. 1(a)]. In all, each small cube has 4 atoms. When joined to each other, they make a regular tetrahedron. Thus, there is one tetrahedral void in each small cube and eight tetrahedral voids in total. Each of the eight small cubes have one void in one unit cell of ccp structure. We know that ccp structure has 4 atoms per unit cell. Thus, the number of tetrahedral voids is twice the number of atoms. Fig. 1: (a) Eight tetrahedral voids per unit cell of ccp structure (b) one tetrahedral void showing the geometry. (b) Locating Octahedral Voids Let us again consider a unit cell of ccp or fcc lattice [Fig. 2(a)]. The body centre of the cube, C is not occupied but it is surrounded by six atoms on face centres. If these face centres are joined, an octahedron is generated. Thus, this unit cell has one octahedral void at the body centre of the cube. Besides the body centre, there is one octahedral void at the centre of each of the 12 edges. [Fig. 2(b)]. It is surrounded by six atoms, four belonging to the same unit cell (2 on the corners and 2 on face centre) and two belonging to two adjacent unit cells. Since each edge of the cube is shared between four adjacent 1 th unit cells, so is the octahedral void located on it. Only of each void belongs 4 to a particular unit cell. (a) (b) Fig. 2: Location of octahedral voids per unit cell of ccp or fcc lattice (a) at the body centre of the cube and (b) at the centre of each edge (only one such void is shown). 17 The Solid State  Thus in cubic close packed structure: Octahedral void at the body-centre of the cube = 1 12 octahedral voids located at each edge and shared between four unit cells 1 = 12  3 4 ∴ Total number of octahedral voids = 4 We know that in ccp structure, each unit cell has 4 atoms. Thus, the number of octahedral voids is equal to this number. 1.7 Packing In whatever way the constituent particles (atoms, molecules or ions) Efficiency are packed, there is always some free space in the form of voids. Packing efficiency is the percentage of total space filled by the particles. Let us calculate the packing efficiency in different types of structures. 1.7.1 Packing Both types of close packing (hcp and ccp) are equally efficient. Let us Efficiency in calculate the efficiency of packing in ccp structure. In Fig. 1.20 let the hcp and ccp unit cell edge length be ‘a’ and face diagonal AC = b. Structures In  ABC AC2 = b2 = BC2 + AB2 = a2+a2 = 2a2 or b= 2a If r is the radius of the sphere, we find b = 4r = 2a 4r or a =  2 2r 2 a (we can also write, r  ) 2 2 We know, that each unit cell in ccp structure, Fig. 1.20: Cubic close packing other has effectively 4 spheres. Total volume of four sides are not provided with spheres for sake of clarity. spheres is equal to 4   4 /3  r 3 and volume of the   3 cube is a 3 or 2 2r. Therefore, Volume occupied by four spheres in the unit cell 100 Packing efficiency = % Total volumeof the unit cell 4   4 / 3  r 3  100  % 2  3 2r 16 / 3  r 3  100  %  74% 16 2r 3 Chemistry 18 1.7.2 Efficiency of From Fig. 1.21, it is clear that the Packing in atom at the centre will be in touch Body- with the other two atoms diagonally Centred arranged. Cubic In Δ EFD, Structures b2 = a2 + a2 = 2a2 b = 2a Now in Δ AFD 2 2 2 2 2 2 c = a + b = a + 2a = 3a c = 3a The length of the body diagonal Fig. 1.21: Body-centred cubic unit c is equal to 4r, where r is the radius cell (sphere along the of the sphere (atom), as all the three body diagonal are shown spheres along the diagonal touch with solid boundaries). each other. Therefore, 3a = 4r 4r a= 3 3 Also we can write, r = a 4 In this type of structure, total number of atoms is 2 and their volume is 2  4 r 3. 3 3 3  4    Volume of the cube, a3 will be equal to  r  or a3   4 r .  3   3  Therefore, Volume occupied by two spheres in the unit cell  100 Packing efficiency = % Total volume of the unit cell 2   4 /3  r 3  100  %   3  4/ 3 r    8/ 3  r 3  100  %  68%  64 / 3 3 r 3  1.7.3 Packing In a simple cubic lattice the atoms are located only on the corners of the Efficiency in cube. The particles touch each other along the edge (Fig. 1.22). Simple Cubic Thus, the edge length or side of the cube ‘a’, and the radius of each particle, Lattice r are related as a = 2r The volume of the cubic unit cell = a3 = (2r)3 = 8r3 Since a simple cubic unit cell contains only 1 atom 4 r 3 The volume of the occupied space = 3 19 The Solid State  ∴ Packing efficiency Volume of one atom = Volume of cubic unit cell  100% 4 3 r = 3   100   100 Fig. 1.22 8r 3 6 Simple cubic unit cell. = 52.36% = 52.4 % The spheres are in contact with each Thus, we may conclude that ccp other along the edge of and hcp structures have maximum the cube. packing efficiency. 1.8 Calculations From the unit cell dimensions, it is possible to calculate the volume of Involving the unit cell. Knowing the density of the metal, we can calculate the mass of the atoms in the unit cell. The determination of the mass of a Unit Cell single atom gives an accurate method of determination of Avogadro Dimensions constant. Suppose, edge length of a unit cell of a cubic crystal determined by X-ray diffraction is a, d the density of the solid substance and M the molar mass. In case of cubic crystal: 3 Volume of a unit cell = a Mass of the unit cell = number of atoms in unit cell × mass of each atom = z × m (Here z is the number of atoms present in one unit cell and m is the mass of a single atom) Mass of an atom present in the unit cell: M m = N (M is molar mass) A Therefore, density of the unit cell mass of unit cell = volume of unit cell z.m z.M zM = = 3 or d = 3 a3 a.N A a NA Remember, the density of the unit cell is the same as the density of the substance. The density of the solid can always be determined by other methods. Out of the five parameters (d, z M, a and NA), if any four are known, we can determine the fifth. Example 1.3 An element has a body-centred cubic (bcc) structure with a cell edge of 288 pm. The density of the element is 7.2 g/cm3. How many atoms are present in 208 g of the element? Solution Volume of the unit cell = (288 pm)3 = (288×10-12 m)3 = (288×10-10 cm)3 = 2.39×10-23 cm3 Chemistry 20 Volume of 208 g of the element mass 208 g    28.88 cm 3 density 7.2 g cm 3 Number of unit cells in this volume 28.88cm 3  = 12.08×1023 unit cells 2.39  1023 cm 3 / unit cell Since each bcc cubic unit cell contains 2 atoms, therefore, the total number of atoms in 208 g = 2 (atoms/unit cell) × 12.08 × 1023 unit cells = 24.16×1023 atoms X-ray diffraction studies show that copper crystallises in an fcc unit Example 1.4 cell with cell edge of 3.608×10-8 cm. In a separate experiment, copper is determined to have a density of 8.92 g/cm3, calculate the atomic mass of copper. In case of fcc lattice, number of atoms per unit cell, z = 4 atoms Solution 3 dN A a Therefore, M = z 8.92 g cm –3  6.022  1023 atoms mol 1  (3.608  10 8 cm)3  4 atoms = 63.1 g/mol Atomic mass of copper = 63.1u Silver forms ccp lattice and X-ray studies of its crystals show that the Example 1.5 edge length of its unit cell is 408.6 pm. Calculate the density of silver (Atomic mass = 107.9 u). Since the lattice is ccp, the number of silver atoms per unit cell = z = 4 Solution –1 -3 –1 Molar mass of silver = 107.9 g mol = 107.9×10 kg mol Edge length of unit cell = a = 408.6 pm = 408.6×10–12 m z.M Density, d = a 3.N A =  4  107.9  103 kg mol 1  = 10.5×103 kg m–3  408.6  10   6.022  10  12 3 23 1 m mol -3 = 10.5 g cm Intext Questions 1.14 What is the two dimensional coordination number of a molecule in square close-packed layer? 1.15 A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids? 21 The Solid State  1.16 A compound is formed by two elements M and N. The element N forms ccp and atoms of M occupy 1/3rd of tetrahedral voids. What is the formula of the compound? 1.17 Which of the following lattices has the highest packing efficiency (i) simple cubic (ii) body-centred cubic and (iii) hexagonal close-packed lattice? 1.18 An element with molar mass 2.7×10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7×103 kg m-3, what is the nature of the cubic unit cell? 1.9 Imperfections Although crystalline solids have short range as well as long range in Solids order in the arrangement of their constituent particles, yet crystals are not perfect. Usually a solid consists of an aggregate of large number of small crystals. These small crystals have defects in them. This happens when crystallisation process occurs at fast or moderate rate. Single crystals are formed when the process of crystallisation occurs at extremely slow rate. Even these crystals are not free of defects. The defects are basically irregularities in the arrangement of constituent particles. Broadly speaking, the defects are of two types, namely, point defects and line defects. Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance, whereas the line defects are the irregularities or deviations from ideal arrangement in entire rows of lattice points. These irregularities are called crystal defects. We shall confine our discussion to point defects only. 1.9.1 Types of Point defects can be classified into three types : (i) stoichiometric defects Point Defects (ii) impurity defects and (iii) non-stoichiometric defects. (a) Stoichiometric Defects These are the point defects that do not disturb the stoichiometry of the solid. They are also called intrinsic or thermodynamic defects. Basically these are of two types, vacancy defects and interstitial defects. (i) Vacancy Defect: When some of the lattice sites are vacant, the crystal is said to have vacancy defect (Fig. 1.23). This results in decrease in density of the substance. This defect can also develop when a substance is heated. (ii) Interstitial Defect: When some constituent particles (atoms or molecules) occupy an interstitial site, the crystal is said to have interstitial defect (Fig. 1.24). This defect increases the density of the substance. Vacancy and interstitial defects as explained above can be shown by non-ionic solids. Ionic solids must always maintain electrical neutrality. Rather than simple vacancy or interstitial defects, they show these defects as Frenkel and Fig. 1.23: Vacancy defects Schottky defects. Chemistry 22  (iii) Frenkel Defect: This defect is shown by ionic solids. The smaller ion (usually cation) is dislocated from its normal site to an interstitial site (Fig. 1.25). It creates a vacancy defect at its original site and an interstitial defect at its new location. Frenkel defect is also Fig. 1.24: Interstitial defects called dislocation defect. It does not change the density of the solid. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions, for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+ and Ag+ ions. (iv) Schottky Defect: It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the number of missing cations and anions are equal (Fig. 1.26). Like simple vacancy defect, Schottky defect also decreases the density of the substance. Number of such defects in ionic solids is quite significant. For example, in NaCl there are approximately 106 Schottky pairs per cm3 at room temperature. In 1 cm 3 there are about 1022 ions. Thus, there is one Schottky defect per 1016 ions. Fig. 1.25: Frenkel defects Fig. 1.26: Schottky defects Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes. For example, NaCl, KCl, CsCl and AgBr. It may be noted that AgBr shows both, Frenkel as well as Schottky defects. (b) Impurity Defects If molten NaCl containing a little amount of SrCl2 is crystallised, some of the sites of Na+ ions are occupied by Sr2+ (Fig.1.27). Each Sr2+ replaces two Na+ ions. It occupies the site of one ion and the other site remains vacant. The cationic vacancies thus produced are equal in number to that of Sr2+ ions. Another similar example is the Fig. 1.27: Introduction of cation vacancy in solid solution of CdCl2 and AgCl. NaCl by substitution of Na+ by Sr 2+ 23 The Solid State  (c) Non-Stoichiometric Defects The defects discussed so far do not disturb the stoichiometry of the crystalline substance. However, a large number of non- stoichiometric inorganic solids are known which contain the constituent elements in non-stoichiometric ratio due to defects in their crystal structures. These defects are of two types: (i) metal excess defect and (ii) metal deficiency defect. (i) Metal Excess Defect  Metal excess defect due to anionic vacancies: Alkali halides like NaCl and KCl show this type of defect. When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The Cl– ions diffuse to the surface of the crystal and combine with Na atoms to give NaCl. This happens by loss of electron by sodium atoms to form Na+ ions. The released electrons diffuse into the crystal and occupy anionic sites (Fig. 1.28). As a result the crystal now has an excess of sodium. The anionic sites occupied by unpaired electrons are called F-centres (from the German word Farbenzenter for colour centre). They impart yellow colour to the crystals of NaCl. The colour results by excitation of these electrons when they absorb energy from the visible light falling on the crystals. Similarly, excess of lithium makes LiCl crystals pink and excess of potassium Fig. 1.28: An F-centre in a crystal makes KCl crystals violet (or lilac).  Metal excess defect due to the presence of extra cations at interstitial sites: Zinc oxide is white in colour at room temperature. On heating it loses oxygen and turns yellow. 1 ZnO  heating Zn 2   O2  2e  2 Now there is excess of zinc in the crystal and its formula becomes 2+ Zn1+xO. The excess Zn ions move to interstitial sites and the electrons to neighbouring interstitial sites. (ii) Metal Deficiency Defect There are many solids which are difficult to prepare in the stoichiometric composition and contain less amount of the metal as compared to the stoichiometric proportion. A typical example of this type is FeO which is mostly found with a composition of Fe0.95O. It may actually range from Fe0.93O to Fe0.96O. In crystals of FeO some Fe2+ cations are missing and the loss of positive charge is made up by the presence of required number of Fe3+ ions. 1.10 Electrical Solids exhibit an amazing range of electrical conductivities, extending Properties –20 7 –1 –1 over 27 orders of magnitude ranging from 10 to 10 ohm m. Solids can be classified into three types on the basis of their conductivities. (i) Conductors: The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors. Metals have conductivities in the order of 107 ohm–1m–1 are good conductors. Chemistry 24  (ii) Insulators : These are the solids with very low conductivities –20 –10 –1 –1 ranging between 10 to 10 ohm m. (iii) Semiconductors : These are the solids with conductivities in the –6 4 –1 –1 intermediate range from 10 to 10 ohm m. 1.10.1 Conduction A conductor may conduct electricity through movement of electrons or of ions. Metallic conductors belong to the former category and electrolytes Electricity to the latter. in Metals Metals conduct electricity in solid as well as molten state. The conductivity of metals depend upon the number of valence electrons available per atom. The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each other as to form a band. If this band is partially filled or it overlaps with a higher energy unoccupied conduction band, then electrons can flow easily under an applied electric field and the metal shows conductivity (Fig. 1.29 a). If the gap between filled valence band and the next higher unoccupied band (conduction band) is large, electrons cannot jump to it and such a substance has very small conductivity and it behaves as an insulator (Fig. 1.29 b). 1.10.2 Conduction In case of semiconductors, the gap between the valence band and of conduction band is small (Fig. 1.29c). Therefore, some electrons may Electricity jump to conduction band and show some conductivity. Electrical in Semi- conductivity of semiconductors increases with rise in temperature, since conductors more electrons can jump to the conduction band. Substances like silicon and germanium show this type of behaviour and are called intrinsic semiconductors. The conductivity of these intrinsic semiconductors is too low to be of practical use. Their conductivity is increased by adding an appropriate amount of suitable impurity. This process is called Fig. 1.29 Distinction among (a) metals (b) insulators and (c) semiconductors. In each case, an unshaded area represents a conduction band. 25 The Solid State  doping. Doping can be done with an impurity which is electron rich or electron deficient as compared to the intrinsic semiconductor silicon or germanium. Such impurities introduce electronic defects in them. (a) Electron – rich impurities Silicon and germanium belong to group 14 of the periodic table and have four valence electrons each. In their crystals each atom forms four covalent bonds with its neighbours (Fig. 1.30 a). When doped with a group 15 element like P or As, which contains five valence electrons, they occupy some of the lattice sites in silicon or germanium crystal (Fig. 1.30 b). Four out of five electrons are used in the formation of four covalent bonds with the four neighbouring silicon atoms. The fifth electron is extra and becomes delocalised. These delocalised electrons increase the conductivity of doped silicon (or germanium). Here the increase in conductivity is due to the negatively charged electron, hence silicon doped with electron-rich impurity is called n-type semiconductor. (b) Electron – deficit impurities Silicon or germanium can also be doped with a group 13 element like B, Al or Ga which contains only three valence electrons. The place where the fourth valence electron is missing is called electron hole or electron vacancy (Fig. 1.30 c). An electron from a neighbouring atom can come and fill the electron hole, but in doing so it would leave an electron hole at its original position. If it happens, it would appear as if the electron hole has moved in the direction opposite to that of the electron that filled it. Under the influence of electric field, electrons would move towards the positively charged plate through electronic holes, but it would appear as if electron holes are positively charged and are moving towards negatively charged plate. This type of semi conductors are called p-type semiconductors. Fig. 1.30: Creation of n-type and p-type semiconductors by doping groups 13 and 15 elements. Chemistry 26  Applications of n-type and p-type semiconductors Various combinations of n-type and p-type semiconductors are used for making electronic components. Diode is a combination of n-type and p-type semiconductors and is used as a rectifier. Transistors are made by sandwiching a layer of one type of semiconductor between two layers of the other type of semiconductor. npn and pnp type of transistors are used to detect or amplify radio or audio signals. The solar cell is an efficient photo-diode used for conversion of light energy into electrical energy. Germanium and silicon are group 14 elements and therefore, have a characteristic valence of four and form four bonds as in diamond. A large variety of solid state materials have been prepared by combination of groups 13 and 15 or 12 and 16 to simulate average valence of four as in Ge or Si. Typical compounds of groups 13 – 15 are InSb, AlP and GaAs. Gallium arsenide (GaAs) semiconductors have very fast response and have revolutionised the design of semiconductor devices. ZnS, CdS, CdSe and HgTe are examples of groups 12 – 16 compounds. In these compounds, the bonds are not perfectly covalent and the ionic character depends on the electronegativities of the two elements. It is interesting to learn that transition metal oxides show marked differences in electrical properties. TiO, CrO2 and ReO3 behave like metals. Rhenium oxide, ReO3 is like metallic copper in its conductivity and appearance. Certain other oxides like VO, VO2, VO3 and TiO3 show metallic or insulating properties depending on temperature. 1.11 Magnetic Properties Every substance has some magnetic properties associated with it. The origin of these properties lies in the electrons. Each electron in an atom behaves like a tiny magnet. Its magnetic moment originates from two types of motions (i) its orbital motion around the nucleus and (ii) its spin around its own axis (Fig. 1.31). Electron being a charged particle and undergoing these motions can be considered as a small loop of current which possesses a magnetic moment. Thus, each electron has a permanent spin and an orbital magnetic moment associated with it. Magnitude of Fig.1.31: Demonstration of the magnetic moment this magnetic moment is very small and associated with (a) an orbiting electron is measured in the unit called Bohr and (b) a spinning electron. magneton, μB. It is equal to 9.27 × 10 A m. –24 2 On the basis of their magnetic properties, substances can be classified into five categories: (i) paramagnetic (ii) diamagnetic (iii) ferromagnetic (iv) antiferromagnetic and (v) ferrimagnetic. (i) Paramagnetism: Paramagnetic substances are weakly attracted by a magnetic field. They are magnetised in a magnetic field in the same direction. They lose their magnetism in the absence of magnetic field. Paramagnetism is due to presence of one or more unpaired electrons which are attracted by the magnetic field. O2, Cu2+, Fe3+, Cr3+ are some examples of such substances. 27 The Solid State  (ii) Diamagnetism: Diamagnetic substances are weakly repelled by a magnetic field. H2O, NaCl and C6H6 are some examples of such substances. They are weakly magnetised in a magnetic field in opposite direction. Diamagnetism is shown by those substances in which all the electrons are paired and there are no unpaired electrons. Pairing of electrons cancels their magnetic moments and they lose their magnetic character. (iii) Ferromagnetism: A few substances like iron, cobalt, nickel, gadolinium and CrO2 are attracted very strongly by a magnetic field. Such substances are called ferromagnetic substances. Besides strong attractions, these substances can be permanently magnetised. In solid state, the metal ions of ferromagnetic substances are grouped together into small regions called domains. Thus, each domain acts as a tiny magnet. In an unmagnetised piece of a ferromagnetic substance the domains are randomly oriented and their magnetic moments get cancelled. When the substance is placed in a magnetic field all the domains get oriented in the direction of the magnetic field (Fig. 1.32 a) and a strong magnetic effect is produced. This ordering of domains persist even when the magnetic field is removed and the ferromagnetic substance becomes a permanent magnet. (iv) Antiferromagnetism: Substances like MnO showing anti- ferromagnetism have domain structure similar to ferromagnetic substance, but their domains are oppositely oriented and cancel out each other's magnetic moment (Fig. 1.32 b). (v) Ferrimagnetism: Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers (Fig. 1.32 c). They are weakly attracted by magnetic field as compared to ferromagnetic substances. Fe3O4 (magnetite) and ferrites like MgFe2O4 and ZnFe2O4 are examples of such substances. These substances also lose ferrimagnetism on heating and become paramagnetic. Fig 1.32: Schematic alignment of magnetic moments in (a) ferromagnetic (b) antiferromagnetic and (c) ferrimagnetic. Chemistry 28  Intext Questions 1.19 What type of defect can arise when a solid is heated? Which physical property is affected by it and in what way? 1.20 What type of stoichiometric defect is shown by: (i) ZnS (ii) AgBr 1.21 Explain how vacancies are introduced in an ionic solid when a cation of higher valence is added as an impurity in it. 1.22 Ionic solids, which have anionic vacancies due to metal excess defect, develop colour. Explain with the help of a suitable example. 1.23 A group 14 element is to be converted into n-type semiconductor by doping it with a suitable impurity. To which group should this impurity belong? 1.24 What type of substances would make better permanent magnets, ferromagnetic or ferrimagnetic. Justify your answer. Summary Solids have definite mass, volume and shape. This is due to the fixed position of their constituent particles, short distances and strong interactions between them. In amorphous solids, the arrangement of constituent particles has only short range order and consequently they behave like super cooled liquids, do not have sharp melting points and are isotropic in nature. In crystalline solids there is long range order in the arrangement of their constituent particles. They have sharp melting points, are anisotropic in nature and their particles have characteristic shapes. Properties of crystalline solids depend upon the nature of interactions between their constituent particles. On this basis, they can be divided into four categories, namely: molecular, ionic, metallic and covalent solids. They differ widely in their properties. The constituent particles in crystalline solids are arranged in a regular pattern which extends throughout the crystal. This arrangement is often depicted in the form of a three dimensional array of points which is called crystal lattice. Each lattice point gives the location of one particle in space. In all, fourteen different types of lattices are possible which are called Bravais lattices. Each lattice can be generated by repeating its small characteristic portion called unit cell. A unit cell is characterised by its edge lengths and three angles between these edges. Unit cells can be either primitive which have particles only at their corner positions or centred. The centred unit cells have additional particles at their body centre (body- centred), at the centre of each face (face-centred) or at the centre of two opposite faces (end-centred). There are seven types of primitive unit cells. Taking centred unit cells also into account, there are fourteen types of unit cells in all, which result in fourteen Bravais lattices. Close-packing of particles result in two highly efficient lattices, hexagonal close-packed (hcp) and cubic close-packed (ccp). The latter is also called face- centred cubic (fcc) lattice. In both of these packings 74% space is filled. The remaining space is present in the form of two types of voids-octahedral voids and tetrahedral voids. Other types of packing are not close-packings and have less 29 The Solid State  efficient packing of particles. While in body-centred cubic lattice (bcc) 68% space is filled, in simple cubic lattice only 52.4 % space is filled. Solids are not perfect in structure. There are different types of imperfections or defects in them. Point defects and line defects are common types of defects. Point defects are of three types - stoichiometric defects, impurity defects and non-stoichiometric defects. Vacancy defects and interstitial defects are the two basic types of stoichiometric point defects. In ionic solids, these defects are present as Frenkel and Schottky defects. Impurity defects are caused by the presence of an impurity in the crystal. In ionic solids, when the ionic impurity has a different valence than the