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Unit 4 Solid State

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Unit 4 Solid State UNIT 4 SOLID STATE Structure Introduction Objectives What are solids? Classification of Solids X-Ray Diffraction of Solids Principles of Dimaction Bragg Law and Bragg Equation Crystal Lattices Crystal systems and Bravais Lattices Cubic Unit Cells Calculation of Density of Solids Close-Packed Structures Voids Struch11.e~of Ionlc Solids Electrical Properties of Solids Metallic Conduction in Solids: Band Theory Ionic Conductioll in Solids Magnetic Properties of Solids Temperature Dependence of Magnetic Properties Summary Ternenal Questions 4.1 INTRODUCTION Matter can exist in seven different states of varying extents of compactness. Of these, we nom~allycome across three states viz., solids, liquids and gases. The other four states are found in the cosmic bodies. In this unit we are going to learn about the solid state, a commonly encountered state of matter characterised by order and regularity. The last twenty years or so have seen a change in the perception of solid state chemistry, in particular the significance of understanding the relationship between chemical structure and physical properties. This has led to the development of newer materials with interesting properties ranging froin semiconductors to superconductors, which find divcrse applications. Study of solids is so very important that material science is one of the most sought after areas of research now a days. However, we are going to take up solid state at a very elementary level. You would learn about the basic structure of the solids, its detem~inationand some of the properties of solids. In the next unit you would learn about basic chemical thermodynamics. Objectives After studying this unit, you should be able to: classify solids on the basis ofthe nature of bonding between the species constituting them, define crystalline solids and differentiate them from amorphous substances, define crystal lattice, and primitive and non prirnitivc unit cells describe the seven crystal systems and the fourteen Bravais lattices, state the principle of X-ray diffraction method for determining the structures of the solids, derive and use Bragg equation, describe close packed structures of metallic solids, discuss the structures of common ionic solids of MX,MX2 and M2X type and exnlain the electrical and mametic properties of solids. Structure 4.2 WHAT ARE SOLIDS? A solid is an almost incompressible state of matter having a well defined rigid structure. It is composed of structural units - atoms, molecules or ions which are in close contact due to strong forces of attraction between one another. These forces of attraction are of different types and are responsible for the differences in the properties of the solids. The force of attraction may be of electrical nature as in case of sodium chloride in which the sodium ions and chloride ions are attracted to each other or these may be of There are four different intermolecular type which hold different molecules together e.g., in ice, water types of solids molecules are held together by intermolecular hydrogen bonding. Other possibilities are ionic, of strong chemical bonds between the constituent atoms as in case of diamond or the molecular, . covalent and metallic bonding in which a large number of positive cores of the atoms are held metallic. together by a sea of electrons. In fact, the solids are sometimes classified on the basis of the forces of interaction or attraction between the structural units. 4.2.1 Classification of Solids There is a vast variety of solids and these can be classified on the basis of the nature of forces of attraction between the structural units constituting the solids as discussed above. Thus there are four different types of solids- ionic, molecular, covalent and metallic. ' Fig. 4.1: Ionic (NaCl), covalent (diamond), molecular (ice) and metallic (copper) solids. The characteristics and the properties of the different types of solids are compiled in Table 4.1. Table 4.1: Characteristics and properties of different types of solids. Constituent Forces of Melting Electrical Solid Species interaction Point conductivity between the constituent species Weak, dipolar or dispersion type - Metallic Hard and Aloms Electron Variable Conducting malleable-- delocalisation - Coulombic Ionic DoairHard and Ions 1 1 1 conducting I rhigh conducting Amorphous and Crystalline Solids Solid State There is another way to classify solids, let us perfom1 an activity to understand this. Take a few common solids like, common salt, sugar, benzoic acid and a piece of glass rod. Observe these solids closely -you may usc a hand lens to observe small particles of salt, sugar and benzoic acid. What do you observe? Thc salt, sugar and benzoic acid exhibit a number of definite smooth surfaces at definite anglcs to each other on the other hand the glass does not have these. Now try to melt these solids (othcr than NaCl, it has very high melting point) on a flame. Sugar and benzoic acid can be melted in a glass capillary while the glass rod can be put directly to the flame. You nlay observe that all thc solids other than glass undergo a sharp change from solid to liquid state at a fixed temperature while glass gradually softens over a range of temperature. The solids having smooth surfaces at definite angles to each other and showing a sharp change from solid to liquid state are called as crystalline solids while solids showing thc ' behaviour displayed by glass arc called as amorphous solids. Another point of differentiation betwecn the amorphous and crystalline solids is that while amorphous solids arc isotropic in naturc is., these exhibit same value of any property in all directions, the crystalline solids arc ai~isotropici.e., thc value ofphysical properties are different in different directions. We will, however, focus our attention on crystalline r solids only. I The regularity and perfection of a crystalline solid suggests of an ordcred internal structure for them. Actually the form of crystal depends on the way it is grown. A slow cooling of a slightly supersaturated solution generally proceeds in such a way that it Thesc interfacial angles are 1 mcasured by an instrument allows all the naturally occurring faces of the crystals to grow and develop highly called as contact symnletrical crystals. On the other hand a sudden cooling of a molten compound or goniometer. i highly supersaturated solution gives imperfect crystals. The quality of the crystal may vary but the anglcs between the perpendiculars to different faces called interfacial I angles are characteristic and distinct for a substance. This fact is known as Huay's law of constancy of interfacial angles. The highly ordercd internal structure of a crystalline solid is represented in terms of a three dimensional structure called lattice. You will lcam about the meaning of lattice and different types of crystal lattices and their representations in section 4.4. 4.3 X-RAY DIFFRACTION OF SOLIDS - In 1912 Laue suggested that the wavelength of X-rays may be of the order of the interatomic distances between atoms in a crystal and the crystal may serve as a diffraction grating for the X-rays. Tt was experimentally found to be so a little later. W.L. Bragg (1913) used monochromatic radiation for the scattcring experiment and in the process determined the structures of some common ionic compounds and provided a fundamental equation named after him. In the course of interaction with the crystal the X-rays are scattered by the electron cloud of an atom. Rragg suggested that the crystal contains a large number of stacks of planes from which the X-rays are reflected. Further, the angle of reflection from a given stack of planes depends on the wavelength of the X-rays and the interplaner distance. Let us learn about the meaning of diffraction and derive an cxprcssion for the diffraction of X-rays from a stack of parallel planes. 4.3.1 Principle of Diffraction The phenomenon of diffraction refers to the interference of waves due to the presence of an obstacle in their path. This can be exemplified by the bending of light round the edges of an object. Consider a beam of light passing through two slits (S, and S?),cut near to each other on a screen and falling on a second screen placed beyond the slits (Fig. 4.2). A series of dark and bright bands are observed on the screen, which are tn fhr rnnotnlrtive and destructive interference of the two beams passing through Structure In phase combination Source of light' combination Fig. 4.2: In phase and out of phase combination of the light waves originating from two point sources leads to bright ( for in-phase) and dark spots ( for out of phase) on the screen. The amplitude is directly When the waves are in phase, the intensity is increased, this is known as constructive related to the intensity of interference; Fig. 4.3(a). When they are out of phase (known as destructive the beam. interference), the intensity is decreased, Fig. 4.3(b). If however, when the two waves are completely out of phase, these cancel each other, Fig. 4.3(c). Fig. 4.3: Interference of two waves a) completely in phase b) partly out of phase and c) completely out of phase. For diffraction to occur the dimensions of the diffracting object should be comparable to the wavelength of the light. Whether the beams are in-phase or out-of-phase will depend on the path difference between the two rays. 4.3.2 Bragg Law and Bragg Equation If the path difference between the two rays is an integral multiple (n = 1,2,3 ...) of the wavelength of X-rays, then the two rays will be in-phase and the diffraction patterns will be bright (i.e.
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