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Introduction to Materials 1.1 INTRODUCTION The importance of the study of solid state physics and materials science for engineers needs no emphasis. The growth of science and technology is intimately linked with the availability of newer and better materials. The social scientists even employ the extent of usage of materials as an index to characterise human societies and civilisations. The use of terms such as the stone age, bronze age and iron age used to describe ancient societies illustrates this idea. Every engineer ought to have an intimate knowledge of the materials he uses in his work. The kind of material he deals with depends on his work and specialisation. A civil engineer would be interested in materials that can be used in the construction of a building or a bridge. An architectural engineer would have to know materials with special reference to their sound absorption to design an auditorium with good acoustics. An aerospace engineer would look for an ideal material for designing an aeroplane or a spacecraft. A mechanical engineer would deal with materials that can be used in designing a variety of machines, (both simple and complex). An electrical engineer has to know the electrical properties of materials which would help to design a circuit or a circuit element. Needless to say, the ongoing revolution in electronics, computer science and information technology has been made possible because of the progress in the preparation and processing of semiconducting materials. It is thus essential for an engineer to have a firm grasp of the underlying principles that govern the different properties of various materials. 1.2 ENGINEERING MATERIALS It is conventional to classify the engineering materials into several broad classes. They are metals, semiconductors, polymers, elastomers, ceramics, glasses, liquid crystals, composites and nanomaterials. The members of each class have similar properties, similar processing routes and often similar applications. There could be exceptions to this general categorisation. Metals have relatively high elastic moduli and are highly ductile and malleable. They are very good thermal and electrical conductors. Some of them are superconductors at very low temperatures. They show interesting magnetic properties. They can function at high temperature. Their main disadvantage is their susceptibility to corrosion. They possess shock resistance and are particularly useful for structural and load bearing applications. Pure metals are occasionally used. Usually a combination of metals called alloys serves the purpose better. Metals are opaque to visible light. They can be polished to high lustre. 1 2 APPLIED SOLID STATE PHYSICS Ceramics and glasses, also, have high elastic moduli. But unlike metals they are brittle and do not exhibit ductility or malleability. Their attractive features are their stiffness, hardness and abrasion as well as corrosion resistance. Usually they are insulators or semiconductors. They possess poor thermal conductivity. They can also be used in high temperature environment. A number of ceramic materials exhibit superconductivity, ferroelectricity, piezoelectricity, pyroelectricity and magnetostriction. These properties are useful in many device applications. They have very high melting point. Polymers and elastomers have low elastic moduli. Their elastic moduli are roughly about 50 times less than those of metals. But they can be strong. They are easy to shape and are corrosion resistant. Their main disadvantage is that they cannot be used at high temperatures. In recent years, polymers showing conducting property have been synthesised. Some of the polymers exhibit piezoelectricity, pyroelectricity and ferroelectricity. The subject of organic electronics is an upcoming field. Polymers are made up of long chains of organic molecules. They include rubber, plastics and many types of adhesives. They have low electrical and thermal conductivity. Thermoplastic polymers in which the long molecular chains are not rigidly connected have good formability. Thermosetting polymers are stronger but more brittle because the molecular chains are rigidly linked. A broad comparison of the properties of these classes of materials is shown in Table 1.1. Table 1.1 Comparisons of properties of metals, ceramics and polymers Property Metals Ceramics Polymers Structure Mostly Crystalline Cubic Systems (FCC, BCC, HCP) Complex Crystalline Structure Amorphous and Semicrystalline Bonding Metallic Predominantly Predominantly Ionic and Covalent Covalent, van der Waal and Hydrogen bonds Density Medium to high Medium Low (g/cc) 2–16 2–17 1–2 Low to high High Low Pb: 32°C, Sn: 232°C, 2000 to 4000°C 70 to 200°C Melting point W : 3400°C Specific heat Low High Medium Hardness Medium High Low Machineability Good Poor Good Tensile strength Medium to high Low Low (MPa) 100 to 2500 10 to 400 30 to 120 Compressive strength Medium to high High Low (MPa) Up to 2500 Up to 5000 Up to 350 Young’s modulus Medium to high High Low (GPa) 40–400 150–450 0.001–3.5 Hight temperature Poor Excellent – creep resistance 3 INTRODUCTION TO MATERIALS Toughness Good some good and some poor and some poor Poor Thermal expansion Medium to high Low to medium Very high Thermal conductivity High Medium but often Low decreases rapidly with temperature Thermal shock Good Generally poor – Wear resistance Medium High Low to moderate Electrical properties Conductors Majority of them are Majority of them are insulators insulators Chemical resistance Low to medium Excellent Generally good Oxidation resistance Poor, except for rare Oxides excellent; at high temperatures metals resistance – SiC and Si3N4 are good Optical properties Opaque to visible Some transparent, Some transparent, light Some opaque Some opaque Semiconductors have interesting electrical and optical properties. Semiconductors are a group of materials having electrical conductivities intermediate between metals and insulators. Their conductivities can be varied by orders of magnitude through variation of temperature and doping. Hence, they are used in electronic devices such as transistors, diodes and integrated circuits. They are the basic materials for microelectronic and optoelectronic devices. Silicon, germanium and a number of compounds such as gallium arsenide are semiconductors. Semiconductors are made use of in photodiodes, light emitting diodes and laser diodes which are routinely used in optical communication. Liquid crystals are materials which have properties in between those of crystals and liquids. In liquid crystals the molecules have an orientational order but are devoid of any translational order. This configuration of molecules enables liquid crystals to possess unique optical and electrical properties. These have been exploited in display devices, which are an important component of computer and information technology. Composite materials: There are many situations in engineering where no single material will be suitable to meet a particular design requirement. However, two materials in combination may posses the desired properties and provide a feasible solution. Composite materials are formed from two or more materials. They have properties that are not found in the materials of which they are composed. Concrete, plywood and fibreglass are typical examples of composite materials. With composites, one can produce light weight, very strong, very stiff, high temperature resistant material or produce hard yet shock resistant cutting tools that would otherwise shatter. Advanced aircraft and aerospace vehicles rely heavily on composites such as carbon reinforced polymers and Kevlar reinforced polymers. Nanomaterials: These materials are made up of grains whose dimensions are less than 100 nm. Nanomaterials could be metals, semiconductors, ceramics or polymers. Their properties are considerably different from those of the bulk and might exhibit novel effects. Their properties ought to be understood on the basis of quantum mechanics. 4 APPLIED SOLID STATE PHYSICS Table 1.2 shows the use of various types of engineering materials and their applications. Table 1.2 Important engineering materials and their applications Materials Applications Properties Metals and Alloys Copper Gray cast iron Conducting wire Automobile engine blocks Electrical conductivity Malleable, castable, machineable, vibration damping Significantly strengthened by heat treatment Alloy steels Wrenches, automobile chassis Titanium alloys, steels Aircraft structures, bridges Load bearing Nb3Sn Superconducting magnets Superconductivity Ceramics and Glasses SiO2–Na2O–CaO Window glass Optically transparent, thermally insulating Al2O3, MgO,SiO2 Refractories (heat resistant lining of furnaces) Thermal insulation, low thermal conductivity BaTiO3 Capacitors for microelectronic Ferroelectric transducer PZT(PbZrxTi1–xO3) Transducer Piezoelectric Silica Optical fibers for communication Refractive index, low optical losses Polymers (Thermoplastics) Polyethylene(PE) Food packaging, flexible bottles, toys, tumblers, battery parts, ice trays, film wrapping materials, wire insulation, household items, tubing Easily formed into thin flexible air tight film, chemically resistant, and electrically insulating; tough and relatively low coefficient of friction; low strength and poor resistance to weathering Polystyrene(PS) Video cassette cases, CD jackets, coffee cups, knives, spoons, cafeteria trays, wall tile, battery cases, toys, indoor lighting panels, housing appliances, packing, insulation foams Excellent electrical properties and optical clarity; good thermal and dimensional stability; relatively inexpensive Acrylonitrilebutadiene styrene (ABS) Refrigerator linings, lawn and garden equipment, toys, highway safety devices, textile fibres Outstanding strength and toughness, resistant to heat distortion; good electrical properties; flammable and soluble in some organic solvents 5 INTRODUCTION TO MATERIALS Materials Applications Properties Acrylics (polymethyl methacrylate; PMMA) Lenses, transparent aircraft enclosures, drafting equipment, outdoor signs, auto rear light covers Outstanding light transmission and resistance to weathering; only fair mechanical properties Fluorocarbons (PTFE or TFE) Polytetrafluoroethylene or Teflon Anticorrosive seals, chemical pipes and valves, bearing, anti-adhesive coatings, high temperature electronic parts Chemically inert in almost all environments, excellent electrical insulating properties; good thermal conductivity, low coefficient of friction; may be used up to 260° C (500°F); relatively weak and poor cold-flow properties Polyamides (PA6) (nylons) Bearings, gears, cams, bushings, handles, and jacketing for wires and cables automotive components, ropes Good mechanical strength, abrasion resistance, and toughness; low coefficient of friction; absorbs water and some other liquids Polycarbonates (PC) Safety helmets, lenses, light globes, base for photographic film, housing and electrical appliances, car board lamp mouldings Dimensionally stable; low water absorption; transparent; very good impact resistance and ductility; chemical resistance not outstanding Polypropylene (PP) Sterilizable bottles, packaging film, TV cabinets, luggage, tanks, carpet fibres, ropes and packing, semi-rigid moulded products, car interior components Resistant to heat distortion; excellent electrical properties and fatigue strength; chemically inert; relatively inexpensive; poor resistance to UV light. This is usually copolymerised with PE Poly vinyl chloride (PVC) Floor coverings, pipe, electrical wire insulation, garden hose, phonograph records Good low cost, general purpose materials; ordinarily rigid, but may be made flexible with plasticisers; often copolymerised; susceptible to distortion by heat Polyethylene tetrapthalate (PET or PETE) Magnetic recording tapes, clothing, automotive tire cords, beverage containers, boil in bag containers One of the toughest of plastic films; excellent fatigue and tear strength, and resistance to humidity, acids, greases, oils and solvents Polyoxy methylene (POM) Engineering mouldings Good mechanical properties, high elastic moduli 6 APPLIED SOLID STATE PHYSICS Materials Applications Properties Polymers (Thermosets) Phenolics Motor housings, telephones, auto distributors, electrical fixtures, Adhesives, coating laminates Excellent thermal stability to over 150°C (300°F); may be compounded with a large number of resins, fillers, etc; inexpensive Unsaturated polyesters Helmets, fibreglass boats, autobody components, chairs, fans, Electrical mouldings, decorative laminates, polyester matrix in fibre glass Excellent electrical properties and low cost; can be formulated for room or high temperature use; often fibre reinforced Epoxies Encapsulation of integrated circuits, sinks, adhesives, protective coatings, used with fibreglass laminates Excellent combination of mechanical properties and corrosion resistance; dimensionally stable; good adhesion; relatively inexpensive; good electrical properties Silicone Adhesives, gaskets, sealants Good adhesive properties Urethanes Fibre coatings, foams, insulation Good thermal properties Semiconductors Silicon Transistors and integrated Unique electrical behaviour circuits GaAs, GaP Optoelectronic systems Lasing properties Composites Graphite-epoxy WCCo Aircraft components High strength to weight ratio (Tungsten-carbidecobalt) Cutting tools High hardness, good shock resistance Titanium clad vessel Reactor vessel High strength of steel and anticorrosive properties 1.3 PROPERTIES OF MATERIALS The properties of materials can be broadly classified as physical properties and chemical properties. 1.3.1 Physical Properties Physical properties describe the response of materials to mechanical force, heat, light, sound, electric fields and magnetic fields. Depending on the nature of stimulus, the physical properties are classified as mechanical, thermal, optical, acoustical, electrical and magnetic (Table 1.3). 7 INTRODUCTION TO MATERIALS Table 1.3 Physical properties of materials Property Stimulus Material parameters for characterisation Mechanical properties Mechanical force Young’s modulus, Bulk modulus, Rigidity modulus, Poisson ratio, Hardness, Yield strength, Fracture strength, Fatigue strength, Creep rate Thermal properties Heat Specific heat, Thermal conductivity, Emissivity and absorbptivity (of surfaces), Thermal expansion coefficient Electrical properties Electric field Resistivity, Temperature, Coefficient of resistivity, Dielectric constant, Dielectric loss, Dielectric breakdown Magnetic properties Magnetic field Magnetic susceptibility, Temperature dependence of magnetic susceptibility, Hysteresis loss (magnetic materials) Acoustical properties Sound Sound absorption and sound transmission coefficients Optical properties Light Reflectivity, Transmittivity, Absorptivity, Refractive index 1.3.2 Mechanical Properties These describe the characteristics of the material when subjected to a mechanical force. They relate to the elastic or plastic behaviour of the material. The parameters characterising the mechanical properties are the following: Moduli of elasticity: This is the ratio of stress to strain. The strain could be linear, volume or shear. The corresponding moduli are denoted as Young’s modulus, Bulk modulus and Rigidity modulus. Yield strength: This is the stress at which the material exhibits a specified deviation from the proportionality of stress and strain. Compressive yield strength: The stress in compression at which a material exhibits a specified deviation from the proportionality of stress and strain. Tensile strength: This is the maximum tensile stress the material is capable of withstanding. Compressive strength: This is the maximum compressive stress that a material is capable of withstanding. Poisson ratio: This is the ratio of the lateral strain to longitudinal strain. Hardness: It is the resistance of the material to plastic deformation. The deformation could be due to indentation (i.e., making a mark on the surface), abrasion, scratching and machining. Impact strength: The amount of energy required to fracture a given volume of the material. Endurance limit: The maximum stress below which a material can theoretically endure an infinite number of stress cycles. 8 APPLIED SOLID STATE PHYSICS Creep: This is the time-dependent permanent strain under stress. Creep strength: This is the constant nominal stress that will cause a specified measure of creep in a given time at constant temperature. Fracture: One of the important effects on applying the load to a material beyoud a limit, is fracture. Fracture is concerned with the initiation and propagation of a crack or cracks in the material until the extent of cracking is such that the applied loading can no longer be sustained by the material. Two basic types of fracture are observed in tension, depending on the material, temperature, strain rate etc. These are termed as ‘brittle’ and ‘ductile’. The main features of the former are that there is little or no plastic deformation, the plane of the fracture is normal to the tensile stress and separation of crystal structure occurs. In the ductile type, the fracture is preceded by a considerable amount of plastic deformation and the fracture is by shear or sliding of the crystal structure on microscopic planes at about 45° to the tensile stress. Thermal properties describe the response of materials to heat. Following are the important thermal parameters for the material. Specific heat or heat capacity: If heat Q is supplied to an object of mass m, the temperature change (Tf – Ti) is related to Q by the relation Q = C (Tf – Ti) where C is the heat capacity of the object. The specific heat ‘c’ of the material (the heat capacity per unit mass) is defined as Q = cm (Tf – Ti) The molar specific heat (the heat capacity per mole of a substance) shows an interesting regularity that helps us to understand the mechanisms in heat absorption. The specific heat depends on the conditions of measurement and is a function of temperature. In the case of gases the specific heat at constant volume or constant pressure has to be specified. Heat of transformation: Heat supplied to a material may change the material’s physical state, for example from solid to liquid (melting) or from liquid to gas (vaporisation) or from solid to gas (sublimation). The amount of heat (Q) required per unit mass for a particular phase change is the heat of transformation and is called the latent heat since the phase change occurs at constant temperature. Q = Lm where L is the heat of transformation and m is the mass. The heat of vaporisation Lv is the amount of heat per unit mass that must be supplied to vaporise a liquid or that must be removed to condense a gas into liquid. The heat of fusion Lf is the amount of heat per unit mass that must be supplied to melt a solid or that must be removed from a liquid to freeze it into a solid. The heat of sublimation Ls is the amount of heat that must be supplied to directly convert the solid into its vapour or removed from a vapour to condense it into a solid. Thermal conductivity: The heat transfer through a solid is characterised by the parameter called the thermal conductivity. The rate H at which heat is conducted through a slab whose faces are maintained at Th and Tc is H = Q/t = kA (Th – Tc)/L in which A and L are the face area and length of the slab. The thermal conductivity ‘k’ is defined as the rate of heat flow through a slab of unit cross-section and whose faces are maintained at unit temperature gradient. INTRODUCTION TO MATERIALS 9 Thermal expansion: All objects change size with changes in temperature. The change ∆l in any linear dimension L for a temperature change ∆T is given by ∆l = Lα∆T in which α is the coefficient of linear expansion. In the case of a planar object the change in area ∆A is given by ∆A = Aβ∆T in which β is the coefficient of a real expansion. The change in volume ∆V of a solid or liquid is given by ∆V = Vγ∆T where γ is the coefficient of volume expansion. It can be shown that β = 2α and γ = 3α. Since, strain is defined as the change in dimension to original dimension, α, β and γ can be defined as the linear, areal and volume strain resulting from a unit change in temperature. Thermal emissivity: All objects radiate heat at any temperature. The rate of energy radiated per unit area depends on the nature of the surface. It is given by E = εσT4 where E is the rate of energy radiated per unit area of cross-section, T is the temperature in Kelvin at which the surface is maintained, ‘σ’ is the Stefen-Boltzmann’s constant and ε is the emissitivity. ε = 1 for a perfect blackbody. Electrical properties describe the response of materials to electric fields (both dc and ac): Resistivity: In a conductor the application of an electric field leads to a flow of charge, which constitutes the current. If an application of an electric field E, leads to a current density j then j=σE where σ is called the conductivity. The resistivity ρ is defined as the reciprocal of σ. ρ = 1/σ The temperature variation of resistivity is also an important parameter. In the case of metals and insulators the resistivity increases with temperature while in the case of semiconductors it decreases with temperature. Electric susceptibility: In an insulator the application of an electric field leads to polarisation. Polarisation is the induced electric dipole moment per unit volume. The polarisation can be classified as ionic, electronic, orientational or space charge. Polarisation depends on the nature of the material and the frequency of the electric field. If the application of an electric field E leads to a polarisation P, then P = χel E where χel is called the electric susceptibility. The dielectric constant ε is related to the electric susceptibility χ by the relation ε = 1 + 4πχel Insulators are used as materials for capacitors. The dielectric constant ε is equal to the ratio of the capacitance of the capacitor with the material and without the material i.e., ε = C/C0 where C is the capacitance of the capacitor with the material and C0 is the capacitance of the capacitor without the material. 10 APPLIED SOLID STATE PHYSICS However, no material is a perfect dielectric. Hence, on the application of an electric field a minute current will flow. This is taken care of by treating ε as a complex quantity. i.e., ε = ε 1 + i ε2 where ε2 is a measure of its conductivity. The insulators are also characterised by another parameter called the dielectric strength. This is the electric field at which there is a sudden increase of current in the material. The phenomenon is known as the dielectric breakdown. Magnetic properties describe the response of material to magnetic field. Following are the important material parameters: Magnetic susceptibility: In the case of magnetic materials the application of a magnetic field H, leads to magnetisation M. Magnetisation is defined as the induced magnetic moment per unit volume. Analogous to electrical susceptibility, magnetic susceptibility χm is defined as H = χm M Magnetic permeability µ is related to magnetic susceptibility by the equation µ = 1 + 4πχm Magnetic materials are classified as diamagnetic, paramagnetic and ferromagnetic depending on whether χ is < 0, χ is > 1 or χ is >>> 1. The ferromagnetic materials exhibit magnetisation even in the absence of magnetic field and exhibit hysteresis loop. On this account the ferromagnetic materials are used as memory devices. The material parameters for ferromagnetic materials include remnant magnetisation, hysteresis loss and coercive field strength. Remnant magnetisation is the magnetisation present in the material when the applied magnetic field is removed. Hysteresis loss is the energy dissipated in moving the domain boundaries during a single magnetisation cycle. Coercive field strength is the magnetic field needed to reverse the magnetisation in the material. The ferromagnetic materials are also characterised by Eddy current loss. This is the power loss in ferromagnetic materials in alternating fields due to induced surface currents in the materials. Optical properties describe the response of materials to light. Optical properties are described by the following parameters. Reflectivity (r): This is a surface property and is defined as the ratio of the intensity of reflected light to that of incident light. Transmittivity (t): This is defined as the ratio of the intensity of light transmitted through the material to that of the incident light. Absorptivity (a): This is defined as the ratio of the intensity of light absorbed by the material to that of incident light. Refractive index (n): The refractive index of a material is a complex quantity (n1 + in2). n1 = c/ν where c is the velocity of light in vacuum and ν is the velocity of light in the material. The imaginary part n2 characterises the optical absorption in the material. The optical properties (r, t, a and n) are functions of wavelength and is usually specified from infrared to the ultraviolet region of the electromagnetic spectrum. Acoustical properties describe the response of the material to sound waves. The acoustical properties of materials are of interest especially to architectural engineers involved in the design of auditoria or noise control. The material is used to maximise sound absorption by promoting frictional processes. The most commonly used materials are porous, such as mineral fibre materials or certain types of open-cell foam polymer materials. The material