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Chapter-10:
Phase Transformations in Metals
10.1 Introduction The goal is to obtain specific microstructures that will improve the mechanical properties of a metal, in addition to grain-size refinement, solid-solution strengthening, and strain-hardening.
10.2 Basic Concepts
Phase transformations that involve a change in the microstructure can occur through: Diffusion Maintaining the type and number of phases (e.g., solidification of a pure metal, allotropic transformation, recrystallization, grain growth. Alteration of phase composition (e.g., eutectoid reactions, see 10.5) Diffusionless Production of metastable phases (e.g., martensitic transformation, see 10.5)
10.3 The Kinetics of Solid-State Reactions
Change in composition implies atomic rearrangement, which requires diffusion. Atoms are displaced by random walk. The displacement of a given atom, d, is not linear in time t (as would be for a straight trajectory) but is proportional to the square root of time, due to the tortuous path: d = c(Dt) 1/2 where c is a constant and D the diffusion constant. This time-dependence of the rate at which the reaction (phase transformation) occurs is what is meant by the term reaction kinetics. D is called a constant because it does not depend on time, but it depends on temperature as we have seen in Ch. 5. Diffusion occurs faster at high temperatures. Phase transformation requires two processes: nucleation and growth. Nucleation involves the formation of very small particles, or nuclei (e.g., grain boundaries, defects). This is similar to rain happening when water molecules condensed around dust particles. During growth, the nuclei grow in size at the expense of the surrounding material. The kinetic behavior often has the S-shape form of Fig. 10.1, when plotting percent of material transformed vs. the logarithm of time. The nucleation phase is seen as an incubation period, where nothing seems to happen. Usually the transformation rate has the form r = A e-Q/RT (similar to the temperature dependence of the diffusion constant), in which case it is said to be thermally activated.
10.4 Multiphase Transformations
To describe phase transformations that occur during cooling, equilibrium phase diagrams are inadequate if the transformation rate is slow compared to the cooling rate. This is usually the case in practice, so that equilibrium microstructures are seldom obtained. This means that the transformations are delayed (e.g., case of supercooling), and metastable states are formed. We then need to know the effect of time on phase transformations. Microstructural and Property Changes in Fe-C Alloys
10.5 Isothermal Transformation Diagrams
We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite (g- phase) to pearlite, that contains ferrite (a) plus cementite (Fe3C or iron carbide). When cooling proceeds below the eutectoid temperature (727 oC) nucleation of pearlite starts. The S-shaped curves (fraction of pearlite vs. log. time, fig. 10.3) are displaced to longer times at higher temperatures showing that the transformation is dominated by nucleation (the nucleation period is longer at higher temperatures) and not by diffusion (which occurs faster at higher temperatures). The family of S-shaped curves at different temperatures can be used to construct the TTT (Time-Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to apply, one needs to cool the material quickly to a given temperature To before the transformation occurs, and keep it at that temperature over time. The horizontal line that indicates constant temperature To intercepts the TTT curves on the left (beginning of the transformation) and the right (end of the transformation); thus one can read from the diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4 also indicates that the transformation occurs sooner at low temperatures, which is an indication that it is controlled by the rate of nucleation. At low temperatures, nucleation occurs fast and grain growth is reduced (since it occurs by diffusion, which is hindered at low temperatures). This reduced grain growth leads to fine-grained microstructure (fine pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading to coarse pearlite. At lower temperatures nucleation starts to become slower, and a new phase is formed, bainite. Since diffusion is low at low temperatures, this phase has a very fine (microscopic) microstructure. Spheroidite is a coarse phase that forms at temperatures close to the eutectoid temperature. The relatively high temperatures caused a slow nucleation but enhances the growth of the nuclei leading to large grains. A very important structure is martensite, which forms when cooling austenite very fast (quenching) to below a maximum temperature that is required for the transformation. It forms nearly instantaneously when the required low temperature is reached; since no thermal activation is needed, this is called an athermal transformation. Martensite is a different phase, a body-centered tetragonal (BCT) structure with interstitial C atoms. Martensite is metastable and decomposes into ferrite and pearlite but this is extremely slow (and not noticeable) at room temperature. In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys, the analysis is the same, but the proeutectoid phase that forms before cooling through the eutectoid temperature is also part of the final microstructure.

10.6 Continuous Cooling Transformation Diagrams - not covered

10.7 Mechanical Behavior of Fe-C Alloys The strength and hardness of the different microstructures is inversely related to the size of the microstructures. Thus, spheroidite is softest, fine pearlite is stronger than coarse pearlite, bainite is stronger than pearlite and martensite is the strongest of all. The stronger and harder the phase the more brittle it becomes.
10.8 Tempered Martensite
Martensite is so brittle that it needs to be modified in many practical cases. This is done by heating it to 250-650 oC for some time (tempering) which produces tempered martensite, an extremely fine-grained and well dispersed cementite grains in a ferrite matrix.

Chapter 11.

Thermal Processing of Metal Alloys

Annealing Processes
11.1 Introduction
Annealing is a heat treatment where the material is taken to a high temperature, kept there for some time and then cooled. High temperatures allow diffusion processes to occur fast. The time at the high temperature (soaking time) is long enough to allow the desired transformation to occur. Cooling is done slowly to avoid the distortion (warping) of the metal piece, or even cracking, caused by stresses induced by differential contraction due to thermal inhomogeneities. Benefits of annealing are: relieve stresses increase softness, ductility and toughness produce a specific microstructure
11.2 Process Annealing
Deforming a piece that has been strengthened by cold working requires a lot of energy. Reverting the effect of cold work by process annealing eases further deformation. Heating allows recovery and recrystallization but is usually limited to avoid excessive grain growth and oxidation.
11.3 Stress Relief
Stresses resulting from machining operations of non-uniform cooling can be eliminated by stress relief annealing at moderately low temperatures, such that the effect of cold working and other heat treatments is maintained.
11.4 Annealing of Ferrous Alloys
Normalizing (or austenitizing) consists in taking the Fe-C alloy to the austenitic phase which makes the grain size more uniform, followed by cooling in air. Full anneal involves taking hypoeutectoid alloys to the austenite phase and hypereutectoid alloys over the eutectoid temperature (Fig. 11.1) to soften pieces which have been hardened by plastic deformation, and which need to be machined. Spheroidizing consists in prolongued heating just below the eutectoid temperature, which results in the soft spheroidite structure discussed in Sect. 10.5. This achieves maximum softness that minimizes the energy needed in subsequent forming operations.
Heat Treatment of Steels 1.5 Hardenability
To achieve a full conversion of austenite into hard martensite, cooling needs to be fast enough to avoid partial conversion into perlite or bainite. If the piece is thick, the interior may cool too slowly so that full martensitic conversion is not achieved. Thus, the martensitic content, and the hardness, will drop from a high value at the surface to a lower value in the interior of the piece. Hardenability is the ability of the material to be hardened by forming martensite. Hardenability is measured by the Jominy end-quench test (Fig. 11.2). Hardenability is then given as the dependence of hardness on distance from the quenched end. High hardenability means that the hardness curve is relatively flat.
11.6 Influence of Quenching Medium, Specimen Size, and Geometry
The cooling rate depends on the cooling medium. Cooling is fastest using water, then oil, and then air. Fast cooling brings the danger of warping and formation of cracks, since it is usually accompanied by large thermal gradients. The shape and size of the piece, together with the heat capacity and heat conductivity are important in determining the cooling rate for different parts of the metal piece. Heat capacity is the energy content of a heated mass, which needs to be removed for cooling. Heat conductivity measures how fast this energy is transported to the colder regions of the piece.
Precipitation Hardening Hardening can be enhanced by extremely small precipitates that hinder dislocation motion. The precipitates form when the solubility limit is exceeded. Precipitation hardening is also called age hardening because it involves the hardening of the material over a prolonged time.
11.7 Heat Treatments
Precipitation hardening is achieved by:
a) solution heat treatment where all the solute atoms are dissolved to form a single-phase solution. b) rapid cooling across the solvus line to exceed the solubility limit. This leads to a supersaturated solid solution that remains stable (metastable) due to the low temperatures, which prevent diffusion. c) precipitation heat treatment where the supersaturated solution is heated to an intermediate temperature to induce precipitation and kept there for some time (aging).
If the process is continued for a very long time, eventually the hardness decreases. This is called overaging. The requirements for precipitation hardening are: appreciable maximum solubility solubility curve that falls fast with temperature composition of the alloy that is less than the maximum solubility
11.8 Mechanism of Hardening
Strengthening involves the formation of a large number of microscopic nuclei, called zones. It is accelerated at high temperatures. Hardening occurs because the deformation of the lattice around the precipitates hinder slip. Aging that occurs at room temperature is called natural aging, to distinguish from the artificial aging caused by premeditated heating.
11.9 Miscellaneous Considerations
Since forming, machining, etc. uses more energy when the material is hard, the steps in the processing of alloys are usually: solution heat treat and quench do needed cold working before hardening do precipitation hardening Exposure of precipitation-hardened alloys to high temperatures may lead to loss of strength by overaging
Chapter 12.
Ceramics - Structures and Properties
12.1 Introduction
Ceramics are inorganic and non-metallic materials that are commonly electrical and thermal insulators, brittle and composed of more than one element (e.g., two in Al2O3) Ceramic Structures
12.2 Crystal Structures
Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on the particular ceramics. The ionic character is given by the difference of electronegativity between the cations (+) and anions (-). Covalent bonds involve sharing of valence electrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths (first two columns of the periodic table) and oxygen or halogens as anions. The building criteria for the crystal structure are two: maintain neutrality charge balance dictates chemical formula achieve closest packing the condition for minimum energy implies maximum attraction and minimum repulsion. This leads to contact, configurations where anions have the highest number of cation neighbors and viceversa. The parameter that is important in determining contact is the ratio of cation to anion radii, rC/rA. Table 13.2 gives the coordination number and geometry as a function of rC/rA. For example, in the NaCl structure (Fig. 13.2), rC = rNa = 0.102 nm, rA =rCl.= 0.181 nm, so rC/rA.= 0.56. From table 13.2 this implies coordination number = 6, as observed for this rock-salt structure. Other structures were shown in class, but will not be included in the test.
12.3 Silicate Ceramics
Oxygen and Silicon are the most abundant elements in Earth’s crust. Their combination (silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si4+ as the cation and O2- as the anion. rSi = 0.04 nm, rO.= 0.14 nm, so rC/rA = 0.286. From table 13.2 this implies coordination number = 4, that is tetrahedral coordination (Fig. 13.9). The tetrahedron is charged: Si4+ + 4 O2- Þ (Si O4)4-. Silicates differ on how the tetrahedra are arranged. In silica, (SiO2), every oxygen atom is shared by adjacent tetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass. Soda glasses melt at lower temperature than amorphous SiO2 because the addition of Na2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to form glass to make, for instance, bottles.

12.4 Carbon

Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a type of ceramic. Diamond has very interesting and even unusual properties: diamond-cubic structure (like Si, Ge) covalent C-C bonds highest hardness of any material known very high thermal conductivity (unlike ceramics) transparent in the visible and infrared, with high index of refraction semiconductor (can be doped to make electronic devices) metastable (transforms to carbon when heated) Synthetic diamonds are made by application of high temperatures and pressures or by chemical vapor deposition. Future applications of this latter, cheaper production method include hard coatings for metal tools, ultra-low friction coatings for space applications, and microelectronics. Graphite has a layered structure with very strong hexagonal bonding within the planar layers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding between layers using the fourth electron. This leads to easy interplanar cleavage and applications as a lubricant and for writing (pencils). Graphite is a good electrical conductor and chemically stable even at high temperatures. Applications include furnaces, rocket nozzles, electrodes in batteries. A recently (1985) discovered formed of carbon is the C60 molecule, also known as fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesic structure that C60 resembles.) Fullerenes and related structures like bucky-onions amd nanotubes are exceptionally strong. Future applications are as a structural material and possibly in microelectronics, due to the unusual properties that result when fullerenes are doped with other atoms.

12.5 Imperfections in Ceramics
Imperfections include point defects and impurities. Their formation is strongly affected by the condition of charge neutrality (creation of unbalanced charges requires the expenditure of a large amount of energy. Non-stoichiometry refers to a change in composition so that the elements in the ceramic are not in the proportion appropriate for the compound (condition known as stoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges (Fig. 13.1). Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a vacancy- interstitial pair of cations (placing large anions in an interstitial position requires a lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation and anion vacancies. Introduction of impurity atoms in the lattice is likely in conditions where the charge is maintained. This is the case of electronegative impurities that substitute a lattice anions or electropositive substitutional impurities. This is more likely for similar ionic radii since this minimizes the energy required for lattice distortion. Defects will appear if the charge of the impurities is not balanced. 12.6 Ceramic Phase Diagrams (not covered)

12.7 Brittle Fracture of Ceramics
The brittle fracture of ceramics limits applications. It occurs due to the unavoidable presence of microscopic flaws (micro-cracks, internal pores, and atmospheric contaminants) that result during cooling from the melt. The flaws need to crack formation, and crack propagation (perpendicular to the applied stress) is usually transgranular, along cleavage planes. The flaws cannot be closely controlled in manufacturing; this leads to a large variability (scatter) in the fracture strength of ceramic materials. The compressive strength is typically ten times the tensile strength. This makes ceramics good structural materials under compression (e.g., bricks in houses, stone blocks in the pyramids), but not in conditions of tensile stress, such as under flexure. Plastic deformation in crystalline ceramics is by slip, which is difficult due to the structure and the strong local (electrostatic) potentials. There is very little plastic deformation before fracture. Non-crystalline ceramics, like common glass deform by viscous flow (like very high-density liquids). Viscosity decreases strongly with increases temperature.

Chapter 13.

Ceramics - Applications and Processing

13.1 Introduction
Ceramics properties that are different from those of metals lead to different uses. In structures, designs must be done for compressive loads. The transparency to light of many ceramics leads to optical uses, like in windows, photographic cameras, telescopes and microscopes. Good thermal insulation leads to use in ovens, the exterior tiles of the Shuttle orbiter, etc. Good electrical isolation are used to support conductors in electrical and electronic applications. The good chemical inertness shows in the stability of the structures thousands of years old.

13.2 Glass Properties
A special characteristic of glasses is that solidification is gradual, through a viscous stage, without a clear melting temperature. The specific volume does not have an abrupt transition at a temperature but rather shows a change in slope at the glass-transition temperature (Fig. 14.3). The melting point, working point, softening point and annealing point are defined in terms of viscosity, rather than temperature (Fig. 14.4), and depend on glass composition..

13.4 Heat Treating Glasses Similar to the case of metals, annealing is used at elevated temperatures is used to remove stresses, like those caused by inhomogeneous temperatures during cooling. Strengthening by glass tempering is done by heating the glass above the glass transition temperature but below the softening point and then quenched in an air jet or oil bath. The interior, which cools later than the outside, tries to contract while in a plastic state after the exterior has become rigid. This causes residual compressive stresses on the surface and tensile stresses inside. To fracture, a crack has first to overcome the residual compressive stress, making tempered glass less susceptible to fracture. This improvement leads to use in automobile windshields, glass doors, eyeglass lenses, etc

Chapter 14.

Polymer Structures

14.1 Introduction

Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk, proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil. Their use has grown exponentially, especially after WW2. The key factor is the very low production cost and useful properties (e.g., combination of transparency and flexibility, long elongation).

14.2 Hydrocarbon Molecules

Most polymers are organic, and formed from hydrocarbon molecules. These molecules can have single, double, or triple carbon bonds. A saturated hydrocarbon is one where all bonds are single, that is, the number of atoms is maximum (or saturated). Among this type are the paraffin compounds, CnH2n+2 (Table 15.1). In contrast, non-saturated hydrocarbons contain some double and triple bonds. Isomers are molecules that contain the same molecules but in a different arrangement. An example is butane and isobutane.

14.3 Polymer Molecules

Polymer molecules are huge, macromolecules that have internal covalent bonds. For most polymers, these molecules form very long chains. The backbone is a string of carbon atoms, often single bonded. Polymers are composed of basic structures called mer units. A molecule with just one mer is a monomer.

14.4 The Chemistry of Polymer Molecules

Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE or Teflon), polypropylene, nylon and polystyrene. Chains are represented straight but in practice they have a three-dimensional, zig-zag structure (Fig. 15.1b). When all the mers are the same, the molecule is called a homopolymer. When there is more than one type of mer present, the molecule is a copolymer.

14.5 Molecular Weight

The mass of a polymer is not fixed, but is distributed around a mean value, since polymer molecules have different lengths. The average molecular weight can be obtained by averaging the masses with the fraction of times they appear (number-average) or with the mass fraction of the molecules (called, improperly, a weight fraction). The degree of polymerization is the average number of mer units, and is obtained by dividing the average mass of the polymer by the mass of a mer unit. Polymers of low mass are liquid or gases, those of very high mass (called high-polymers, are solid). Waxes, paraffins and resins have intermediate masses.

14.6 Molecular Shape
Polymers are usually not linear; bending and rotations can occur around single C-C bonds (double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead to entanglement, like in the spaghetti structure shown in Fig. 15.6.

14.7 Molecular Structure

Typical structures are (Fig. 15.7): linear (end-to-end, flexible, like PVC, nylon) branched cross-linked (due to radiation, vulcanization, etc.) network (similar to highly cross-linked structures). 14.8 Molecular Configurations The regularity and symmetry of the side-groups can affect strongly the properties of polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like H, O, methyl, etc. If the radicals are linked in the same order, the configuration is called isostatic In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides in the chain. In the atactic configuration, the radical groups are positioned at random.

14.9 Copolymers

Copolymers, polymers with at least two different types of mers can differ in the way the mers are arranged. Fig. 15.9 shows different arrangements: random, alternating, block, and graft.

14.10 Polymer Crystallinity Crystallinity in polymers is more complex than in metals (fig. 15.10). Polymer molecules are often partially crystalline (semicrystalline), with crystalline regions dispersed within amorphous material. . Chain disorder or misalignment, which is common, leads to amorphous material since twisting, kinking and coiling prevent strict ordering required in the crystalline state. Thus, linear polymers with small side groups, which are not too long form crystalline regions easier than branched, network, atactic polymers, random copolymers, or polymers with bulky side groups. Crystalline polymers are denser than amorphous polymers, so the degree of crystallinity can be obtained from the measurement of density.

14.11 Polymer Crystals Different models have been proposed to describe the arrangement of molecules in semicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) are embedded in an amorphous matrix (Fig.15.11). Polymer single crystals grown are shaped in regular platelets (lamellae) (Fig. 15.12). Spherulites (Fig. 15.4) are chain-folded crystallites in an amorphous matrix that grow radially in spherical shape “grains”.

Chapter 15.

Polymers. Characteristics, Applications and Processing

15.1 Introduction

15.2 Stress-Strain Behavior

The description of stress-strain behavior is similar to that of metals, but a very important consideration for polymers is that the mechanical properties depend on the strain rate, temperature, and environmental conditions. The stress-strain behavior can be brittle, plastic and highly elastic (elastomeric or rubber-like), see Fig. 16. 1. Tensile modulus (modulus) and tensile strengths are orders of magnitude smaller than those of metals, but elongation can be up to 1000 % in some cases. The tensile strength is defined at the fracture point (Fig. 16.2) and can be lower than the yield strength. Mechanical properties change dramatically with temperature, going from glass-like brittle behavior at low temperatures (like in the liquid-nitrogen demonstration) to a rubber-like behavior at high temperatures (Fig. 16.3). In general, decreasing the strain rate has the same influence on the strain-strength characteristics as increasing the temperature: the material becomes softer and more ductile.

15.3 Deformation of Semicrystalline Polymers
Many semicrystalline polymers have the spherulitic structure and deform in the following steps (Fig. 16.4): elongation of amorphous tie chains tilting of lamellar chain folds towards the tensile direction separation of crystalline block segments orientation of segments and tie chains in the tensile direction The macroscopic deformation involves an upper and lower yield point and necking. Unlike the case of metals, the neck gets stronger since the deformation aligns the chains so increasing the tensile stress leads to the growth of the neck. (Fig. 16.5).

15.4 Factors that Influence the Mechanical Properties of Polymers
The tensile modulus decreases with increasing temperature or diminishing strain rate. Obstacles to the steps mentioned in 16.4 strengthen the polymer. Examples are cross-linking (aligned chains have more van der Waals inter-chain bonds) and a large mass (longer molecules have more inter-chain bonds). Crystallinity increases strength as the secondary bonding is enhanced when the molecular chains are closely packed and parallel. Pre-deformation by drawing, analogous to strain hardening in metals, increases strength by orienting the molecular chains. For undrawn polymers, heating increases the tensile modulus and yield strength, and reduces the ductility - opposite of what happens in metals.

15.5 Crystallization, Melting, and Glass Transition Phenomena
Crystallization rates are governed by the same type of S-curves we saw in the case of metals (Fig. 16.7). Nucleation becomes slower at higher temperatures. The melting behavior of semicrystalline polymers is intermediate between that of crystalline materials (sharp density change at a melting temperature) and that of a pure amorphous material (slight change in slope of density at the glass-transition temperature). The glass transition temperature is between 0.5 and 0.8 of the melting temperature. The melting temperature increases with the rate of heating, thickness of the lamellae, and depends on the temperature at which the polymer was crystallized. Melting involves breaking of the inter-chain bonds, so the glass and melting temperatures depend on: chain stiffness (e.g., single vs. double bonds) size, shape of side groups size of molecule side branches, defects cross-linking Rigid chains have higher melting temperatures.

15.6 Thermoplastic and Thermosetting Polymers
Thermoplastic polymers (thermoplasts) soften reversibly when heated (harden when cooled back) Thermosetting polymers (thermosets) harden permanently when heated, as cross-linking hinder bending and rotations. Thermosets are harder, more dimensionally stable, and more brittle than thermoplasts.

15.7 Viscoelasticity
At low temperatures, amorphous polymers deform elastically, like glass, at small elongation. At high temperatures the behavior is viscous, like liquids. At intermediate temperatures, the behavior, like a rubbery solid, is termed viscoelastic. Viscoelasticity is characterized by the viscoelastic relaxation modulus Er = s(t)/e0. If the material is strained to a value e0.it is found that the stress needs to be reduced with time to maintain this constant value of strain (see figs. 16.11 and 16.12). In viscoelastic creep, the stress is kept constant at s0 and the change of deformation with time e(t) is measured. The time-dependent creep modulus is given by Ec = s0/e(t).

15.8 Deformation and Elastomers
Elastomers can be deformed to very large strains and the spring back elastically to the original length, a behavior first observed in natural rubber. Elastic elongation is due to uncoiling, untwisting and straightening of chains in the stress direction. To be elastomeric, the polymer needs to meet several criteria: must not crystallize easily have relatively free chain rotations delayed plastic deformation by cross-linking (achieved by vulcanization). be above the glass transition temperature

15.9 Fracture of Polymers
As other mechanical properties, the fracture strength of polymers is much lower than that of metals. Fracture also starts with cracks at flaws, scratches, etc. Fracture involves breaking of covalent bonds in the chains. Thermoplasts can have both brittle and ductile fracture behaviors. Glassy thermosets have brittle fracture at low temperatures and ductile fracture at high temperatures. Glassy thremoplasts often suffer grazing before brittle fracture. Crazes are associated with regions of highly localized yielding which leads to the formation of interconnected microvoids (Fig. 16.15). Crazing absorbs energy thus increasing the fracture strength of the polymer.

15.10 Miscellaneous Characteristics
Polymers are brittle at low temperatures and have low impact strengths (Izod or Charpy tests), and a brittle to ductile transition over a narrow temperature range. Fatigue is similar to the case of metals but at reduced loads and is more sensitive to frequency due to heating which leads to softening.

15.11 Polymerization
Polymerization is the synthesis of high polymers from raw materials like oil or coal. It may occur by: addition (chain-reaction) polymerization, where monomer units are attached one at a time condensation polymerization, by stepwise intermolecular chemical reactions that produce the mer units.

15.12 Elastomers

In vulcanization, crosslinking of the elastomeric polymer is achieved by an irreversible chemical reaction usually at high temperatures (hence ‘vulcan’), and usually involving the addition of sulfur compounds. The S atoms are the ones that form the bridge cross-links. Elastomers are thermosetting due to the cross-linking. Rubbers become harder and extend less with increasing sulfur content. For automobile applications, synthetic rubbers are strengthened by adding carbon black. In silicone rubbers, the backbone C atoms are replaced by a chain of alternating silicon and oxygen atoms. These elastomers are also cross-linked and are stable to higher temperatures than C-based elastomers.

Chapter 16.

Composites

16.1 Introduction

The idea is that by combining two or more distinct materials one can engineer a new material with the desired combination of properties (e.g., light, strong, corrosion resistant). The idea that a better combination of properties can be achieved is called the principle of combined action. New - High-tech materials, engineered to specific applications Old - brick-straw composites, paper, known for > 5000 years. A type of composite that has been discussed is perlitic steel, which combines hard, brittle cementite with soft, ductile ferrite to get a superior material. Natural composites: wood (polymer-polymer), bones (polymer-ceramics). Usual composites have just two phases: matrix (continuous) dispersed phase (particulates, fibers) Properties of composites depend on properties of phases geometry of dispersed phase (particle size, distribution, orientation) amount of phase Classification of composites: three main categories: particle-reinforced (large-particle and dispersion-strengthened) fiber-reinforced (continuous (aligned) and short fibers (aligned or random) structural (laminates and sandwich panels) Particle-reinforced composites These are the cheapest and most widely used. They fall in two categories depending on the size of the particles: large-particle composites, which act by restraining the movement of the matrix, if well bonded. dispersion-strengthened composites, containing 10-100 nm particles, similar to what was discussed under precipitation hardening. The matrix bears the major portion of the applied load and the small particles hinder dislocation motion, limiting plastic deformation.

16.2 Large-Particle Composites

Properties are a combination of those of the components. The rule of mixtures predicts that an upper limit of the elastic modulus of the composite is given in terms of the elastic moduli of the matrix (Em) and the particulate (Ep) phases by: Ec = EmVm + EpVp where Vm and Vp are the volume fraction of the two phases. A lower bound is given by: Ec = EmEp / (EpVm + EmVp) Fig. 17.3 - modulus of composite of WC particles in Cu matrix vs. WC concentration. Concrete The most common large-particle composite is concrete, made of a cement matrix that bonds particles of different size (gravel and sand.) Cement was already known to the Egyptians and the Greek. Romans made cement by mixing lime (CaO) with volcanic ice. In its general from, cement is a fine mixture of lime, alumina, silica, and water. Portland cement is a fine powder of chalk, clay and lime-bearing minerals fired to 1500o C (calcinated). It forms a paste when dissolved in water. It sets into a solid in minutes and hardens slowly (takes 4 months for full strength). Properties depend on how well it is mixed, and the amount of water: too little - incomplete bonding, too much - excessive porosity. The advantage of cement is that it can be poured in place, it hardens at room temperature and even under water, and it is very cheap. The disadvantages are that it is weak and brittle, and that water in the pores can produce crack when it freezes in cold weather. Concrete is cement strengthened by adding particulates. The use of different size (stone and sand) allows better packing factor than when using particles of similar size. Concrete is improved by making the pores smaller (using finer powder, adding polymeric lubricants, and applying pressure during hardening. Reinforced concrete is obtained by adding steel rods, wires, mesh. Steel has the advantage of a similar thermal expansion coefficient, so there is reduced danger of cracking due to thermal stresses. Pre-stressed concrete is obtained by applying tensile stress to the steel rods while the cement is setting and hardening. When the tensile stress is removed, the concrete is left under compressive stress, enabling it to sustain tensile loads without fracturing. Pre-stressed concrete shapes are usually prefabricated. A common use is in railroad or highway bridges. Cermets are composites of ceramic particles (strong, brittle) in a metal matrix (soft, ductile) that enhances toughness. For instance, tungsten carbide or titanium carbide ceramics in Co or Ni. They are used for cutting tools for hardened steels. Reinforced rubber is obtained by strengthening with 20-50 nm carbon-black particles. Used in auto tires

16.3 Dispersion-Strengthened Composites

Use of very hard, small particles to strengthen metals and metal alloys. The effect is like precipitation hardening but not so strong. Particles like oxides do not react so the strengthening action is retained at high temperatures. Fiber-reinforced composites In many applications, like in aircraft parts, there is a need for high strength per unit weight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers. The strength depends on the fiber length and its orientation with respect to the stress direction. The efficiency of load transfer between matrix and fiber depends on the interfacial bond

16.4 Influence of Fiber Length

Normally the matrix has a much lower modulus than the fiber so it strains more. This occurs at a distance from the fiber. Right next to the fiber, the strain is limited by the fiber. Thus, for a composite under tension, a shear stress appears in the matrix that pulls from the fiber. The pull is uniform over the area of the fiber. This makes the force on the fiber be minimum at the ends and maximum in the middle, like in the tug-of-war game. To achieve effective strengthening and stiffening, the fibers must be larger than a critical length lc, defined as the minimum length at which the center of the fiber reaches the ultimate (tensile) strength sf, when the matrix achieves the maximum shear strength tm: lc = sf d /2 tm Since it is proportional to the diameter of the fiber d, a more unified condition for effective strengthening is that the aspect ratio of the fiber is l/d > sf /2 tm.

16.5 Influence of Fiber Orientation

The composite is stronger along the direction of orientation of the fibers and weakest in a direction perpendicular to the fiber. For discontinuous, random fibers, the properties are isotropic.

16.6 Polymer Matrix Composites
Largest and most diverse use of composites due to ease of fabrication, low cost and good properties. Glass-fiber reinforced composites (GFRC) are strong, corrosion resistant and lightweight, but not very stiff and cannot be used at high temperatures. Applications include auto and boat bodies, aircraft components. Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the highest specific module (module divided by weight). CFRC are strong, inert, allow high temperature use. Applications include fishing rods, golf clubs, aircraft components. Kevlar, and aremid-fiber composite (Fig. 17.9) can be used as textile fibers. Applications include bullet-proof vests, tires, brake and clutch linings. Wood: This is one of the oldest and the most widely used structural material. It is a composite of strong and flexible cellulose fibers (linear polymer) surrounded and held together by a matrix of lignin and other polymers. The properties are anisotropic and vary widely among types of wood. Wood is ten times stronger in the axial direction than in the radial or tangential directions

Chapter 17.

Electrical Properties

Electrical Conduction

17.2 Ohm’s Law
When an electric potential V is applied across a material, a current of magnitude I flows. In most metals, at low values of V, the current is proportional to V, according to Ohm's law: I = V/R where R is the electrical resistance. R depends on the intrinsic resistivity r of the material and on the geometry (length l and area A through which the current passes). R = rl/A

17.3 Electrical Conductivity

The electrical conductivity is the inverse of the resistivity: s = 1/r. The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of the current density j = I/A as: j = s E The conductivity is one of the properties of materials that varies most widely, from 107 (W-m) typical of metals to 10-20 (W-m) for good electrical insulators. Semiconductors have conductivities in the range 10-6 to 104 (W-m).

17.4 Electronic and Ionic Conduction

In metals, the current is carried by electrons, and hence the name electronic conduction. In ionic crystals, the charge carriers are ions, thus the name ionic conduction (see Sect. 19.15).

17.5 Energy Band Structures in Solids

When atoms come together to form a solid, their valence electrons interact due to Coulomb forces, and they also feel the electric field produced by their own nucleus and that of the other atoms. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same property (which include the energy). As a result of all these effects, the valence electrons of atoms form wide valence bands when they form a solid. The bands are separated by gaps, where electrons cannot exist. The precise location of the bands and band gaps depends on the type of atom (e.g., Si vs. Al), the distance between atoms in the solid, and the atomic arrangement (e.g., carbon vs. diamond). In semiconductors and insulators, the valence band is filled, and no more electrons can be added, following Pauli's principle. Electrical conduction requires that electrons be able to gain energy in an electric field; this is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap. In metals, the electrons occupy states up to the Fermi level. Conduction occurs by promoting electrons into the conduction band, that starts at the Fermi level, separated by the valence band by an infinitesimal amount.

17.6 Conduction in Terms of Band and Atomic Bonding Models

Conduction in metals is by electrons in the conduction band. Conduction in insulators is by electrons in the conduction band and by holes in the valence band. Holes are vacant states in the valence band that are created when an electron is removed. In metals there are empty states just above the Fermi levels, where electrons can be promoted. The promotion energy is negligibly small so that at any temperature electrons can be found in the conduction band. The number of electrons participating in electrical conduction is extremely small. In insulators, there is an energy gap between the valence and conduction bands, so energy is needed to promote an electron to the conduction band. This energy may come from heat, or from energetic radiation, like light of sufficiently small wavelength. A working definition for the difference between semiconductors and insulators is that in semiconductors, electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot. The probability that an electron reaches the conduction band is about exp(-Eg/2kT) where Eg is the band gap and kT has the usual meaning. If this probability is, say, < 10-24 one would not find a single electron in the conduction band in a solid of 1 cubic centimeter. This requires Eg/2kT > 55. At room temperature, 2kT = 0.05 eV; thus Eg > 2.8 eV can be used as the condition for an insulator. Besides having relatively small Eg, semiconductors have covalent bond, whereas insulators usually are partially ionic bonded.

17.7 Electron Mobility
Electrons are accelerated in an electric field E, in the opposite direction to the field because of their negative charge. The force acting on the electron is -eE, where e is the electric charge. This force produces a constant acceleration so that, in the absence of obstacles (in vacuum, like inside a TV tube) the electron speeds up continuously in an electric field. In a solid, the situation is different. The electrons scatter by collisions with atoms and vacancies that change drastically their direction of motion. Thus electrons move randomly but with a net drift in the direction opposite to the electric field. The drift velocity is constant, equal to the electric field times a constant called the mobility m, vd= – me E which means that there is a friction force proportional to velocity. This friction translates into energy that goes into the lattice as heat. This is the way that electric heaters work. The electrical conductivity is: s = n |e| me where n is the concentration of electrons (n is used to indicate that the carriers of electricity are negative particles).

17.8 Electrical Resistivity of Metals

The resistivity then depends on collisions. Quantum mechanics tells us that electrons behave like waves. One of the effects of this is that electrons do not scatter from a perfect lattice. They scatter by defects, which can be: atoms displaced by lattice vibrations vacancies and interstitials dislocations, grain boundaries impurities One can express the total resistivity rtot by the Matthiessen rule, as a sum of resistivities due to thermal vibrations, impurities and dislocations. Fig. 19.8 illustrates how the resistivity increases with temperature, with deformation, and with alloying.

17.9 Electrical Characteristics of Commercial Alloys

The best material for electrical conduction (lower resistivity) is silver. Since it is very expensive, copper is preferred, at an only modest increase in r. To achieve low r it is necessary to remove gases occluded in the metal during fabrication. Copper is soft so, for applications where mechanical strength is important, the alloy CuBe is used, which has a nearly as good r. When weight is important one uses Al, which is half as good as Cu. Al is also more resistant to corrosion. When high resistivity materials are needed, like in electrical heaters, especially those that operate at high temperature, nichrome (NiCr) or graphite are used.

17.10 Intrinsic Semiconduction
Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the conductivity depends on the concentration of impurities. Conduction is by electrons and holes. In an electric field, electrons and holes move in opposite direction because they have opposite charges. The conductivity of an intrinsic semiconductor is: s = n |e| me + p |e| mh where p is the hole concentration and mh the hole mobility. One finds that electrons move much faster than holes: me > mh In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Thus: n = p Thus, s = 2 n |e| (me + mh) (only for intrinsic semiconductors).

17.11 Extrinsic Semiconduction

Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p>n and n-type if n>p. They are made by doping, the addition of a very small concentration of impurity atoms. Two common methods of doping are diffusion and ion implantation. Excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. For instance phosphorous, with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Thus, elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge. The energy level of the donor state is close to the conduction band, so that the electron is promoted (ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this hole is unlike a hole in the matrix, it does not move easily by capturing electrons from adjacent atoms. This means that the conduction occurs mainly by the donated electrons (thus n-type). Excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix. This is the case of elements of group II and III in column IV semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can capture or accept electrons from adjacent silicon atoms. They are called acceptors. The energy level of the acceptor is close to the valence band, so that an electron may easily hop from the valence band to complete the bond leaving a hole behind. This means that conduction occurs mainly by the holes (thus p-type).

17.12 The Temperature Variation of Conductivity and Carrier Concentration

Temperature causes electrons to be promoted to the conduction band and from donor levels, or holes to acceptor levels. The dependence of conductivity on temperature is like other thermally activated processes: s = A exp(–Eg/2kT) where A is a constant (the mobility varies much more slowly with temperature). Plotting ln s vs. 1/T produces a straight line of slope Eg/2k from which the band gap energy can be determined. Extrinsic semiconductors have, in addition to this dependence, one due to the thermal promotion of electrons from donor levels or holes from acceptor levels. The dependence on temperature is also exponential but it eventually saturates at high temperatures where all the donors are emptied or all the acceptors are filled. This means that at low temperatures, extrinsic semiconductors have larger conductivity than intrinsic semiconductors. At high temperatures, both the impurity levels and valence electrons are ionized, but since the impurities are very low in number and they are exhausted, eventually the behavior is dominated by the intrinsic type of conductivity.

17.14 Semiconductor Devices

A semiconductor diode is made by the intimate junction of a p-type and an n-type semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that passes through the material depends on the polarity of the applied voltage. If the positive side of a battery is connected to the p-side, a situation called forward bias, a large amount of current can flow since holes and electrons are pushed into the junction region, where they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates under reverse bias. Holes and electrons are removed from the region of the junction, which therefore becomes depleted of carriers and behaves like an insulator. For this reason, the current is very small under reverse bias. The asymmetric current-voltage characteristics of diodes (Fig. 19.20) is used to convert alternating current into direct current. This is called rectification. A p-n-p junction transistor contains two diodes back-to-back. The central region is very thin and is called the base. A small voltage applied to the base has a large effect on the current passing through the transistor, and this can be used to amplify electrical signals (Fig. 19.22). Another common device is the MOSFET transistor where a gate serves the function of the base in a junction transistor. Control of the current through the transistor is by means of the electric field induced by the gate, which is isolated electrically by an oxide layer.

17.15 Conduction in Ionic Materials

In ionic materials, the band gap is too large for thermal electron promotion. Cation vacancies allow ionic motion in the direction of an applied electric field, this is referred to as ionic conduction. High temperatures produce more vacancies and higher ionic conductivity. At low temperatures, electrical conduction in insulators is usually along the surface, due to the deposition of moisture that contains impurity ions.

17.16 Electrical Properties of Polymers
Polymers are usually good insulators but can be made to conduct by doping. Teflon is an exceptionally good insulator. Dielectric Behavior A dielectric is an electrical insulator that can be made to exhibit an electric dipole structure (displace the negative and positive charge so that their center of gravity is different).

17.17 Capacitance When two parallel plates of area A, separated by a small distance l, are charged by +Q, –Q, an electric field develops between the plates E = D/ee0 where D = Q/A. e0 is called the vacuum permittivity and e the relative permittivity, or dielectric constant (e = 1 for vacuum). In terms of the voltage between the plates, V = E l, V = Dl/ee0 = Q l/Aee0 = Q / C The constant C= Aee0/l is called the capacitance of the plates.

17.18 Field Vectors and Polarization

The dipole moment of a pair of positive and negative charges (+q and –q) separated at a distance d is p = qd. If an electric field is applied, the dipole tends to align so that the positive charge points in the field direction. Dipoles between the plates of a capacitor will produce an electric field that opposes the applied field. For a given applied voltage V, there will be an increase in the charge in the plates by an amount Q' so that the total charge becomes Q = Q' + Q0, where Q0 is the charge of a vacuum capacitor with the same V. With Q' = PA, the charge density becomes D = D0 E + P, where the polarization P = e0 (e–1) E .

19.19 Types of Polarization

Three types of polarization can be caused by an electric field: Electronic polarization: the electrons in atoms are displaced relative to the nucleus. Ionic polarization: cations and anions in an ionic crystal are displaced with respect to each other. Orientation polarization: permanent dipoles (like H2O) are aligned. 17.20 Frequency Dependence of the Dielectric Constant Electrons have much smaller mass than ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at very high frequencies (such as light) only electronic polarization can occur. At smaller frequencies, the relative displacement of positive and negative ions can occur. Orientation of permanent dipoles, which require the rotation of a molecule can occur only if the oscillation is relatively slow (MHz range or slower). The time needed by the specific polarization to occur is called the relaxation time.

17.21 Dielectric Strength

Very high electric fields (>108 V/m) can free electrons from atoms, and accelerate them to such high energies that they can, in turn, free other electrons, in an avalanche process (or electrical discharge). This is called dielectric breakdown, and the field necessary to start the is called the dielectric strength or breakdown strength. 17.22 Dielectric Materials Capacitors require dielectrics of high e that can function at high frequencies (small relaxation times). Many of the ceramics have these properties, like mica, glass, and porcelain). Polymers usually have lower e.

17.23 Ferroelectricity

Ferroelectric materials are ceramics that exhibit permanent polarization in the absence of an electric field. This is due to the asymmetric location of positive and negative charges within the unit cell. Two possible arrangements of this asymmetry results in two distinct polarizations, which can be used to code "0" and "1" in ferroelectric memories. A typical ferroelectric is barium titanate, BaTiO3, where the Ti4+ is in the center of the unit cell and four O2- in the central plane can be displaced to one side or the other of this central ion (Fig. 19.33).

17.24 Piezoelectricity

In a piezolectric material, like quartz, an applied mechanical stress causes electric polarization by the relative displacement of anions and cations

[swananddeodhar]

Total of 35 pages to read and understand. Thanks for everything. I expect to clear Winter 2010 the exams. But still I am afraid that I might fall back on computing and informatics.