Saturday, January 12, 2008

Chapter-9: PHASE DIAGRAMS

9.1 Introduction

Definitions
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics

9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content (like when cooling) leads to precipitation.

9.3 Phases
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.

9.4 Microstructure
The properties of an alloy do not depend only on concentration of the phases but how they are arranged structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.
A binary alloy may be
a. a single solid solution
b. two separated, essentially pure components.
c. two separated solid solutions.
d. a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a different rate) and observe the surface under a microscope.

9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable. This is called a metastable state.
A less strict, operational, definition of equilibrium is that of a system that does not change with time during observation.
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.

9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
a. locate composition and temperature in diagram
b. In two phase region draw tie line or isotherm
c. note intersection with phase boundaries. Read compositions.
Fractions: lever rule
a. construct tie line (isotherm)
b. obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)

9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.
Note:
· the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
· At most two phases can be in equilibrium within a phase field.
· Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase

9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.

9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2

9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids.

9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
· a-ferrite (BCC) Fe-C solution
· g-austenite (FCC) Fe-C solution
· d-ferrite (BCC) Fe-C solution
· liquid Fe-C solution
· Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)

9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: a-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.

9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.

Chapter 2. ATOMIC STRUCTURE AND BONDING

2.2 Fundamental Concepts
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3 in a piece of material of density d (g/cm3).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.
Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.

2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n, which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle, only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n) and subshells (given by l).

2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.

2.5 Bonding Forces and Energies
The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center.
When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay.
The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related. The interaction energy is a minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms.

2.6 Primary Interatomic Bonds

Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp(-0.25 (XA – XB)2], where XA and XB are the electronegativities of the two atoms, A and B, forming the molecule.

Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.

Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.
2.7 Secondary Bonding (Van der Waals)

Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.

Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole.

2.8 Molecules
If molecules formed a closed shell due to covalent bonding (like H2, N2) then the interaction between molecules is weak, of the van der Waals type. Thus, molecular solids usually have very low melting points

Chapter 1. INRODUCTION

1 .1 Historical Perspective
Materials are so important in the development of civilization that we associate Ages with them. In the origin of human life on Earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood. When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world.

1.2 Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties was only possible with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed designing materials and provided a knowledge base for the engineering applications (Materials Engineering).
Structure:
· At the atomic level: arrangement of atoms in different ways. (Gives different properties for graphite than diamond both forms of carbon.)
· At the microscopic level: arrangement of small grains of material that can be identified by microscopy. (Gives different optical properties to transparent vs. frosted glass.)
Properties are the way the material responds to the environment. For instance, the mechanical, electrical and magnetic properties are the responses to mechanical, electrical and magnetic forces, respectively. Other important properties are thermal (transmission of heat, heat capacity), optical (absorption, transmission and scattering of light), and the chemical stability in contact with the environment (like corrosion resistance).
Processing of materials is the application of heat (heat treatment), mechanical forces, etc. to affect their microstructure and, therefore, their properties.
1.3 Why Study Materials Science and Engineering?
· To be able to select a material for a given use based on considerations of cost and performance.
· To understand the limits of materials and the change of their properties with use.
· To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial", like software or system engineering depend on the development of new materials, which in turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complex environmental systems.
1.4 Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle the complexity. One could classify them according to structure, or properties, or use. The one that we will use is according to the way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.
Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are lightweight. Other properties vary greatly. Examples: plastics (nylon, Teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies composites, made of different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties. Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human body parts.

1.5 Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance, and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.
1.6 Modern Material's Needs
· Engine efficiency increases at high temperatures: requires high temperature structural materials
· Use of nuclear energy requires solving problem with residues, or advances in nuclear waste processing.
· Hypersonic flight requires materials that are light, strong and resist high temperatures.
· Optical communications require optical fibers that absorb light negligibly.
· Civil construction – materials for unbreakable windows.
· Structures: materials that are strong like metals and resist corrosion like plastics.

Syllabus of Material Science

MATERIAL SCIENCE AND ENGINEERING
Group A
Introduction to materials . Metal and alloys, ceramics, polymers and semi conducting materials-introduction and application as engineering materials.
Defects in solids . Point, line and surface defects. Diffusion in solids.
Phase diagrams . Mono-component and binary systems, non-equilibrium system, phase diagram and. application in crystalline and non-crystalline solids.
Mechanical properties . Tensile strength, yield strength, elastic and viscoelastic properties, creep, stress relaxation and impact. Fracture behaviour. Ductile fracture, Griffith theory, effect of heat treatment and temperature on properties of metals.
Deformation of metals. Elastic and plastic deformation, slip, twin, dislocation theory, critical resolved shear stress, deformation in polycrystalline materials; season cracking, Bachinger's effect, strengthening mechanics; work hardening recovery, crystallization and grain growth, cold and hot working. .

Group B
Heat treatment . Iron-carbon system. Annealing, normalising, hardening,. critical cooling rate, hardenability, age hardening, surface hardening, tempering.
Thermal properties . High temperature materials; materials for cryogenic application, thermally insulating materials. (Specific heat, thermal conductivity, thermal expansion).
Ceramic materials and polymers . Silicon structures, polymerism . in glass, electrical properties of ceramic phases, rocks, building stones, refractories.
Polymerisation mechanism , structural properties of polymer, thermoplastics, thermosets, elastomer, resins, composites, particles and fibre reinforced composite. Composite material including nano material.
Electronic properties . Magnetism, diamagnetism, paramagnetism, ferromagnetism, magnetic energy, zone theory of solids, zones in conductors and insulators.