Material science

                                      UNIT 1 CRYSTALLOGRAPHY

Introduction to Crystallography Amorphous solids are homogeneous and isotropic because there is no long range order or periodicity in their internal atomic arrangement. By contrast, the crystalline state is characterized by a regular arrangement of atoms over large distances. Crystals are therefore an isotropic – their properties vary with direction.

For example, the inter atomic spacing varies with orientation within the crystal, as does the elastic response to an applied stress. Engineering materials are usually aggregates of many crystals of varying sizes and shapes; these poly crystalline materials have properties which depend on the nature of the individual crystals, but also on aggregate properties such as the size and shape distributions of the crystals, and the orientation relationships between the individual crystals. The randomness in the orientation of the crystals is a measure of texture, which has to be controlled in the manufacture of transformer steels, uranium fuel rods and beverage cans. The crystallography of interfaces connecting adjacent crystals can determine the deformation behavior of the poly crystalline aggregate; it can also influence the toughness through its effect on the degree of segregation of impurities to such interfaces.  

Crystallographic methods now depend on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most commonly used; other beams used include electrons or neutrons. This is facilitated by the wave properties of the particles. 

Crystallography often explicitly state the type of beam used, as in the terms X-ray crystallography, neutron diffraction and electron diffraction. These three types of radiation interact with the specimen in different ways.

• X-rays interact with the spatial distribution of electrons in the sample.

• Electrons are charged particles and therefore interact with the total charge distribution of both the atomic nuclei and the electrons of the sample.

• Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered bymagnetic fields. When neutrons are scattered from hydrogen-containing materials, they produce diffraction patterns with high noise levels. However, the material can sometimes be treated to substitute deuterium for hydrogen.

Lattice crystal :

The Lattice Crystals have translational symmetry: it is possible to identify a regular set of points, known as the lattice points, each of which has an identical environment. The set of these lattice points constitutes a three dimensional lattice. A unit cell may be defined within this lattice as a space–filling parallelepiped with origin at a lattice point, and with its edges defined by three non-coplanar basis vectors a1 , a2 and a3 , each of which represents translations between two lattice points. 

The entire lattice can then be generated by stacking unit cells in three dimensions. Any vector representing a translation between lattice points is called a lattice vector. The unit cell defined above has lattice points located at its corners. Since these are shared with seven other unit cells, and since each cell has eight corners, there is only one lattice point per unit cell. Such a unit cell is primitive and has the lattice symbol P. 

Non–primitive unit cells can have two or more lattice points, in which case, the additional lattice points will be located at positions other than the corners of the cell. A cell with lattice points located at the centres of all its faces has the lattice symbol F; such a cell would contain four lattice points. Not all the faces of the cell need to have face–centering lattice points; when a cell containing two lattice points has the additional lattice point located at the centre of the face defined by a2 and a3 , the lattice symbol is A and the cell is said to be A-centred. B-centred and C-centred cells have the additional lattice point located on the face defined by a3 & a1 or a1 & a2 respectively. 

Imperfections in Solids

 Introduction

Materials are often stronger when they have defects.  The study of defects is divided according to their dimension:

0D (zero dimension) – point defects: vacancies and interstitials. Impurities.

1D – linear defects: dislocations (edge, screw, mixed)

2D – grain boundaries, surfaces.

3D – extended defects: pores, cracks.

Point Defects

 Vacancies and Self-Interstitials

A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations.

An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity atom.

In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect.

The number of vacancies formed by thermal agitation follows the law:

N_V = N_A × exp (-Q_V/kT)

where N_A is the total number of atoms in the solid, Q_V is the energy required to form a vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in ^oC or ^oF).

When Q_V is given in joules, k = 1.38 × 10^-23 J/atom-K. When using eV as the unit of energy, k = 8.62 × 10^-5 eV/atom-K.

Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation energies. For instance, Q_V(Cu) = 0.9 eV/atom. This means that N_V/N_A at room temperature is exp(-36) = 2.3 × 10^-16, an insignificant number. Thus, a high temperature is needed to have a high thermal concentration of vacancies. Even so, N_V/N_A is typically only about 0.0001 at the melting point.

Impurities in Solids

All real solids are impure. A very high purity material, say 99.9999% pure (called 6N – six nines) contains ~ 6 × 10¹⁶ impurities per cm³.

Impurities are often added to materials to improve the properties. For instance, carbon added in small amounts to iron makes steel, which is stronger than iron. Boron impurities added to silicon drastically change its electrical properties.

Solid solutions are made of a host, the solvent or matrix) which dissolves the solute (minor component). The ability to dissolve is called solubility. Solid solutions are:

• homogeneous
• maintain crystal structure
• contain randomly dispersed impurities (substitutional or interstitial)

Factors for high solubility

• Similar atomic size (to within 15%)
• Similar crystal structure
• Similar electro negativity (otherwise a compound is formed)
• Similar valence

Composition can be expressed in weight percent, useful when making the solution, and in atomic percent, useful when trying to understand the material at the atomic level.

Miscellaneous Imperfections
 Dislocations—Linear Defects

Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid. They occur in high density and are very important in mechanical properties of material. They are characterized by the Burgers vector, found by doing a loop around the dislocation line and noticing the extra interatomic spacing needed to close the loop. The Burgers vector in metals points in a close packed direction.

Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end of the plane. In an edge dislocation, the Burgers vector is perpendicular to the dislocation line.

Screw dislocations result when displacing planes relative to each other through shear. In this case, the Burgers vector is parallel to the dislocation line.

 Interfacial Defects

The environment of an atom at a surface differs from that of an atom in the bulk, in that the number of neighbors (coordination) decreases. This introduces unbalanced forces which result in relaxation (the lattice spacing is decreased) or reconstruction (the crystal structure changes).

The density of atoms in the region including the grain boundary is smaller than the bulk value, since void space occurs in the interface.

Surfaces and interfaces are very reactive and it is usual that impurities segregate there. Since energy is required to form a surface, grains tend to grow in size at the expense of smaller grains to minimize energy. This occurs by diffusion, which is accelerated at high temperatures.

Twin boundaries: not covered

 Bulk or Volume Defects

A typical volume defect is porosity, often introduced in the solid during processing. A common example is snow, which is highly porous ice.

 Atomic Vibrations

Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and increase in amplitude with temperature.

POINT DEFECT

Point defects are defects that occur only at or around a single lattice point. They are not extended in space in any dimension. Strict limits for how small a point defect is are generally not defined explicitly, typically; however, these defects involve at most a few extra or missing atoms. Larger defects in an ordered structure are usually considered dislocation loops. For historical reasons, many point defects, especially in ionic crystals, are called centers: for example a vacancy in many ionic solids is called a luminescence center, a color center, or F-center. These dislocations permit ionic transport through crystals leading to electrochemical reactions. These are frequently specified using Kröger–Vink Notation.

·         Vacancy defects are lattice sites which would be occupied in a perfect crystal, but are vacant. If a neighboring atom moves to occupy the vacant site, the vacancy moves in the opposite direction to the site which used to be occupied by the moving atom. The stability of the surrounding crystal structure guarantees that the neighboring atoms will not simply collapse around the vacancy. In some materials, neighboring atoms actually move away from a vacancy, because they experience attraction from atoms in the surroundings. A vacancy (or pair of vacancies in an ionic solid) is sometimes called a Schottky defect.

·         Interstitial defects are atoms that occupy a site in the crystal structure at which there is usually not an atom. They are generally high energy configurations. Small atoms in some crystals can occupy interstices without high energy, such as hydrogen in palladium.

Schematic illustration of some simple point defect types in a monatomic solid

·         A nearby pair of a vacancy and an interstitial is often called a Frenkel defect or Frenkel pair. This is caused when an ion moves into an interstitial site and creates a vacancy.

·         Due to fundamental limitations of material purification methods, materials are never 100% pure, which by definition induces defects in crystal structure. In the case of an impurity, the atom is often incorporated at a regular atomic site in the crystal structure. This is neither a vacant site nor is the atom on an interstitial site and it is called a substitutional defect. The atom is not supposed to be anywhere in the crystal, and is thus an impurity. In some cases where the radius of the substitutional atom (ion) is substantially smaller than that of the atom (ion) it is replacing, its equilibrium position can be shifted away from the lattice site. These types of substitutional defects are often referred to as off-center ions. There are two different types of substitutional defects: Isovalent substitution and aliovalent substitution. Isovalent substitution is where the ion that is substituting the original ion is of the same oxidation state as the ion it is replacing. Aliovalent substitution is where the ion that is substituting the original ion is of a different oxidation state than the ion it is replacing. Aliovalent substitutions change the overall charge within the ionic compound, but the ionic compound must be neutral. Therefore, a charge compensation mechanism is required. Hence either one of the metals is partially or fully oxidised or reduced, or ion vacancies are created.

·         Antisite defects occur in an ordered alloy or compound when atoms of different type exchange positions. For example, some alloys have a regular structure in which every other atom is a different species; for illustration assume that type A atoms sit on the corners of a cubic lattice, and type B atoms sit in the center of the cubes. If one cube has an A atom at its center, the atom is on a site usually occupied by a B atom, and is thus an antisite defect. This is neither a vacancy nor an interstitial, nor an impurity.

·         Topological defects are regions in a crystal where the normal chemical bonding environment is topologically different from the surroundings. For instance, in a perfect sheet of graphite (graphene) all atoms are in rings containing six atoms. If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed. An example is the Stone Wales defect in nanotubes, which consists of two adjacent 5-membered and two 7-membered atom rings.

Schematic illustration of defects in a compound solid, using Ga As as an example.

·         Also amorphous solids may contain defects. These are naturally somewhat hard to define, but sometimes their nature can be quite easily understood. For instance, in ideally bonded amorphous silica all Si atoms have 4 bonds to O atoms and all O atoms have 2 bonds to Si atom. Thus e.g. an O atom with only one Si bond (a dangling bond) can be considered a defect in silica. Moreover, defects can also be defined in amorphous solids based on empty or densely packed local atomic neighbourhoods, and the properties of such 'defects' can be shown to be similar to normal vacancies and interstitials in crystals,.

·         Complexes can form between different kinds of point defects. For example, if a vacancy encounters an impurity, the two may bind together if the impurity is too large for the lattice. Interstitials can form 'split interstitial' or 'dumbbell' structures where two atoms effectively share an atomic site, resulting in neither atom actually occupying the site.

Line defects

Line defects can be described by gauge theories.

Dislocations are linear defects around which some of the atoms of the crystal lattice are misaligned There are two basic types of dislocations, the edge dislocation and the screwdislocation. "Mixed" dislocations, combining aspects of both types, are also common.

An edge dislocation is shown. The dislocation line is presented in blue, the Burgers vector b in black.

Edge dislocations are caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the adjacent planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. The analogy with a stack of paper is apt: if a half a piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable at the edge of the half sheet.

The screw dislocation is more difficult to visualise, but basically comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes of atoms in the crystal lattice.

The presence of dislocation results in lattice strain (distortion). The direction and magnitude of such distortion is expressed in terms of a Burgers vector (b). For an edge type, b is perpendicular to the dislocation line, whereas in the cases of the screw type it is parallel. In metallic materials, b is aligned with close-packed crystallographic directions and its magnitude is equivalent to one interatomic spacing.

Dislocations can move if the atoms from one of the surrounding planes break their bonds and rebond with the atoms at the terminating edge.

It is the presence of dislocations and their ability to readily move (and interact) under the influence of stresses induced by external loads that leads to the characteristic malleability of metallic materials.

Dislocations can be observed using transmission electron microscopy, field ion microscopy and atom probe techniques. Deep level transient spectroscopy has been used for studying the electrical activity of dislocations in semiconductors, mainly silicon.

Disclinations are line defects corresponding to "adding" or "subtracting" an angle around a line. Basically, this means that if you track the crystal orientation around the line defect, you get a rotation. Usually, they were thought to play a role only in liquid crystals, but recent developments suggest that they might have a role also in solid materials, e.g. leading to the self-healing of crack.

Planar defects

Origin of stacking faults: Different stacking sequences of close-packed crystals

·         Grain boundaries occur where the crystallographic direction of the lattice abruptly changes. This usually occurs when two crystals begin growing separately and then meet.

·         Antiphase boundaries occur in ordered alloys: in this case, the crystallographic direction remains the same, but each side of the boundary has an opposite phase: For example, if the ordering is usually ABABABAB (hexagonalclose-packed crystal), an antiphase boundary takes the form of ABABBABA.

·         Stacking faults occur in a number of crystal structures, but the common example is in close-packed structures. They are formed by a local deviation of the stacking sequence of layers in a crystal. An example would be the ABABCABAB stacking sequence.

·         A twin boundary is a defect that introduces a plane of mirror symmetry in the ordering of a crystal. For example, in cubic close-packed crystals, the stacking sequence of a twin boundary would be ABCABCBACBA.

·         On surfaces of single crystals, steps between atomically flat terraces can also be regarded as planar defects. It has been shown that such defects and their geometry have significant influence on the adsorption of organic molecules^[14]

Bulk defects[edit]

·         three-dimensional macroscopic or bulk defects, such as pores, cracks, or inclusions

·         Voids — small regions where there are no atoms, and which can be thought of as clusters of vacancies

·         Impurities can cluster together to form small regions of a different phase. These are often called 

DEFORMATION OF METAL

 A temporary shape change that is self-reversing after the force is removed, so that the object returns to its original shape, is called elastic deformation. In other words, elastic deformation is a change in shape of a material at low stress that is recoverable after the stress is removed.

Elastic/Plastic Deformation

When a sufficient load is applied to a metal or other structural material, it will cause the material to change shape. This change in shape is called deformation. A temporary shape change that is self-reversing after the force is removed, so that the object returns to its original shape, is called elastic deformation. In other words, elastic deformation is a change in shape of a material at low stress that is recoverable after the stress is removed. This type of deformation involves stretching of the bonds, but the atoms do not slip past each other.

When the stress is sufficient to permanently deform the metal, it is called plastic deformation. As discussed in the section on crystal defects, plastic deformation involves the breaking of a limited number of atomic bonds by the movement of dislocations. Recall that the force needed to break the bonds of all the atoms in a crystal plane all at once is very great. However, the movement of dislocations allows atoms in crystal planes to slip past one another at a much lower stress levels. Since the energy required to move is lowest along the densest planes of atoms, dislocations have a preferred direction of travel within a grain of the material. This results in slip that occurs along parallel planes within the grain. These parallel slip planes group together to form slip bands, which can be seen with an optical microscope. A slip band appears as a single line under the microscope, but it is in fact made up of closely spaced parallel slip planes as shown in the image.

Metal forming is the backbone of modern manufacturing industry besides being a major industry in itself. Throughout the world hundreds of million tons of metals go through metal forming processes every year. As much as 15–20% of GDP of industrialized nations comes from metal forming industry. Besides, it fulfils a social cause by providing job opportunities to millions of workers. Metal forming industry, in general, is a bulk producer of semi-finished and finished goods and this is one reason that it is viable to undertake large scale research and development projects because even a small saving per ton adds up to huge sums. In metal forming processes, the product shapes are produced by plastic deformation. Hence it is important to know the plastic flow properties of metals and alloys for optimizing the processes. Also the resulting component properties depend upon the intensity and the conditions of plastic deformation during forming. Many forming processes produce raw materials for other processes which in turn produce finished or semi-finished products. 

For example, steel plants produce sheet metal which is used by automobile industry to manufacture components of automobiles and their bodies. In fact sheet metal is used by a number of manufacturers for producing a large variety of household and industrial products. Similarly billets produced by steel plants are used by re-rolling mills for rolling into products like angles, channels, bars etc. Bars may be further used for manufacturing forgings, wires, bright bars and machined products. Similarly the manufacturers of rivets, screws, bolts and nuts buy wire from wire manufacturers and process them further. Therefore, the producers of semi-finished materials such as sheet metal, bar stock and wires, etc. have to consider that they produce such properties in their products which are required by down stream industry engaged in further processing of these products. 
For example, deep drawability of sheet metal increases with increase in anisotropy ratio (see Section 1.9), therefore, rolling parameters such as finishing temperature, cold reduction etc, are adjusted to produce higher anisotropy ratio in the sheet metal which is to be used for deep drawing. The properties of metals and alloys are highly influenced by their microstructure which may be modified or altered by alloying elements, by heating or heat treatment or by plastic deformation. For example, metals and alloys may be hardened by plastic deformation. It would, therefore, be helpful if we look at metals at the micro level.
                               UNIT 3 HEAT TREATMENT PROCESS

Engineering properties are modified by heat treatment processes so that structural components are able withstand specified operating conditions and have desired useful life.

·     Heat treatment is the heating and cooling of metals to change their physical and mechanical properties, without letting it change its Heat treatment could be said to be a method for strengthening materials but could also be used to alter some mechanical properties such as improving formability, machining, etc. The most common application is metallurgical but heat treatment can also be used in manufacture of glass, aluminum, steel and many more materials. 

The process of heat treatment involves the use of heating or cooling, usually to extreme temperatures to achieve the wanted result. It is very important manufacturing processes that can not only help manufacturing process but can also improve product, its performance, and its characteristics in many ways.

        Heat Treatment Processes

Hardening

Hardening involves heating of steel, keeping it at an appropriate temperature until all pearlite is transformed into austenite, and then quenching it rapidly in water or oil. The temperature at which austentizing rapidly takes place depends upon the carbon content in the steel used. The heating time should be increased ensuring that the core will also be fully transformed into austenite. The microstructure of a hardened steel part is ferrite, martensite, or cementite.

Tempering

Tempering involves heating steel that has been quenched and hardened for an adequate period of time so that the metal can be equilibrated. The hardness and strength obtained depend upon the temperature at which tempering is carried out. Higher temperatures will result into high ductility, but low strength and hardness. Low tempering temperatures will produce low ductility, but high strength and hardness. In practice, appropriate tempering temperatures are selected that will produce the desired level of hardness and strength. This operation is performed on all carbon steels that have been hardened, in order to reduce their brittleness, so that they can be used effectively in desired applications.

Annealing

Annealing involves treating steel up to a high temperature, and then cooling it very slowly to room temperature, so that the resulting microstructure will possess high ductility and toughness, but low hardness. Annealing is performed by heating a component to the appropriate temperature, soaking it at that temperature, and then shutting off the furnace while the piece is in it. Steel is annealed before being processed by cold forming, to reduce the requirements of load and energy, and to enable the metal to undergo large strains without failure.

Normalizing

Normalizing involves heating steel, and then keeping it at that temperature for a period of time, and then cooling it in air. The resulting microstructure is a mixture of ferrite and cementite which has a higher strength and hardness, but lower ductility. Normalizing is performed on structures and structural components that will be subjected to machining, because it improves the machinability of carbon steels.

Carburization

It is a heat treatment process in which steel or iron is heated to a temperature, below the melting point, in the presence of a liquid, solid, or gaseous material which decomposes so as to release carbon when heated to the temperature used. The outer case or surface will have higher carbon content than the primary material. When the steel or iron is rapidly cooled by quenching, the higher carbon content on the outer surface becomes hard, while the core remains tough and soft.

Surface Hardening

In many engineering applications, it is necessary to have the surface of the component hard enough to resist wear and erosion, while maintaining ductility and toughness, to withstand impact and shock loading. This can be achieved by local austentitizing and quenching, and diffusion of hardening elements like carbon or nitrogen into the surface. Processes involved for this purpose are known as flame hardening, induction hardening, nitriding and carbonitriding

PHASE DIAGRAM

IRON CARBON DIAGRAM

Introduction

Cooling curve for pure iron

Definition of structures

Iron-Carbon equilibrium phase diagram – Sketch

The Iron-Iron Carbide Diagram - 

Ø The Austenite to ferrite / cementite transformation

Ø Nucleation & growth of pearlite

Ø Effect of C %age on the microstructure of steel

Ø Various phases that appear on the Iron-Carbon equilibrium phase diagram are as under:

Ø Austenite

Ø Ferrite

Ø Pearlite

Ø Cementite

Ø Martensite*

Ø Ledeburite

Ø Relationship b/w C %age & mechanical properties of steel

Ferrite is known as α solid solution.

Ø It is an interstitial solid solution of a small amount of carbon dissolved in α (BCC) iron.

Ø stable form of iron below 912 deg.C

Ø The maximum solubility is 0.025 % C at 723°C and it dissolves only 0.008 % C at room temperature.

Ø It is the softest structure that appears on the diagram.

Pearlite is the eutectoid mixture containing 0.80 % C and is formed at 723°C on very slow cooling.

Ø It is a very fine platelike or lamellar mixture of ferrite and cementite.

Ø The white ferritic background or matrix contains thin plates of cementite (dark).

 Cementite or iron carbide, is very hard, brittle intermetallic compound of iron & carbon, as Fe₃C, contains 6.67 % C.

  It is the hardest structure that appears on the diagram, exact melting point unknown.

  Its crystal structure is orthorhombic.

  It is has

q low tensile strength (approx. 5,000 psi), but

q high compressive strength.

Peritectic, at 1490 deg.C, with low wt% C alloys (almost no engineering importance).

  Eutectic, at 1130 deg.C, with 4.3wt% C, alloys called cast irons.

Eutectoid, at 723 deg.C with eutectoid composition of 0.8wt% C, two-phase mixture (ferrite & cementite). They are steels. 

In order to understand the transformation processes, consider a steel of the eutectoid composition. 0.8% carbon, being slow cooled along line x-x‘.

 At the upper temperatures, only austenite is present, with the 0.8% carbon being dissolved in solid solution within the FCC. When the steel cools through 723°C, several changes occur simultaneously.

  

The net reaction at the eutectoid  is the formation of pearlitic structure.

 Since the chemical separation occurs entirely within crystalline solids, the resultant structure is a fine mixture of ferrite and cementite.

 As the carbon-rich phase nucleates and grows, the remaining austenite decreases in carbon content, again reaching the eutectoid composition at 723°C.

  This austenite transforms to pearlite upon slow cooling through the eutectoid temperature.

 The resulting structure consists of primary cementite and pearlite.

  The continuous network of primary cementite will cause the material to be extremely brittle.

  -Iron-Carbon alloys of 2.11%C or more are cast irons.

  -Typical composition: 2.0-4.0%C,0.5-3.0% Si, less than 1.0% Mn and less than 0.2% S.

n  -Si-substitutes partially for C and promotes formation of graphite as the carbon rich component instead.
gGIBBS PHASE RULE
 The Gibbs Phase Rule 

 The phase rule allows one to determine the number of degrees of freedom (F) or variance of a chemical system. 

This is useful for interpreting phase diagrams. F = 2 + C - P

Where F is the number of degrees of freedom, C is the number of chemical components and P is the number of phases in the system. The number two is specified because this formulation assumes that both T and P can be varied.

Thermodynamics of Solutions • Phases: Part of a system that is chemically and physically homogeneous, bounded by a distinct interface with other phases and physically separable from other phases. • Components: Smallest number of chemical entities necessary to describe the composition of every phase in the system. •

Solutions: Homogeneous mixture of two or more chemical components in which their concentrations may be freely varied within certain limits.

These define the limits of stability fields. These represent values of parameters where phases in adjacent fields coexist. – Triple points: Points where equilibrium boundary lines meet.

 All phases in the adjacent stability fields must coexist. Silica Phase Diagram and Phase Rule Single Component System: F = 2 + C - P = 3 - P Stability Field P = 1; F = 2; divariant Boundary Line Triple Point P = 2; F = 1; univariant P = 3; F = 0; invariant From Swamy et al., 1994 Wet and Dry Melting Relations for Albite From Burham & Davis, 1974; Boettcher et al., 1982 Dry Melting Curve Water Saturated Melting Curve Water Undersaturated Melting Curves (2, 5, & 8 kbar) Binary Phase Relations - Definitions •

 Liquidus line: the line that represents the locus of depressed freezing points as a second component is added to the system. Solid phases are not stable at temperatures above those defined by the liquidus line or surface. Di-An Binary Eutectic Phase Diagram Binary Phase Diagram Definitions •

Eutectic point: Lowest T point on the liquidus at which a unique melt of fixed composition is in equilibrium with two or more phases. • Isopleth: line of constant chemical composition. • Isotherm: line of constant temperature • Tie line: portion of isotherm that connects two stable coexisting phases, in this case L (representing the silicate liquid) and S (pure crystalline anorthite feldspar) The Lever Rule Follows directly from the Law of Conservation of Mass. Allows one to calculate either algebraically or graphically the modal abundance of each phase at every temperature.

MASS OF LIQUID MASS OF SOLID BULK COMPOSITION

L = y (x + y) S = x (x + y)

Equilibrium vs. Fractional Crystallization Equilibrium Crystallization: crystals continuously react and re-equilibrate with the melt at P-T-X conditions change. Melt-xtal reactions are reversible. Fractional Crystallization: Crystals are immediately isolated, removed, or fractionated from the residual melt so that no further reactions can occur. Melt-xtal reactions are irreversible. Binary Phase Loop with Solid Solution liquidus solidus Plagioclase Differentiation Mechanisms Gabbro - Plane Polarized Light Plagioclase zoning zoned Crystal Settling plag Perthitic pyroxene Hawaiian Basalt Phase Relations at 1 atm From Wright & Okamura, 1977 Temperatures measured in borehole 1170°C 1130°C 1075°C 1020°C Generalized Basalt Phase Diagram From Green, 1982.