MATERIAL SCIENCE (Group A -part2)

Schottky defectsWhen two oppositely charged ions are missing from an ionic crystal, action-anion divacancy is created which is known as schottky imperfection.Frenkel defectsIf a positive cation moves into an interstitial site in an ionic crystal, a cation vacancy is created in the normal ion site. This vacancy-interstitialcy pair is called the Frenkel imperfection.Screw dislocationA screw dislocation is much harder to visualize. Imagine cutting a crystal along a plane and slipping one half across the other by a lattice vector, the halves will fit back together without leaving a defect. If the cut only goes part way through the crystal, and then slipped, the boundary of the cut is a screw dislocation. Despite the difficulty in visualization, the stresses caused by a screw dislocation are less complex than those of an edge dislocation. These stresses need only one equation, as symmetry allows only one radial coordinate to be used: [1]

Where μ is the shear modulus of the material, b is the Burgers vector, and r is a radial coordinate. This equation suggests a long cylinder of stress radiating outward from the cylinder and decreasing with distance. Please note, this simple model results in an infinite value for the core of the dislocation at r=0 and so it is only valid for stresses outside of the core of the dislocation.[1]

Edge dislocation

An edge dislocation is a defect where an extra half-plane of atoms is introduced mid way through the crystal, distorting nearby planes of atoms. When enough force is applied from one side of the crystal structure, this extra plane passes through planes of atoms breaking and joining bonds with them until it reaches the grain boundary. A simple schematic diagram of such atomic planes can be used to illustrate lattice defects such as dislocations. (Figure B represents the "extra half-plane" concept of an edge type dislocation).

The stresses caused by an edge dislocation are complex due to its inherent asymmetry. These stresses are described by three equations: [1]

Where μ is the shear modulus of the material, b is the Burgers vector, ν is Poisson's ratio and x and y is coordinates. These equations suggest a vertically oriented dumbbell of stresses surrounding the dislocation, with compression experienced by the atoms near the "extra" plane, and tension experienced by those atoms near the "missing" plane.

Burger vector

The Burgers vector, often denoted by b, is a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice.[1]

The direction of the vector depends on the plane of dislocation, which is usually on the closest-packed plane of unit cell. The magnitude is usually represented by equation:

Where a is the unit cell length of the crystal, ||b|| is the magnitude of Burgers vector and h, k, and l are the components of Burgers vector, b = <h k l>. In most metallic materials, the magnitude of the Burgers vector for a dislocation is of a magnitude equal to the interatomic spacing of the material, since a single dislocation will offset the crystal lattice by one close-packed crystallographic spacing unit.

In edge dislocations, the Burgers vector and dislocation line are at right angles to one another. In screw dislocations, they are parallel.

The Burgers Vector is significant in determining the strength of a material: it affects solute hardening, precipitation hardening and work hardening, all of which affect yield strength.

Diffusion MechanismsDiffusion describes the spread of particles through random motion from regions of higher concentration to regions of lower concentration.

Kirkendal effectErnest Kirkendall reported the results of experiments on the inter diffusion between copper and zinc in brass and observed the movement of the interface between the different phases due to high-temperature inter diffusion, now called the Kirkendall Effect.Today, the effect has been taken into account in various fields in materials science and technology such as structural materials welding, metals and ceramics powders sintering, thin films, and large-scale integration.

(OR)In binary solution, two different elements, rate at which they diffuse are not necessarily equal. Usually, the lower melting component diffuses much faster than the other. If an inert marker (say, thin rod of a high melting point substance which is insoluble in the diffusion matrix) is placed at the weld joint of the couple, prior to the diffusion anneal, the marker is found to shifting during annealing in the same direction as the slower moving species. This phenomenon is termed as Kirkendall effect.Invariant reactionIn a binary (component, C=2) phase diagram, If three phases (P=3) coexist then the degree of freedom (F) at the point is zero (F=C-P+1 => F=2-3+1 => F=0). The degree of freedom zero means this can occur only at a particular temperature and particular composition and the point in the phase diagram is known as the invariant point. Any reaction or transaction occurred at that point is termed as invariant reaction.

PhaseA phase in a material in terms of its micro-structure is a region that differs in structure and or composition from another region.

(OR)In thermodynamics a chemically and physically uniform quantity of matter that can be separated mechanically from a non homogeneous mixture. It may consist of a single substance or of a mixture of substances. The three basic phases of matter are solid, liquid, and gas; other phases that are considered to exist include crystalline (see crystal), colloidal (see colloid), glass, amorphous, and plasma. The different phases of a pure substance are related to each other in terms of temperature and pressure. For example, if the temperature of a solid is raised enough, or the pressure is reduced enough, it will become a liquid.

Phase diagramA phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically-distinct phases can occur at equilibrium. In mathematics and physics, "phase diagram" is used with a different meaning: a synonym for a phase space.

OverviewCommon components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.

Types of phase diagrams

1. 2D phase diagrams2. 3D phase diagrams :

It is possible to envision three-dimensional (3D) graphs showing three thermodynamic quantities.

3. Binary phase diagrams :

Other much more complex types of phase diagrams can be constructed, particularly when more than one pure component is present. In that case concentration becomes an important variable. Phase diagrams with more than two dimensions can be constructed that show the effect of more than two variables on the phase of a substance.

4. Crystal phase diagrams:

Polymorphic and polyamorphic substances have multiple crystal or amorphous phases, which can be graphed in a similar fashion to solid, liquid, and gas phases.

In liquid crystal physics, phase diagrams are used in the case of mixing of nematogenic compounds to distinguish between the isotropic liquid phase, the nematic liquid phase.

Lever ruleUsing the lever rule one can determine quantitatively the relative composition of a mixture in a two-phase region in a phase diagram. The distances l from the mixture point along a horizontal tie line to both phase boundaries give the composition: [1]

Where: represents the amount of phase α Represents the amount of phase β. It can be conveniently expressed as: [2]

%α = (x * L) / (α * L) * 100%L = (α * x) / (α * L) * 100

Tensile strengthUltimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength,[1][2] is the maximum stress that a material withstand before necking. The UTS is usually found by performing a tensile test and recording the stress versus strain; the highest point of the stress-strain curve is the UTS. It is an intensive property, therefore its value does not depend on the size of the test specimen. However, it is dependent on other factors, such as the preparation of the specimen and the temperature of the test environment and material.

(Or simply)The strength of material expressed as the greatest longitudinal stress it can bear without tearing apart,

Elastic and plastic deformationWhen 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.Plastic DeformationWhen a material is stressed below its elastic limit, the resulting deformation or strain is temporary. Removal of stress results in a gradual return of the object to its original dimensions. When a material is stressed beyond its elastic limit, plastic or permanent deformation takes place, and it will not return to its original shape by the application of force alone. The ability of a metal to undergo plastic deformation is probably its most outstanding characteristic in comparison with other materials. All shaping operations such as stamping, pressing, spinning, rolling, forging, drawing, and extruding involve plastic deformation of metals. Various machining operations such as milling, turning, sawing, and punching also involve plastic deformation. Plastic deformation may take place by:-

1. Slip 2.Twinning 3.Combination of slip and twinning

Engineering stress

The stress , or intensity of internal forces, can be obtained by dividing the total normal force , determined from the equilibrium of forces, by the cross-sectional area of the prism it is acting upon. The normal force can be a tensile force if acting outward from the plane, or compressive force if acting inward to the plane. In the case of a prismatic bar axially loaded, the stress is represented by a scalar called engineering stress or nominal stress that represents an average stress ( ) over the area, meaning that the stress in the cross section is uniformly distributed. Thus, we have

Engineering strainThe (Cauchy strain or) engineering strain is expressed as the ratio of total deformation to the initial dimension of the material body in which the forces are being applied. The engineering normal strain or engineering extensional strain e of a material line element or fiber axially loaded is expressed as the change in length ΔL per unit of the original length L of the line element or fibers. The normal strain is positive if the material fibers are stretched or negative if they are compressed. Thus, we have

Where is the engineering normal strain, L is the original length of the fiber and is the final length of the fiber.

The engineering shear strain is defined as the change in the angle between two material line elements initially perpendicular to each other in the no deformed or initial configuration.

True stress

Engineering stress is Force / prime (early) Area = F/A0True stress is Force / Area in any time = F/Aengineering strain is (Lf-L0)/L0 while Lf is length of sample after deformation and L0 is early length of sample (before deformation)True stress is defined is d (Epsilon) = dL/L therefore Epsilon = ln (Lf/L0).Therefore: True Stress = Eng. Stress X (1+Eng. Strain)and True Strain = ln(1+Eng. Strain)

True strainThe logarithmic strain ε, also called natural strain, true strain or Hencky strain. Considering an incremental strain (Ludwik)

The logarithmic strain is obtained by integrating this incremental strain:

Where e is the engineering strain. The logarithmic strain provides the correct measure of the final strain when deformation takes place in a series of increments, taking into account the influence of the strain path.[2]

Shear strain

The engineering shear strain is defined as the change in angle between two originally orthogonal material lines. In the figure above, the engineering shear strain (γxy) is the change in angle between lines and . Therefore,

From the geometry of the figure, we have

For small displacement gradients we have

For small rotations, i.e., and are we have . Therefore,

Thus

By interchanging and and and , it can be shown that

Similarly, for the - and - planes, we have

The tonsorial shear strain components of the infinitesimal strain tensor can then be expressed using the engineering strain definition, , as

Shear strainExpressed in (SI unit): 1, or radianCommonly used symbols: γ or ϵExpressed in other quantities: γ = τ / G

Modulus elasticityModulus of elasticity, also known as elastic modulus or Young’s Modulus, is a measure of how a material or structure will deform and strain when placed under stress. Materials deform differently when loads and stresses are applied, and the relationship between stress and strain typically varies. The ability of matter to resist or transmit stress is important, and this property is often used to determine if a particular material is suitable for a specific purpose.

(OR) When a material is subjected to an external load it becomes distorted or strained. With metals, provided the loading is not too great, they return to their

original dimensions when the load is removed, i.e. they are elastic. Within the limits of elasticity, the ratio of the linear stress to the linear strain is termed the modulus of elasticity or more commonly known as Young's Modulus.

Yield strengthThe yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the

deformation will be permanent and non-reversible.In the three-dimensional space of the principal stresses (σ1,σ2,σ3), an infinite number of yield points form together a yield surface.Knowledge of the yield point is vital when designing a component since it generally represents an upper limit to the load that can be applied. It is also important for the control of many materials production techniques such as forging, rolling, or pressing. In structural engineering, this is a soft failure mode which does not normally cause catastrophic failure or ultimate failure unless it accelerates buckling.

ResilienceResilience is the property of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered. In other words, it is the maximum energy per unit volume that can be elastically stored. It is represented by the area under the curve in the elastic region in the Stress-Strain diagram.

Modulus of Resilience, Ur, can be calculated using the following formula: ,

where σ is yield stress, E is Young's modulus, and ε is strain.

Elastic behavior

A. Material acts like a spring

B. Any kind of strain is completely and instantaneously recoverable

C. Hookian behavior:

d = E

E = constant, Young’s modulus

E = d /

D. E describes the elastic properties of a material

1. E defines the slope on verses plot

2. E is a way to quantify how stiff a rock is in terms of its elastic behavior

3. Large E = stiff rocks, requires large amounts of stress to obtain a certain amount of strain

4. Small E = soft rocks, more strain for less stress

5. Elastic behavior has no dependence on time

a. 0 - apply stress, material strains as long as stress is held

b. 1 - remove stress, strain is instantaneously removed

Group B