• These notes in this section were copied from Paul Johnson’s web site and placed here.



1.6.1 Atomic Bonding and Structure - Atomic Structure


A.Fundamental Concepts

1.Atomic number - # of protons in nucleus

2.Atomic mass - sum of protons and neutrons

3.Atomic weight - weighted average of atomic masses of natural isotopes

4.Atomic mass unit (amu) - 1/12th the mass of 12C

5.Mole - Avogadro's Number (6.023 x 1023) units (atoms or molecules) of a substance

B.Atomic Models

1.Bohr model

a.Quantized energy levels for electrons in atom

b.Discrete (particle like) electrons in an orbital

c.Energy levels are negative with respect to zero energy for a free electron

2.Wave-Mechanical model

a.Wave is neither wave nor particle, but can act like either in certain situations

b.Electron described as an electron 'cloud'

c.Energy levels divided into subshells with discrete states for each pair of electrons given by

quantum numbers

1.Principal quantum number n = 1, 2, 3, 4, 5, 6, 7

2.2nd quantum number, subshell, l = s, p, d, f

3.3rd quantum number, energy states in subshell, mi = 1(s), 3(p), 5(d), 7(f)

4.4th quantum number, spin moment, ms = +½, -½

d.Ground state - all electrons in atom filling lowest energy level states

e.Valence electrons - electrons in highest energy shell in ground state - Periodic Table

A.Metallic elements

1.1 to 3 valence electrons

2.Electropositive - tend to give up electrons in bonding


1.1 to 3 electrons short of full valence level

2.Electronegative - tend to add electrons in bonding

C.Intermediate elements

1.Metallic and non-metallic characteristics

2.Includes semiconductors

3.May gain or lose electrons in bonding

III.Atomic Bonding

A.Bonding Reactions

1.Bonding forces

a.Attractive force due to bond

b.Repulsive force due to electron clouds

c.Equilibrium when net force is zero

2.Bonding Energy - Equilibrium when energy is minimum

B.Primary (Strong) Bonding


a.Transfer of electrons from electropositive to electronegative atoms

b.Coulombic attraction between ions


a.Sharing of electrons between 2 (or a few) atoms

b.Number of bonds are those needed to fill valence level

c.Bonds between atoms with similar electronegativities


a.Sharing of electrons among many atoms

b.Valence electrons 'free' to move

c.Weak (Secondary) Bonding

4.Induced Dipole

a.Temporary, short term shifts in charge creating dipoles

b.Coulombic attraction between dipoles

5.Polar Molecules

a.Permanent dipoles

b.Large differences in attraction for electrons

c.Coulombic attraction between dipoles

6.Hydrogen Bonding

a.Special case of polar molecule bonding

b.Dipoles formed between Hydrogen and highly electronegative atoms (e.g. H2O)



1.6.2 Ideal Crystal Structure


I.Crystal Structure Fundamentals

A.Crystal structure - atoms arranged in regular, repeating pattern over large distances

compared to atomic size

B.Solid sphere model of atoms

C.Lattice - 3-dimensional array of points arranged in a regular, repeating periodic structure

D.Unit cell - the smallest portion of a lattice which represents the symmetry and structure of

the entire lattice

E.Equivalent sites - points in a lattice which are indistinguishable from other points in the

lattice - in a real crystal each equivalent site is associated with an identical atom or group of


F.Lattice geometry

1.Crystallographic axes - x, y, z

2.Crystallographic angles - a, b , g

3.Unit cell dimensions

a.in +x direction

b.in +y direction

c. in +z direction

II.Crystal Systems and Structures

A.Cubic Crystal System

1.a = b = c, a = b = g = 90°

2.Simple Cubic (SC)

a.1 equivalent site per unit cell

b.no crystals with only 1 atom per equivalent site

3.Face-Centered Cubic (FCC) lattice

a.4 equivalent sites per unit cell

b.common metals with 1 atom per equivalent site include - Al, Cu, Ni

4.Body-Centered Cubic (BCC) lattice

a.2 equivalent sites per unit cell

b.common metals with 1 atom per equivalent site include - Fe, Cr, W

B.Hexagonal Crystal System

1.a = b ¹ c, a = b = 90° , g = 120°

2.1 equivalent site per unit cell

3.Face-Centered Hexagonal (FCC)

a.2 atoms per equivalent site with close packed arrangement

b.common metals with HCP structure include - Zn, Mg, Ti

C.Tetragonal Crystal System

a = b ¹ c, a = b = g = 90°

D.Orthorhombic Crystal System

a ¹ b ¹ c, a = b = g = 90°

E.Rhombohedral Crystal System

a = b = c, a = b = g ¹ 90°

F.Monoclinic Crystal System

a ¹ b ¹ c, a = g = 90° ¹ b

G.Triclinic Crystal System

a ¹ b ¹ c, a ¹ b ¹ g ¹ 90°

III.Crystal Geometry

A.Points in a crystal

1.Set origin for crystal system

2.Points identified by translation from the origin

B.Direction vectors

1.Move origin to tail of vector or draw parallel vector from origin

2.Determine translation to tip point

3.May also use tip minus tail to find translation

4.Convert indices obtained to lowest integer form

5.Place indices into brackets in form [uvw]

6.Negative indices indicated by a bar over the number

C.Plane indices

1.Find intercepts of plane with the three crystallographic axes

2.If plane includes the origin, move either the plane or the origin

3.Invert intercept values obtained

4.Convert reciprocals to lowest integer form

5.Place indices in parentheses in form (hkl)

6.Negative indices indicated by a bar over the number

D.Families of directions and planes

1.Families refer to directions or planes in a crystal which have exactly the same arrangement

and spacing of equivalent sites and atoms

2.Families of directions have the same atomic spacing

3.A family of directions is indicated by placing the indices for any one member of the family in

pointed brackets in the form <uvw>

4.Families of planes have the same planar arrangement of equivalent sites and atoms

5.A family of planes is indicated by placing the indices for any one member of the family in

braces in the form {hkl}

E.Linear and Planar densities

1.Linear density

a.Fraction (or %) of a vector which passes through atoms

b.Vector must pass through the center of the atom for the atoms to be counted

2.Planar density

a.Fraction (or %) of the plane which is covered by the atoms spheres

b.Only atoms whose center lies on the plane are counted

3.Close packed crystals

a.Densest possible packing of identical size spheres

b.FCC and HCP structures for metals are close packed

c.Stacking of close packed layers of atoms



F.Structure variations

1.Single crystals - some materials can exist as large (macroscopic) single crystals

a.Si in semiconductors

b.Turbine blades

2.Polycrystalline - most materials exist as a set of contiguous small crystals

Grain boundary - interface between individual crystals

3.Isotropic vs. anisotropic

a.Isotropic materials have randomly oriented polycrystals - thus physical

properties are the same in all directions

b.Anisotropic materials have non-random orientations of the crystallographic

axes - thus physical properties vary with direction in the material

4.Amorphous materials - no long range orientation of the atoms to each other

5.Polymorphic and Allotropic Materials



1.6.3 Crystal Imperfections


I.Point Defects - crystal structure irregularities at a single point


1.Atom missing from crystal lattice

2.Lattice distortions around the vacancy


1.Extra atom squeezed into interstice of the lattice

2.Very rare in normal, densely packed structures

3.Extreme lattice distortions around the extra atom

C.Solid Solutions - alloys containing two or more different types of atoms

1.Interstitial Solid Solution

a.Small solute atoms in some of the interstices of the larger solvent atoms

b.Very dilute solutions due to large stresses involved

2.Substitutional Solid Solution

a.Atoms on solvent lattice replaced by solute atoms of a different type

b.Solubility limits dependent on

1.Atomic size - must be similar for large solubility

2.Crystal structure - greatest solubility if same lattice

3.Electronegativity - similar or intermetallic or ceramic may form

4.Valence - solute with same or higher valence than solvent for highest solubility

3.Composition specifications

a.Atomic - fraction or % of atoms for each component present

b.Weight - fraction or % of the weight of each component

c.Conversions between wt. % and at. %

II.Linear Defects - crystal structure irregularities in one dimension

A.Edge dislocation

1.'Extra' half plane of atoms in crystal

2.Burger's Vector perpendicular to line of dislocation

3.Movement of dislocation leads to crystal offset equal to Burger's vector

B.Screw dislocation

1.Helical arrangement of atoms around the dislocation line

2.Burger's Vector parallel to line of dislocation

3.Movement of dislocation leads to crystal offset equal to Burger's vector

C.Mixed dislocation - most real dislocations in materials

1.Regions with edge, screw and mixed screw-edge character

2.Movement of dislocation leads to crystal offset equal to Burger's vector

III.Interfacial Defects - crystal structure irregularities in two dimensions

A.External surfaces

1.Atoms on surface have smaller coordination number than atoms in bulk

2.Coordination number - number of nearest neighbors

B.Grain boundaries

1.Region between individual crystals with less perfect bonding than in bulk of crystal

2.Lower coordination number - depends on degree of mismatch between crystals

C.Twin boundaries

1.Similar to a grain boundary but occurring within grains

2.Lattice on opposite sides of boundary are mirror images

IV.Bulk or Volume Defects - crystal structure irregularities in three dimensions - cracks, voids,

porosity, inclusions


A.Polish surface of metal to mirror finish

B.Etch to preferentially erode atoms with lowest coordination number (weakest bonding)

C.Examine microscopically to see grain structure



1.6.4 Diffusion


I.Diffusion Processes


1.Random motion of atoms within a 'pure' material

2.Measurable only by radioactive isotope diffusion


1.Random motion of atoms in an alloy

2.Net flux down a concentration gradient

3.Homogenization of alloy

II.Diffusion Mechanisms

A.Vacancy Diffusion

1.Thermal vibration leading to motion

2.Movement of surrounding atom into vacancy

3.Energy to move in lattice directed toward vacancy

B.Interstitial Diffusion

1.Thermal vibration leading to motion

2.Movement of atom from interstice to interstice

3.Energy to move in lattice

4.At low concentrations neighboring interstice usually empty

III.Steady State Diffusion

A.Flux and concentration gradient assumed NOT to change with time

B.Fick's First Law -

1.J - net flux of atoms down the concentration gradient -

2.D - diffusivity depending on energy required to move atoms in lattice and thermal excitation -

3.dC/dx - concentration gradient -

C.Diffusivity -

1.D0 - pre-exponential diffusivity - an empirical constant for a given diffusion couple

2.Qd - average energy required to get atom to move in lattice

3.R - gas constant in units appropriate to the energy

4.T - temperature in absolute units - usually degrees kelvin

IV.Non-Steady State Diffusion

A.Concentration gradient and flux are a function of time

(most real situations)

B.Fick's second law -

V.Factors Affecting Diffusion

A.Atomic packing


C.Atomic size

D.Diffusion path

1.Bulk diffusion

2.Grain boundary diffusion

3.Surface diffusion



1.6.5 Mechanical Properties of Metals


I.Stress and Strain

A.Stress - the loading of a specimen

B.Strain - the response of the system

C.Tensile Testing

1.Axial loading of a specimen

2.Uniform round or rectangular cross-section

3.Stress -

4.Strain -

a.Linear -

b.Cross-sectional -

D.Compression Testing

1.'Squat' specimens needed to avoid bending

2.For brittle materials

3.For materials used under heavy compressive loads

E.Shear and Torsion Testing

1.Stress -

2.Strain -


III.Elastic Behavior

A.Hooke's Law

1.Stress proportional to strain in elastic region

2.Followed to considerable extent by most metals


4.E = modulus of elasticity or Young's modulus

B.Non-linear materials

1.Tangent modulus

Slope of stress-strain curve at point of interest

2.Secant modulus

Slope of stress strain from origin to some point on the line


1.Time dependent strain under load

2.Not significant for metals

3.High hysteresis for many polymers (pseudoplastic behavior)

D.Poisson's Ratio

1.Relation between strain in direction of applied stress and strain in transverse directions

2. where the applied stress is in the z direction

3.n =0.5 indicates no net change in volume

IV.Plastic Behavior

A.Onset of plastic deformation -

1.When dislocations begin moving in most metals

2.Viscous flow in amorphous materials

3.Twinning in some metals

B.Yielding -

1.Elastic limit - point at which deformation just begins -

not easily determinable

2.Proportional limit - point at which Hooke's law no longer is followed

3.Yield point phenomenon - abrupt onset of dislocation movement for solute 'pinned' dislocations

4.0.2% Yield Strength - stress at 0.002 strain

C.Tensile Strength (Ultimate Tensile Strength)

1.Maximum Engineering Stress Level reached

2.Based on starting cross sectional area

D.Fracture Strength

1.Stress at point of sample separation

2.Variable and not often used in engineering design


1.% elongation -

2.% reduction in area -


1.Amount of energy absorbed up to fracture

2.Equal to area under plastic portion of stress-strain curve


1.Energy absorbed by a specimen in elastic deformation

2.Equal to area under elastic portion of stress-strain curve

H.True Stress and Strain

1.Based on actual cross sectional area rather than original area

2.Higher values of stress and strain due to non-uniform deformation in neck


A.Hardness measurement concepts

1.Resistance to plastic deformation of surface



c.Most polymers

2.Resistance to elastic deformation of surface


b.Some other polymers

B.Hardness testing

1.Moh's hardness scale - hardness relative to naturally occurring minerals

2.Rockwell hardness scales

a.Relative depth of indentation of indenter into surface

b.Pre-load of indenter to penetrate surface scale and irregularities

c.Loads from 60 kg (soft materials) to 150 kg (hard materials)

3.Superficial Rockwell hardness scales

a.Relative depth of indentation into surface

b.Light loads (15 to 45 kg) to measure surface properties

4.Brinell hardness scale

a.Indentation of hardened ball into surface

b.Loads from 500 to 3000 kg

5.Vickers and Knoop microhardness scales

a.Very small diamond indenter

b.Indented into surface features using microscope on metallographic specimen

c.Hardness of individual phase regions of sample

6.Hardness conversions

a.Conversions between hardness scales not generally possible since different materials react

differently to different types of testing

b.Conversion scales available for specific material types

VI.Variability of Material Properties

A.Repeat testing necessary to determine material properties

B.Range of values often used to report strength or hardness in order to represent variability

VII.Safety Factors

A.Impossible to perfectly analyze stresses and material properties in any design problem

B.Safety factor used to account for unknowns in design parameters

C.Range of safety factors

1.Low safety factor when over-design may make product unusable

a.Select materials with small variability of properties (higher cost)

b.Increase inspections to detect incipient failures

2.High safety factor when safety is of ultimate concern and high cost and inspection are not practical



1.6.6 Dislocations and Strengthening Mechanisms


I.Dislocation Slip

A.Dislocation on closest packed plane, moving in close packed direction

B.Burger's vector offset - 1 inter-atomic spacing

C.Dislocation density

1.Usually 105 to 106 dislocations per cm2 (cm dislocations per cm3)

2.Cold worked materials up to 1010 / cm2

3.Dislocation formation due to interaction of dislocations with each other and other defects in the


D.Slip systems

1.Closest packed (or nearly so) planes

2.Close packed directions lying in the plane

3.Number and orientation of slip systems determines ductility

E.Single crystal slip

1.Resolved shear stress -


f = angle between applied force and normal to slip plane

l = angle between applied force and slip direction

3.Critical Resolved Shear Stress (CRSS) - t crss - stress on dislocation required to make it move

4.Minimum applied stress when f = l = 45°

F.Polycrystalline slip

1.Grain deformation constrained by contiguity with adjoining grains

2.Stress level in each grain not the same

3.Distortion of grain shape due to deformation

4.Crystal 'texture' due to grain rotation

5.Deformation by twinning

G.Strengthening mechanisms

1.Grain size reduction

2.Solid solution strengthening

3.Strain hardening

a.Cold working

b.%CW = ((A0-Ad)/A0) x 100%

c.Hot working


A.Elimination of effects of cold work by heat treatment



a.Reduction in strain energy

b.Elimination of some point defects

c.Improved conductivity


a.Nucleation and growth of new more perfect grains

b.Grain refinement

c.Recovery of ductility and toughness

d.Strength reduced from CW'd state but higher than before CW

3.Grain Growth

a.Increase in grain size to eliminate grain boundary defects

b.Reduction of strength



1.6.7 Phase Diagrams




1.Phase - a homogeneous portion of a system that has uniform chemical and physical characteristics - i.e., the

same crystal structure throughout with no discontinuous changes in composition or dimensions

2.Component - the chemical elements (or occasionally compounds) which compose an alloy

3.Solvent - the component of a solution present in the greatest amount

4.Solute - the component of a solution present in a minor amount (note that the distinction between solute and

solvent is sometimes blurred)

5.Solubility Limit - the maximum concentration of solute which can be dissolved in a solvent

6.Equilibrium - a system in its most stable or lowest energy configuration - reaching equilibrium may take a

very long time

B.Sugar - Water Phase Diagram

II.Solid State Phase Diagrams

A.Binary Isomorphous Systems (Cu-Ni)

1.Contain a single solid phase

2.Melting point range for all but pure components

3.Phase compositions in 2 phase regions - given by solubility limits of each phase

4.Phase amounts in 2 phase regions - given by position along tie line

5.Inverse Lever Arm Rule

a.Amount of given phase proportional to the length of tie line on opposite side of line

b.Calculated from phase compositions at solubility limits and composition of overall alloy

6.Equilibrium melting and solidification

7.Non-equilibrium solidification

a.Coring - varying composition of solid phase(s)

b.Suppression of melting point

8.Mechanical properties

a.Solid solution strengthening due to solute addition

b.Ductility reduction usually (but not always) occurs with strengthening

B.Binary Eutectic Systems

(Eutectic - having a low melting point)

1.Eutectic point (invariant point) - melting at a specific temperature

2.Three phases in equilibrium at eutectic point compositions and temperature

3.L Û a + b

a.Written as a cooling reaction

b.Phase compositions and temperatures included


a.Terminal solid solutions - phases containing the pure components

b.Hypoeutectic - having a composition less than eutectic

c.Hypereutectic - having a composition greater than eutectic

d.Proeutectic phases - form before (higher T) eutectic

e.Liquidus - line above which all of alloy is liquid

f.Solidus - line below which all of alloy is solid

g.Solvus - boundaries between solid phase regions

5.Eutectic microstructures

a.Eutectic alloys - often lamellar

b.Precipitation from terminal solid solutions

c.Hypo- and Hypereutectic alloy structures

C.Phase Diagrams with Intermediate (or Intermetallic) Phases

1.Phases present other than terminal solid solutions

a.Intermediate phases - solid solutions at intermediate compositions

b.Intermetallic compounds - stoichiometric phases with very small range of solubility

2.Eutectoid reaction (Eutectic like)

a.a Û b + g

b.Cools from one solid phase to two different solid phases

3.Peritectic reaction

a.a + L Û b

b.Cools from a mixture of liquid and a solid phase to a different solid phase

4.Peritectoid reaction

a.a + b Û g

b.Cools from a mixture of two solid phases to a different solid phase

5.Congruent transformations

a.L Û a or a Û b

b.A transformation with no change in composition of the phases

D.Gibb's Phase Rule

1.Determines the number of degrees of freedom of an alloy system with a certain number of phases in


2.P + F = C + N

P = number of phases in equilibrium

F = number of degrees of freedom

C = number of components in the alloy system

N = number of non-compositional variables (e.g., temperature and pressure)

III.Iron-Carbon Alloys (Fe-Fe3C phase diagram)


1.Ferrite - a iron

2.Austenite - g iron

3.Delta ferrite - d iron

4.Cementite (Iron Carbide) - Fe3C

B.Invariant reactions

1.Eutectic transformation - L ® g + Fe3C

2.Eutectoid transformation - g ® a + Fe3C

3.Peritectic transformation - d + L ® g

C.Eutectoid microstructures

1.Pearlite from eutectoid composition alloy

2.Hypoeutectoid alloys - proeutectoid ferrite

3.Hypereutectoid alloys - proeutectoid carbide

4.Rapidly cooled alloys





1.6.8 Phase Transformations


I.Nucleation and Growth Transformations

A.Nucleation time - slow transformation as nuclei form

B.Growth time - rapid growth initially followed by slowing growth (Fig 10.1)

C.Rate of reaction generally taken as r = 1/t0.5

D.Nucleation process - fastest when old phase(s) most unstable

E.Growth rate - fastest at higher temperatures (diffusion)

F.Reactions on heating - faster as T increases

G.Reactions on cooling

1.Nucleation faster as T decreases

2.Growth rate faster as T increases

II.Fe-Fe3C Transformations

A.Pearlite transformation

1.Rate increases as T decreases - down to about 550 ° C

2.Higher nucleation rate at lower T gives finer Pearlite

3.Isothermal Transformation Diagrams - transformation from austenite to ferrite and carbide when

held at constant T

B.Bainite transformation

1.Homogeneous nucleation at lower T produces Bainite

2.Transformation rate decreases as T decreases due to slower growth

3.Rapid cooling required to form Bainite

C.Spheroidite production

1.Coarse carbide particles in a ferrite matrix

2.NOT produced directly from austenite

3.Reheating of some other ferrite and carbide structure to coarsen carbides


1.Rapid cooling of austenite to temperature where austenite is very unstable but transformation

rate to ferrite and carbide is very slow

2.Body centered tetragonal lattice produced (BCC ferrite with supersaturation of carbon)

3.Athermal transformation - not time dependent

4.Degree of transformation dependent on temperature (Ms & Mf)

E.Tempered Martensite

1.Produced by reheating of Martensite

2.Martensite transforms to very fine ferrite and carbide

3.Structure similar to Bainite but easier to produce

4.Potential for warping and cracking in quench

F.Proeutectoid phase formation

1.Phases form only at higher temperatures where diffusion is fast

2.Proeutectoid ferrite for hypoeutectoid alloys

3.Proeutectoid carbide for hypereutectoid alloys

III.Isothermal Transformation Diagrams


1.Describe only the transformation of austenite when held at a fixed temperature

2.After austenite has been transformed, IT diagram no longer applies

3.Reheating will not reverse the transformation

4.IT diagrams apply to

a.a specific alloy composition

b.a specific austenitizing temperature and time

c.a specific austenite grain size

B.Plain Carbon Steel Alloys

1.Eutectoid Steel IT

a.Pearlite produced at higher temperatures - becomes finer as transformation T decreases

b.Bainite produced at medium temperatures - becomes finer as transformation T decreases

c.Martensite produced when quenched

2.Hypoeutectoid Steel IT

a.Proeutectoid ferrite produced if transformed above or just below eutectoid T

b.At lower T's, no proeutectoid regions

3.Hypereutectoid Steel IT

a.Proeutectoid carbide produced if fully austenitized and transformed above or just below

eutectoid T - NOT desirable

b.At lower T's, no proeutectoid regions

4.Martensite transformations

a.Ms & Mf decrease as carbon content increases

b.Higher carbon gives more strained M lattice

C.Alloy Steels

1.Alloying elements used to slow transformations (more diffusion required)

2.Pearlite transformation slowed more than bainite

3.Slower cooling and bainite formation possible

IV.Continuous Cooling Transformation Diagrams

A.CCT diagrams shifted to right and down from IT diagrams

B.Represent more realistic cooling in manufacturing

V.Mechanical Behavior

A.Effect of carbon content on mechanical properties

1.Higher C - higher strength and hardness

2.Higher C - lower ductility and toughness

B.Effect of microstructure on mechanical properties

1.Finer distribution of carbide - higher strength and hardness

2.Finer distribution of carbide - lower ductility and toughness



1.6.9 Metal Alloys


I.Fabrication Processes

A.Forming Operations

1.Cold working - deformation at temperature where a deformation structure is created

2.Hot working - deformation at temperature where dynamic recrystallization can occur

3.Forging - forcing metal to take the shape of a die by applying high pressure

4.Rolling - passing metal through restricted rollers to reduce thickness and/or produce a shape

5.Extrusion - pushing metal through a restricted opening to change its dimensions and/or shape

6.Drawing - pulling metal through a die to change its dimensions and/or shape

B.Casting Operations

1.Sand casting - pouring molten metal into a cavity formed by packing sand around a pattern

2.Die casting - forcing molten metal under pressure into a permanent cavity in a metal mold

3.Investment casting (lost wax process) - pouring molten metal into a cavity created by a wax pattern

surrounded by a ceramic shell

4.Continuous casting - casting of a continuous 'ingot' strand - not normally used to produce a finished product

C.Powder Metallurgy

1.Powdered metal compacted under high pressures to produce a 'green' compact

2.Green compact is sintered (heated) to produce fusion of the metal powder

II.Ferrous Alloys

A.Steels - up to approximately 1.4 % C

1.Low alloy

a.Low carbon < 0.25 % C

1.Plain carbon

a.Low carbon steels - not heat treatable as is

b.Inexpensive and easily formable

2.High strength low alloy

a.Small amounts of alloying elements to increase strength

b.Improved corrosion resistance

c.Higher cost

b.Medium carbon 0.25 to 0.60 % C

1.Plain carbon

a.Difficult to harden except for small parts

2.Low alloy

a.Alloying elements added to improve hardenability

b.Generally quenched and tempered or cooled to form bainite

c.High carbon > 0.60 % C

1.Plain carbon

a.Low cost tool steels

b.Hardened only by severe quenching

c.Soften easily in high speed cutting

2.Alloy tool steels

a.Alloying elements added to form stabile carbides

b.Hardened by moderate quenching

c.Hold edge at high speeds

2.High alloy

a.Stainless steels


a.FCC stabilized by Ni and/or Mn additions

b.Not hardenable


a.BCC stabilized by Cr additions

b.Low carbon, not hardenable


a.FCC and BCC lattices possible

b.C sufficient to form martensite

4.Precipitation Hardenable (PH)

a.Alloy precipitate formed

b.Not hardenable by eutectoid transformation

B.Cast Irons - carbon content in eutectic region

1.Gray Iron

a.2.5 - 4.0 wt. % C and 1.0 to 3.0 wt. % Si

b.Graphite flakes formed on solidification

c.High damping capability

d.Weak in tension

e.Alloy matrix



2.Ductile (Nodular) Iron

a.Graphite spheres formed on solidification

b.Additions of Mg or Rare Earths to change surface tension of C

c.More ductile than gray iron

d.Alloy matrix



3.martensite (tempered)

3.White Iron

a.Based on metastable Fe-Fe3C phase diagram

b.Low Si (<1%) and moderate C to alloy metastable Fe-Fe3C alloy

c.High hardness and wear resistance, brittle

III.Nonferrous Alloys

A.Copper and Alloys

1.Copper (nominally pure)

a.High conductivity

b.Soft and malleable


a.Cu-Zn alloys


1.single phase FCC lattice

2.soft and ductile


1.mixture of alpha and beta prime (ordered beta phase) phases

2.heavily strengthened by presence of hard beta prime' phase


a.Cu alloyed with Sn, Al, Si and/or Ni

b.Strong with good corrosion resistance

4.Precipitation hardened Be-Cu alloys

a.High strength and tough

b.Reasonably good conductors

c.Electrical contacts and springs

d.High strength tools and parts

B.Aluminum and Alloys

1.Wrought alloys

a.Designed to be formed by working processes

b.Heat treatable alloys can form a precipitate

c.Non-heat treatable alloys strengthened by solid solution only

2.Cast alloys

a.Designed to be formed only by casting - generally brittle if deformed

b.Heat treatable alloys are precipitation hardened

3.Temper designations

a.Describe heat treatment/cold work processes

b.F- as fabricated

c.H - strain hardened

d.O - annealed (softened)

e.T - hardened - various subtypes indicating combinations of cold work and aging

C.Other Nonferrous Alloys

1.Magnesium alloys

a.Used for their light weight

b.Chemically reactive, corrode easily

2.Titanium alloys

a.High strength, low weight alloys

b.Corrosion resistant

c.High cost

3.Refractory metals

a.High strength strongly bonded metals

b.Temperature resistant, but oxidize readily at high temperatures

c.Used primarily as alloying elements


a.Alloys based on Fe, Ni or Co

b.High strength, corrosion resistance and temperature resistance

c.Often include 10 or more other alloying elements

5.Noble metals

a.Expensive, corrosion resistant metals such as Au, Ag, Pd, Pt, etc.

b.Used for jewelry, catalysts, etc.



1.6.10 Ceramics


I.Ceramic Structures

A.Ionic ceramics

1.Ionic character based on difference in electronegativity

2.Charge neutrality required

3.Coordination number based on radius ratios of ions

4.AX Crystals

a.Rock salt (NaCl) CN = 6

b.CsCl CN = 8

c.ZnS CN = 4

5.AmXp Crystals


6.AmBnXp Crystals


B.Silicate ceramics

1.Tetrahedral bonding - highly covalent

2.Crystalline SiO2

3.Silica glasses - amorphous

C.Carbon polymorphs

1.Diamond - cubic crystal

2.Graphite - ordered structure in 2-D layers

3.Fullerenes - "buckyballs" - complex 3-D structures

II.Defects in Ceramics

A.Schottky defect - ion pair vacancy

B.Frenkel defect - cation vacancy/cation interstitial pair

C.Vacancies in crystals with polyvalent ions

e.g., FeO with Fe+2 and Fe+3

D.Interstitial solute

E.Substitutional solute

III.Phase Diagrams

Components often stable compounds

IV.Mechanical Behavior

A.Flexure testing

B.Brittle fracture

C.Viscous flow in amorphous ceramics (creep)

Chapter 15 - Polymer Structures


I.Hydrocarbons and Polymers

A.Saturated Hydrocarbons (CnH2n+2)

1.Covalent bonds in molecules

2.Weak van der Waals bonds between molecules

3.Melting point and strength increase with molecule size

B.Isomers - same chemical formula but different structure

II.Thermoplastic vs. Thermosetting

A.Thermoplastic polymers

1.Large molecules bonded to each other with weak bonding forces

2.Soften on heating

B.Thermosetting polymers

1.3-D network of strong (usually covalent) bonds throughout polymer structure

2.Smaller molecules may be trapped in the 3-D network

3.Will NOT soften on heating once 3-D structure is created

III.Common Polymers


1.Polymers based on mer C2H3X


3.Polyvinyl chloride



B.Vinylidenes - Polymethyl methacrylate

C.Teflon - PTFE

D.Bakelite (Phenyl-formaldehyde) - thermoset

E.Other thermoplastics

1.Nylon 6,6




A.Monomer - basic building block of the polymer

B.Mer - the smallest repeating unit of a polymer

C.Addition polymerization

1.Active radical (such as HO· ) breaks bond in monomer

2.Active site breaks bond in additional monomer and adds it to chain

V.Molecular Weight

A.Polymer properties partially based on average molecular weight

B.- the number average molecular weight

C.- the weight average molecular weight

D.Degree of polymerization - average number of mers per molecule

VI.Polymer Structures

A.'Random walk' arrangement for linear polymer mers able to rotate freely

B.Branched polymers

C.Crosslinked polymers (vulcanized)

D.Network polymers (thermosets)


1.Stereoisomers - same bonds but different positioning of side groups on adjoining mers




2.Geometrical isomers - side groups bonded to same atoms but different positions within the mer


1.natural rubber

2.elastic material due to 'arched' mer


1.gutta percha

2.hard brittle material due to linear mer

F.Copolymers - more than one mer in a linear polymer

1.Random - random arrangement of mers in chain

2.Alternating - alternating arrangement of mers in chain

3.Block - blocks of each type of mer in chain

4.Graft - backbone of one mer and chains of other mer grafted into backbone


1.Mers must have a regular arrangement in linear chain

2.Regions of crystallinity - never completely a crystal



1.6.11 Electrical Properties


I.Electrical Conductivity

A.Ohm's Law - V = I R

B.Resistivity (Conductivity) -

C.Conduction by electrons or by ions

II.Band Structures in Solids

A.Discrete energy levels in isolated atoms

B.Energy bands for valence electrons as the atoms come close together and bond

C.Valence band - energy band containing valence electrons in lowest energy state

D.Conduction band - energy band with next highest energy levels beyond valence band - no electrons at

lowest energy state

E.Fermi energy - highest filled energy state at 0K (lowest energy state)

F.Energy band gap - energy difference between energy of highest energy electron at 0K and the next

empty state

III.Conduction Models

A.Metallic Materials

1.Very small energy band gap - highest filled state and next state adjacent to each other

2.Partially filled valence band

3.Overlapping valence and conduction bands


1.Strong ionic or covalent bonding holds electrons tightly

2.Large energy band gap between filled valence band and conduction band

3.High amount of activation energy required to boost electron from valence to conduction band


1.Weaker covalent bonding

2.Small energy band gap between filled valence band and conduction band

3.Small amount of activation energy required to boost electron from valence to conduction band


1.Ability of an electron to move under the force of an applied electric field

2.Conductivity given by number of carriers, charge of carrier and mobility of carrier -

E.Electrical Resistivity

1.Metallic materials

a.Temperature effects

1.Resistivity increases with temperature

2.Change approximately linear for metals in normal temperature range of application -

b.Alloying effects

1.Adding alloying elements to a pure material increases resistivity

2.Multiphase materials have net resistivity approximately proportional to resistivity and amount

of each phase

c.Deformation effects - Cold work increases resistivity due to distorted lattice


A.Intrinsic Semiconduction

1.Conduction due to excitation of valence electrons into conduction band

2.Equal number of electron carriers in conduction band and empty sites (holes) in valence band

3.Hole - treated as a positive carrier with charge magnitude same as electron (electrons actually move)

4.Conductivity due to sum of conductivity of electrons and holes -


where n = p for intrinsic conduction


B.Extrinsic Semiconduction

1.Conduction primarily due to either electrons or holes

2.n-type extrinsic semiconduction

a.Addition of impurity with extra valence electron

b.Donor electron will have energy close to conduction band

c.n >> p at operating temperatures,

3.p-type extrinsic semiconduction

a.Addition of impurity with one less valence electron

b.Acceptor site will have energy close to valence band

c.p >> n at operating temperatures,

C.Effects of Temperature on Conduction

1.Electron mobility decreases with temperature

2.Number of carriers increases with temperature in a semiconductor

3.Intrinsic semiconductors

a.Equal numbers of n and p carriers

b.Carriers increase faster than mobility decreases

4.Extrinsic semiconductors

a.p-type semiconductors

1.more holes than electrons

2.saturation level for normal operation

b.n-type semiconductors

1.more electrons than holes

2.exhaustion level for normal operation

V.Hall Effect

A.Moving carriers subjected to a magnetic field

B.Positive and negative carriers deflected in opposite directions

C.Voltage induced perpendicular to current flow

VI.Semiconductor Devices


1.p-n junction

2.movement of charge carriers from junction leads to rectification

a.forward bias - carriers pushed to junction region and combine

b.reverse bias - carriers pulled away from junction - few carriers to combine and carry


3.I-V characteristics of a diode

a.large forward current

b.small reverse current

c.breakdown at high reverse voltages


1.Bipolar Junction Transistors (BJT's)

a.3 semiconducting regions - NPN or PNP

b.emitter-base junction forward biased

c.base-collector junction reverse biased

d.pnp operation

1.narrow base region allows holes to pass from emitter to collector through the base

2.small base-emitter current controls larger emitter-collector current

e.npn operation

1.narrow base region allows electrons to pass from emitter to collector through the base

2.small base-emitter current controls larger emitter-collector current

2.Metal Oxide Silicon Field Effect Transistor (MOSFET)

a.single charge carrier active but controlled by a narrow channel which carriers must pass


b.very small gate current can control large source-drain current (high input impedance)

c.p-channel FET

1.positive charge on gate will reduce hole carriers in p-type Si

2.negative charge on gate will allow passage of holes

d.n-channel FET

1.negative charge on gate will reduce electron carriers in n-type Si

2.positive charge on gate will allow passage of electrons

VII.Conductivity in Ceramics and Polymers

A.Ionic Ceramics

1.Conduction primarily due to ion motion

2.Generally insulating materials until at or near melting


1.Generally insulating due to covalently bonded electrons

2.Conduction possible by doping with appropriate compounds (sometimes filled with conducting elements)

VIII.Dielectric Behavior

A.Dielectric Materials - insulators with internal dipoles capable of aligning with an external field


1.Relative ability of a device to store charge

C = Q/V (units of farads or coulombs/volt)

2.Parallel plate capacitor

C = e (A/l)

a.e is the permittivity of the material between the plates

b.A is the area of the plates

c.l is the distance between the plates


a.in a vacuum - e 0 = 8.85 x 10-12 F/m

b.relative permittivity (dielectric constant) - e r = e /e 0

c.dielectric strength - resistance to breakdown in presence of an electric field



1.6.12 Thermal Properties


I.Background for interest in thermal properties

A.Thermal expansion variations in circuit parts

B.Thermal conductivity for energy removal from circuits

C.Component property variation with temperature

II.Heat Capacity

A.Measure of the amount of thermal energy which can be absorbed

1.C = dQ/dT in J/mol-K

2.Specific heat equals heat capacity per unit mass (J/kg-K)

3.May be measured as heat capacity at constant volume, Cv, or heat capacity at constant pressure, Cp. For

solids they are approximately equal

B.Vibrational Heat Capacity

1.Quantized vibrational energy in atoms (electrons)

2.Phonon - quantum of vibrational energy

3.Scattering of electrons due to vibration

C.Temperature Dependence

1.Cv = AT3 at low temperatures, i.e., increases rapidly with temperature up to the Debye temperature

2.Cv approximately constant at higher temperatures

Cv @ 3 R = 25 J/mol-K above q d (Debye Temperature)

D.Other Factors

1.Electron excitation - small contribution by free valence electrons

2.Randomization of electron spins at Curie temperature

III.Thermal Expansion

A.Linear Thermal Expansion Coefficient

1.D l/l0 = a l D T where a l is the thermal expansion coefficient at room temperature (usually about 25 ° C)

2.Thermal expansion varies slightly with temperature - correction needed far from room temperature

3.Related to average atomic spacing as temperature increases - refer to atomic bonding curves

B.Bulk Thermal Expansion Coefficient

a v @ 3 a l

IV.Thermal Conductivity

A.Steady State Heat Flux -

1.Analogous to diffusion - flow of heat from high temperature region to low temperature region

2.Flux proportional to temperature gradient

B.Conduction mechanisms

1.Lattice vibration waves (phonons) - primarily in insulators

2.Electron motion - primarily in conductors

3.Thermal conductivity, k, related to electronic conductivity in metals by Wiedemann-Franz Law - k = Ls T

V.Thermal Stresses

A.Stresses can be created by thermal expansion (contraction) of a restrained object

B.Stresses can be created by differential thermal expansion (contraction)

C.Thermal shock

1.Stresses due to rapid temperature change

2.Resistance improved by

a.High fracture strength

b.High thermal conductivity

c.Low moduli of elasticity

d.Low thermal expansion coefficients (often at odds with c.)



1.6.13 Magnetic Properties of Materials


I.Magnetic Induction

A.Magnetic field induced by electrical current

1.Magnetic Field Strength -

H - magnetic field strength (amperes/meter)

N - number of turns in coil

I - current in coil

l - length of coil

2.Magnetic Flux Density - indicates response of material subjected to a Magnetic Field


B - Magnetic Flux Density (teslas - webers/square meter)

m - magnetic permeability (Wb/A-m)

3.Magnetic Field Strength in a vacuum given by

where m 0 is the permeability of a vacuum (4p x10-7 H/m)

4.Relative permeability - indicates the relative ability of a material to be magnetized by an external

magnetic field.

5.Magnetization - M - represents the magnetic field strength contributed by the magnetization of the medium

in the magnetic field



where c m is the magnetic susceptibility which is also given by c m = m r - 1


B.Material Response to a Magnetic Field


a.No permanent magnetic dipoles

b.Induced magnetic dipoles in atoms align in a direction opposite to the applied field

c.The magnetic flux density is thus slightly less than it would be in a vacuum, m r < 1


a.Permanent magnetic dipoles randomly arranged when no field applied - thus no magnetism


b.Magnetic dipoles in atoms align in the same direction as the applied field

c.The magnetic flux density is thus slightly greater than it would be in a vacuum, m r > 1


a.Strong permanent magnetic dipoles

b.M >> H, thus B @ m 0M

c.Atomic dipoles tend to align over relatively large areas even without an applied field

(magnetic domains)

d.Saturation magnetization (Ms) occurs when all dipoles align with external field

e.Contribution of individual atoms to magnetization sums to total Ms


a.Permanent magnetic dipoles naturally align in opposing orientations

b.No net magnetic moment results


a.Ceramics may exhibit permanent magnetization

b.Magnetization depends on crystallographic orientation of atoms in lattice

II.Temperature and Magnetization

A.Saturation magnetization decreases with increased temperature

B.Curie Temperature - Tc - temperature at which ferromagnetism ceases, 768° C for iron

III.Magnetic Domains and Hysteresis


1.Magnetic dipoles in a domain aligned

2.Dipole arrangement varies from domain to domain

3.Domains usually smaller than grain size

4.Dipole orientation transition across domain wall boundary

5.Random domain orientation gives unmagnetized material


1.Magnetization curve

a.Applied H field causes domains to align

b.Reducing H field to zero leaves permanent magnetization in ferromagnetic material

(Remanence - Br)

c.H field required to reduce B to zero is the Coercivity, Hc

d.Energy absorbed in cycling through hysteresis loop - proportional to area inside curve

e.Demagnetization by cycling hysteresis curve from large amplitude down to zero

C.Soft vs. Hard Magnetic Materials

1.Hard magnetic materials

a.High Remanence and Coercivity (large hysteresis)

b.Difficult to demagnetize

c.High energy loss in cyclic field

d.Good for permanent magnets

2.Soft magnetic materials

a.Low Remanence and Coercivity (small hysteresis)

b.Easy to demagnetize

c.Low energy loss in cyclic field

d.Good for motor and solenoid cores



1.6.14 Optical Properties of Materials


I.Electromagnetic Radiation








7.g -rays


1.Wave Model

a.Electric field component

b.Magnetic field component

c.Speed of propagation 3x108 m/sec in a vacuum

1.e 0 - electric permittivity of a vacuum

2.m 0 - magnetic permeability of a vacuum

d.Relationship of frequency (n ) and wavelength (l ) - c = l n

2.Particle Model

a.Quantized photons of energy



where h = Planck's constant


II.Interactions with Matter

A.Electron excitation

1.Photon energy transferred to electron if change of energy D E puts the electron at an allowable energy state

2.D E = hn

B.Reemission of photon

1.Excited electron will fall back to lower energy state with emission of photon

2.Emission in visible range can be created by excitation from electron or other particle (CRT)

C.Interaction with semiconductors

1.Electron - hole pair created if hn > Eg

2.Recombination of electron and hole emitting photon of radiation

III.Applications in Electrical Devices


1.Excited electrons dropping back to a lower energy state emitting photon of light

2.Electroluminescence (LED)

a.Electron - hole recombination at p-n junction can produce photon of light

b.Optical range of emission

1.1.8 eV - red LED's (GaAs)

2.3.1 eV - blue/violet LED's (Diamond)


a.Activation of electrons from valence band to conduction band

b.Increase in carriers increases conductivity



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