Materials Engineering and Technology Notes

Materials Science and Engineering Tetrahedron

• Materials Science and Engineering is a multidisciplinary field.

• It explores the structure, properties, processing, and performance of materials.

• The Materials Science and Engineering Tetrahedron provides a framework to understand the four major components that contribute to this field

  • Processing

  • Structure

  • Properties

  • Performance

• The tetrahedron also considers:

  • Sustainability/Criticality

Processing

• The techniques and methods used to modify and shape materials.

• Example: Heat Treatment

  • Heat treatment alters the microstructure of materials to enhance their properties.

  • Examples: Annealing, quenching, tempering.

• Processing Steps:

  • Extraction of ore

  • Separation of metal compounds from sand and rock

  • Chemical separation of metal from other elements

• Common processing methods:

  • Forging: Applying powerful impact on hot metal workpiece.

  • Drawing: Pulling metal through a die.

  • Rolling: Passing hot or cold metal between upper and lower rolls.

  • Casting: Pouring liquid metal into a mold/die and let it solidified.

Structure

• The study of the arrangement of atoms, ions, or molecules in a material.

• Example: Crystal Structure

  • Understanding the atomic arrangement in a crystal lattice provides insights into its properties and behavior.

  • Examples: Diamond, Sodium Chloride (NaCl) crystal lattice.

• Scales:

  • 10^{-9} m: Quantum Physics

  • 10^{-6} m: Chemistry

  • 10^{-3} m: Materials Science

  • 10^{0} m: Traditional Engineering (Civil, Mechanical)

  • 10^{3} m: Geology

  • 10^{6} m: Astrophysics

• Examples of structure:

  • Graphite Sheets: Individual Layer is "Graphene"

  • Diamond Structure

Properties

• Investigating the physical and chemical characteristics of materials.

• Example: Mechanical Properties

  • Mechanical properties describe how a material responds to external forces.

  • Examples: Tensile strength, hardness, elasticity.

• Examples of hardness (Softer to Harder):

  • Air, Butter, Steel, Diamond

• Steel Microstructure:

  • Steel Consists of Two Phases: Iron and Cementite

  • Fe: Pure Iron Matrix

  • Fe_3C: Cementite Precipitates

• Examples of Material Properties:

  • Mechanical

  • Thermal

  • Chemical

  • Optical

  • Magnetic

  • Electronic

  • Processing

Performance

• Evaluating how materials perform under specific conditions and applications.

• Example: Corrosion Resistance

  • Assessing a material's ability to resist chemical reactions with its surroundings.

  • Example: Stainless steel's resistance to rust and corrosion.

• Ashby Diagrams:

  • Used for materials selection.

  • Plot Young's Modulus (GPa) vs. Density (kg/m^3) on logarithmic scales.

  • Material groups are plotted such as Ceramics, Composites, Natural materials, Foams, Metals, Polymers, Elastomers

Classification of Materials

• Metals

• Ceramics

• Polymers

• Composites

• Advanced Materials

  • Semiconductors

  • Biomaterials

  • Smart Materials

  • Nanomaterials

Classification of Functional Materials

• Structural Materials

  • Steels, Aluminum alloys, Concrete, Fiberglass, Plastics, Wood

• Aerospace Materials

  • C-C composites, SiO_2, Amorphous silicon, Al-alloys, Superalloys, Zerodur™

• Biomedical Materials

  • Hydroxyapatite, Titanium alloys, Stainless steels, Shape-memory alloys, Plastics, PZT

• Smart Materials

  • PZT, Ni-Ti shape-memory alloys, MR fluids, Polymer gels

• Electronic Materials

  • Si, GaAs, Ge, BaTiO3, PZT, YBa2Cu3O{7-x}, Al, Cu, W, Conducting polymers

• Optical Materials

  • SiO2, GaAs, Glasses, Al2O_3, YAG, ITO

• Magnetic Materials

  • Fe, Fe-Si, NiZn and MnZn ferrites, Co-Pt-Ta-Cr, γ-Fe2O3

• Energy Technology and Environmental Materials

  • UO2, Ni-Cd, ZrO2, LiCoO_2, Amorphous Si:H

Material Properties Comparison

• Density (g/cm³): Metals (high), Ceramics, Composites, Polymers (low)

• Stiffness [(Elastic (or Young's) Modulus (in units of gigapascals)]: Ceramics (high),Metals, Composites, Polymers (low)

• Strength (Tensile Strength, in units of megapascals): Metals (high), Ceramics, Composites, Polymers (low)

• Resistance to Fracture (Fracture Toughness, in units of MPa\/m): Metals (high), Composites, Polymers, Ceramics(low)

• Electrical Conductivity (in units of reciprocal ohm-meters): Metals (high), Semiconductors, Ceramics, Polymers (low)

Structure of Crystalline Solids

• Crystalline material is a material in which the atoms are situated in a repeating or periodic array over large atomic distances; that is, long-range order exists

• Atoms position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms.

• All metals, many ceramic materials, and certain polymers form crystalline structures under normal solidification conditions.

• Noncrystalline or amorphous materials do not have long-range atomic order.

• Crystal structure is the manner in which atoms, ions, or molecules are spatially arranged.

• Some of the properties depend on the crystal structure.

• Atomic hard-sphere model assumes atoms are hard spheres that touch each other.

• Lattice is a three-dimensional array of points coinciding with atom positions (or sphere centers).

• Unit Cell: The smallest building block of a crystal, consisting of atoms, ions, or molecules, whose geometric arrangement defines a crystal's characteristic symmetry and whose repetition in space produces a crystal lattice.

Common Metallic Crystal Structures

• Face-Centered Cubic (FCC)

  • Cubic geometry with atoms at corners and face centers.

  • Examples: copper, aluminum, silver, and gold.

  • Each corner atom is shared among eight unit cells (8 corners * 1/8), each face-centered atom is shared by two unit cells (6 faces * 1/2).

  • A total of four whole atoms may be assigned to a given unit cell.

  • Coordination number: 12 (number of nearest-neighbor atoms).

  • Atomic Packing Factor (APF): 0.74 (maximum packing possible for spheres).

    • Defined as the sum of the sphere volumes of all atoms within a unit cell (hard-sphere model) divided by the unit cell volume.

    • APF = \frac{volume \ of \ atoms \ in \ a \ unit \ cell}{total \ unit \ cell \ volume} = \frac{Vs}{Vc}

    • APF = \frac{(4) \frac{4}{3}πR^3}{16R^3 \sqrt{2}} = 0.74

  • Cube edge length a and atomic radius R are related through: a = 2R\sqrt{2}.

    • This comes from atoms touching one another across a face-diagonal.

• Body-Centered Cubic (BCC)

  • Cubic geometry with atoms at all eight corners and a single atom at the cube center.

  • Examples: Chromium, iron, tungsten.

  • Two atoms are associated with each BCC unit cell: one from the eight corners, and the single center atom.

  • Coordination number: 8.

  • BCC unit cell length a and atomic radius R are related through: a = \frac{4R}{\sqrt{3}}.

    • The relationship is derived using geometry: a^2 + a^2 = (4R)^2 \implies a = 2R\sqrt{2}

  • Atomic Packing Factor (APF): 0.68.

    • Show that the atomic packing factor for BCC is 0.68: APF = \frac{Vs}{Vc} = \frac{(2) \frac{4}{3}πR^3}{a^3} = \frac{(2) \frac{4}{3}πR^3}{(\frac{4R}{\sqrt{3}})^3} = 0.68

Theoretical Density for Metals

• The theoretical density of a metallic solid can be computed through the relationship: \rho = \frac{nA}{Vc NA}

  • n = number of atoms associated with each unit cell

  • A = atomic weight

  • VC = volume of the unit cell

  • N_A = Avogadro’s number (6.022 \times 10^{23} atoms/mol). Copper example:

    • Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. The literature value for the density of copper is 8.94 g/cm3.

    • Because the crystal structure is FCC, n = 4. Also, A(Cu) = 63.5 g/mol.

    • Unit cell volume: Vc = a^3 = (2R\sqrt{2})^3 = 16R^3\sqrt{2}. Vc = (16)(\sqrt{2})(1.28 \times 10^{-8} cm)^3 = 3.73 \times 10^{-23} cm^3/unit cell.

    • Substitution into the density equation yields: \rho = \frac{nA}{Vc NA} = \frac{(4 \ atoms/unit \ cell)(63.5 \frac{g}{mol})} {(3.73 \times 10^{-23} \frac{cm^3}{unit \ cell})(6.022 \times 10^{23} \frac{atoms}{mol})} = 9.0 \frac{g}{cm^3}

Polymorphism and Allotropy

• Polymorphism: Some metals and nonmetals have more than one crystal structure.

• Allotropy: When polymorphism is found in elemental solids.

• The prevailing crystal structure depends on temperature and external pressure.

• Examples:

  • Carbon: Graphite (stable at ambient conditions), Diamond (formed at extremely high pressures).

  • Iron: BCC at room temperature, changes to FCC at 912 °C.

• A modification of the density and other physical properties accompanies a polymorphic transformation.

Crystal Systems

• Crystal structures are divided into groups according to unit cell configurations.

• Based on unit cell geometry.

• An xyz coordinate system is established with its origin at one of the unit cell corners.

• Lattice Parameters:

  • The unit cell geometry is completely defined in terms of six parameters: the three edge lengths a, b, and c, and the three interaxial angles α, β, and γ.

• Seven Crystal Systems:

  • Cubic: a = b = c, α = β = γ = 90°

  • Hexagonal: a = b ≠ c, α = β = 90°, γ = 120°

  • Tetragonal: a = b ≠ c, α = β = γ = 90°

  • Rhombohedral (Trigonal): a = b = c, α = β = γ ≠ 90°

  • Orthorhombic: a ≠ b ≠ c, α = β = γ = 90°

  • Monoclinic: a ≠ b ≠ c, α = γ = 90° ≠ β

  • Triclinic: a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90°

Crystallographic Points, Directions, and Planes

• Point coordinates: positions within a unit cell specified as fractional multiples of the edge lengths (a, b, c).

• Crystallographic Directions:

  1. A vector of convenient length is positioned such that it passes through the origin of the coordinate system.

  2. The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c.

  3. These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values.

  4. The three indices, not separated by commas, are enclosed in square brackets, thus: [uvw]. The u, v, and w integers correspond to the reduced projections along the x, y, and z axes, respectively.

• Negative indices are represented by a bar over the appropriate index.

• Miller-Bravais indices are used for hexagonal crystals. The three a1, a2, and a3 axes are all contained within a single plane (called the basal plane) and are at 120˚ angles to one another, and the z-axis is perpendicular to this basal plane. Directional indices, which are obtained as described earlier, will be denoted by four indices, as [uvtw]; by convention, the first three indices pertain to projections along the respective a1, a2, and a3 axes in the basal plane. The conversion from the three-index system to the four-index system, is accomplished by the following formulas:

  • u = \frac{1}{3}(2u' - v'), v = \frac{1}{3}(2v' - u'), t = -(u + v), w = w'

• Crystallographic Planes:

  1. If the plane passes through the selected origin, either another parallel plane must be constructed within the unit cell by an appropriate translation, or a new origin must be established at the corner of another unit cell.

  2. At this point the crystallographic plane either intersects or parallels each of the three axes; the length of the planar intercept for each axis is determined in terms of the lattice parameters a, b, and c.

  3. The reciprocals of these numbers are taken. A plane that parallels an axis may be considered to have an infinite intercept, and, therefore, a zero index.

  4. If necessary, these three numbers are changed to the set of smallest integers by multiplication or division by a common factor.

  5. Finally, the integer indices, not separated by commas, are enclosed within parentheses, thus: (hkl).

• For cubic crystals, the angle, θ between two planes, (h1 k1 l1) and (h2 k2 l2) is given by:

  • cos \theta = \frac{h1h2 + k1k2 + l1l2}{\sqrt{(h1^2 + k1^2 + l1^2)(h2^2 + k2^2 + l2^2)}}

• Planar Atomic Arrangements:

  • A family of planes contains all planes that are crystallographically equivalent—that is, having the same atomic packing.

  • A family is designated by indices enclosed in braces—such as {100}.

• Linear Density (LD):

  • Number of atoms per unit length whose centers lie on the direction vector for a specific crystallographic direction. LD = \frac{number \ of \ atoms \ centered \ on \ direction \ vector}{length \ of \ direction \ vector}

• Planar Density (PD):

  • Number of atoms per unit area that are centered on a particular crystallographic plane. PD = \frac{number \ of \ atoms \ centered \ on \ a \ plane}{area \ of \ plane}

• Slip occurs on the most densely packed crystallographic planes and, in those planes, along directions having the greatest atomic packing.

Crystalline and Non-Crystalline Materials

• Single Crystals:

  • The periodic and repeated arrangement of atoms is perfect or extends throughout the entirety of the specimen without interruption.

  • Single crystals exist in nature, but they can also be produced artificially.

  • Extremely important in many modern technologies; electronic microcircuits.

• Polycrystalline Materials:

  • Composed of a collection of many small crystals or grains.

  • Most crystalline solids are polycrystalline.

  • Grains grow and form irregular shapes upon completion of solidification.

  • Grain boundaries: areas where crystals of different orientations meet

• Anisotropy

• The physical properties of single crystals of some substances depend on the crystallographic direction in which measurements are taken.

• This directionality of properties is termed anisotropy, and it is associated with the variance of atomic or ionic spacing with crystallographic direction.

• Substances in which measured properties are independent of the direction of measurement are isotropic.
  *Non-crystalline materials

• lack systematic and regular arrangement of atoms over relatively large atomic distances.

• Sometimes such materials are also called amorphous

Imperfections in Solids

• All crystalline materials contain large numbers of various defects or imperfections.

• Classification:

  • Point Defects: associated with one or two atomic positions.

  • Linear (or One-Dimensional) Defects: Dislocations

  • Interfacial Defects: Grain Boundaries

  • Volume Defects: Pores, cracks

Point Defects

• Vacancy: A vacant lattice site, one normally occupied from which an atom is missing.

  • The equilibrium number of vacancies depends on and increases with temperature according to: Nv = N \exp(-\frac{Qv}{kT})

    • Nv is the number of vacancies

    • N is the total number of atomic sites

    • Qv is the energy required for the formation of a vacancy

    • T is the absolute temperature in kelvins

    • k is the gas or Boltzmann’s constant (1.38 \times 10^{-23} J/atom-K, or 8.62 \times 10^{-5} eV/atom-K).

• Self-Interstitial: An atom from the crystal that is crowded into an interstitial site.

  • Formation is not highly probable and exists in very small concentrations.

Linear Defects

• Dislocation: A linear or one-dimensional defect around which some of the atoms are misaligned.

  • Edge Dislocation: An extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal.

    • Dislocation line: the line that is defined along the end of the extra half-plane of atoms (perpendicular to the plane of the page).

  • Screw Dislocation: is thought of as being formed by a shear stress that is applied to produce the distortion

• Mixed Dislocations: Exhibit components of both edge and screw types.

• Burgers Vector: The magnitude and direction of the lattice distortion associated with a dislocation.

  • For edge dislocations, the burgers vector and dislocation line are perpendicular.

  • For screw dislocations, the burgers vector and dislocation line are parallel.

  • For metallic materials, the Burgers vector will point in a close-packed crystallographic direction and will be of magnitude equal to the interatomic spacing.

• Slip: Permanent deformation of most crystalline materials is by the motion of dislocations

• Slip planes and directions in metallic structures

  • Depends on the type of lattice, different slip systems are present in the material. More specifically, slip occurs on close- packed planes (those containing the greatest number of atoms per area), and in close-packed directions (most atoms per length).

Planar Defects

• Boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and\/or crystallographic orientations.

  • External Surfaces

    • Surface atoms are not bonded to the maximum number of nearest neighbors and are in a higher energy state than the atoms at interior positions.

    • Surface energy: expressed in units of energy per unit area (J/m2).

  • Grain Boundaries

    • Separate regions of different crystalline orientation (i.e., grains) within a polycrystalline solid.

    • Small- (or Low-) Angle Grain Boundary: When the orientation mismatch is slight.

    • High-Angle Grain Boundaries: When the orientation mismatch is significantly higher.

  • Phase Boundaries

    • Exist in multiphase materials, wherein a different phase exists on each side of the boundary

Volume Defects

• Exist in all solid materials that are much larger than those heretofore discussed.

• Include pores, cracks, foreign inclusions, and other phases.

• Normally introduced during processing and fabrication steps.

Solid Solutions

• A solid-state solution of one or more solutes in a solvent.

  • The crystal structure of the solvent remains unchanged by the addition of the solutes.

  • The mixture remains in a single homogeneous phase.

• Types of Solid Solutions

  • Substitutional

  • Interstitial
    *Solubility: is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent.
    *Unlimited
    *Limited

• Hume-Rothery Rules
  * Used to determine conditions for unlimited solid solubility:
  1. Atomic radius difference less than 15%.
  2. Similar crystal structures.
  3. Similar valency.
  4. Similar electronegativity.

Phases and Phase Diagrams

• Phase: A homogeneous portion of a system that has uniform physical and chemical characteristics, bounded by a surface that separates it from any other portions.

  • The same structure or atomic arrangement throughout

  • Roughly the same composition and properties throughout.

  • A definite interface between the phase and any surrounding or adjoining phases.

• Cooling Curve: A graphical plot of the changes in temperature with time for a material over the entire temperature range through which it cools.

Phase Diagram

• A graphical representation of the physical states of a substance under different conditions of temperature and pressure.

• Shows the phases and their compositions at any combination of temperature and alloy composition.

Isomorphous Phase Diagrams

• Binary phase diagram: When only two elements or two compounds are present in a material.
  * Only one solid phase forms
  * The two components in the system display complete solid solubility
  * ex: Cu-Ni

• Liquidus Temperature: The temperature above which a material is completely liquid.

• Solidus Temperature: The temperature below which the alloy is 100% solid.
  *Freezing range: The temperature difference between the liquidus and the solidus is the freezing range of the alloy.
  Composition of Each Phase:
  *We can use a tie line to determine the composition of the two phases.
  A tie line is a horizontal line within a two-phase region drawn at the temperature of interest

• In an isomorphous system, the tie line connects the liquidus and solidus points at the specified temperature.
  The ends of the tie line represent the compositions of the two phases in equilibrium

• Amount of Each Phase ( the Lever Rule)
  To calculate the amounts of liquid and solid, we construct a lever on our tie line, with the fulcrum of our lever being the original composition of the alloy.
  The leg of the lever opposite to the composition of the phase, the amount of which we are calculating, is divided by the total length of the lever to give the amount of that phase.
  The lever rule in general can be written as

Binary Eutectic Phase Diagram

*The below binary eutectic phase diagram explains the chemical behaviour of two elements with limited solubility in solid state but are completely soluble in liquid state

Binary Eutectic Phase Diagram: Terminology

Terminal solid solutions
Liquidus
Solidus
Solvus
Eutectic point
Eutectic isotherm
Hypo-eutectic
Hyper-eutectic
*Copper silver system example - A number of features of this phase diagram are important

IRON IRON-CARBON DIAGRAM

*Cooling curve for pure iron

Definition of structures

Various phases that appear on the Iron-Carbon equilibrium phase diagram are as under:
*Austenite
*Ferrite
*Pearlite
*Cementite
Martensite*
*Ledeburite

Unit Cells of Various Phases

FIGURE - The unit cell for (a) austenite, (b) ferrite, and (c) martensite. The effect of the percentage of carbon (by weight) on the lattice dimensions for martensite is shown in (d). Note the interstitial position of the carbon atoms and the increase in dimension c with increasing carbon content. Thus, the unit cell of martensite is in the shape of a rectangular prism.
Microstructure of different phases

Definition of structures 1. Ferrite is known as α solid solution. 2. It is an interstitial solid solution of a small amount of carbon dissolved in α (BCC) iron. 3. stable form of iron below 912 deg. C 4.The maximum solubility is 0.025 % C at 723°C and it dissolves only 0.008 % C at room temperature. 5. It is the softest structure that appears on the diagram.

*Pearlite
*Austenite
Cementite
Martensite
Ledeburite
Various
Invariant Reactions
*Fe-Fe diagram with regions
The diagram shows three horizontal lines which indicate isothermal reactions (on cooling \/ heating):

• Delta region of Fe-Fe carbide diagram
  Ferrite region of Fe-Fe Carbide diagram
  The Austenite to ferrite \/ cementite transformation in relation to Fe-C diagram

Pearlitic Structure

*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.

Hypo-Eutectoid Steels

*Hypo-eutectoid steels: Steels having less than 0.8% carbon are called hypo-eutectoid steels (hypo means "less than").
*At high temperatures the material is entirely austenite.

Hyper-eutectoid steels (hyper means "greater than") are those that contain more than the eutectoid amount of Carbon.

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
.HYpoeutectoid diagram

Principal phases of steel and their Characteristics

Invariant Reactions

Uses of Phase Diagrams
Time-temperature-transformation (TTT) diagram
Continuous Cooling Transformation (CCT) Diagram

Heat Treatment and Surface Heat treatment

Heat treatment is a controlled process used to alter the microstructure of metals and alloys such as steel and aluminium to impart properties which benefit the working life of a component Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve a desired result such as hardening or softening of a material.
The term heat treatment applies only to processes where the heating and cooling are done for the specific purpose of altering properties intentionally.
Simple heat treatments commonly used for steels are
Process annealing,
*Annealing,
*Normalizing, and
*Spheroidizing