Materials Science II

Point defects

Zero-dimensional lattice defects such as vacancies, interstitials, and substitutional atoms.

Vacancy

A missing atom from a lattice site.

Interstitial defect

An atom positioned in the spaces between lattice sites.

Substitutional defect

A foreign atom replacing a host atom in the lattice.

Linear defect (dislocation)

One-dimensional defect in a crystal lattice responsible for plastic deformation.

Volume (bulk) defect

Three-dimensional defect such as pores, cracks, or inclusions.

Dislocation

A line defect that allows slip and plastic deformation in crystals.

Tension

Loading mode that stretches a material.

Compression

Loading mode that squeezes a material.

Shear

Loading where forces act parallel and opposite, causing sliding deformation.

Torsion

Twisting deformation caused by applied torque.

Bending

Deformation caused by moments producing curvature.

Stress

Force per unit area (σ = F/A).

Strain

Relative deformation (ε = ΔL/L₀).

Stiffness

Resistance to elastic deformation measured by Young’s modulus.

Strength

Maximum stress a material can withstand before failure.

Young’s modulus

Ratio of stress to strain in the elastic region.

Tensile test

Experiment measuring material response under uniaxial tension.

Elastic region

Region where deformation is reversible.

Plastic region

Region where deformation is permanent.

Yield point

Stress at which plastic deformation begins.

Fracture point

Point at which material breaks.

Young’s modulus (E)

Slope of elastic stress–strain curve.

Shear modulus (G)

Ratio of shear stress to shear strain.

Bulk modulus (K)

Resistance to uniform compression.

High Young’s modulus

Indicates a stiff material.

Elastic deformation

Reversible deformation after unloading.

Plastic deformation

Permanent deformation after unloading.

Proportional limit

End of linear stress–strain relationship.

Anelasticity

Time-dependent elastic deformation.

Elasticity

Instantaneous reversible deformation.

Cause of anelasticity

Time-dependent atomic or microscopic rearrangements.

Poisson’s ratio

Ratio of lateral strain to axial strain (with negative sign).

Typical Poisson’s ratio for metals

Approximately 0.25–0.35.

Maximum Poisson’s ratio

0.5 (no volume change).

Cause of plastic deformation

Dislocation motion in crystals.

Yield strength

Stress at which plastic deformation begins.

Tensile strength

Maximum stress before fracture.

Strain hardening effect

Increase in strength after plastic deformation.

Ductility

Ability to undergo plastic deformation before fracture.

Percent elongation

Measure of ductility based on change in length.

Percent reduction in area

Measure of ductility based on cross-sectional change.

Modulus of resilience

Elastic energy absorbed per unit volume.

Toughness

Total energy absorbed before fracture.

True stress

Stress based on instantaneous cross-sectional area.

True strain

Natural logarithmic strain (ln(L/L₀)).

Engineering stress

Stress based on original area.

Engineering strain

Strain based on original length.

Elastic recovery

Recovery of elastic strain after unloading.

Permanent strain

Remaining deformation after plastic deformation.

Hardness

Resistance to localized plastic deformation.

Hardness test advantage

Simple, fast, and nondestructive.

Hardness test limitation

Not precise for design calculations.

Ideal strength

Theoretical maximum strength of a perfect crystal.

Approximate ideal strength

σ ≈ E/15.

Reason real materials are weaker

Presence of defects, especially dislocations.

Slip

Movement of atomic planes along a crystal.

Plasticity in metals

Caused primarily by dislocation motion.

Driving force for dislocation motion

Applied shear stress.

Burgers vector

Measure of lattice distortion caused by a dislocation.

Solubility limit

Maximum solute concentration in a solid solution.

Phase diagram

A graphical representation of phases present under equilibrium conditions as a function of temperature, pressure, and composition.

Unary phase diagram

Phase diagram for a single-component system (variables: temperature and pressure).

Binary phase diagram

Phase diagram for a two-component system at constant pressure showing temperature vs composition.

Equilibrium phase diagram

Diagram showing stable phases under equilibrium conditions.

Exceeding solubility limit

Leads to formation of a second phase.

Phase boundary

Line separating two phases in equilibrium.

Triple point

Condition where solid, liquid, and vapor phases coexist in equilibrium.

Melting point

Temperature where solid and liquid phases coexist at a given pressure.

Boiling point

Temperature where liquid and vapor phases coexist.

Binary isomorphous system

Binary alloy system with complete solid solubility in all proportions.

Solid solution (α phase)

Single solid phase containing both components in a substitutional lattice.

Liquidus line

Boundary above which only liquid exists.

Solidus line

Boundary below which only solid exists.

Two-phase region

Region where both solid and liquid phases coexist.

Tie line

Horizontal line used in a two-phase region to determine phase compositions.

Phase composition

Composition of each individual phase in equilibrium.

Rule for phase composition

Determined by intersections of tie line with phase boundaries.

Lever rule

Method used to calculate mass fractions of phases in a two-phase region.

Mass fraction of phase

Fraction of total alloy present as a given phase.

Lever rule principle

Based on conservation of mass using tie-line segment ratios.

Inverse lever rule

Alternative name emphasizing segment ratio interpretation.

Phase fraction calculation

Ratio of opposite tie-line segment to total tie-line length.

Microstructure

Structural features of a material visible under microscope.

Grain

Individual crystal in a polycrystalline material.

Grain boundary

Interface between two differently oriented grains.

Phase equilibrium

Condition where phases coexist without change over time.

Free energy (Gibbs free energy)

Thermodynamic function determining phase stability.

Equilibrium condition

State of minimum Gibbs free energy.

Entropy

Measure of atomic disorder in a system.

Gibbs phase rule

Relationship between number of phases, components, and degrees of freedom: F = C − P + 1 (for constant pressure).

Degrees of freedom

Number of independent variables (T, composition) that can be changed without changing number of phases.

Component

Chemically independent species in a system.

Nucleation

Initial formation of a new phase within a parent phase.

Homogeneous nucleation

Nucleation occurring uniformly throughout the parent phase.

Heterogeneous nucleation

Nucleation occurring at surfaces, grain boundaries, or defects.

Gibbs free energy change

Driving force for phase transformation.

Volume free energy (ΔGv)

Energy change due to phase transformation per unit volume.

Surface energy (γ)

Energy required to create a new interface.

Critical nucleus

Minimum-sized stable nucleus that can grow.