Materials Science Glossary

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Atomic packing factor

The fraction of the unit-cell volume occupied by atoms, treating atoms as hard spheres. About 0.52 for SC, about 0.68 for BCC and about 0.74 for FCC and HCP.

Body-centered cubic

A crystal structure (BCC) with atoms at the corners and the center of the cube. The unit cell contains 2 atoms; the coordination number is 8 and the packing factor about 0.68. Examples include α-iron, Cr and W.

Face-centered cubic

A crystal structure (FCC) with atoms at the corners of the cube and at the center of each face. The unit cell contains 4 atoms; the coordination number is 12 and the packing factor about 0.74. Examples include Cu, Al and Ni.

Hexagonal close-packed

A crystal structure (HCP) formed by stacking close-packed planes in an ABAB… sequence. The coordination number is 12 and the ideal c/a is about 1.633. Examples include Mg, Ti and Zn.

Miller indices

Sets of integers that describe planes and directions in a crystal. For a plane, the reciprocals of its intercepts on the axes are reduced to the smallest integer ratio and written (hkl); a direction is written [uvw].

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Burgers vector

The vector giving the closure failure of a circuit taken around a dislocation. For a perfect dislocation in FCC it is (a/2)<110>. It determines the type and energy of the dislocation.

Diffusion coefficient

The coefficient D expressing how readily atoms diffuse, in units of m²/s. It depends on temperature in the Arrhenius form D = D₀exp(−Q/RT).

Dislocation

A defect in which the arrangement of atoms in a crystal is disturbed along a line. Metals deform plastically as dislocations move on slip planes. There are edge, screw and mixed dislocations.

Fick's laws

The basic laws of diffusion. The first law states that the flux is proportional to the concentration gradient, J = −D(dC/dx); the second gives the change of concentration with time, ∂C/∂t = D(∂²C/∂x²).

Vacancy

A point defect in which an atom is missing from a lattice site. Its equilibrium concentration rises with temperature as exp(−Q/kT), and vacancies carry the diffusion of substitutional atoms.

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0.2% offset yield strength

For materials without a distinct yield point, the stress that leaves a permanent strain of 0.2% after unloading. It is found where a line parallel to the elastic line, offset by 0.2% strain, meets the stress–strain curve.

Creep

Deformation that progresses over time under a constant load. It becomes significant above roughly 0.4 times the melting point (in absolute temperature) and passes through primary, secondary (steady-state) and tertiary stages before rupture.

Fatigue limit

The stress amplitude below which a material effectively no longer fails under cyclic loading. It often appears at around 10⁶–10⁷ cycles in carbon steels but is not distinct in aluminum alloys.

Fracture toughness

The ability of a cracked material to resist fracture. It is expressed as the critical value of the stress intensity factor, K_IC (in MPa·√m), and fracture is judged by comparing it with K = Yσ√(πa).

Young's modulus

The ratio of stress to strain in the elastic region, E = σ/ε. It is set by interatomic bonding: about 200 GPa for steel and about 70 GPa for aluminum, and it hardly changes with heat treatment.

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Coefficient of linear thermal expansion

The fractional change in length when the temperature rises by 1 K. It arises from the anharmonicity of the interatomic potential and tends to be smaller in strongly bonded materials with high melting points.

Debye temperature

The highest frequency of lattice vibration converted, via its energy, to a temperature. Well below it, the lattice heat capacity is proportional to T³, and at high temperatures it approaches about 3R.

Dulong–Petit law

The law that the molar heat capacity of many solid elements near room temperature is about 3R (about 25 J/(mol·K)). It corresponds to the classical limit of lattice vibrations at high temperature.

Invar

An Fe-36%Ni alloy. Its magnetovolume effect cancels ordinary thermal expansion, giving a very small linear expansion coefficient of about 1×10⁻⁶ K⁻¹ near room temperature.

Phonon

A particle-like quantum of the lattice vibrations of a crystal. Phonons carry heat and heat capacity in insulators and also cause the scattering of electrons.

Thermal diffusivity

The quantity α = κ/(ρc), the thermal conductivity divided by the heat capacity per unit volume. It expresses how quickly a change in temperature spreads through a material and has units of m²/s.

Umklapp process

Phonon-phonon scattering in which the total momentum changes by a reciprocal lattice vector. It counteracts heat flow and is the main reason the thermal conductivity of insulators falls at high temperatures.

Wiedemann–Franz law

The law that the ratio of a metal's thermal conductivity κ to its electrical conductivity σ is proportional to absolute temperature, κ = LσT, where L is the Lorenz number, about 2.44×10⁻⁸ W·Ω/K².

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Eutectic reaction

A reaction in which two solid phases crystallize simultaneously from the liquid on cooling, L → α + β. In a binary system it occurs at a fixed temperature and composition and produces eutectic structures such as lamellae.

Eutectoid reaction

A reaction in which two solid phases form simultaneously from one solid phase on cooling. In steel, γ → α + Fe₃C occurs at 0.76 wt% C and 727 °C, producing pearlite.

Gibbs phase rule

The rule F = C − P + 2 giving the number of degrees of freedom F at equilibrium from the number of components C and the number of phases P. For condensed systems at constant pressure, F = C − P + 1 is used.

Lever rule

A rule for finding the mass fraction of each phase in a two-phase region of a phase diagram from ratios of distances along the tie line. The fraction of a phase is proportional to the distance from the alloy composition to the opposite phase.

Pearlite

The microstructure formed by the eutectoid reaction in steel, with alternating lamellae of ferrite and cementite. The faster the cooling, the finer the lamellar spacing and the harder the pearlite.

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Hall–Petch relationship

The relation σy = σ₀ + k/√d in which the yield stress increases in inverse proportion to the square root of the grain size d. Grain boundaries obstruct dislocation motion, so finer grains give higher strength.

Hardenability

The depth to which martensite can be obtained by quenching (how readily a steel hardens). It increases when alloying elements such as Mn, Cr and Mo shift the nose of the TTT diagram to longer times.

Martensite

The microstructure formed by a diffusionless, shear-type transformation when austenite is quenched. In steel it is body-centered tetragonal, supersaturated with carbon, and very hard.

Precipitation hardening

Strengthening by dispersing fine precipitates through solution treatment, quenching and aging, so that they obstruct dislocation motion. Used in alloys such as Al-Cu; aging too long causes softening by overaging.

Tempering

A heat treatment that reheats quenched steel to a temperature below the A1 temperature (727 °C). It restores toughness and reduces internal stresses at the cost of some hardness.

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Carbon equivalent

The sum of the effects of a steel's alloying elements on hardenability, converted into an amount of carbon. The higher the Ceq, the more the weld heat-affected zone hardens and the more likely cold cracking is.

Extrusion

Plastic working in which a billet in a container is pushed by a ram through a die opening to make long products of constant cross section. Aluminum profiles are a typical example.

Heat-affected zone

The part of the base metal that did not melt during welding but whose microstructure and properties were changed by the welding heat. Also called the HAZ; hardening, softening, grain coarsening and sensitization can occur there.

Hot isostatic pressing

A method that applies an equally high pressure from all directions with an inert gas at high temperature, to densify powder or eliminate closed internal pores in castings and sintered bodies. Abbreviated HIP.

Investment casting

A precision casting method in which a wax pattern is coated with refractory and hardened, and melt is poured into the mold left after the wax is melted out. Also called the lost-wax process; used for turbine blades and the like.

Sensitization

The phenomenon in which stainless steel heated to about 500 to 800°C precipitates Cr carbides at grain boundaries, depleting the Cr around them and making the steel prone to intergranular corrosion.

Shrinkage cavity

A void in a casting where solidification shrinkage could not be made up by melt. It tends to form in thick sections that solidify last and is prevented by the design of risers and the order of solidification.

Springback

The partial recovery of shape by elastic recovery when the load is removed after bending or other working. It is larger for materials with a higher yield stress and a lower Young's modulus.

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Activity

The thermodynamic effective concentration of a component in a solution or solid solution, satisfying μ = μ° + RT ln a. It is 1 for the pure substance and equals the mole fraction in an ideal solution.

Chemical potential

The rate at which the Gibbs energy of a system increases when 1 mol of a component is added (the partial molar Gibbs energy). In phase equilibrium, the chemical potential of each component is equal in all phases.

Ellingham diagram

A diagram plotting the standard Gibbs energy change of formation of oxides and similar compounds, normalized per mol of O₂, against temperature. The lower its line, the more stable the oxide a metal forms.

Entropy of mixing

The entropy that arises because mixing increases the number of ways atoms can be arranged. In an ideal solution it is −R[x ln x + (1 − x) ln(1 − x)], with its maximum at x = 0.5.

Equilibrium oxygen partial pressure

The oxygen partial pressure at which a metal and its oxide coexist in equilibrium. It is found from ΔG° = RT ln pO₂; above it the metal is oxidized, and below it the oxide is reduced.

Gibbs energy

A state function defined by G = H − TS. At constant temperature and pressure, changes proceed spontaneously in the direction that lowers G, and the state of minimum G is equilibrium.

Regular solution

A solution model in which the entropy of mixing is the same as for an ideal solution and the enthalpy of mixing is Ωx(1 − x). When Ω is positive, a miscibility gap appears at low temperature.

Spinodal decomposition

Phase separation into 2 phases at compositions where the free energy curve is convex upward, in which composition fluctuations grow without a nucleation barrier. Uphill diffusion produces a periodic structure.

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Perovskite structure

An ABO₃ crystal structure in which the B-site cation sits at the center of an oxygen octahedron (coordination number 6) and the A-site cation in the space between octahedra (coordination number 12). BaTiO₃ is an example.

Piezoelectric effect

The phenomenon in which applying stress produces polarization and, conversely, applying an electric field produces deformation. It occurs in crystals without a center of symmetry; quartz and PZT are used in sensors and resonators.

Sintering

The process of heating a powder compact at a high temperature below the melting point so that the particles bond and the compact densifies. The driving force is the reduction in surface energy.

Transformation toughening

The mechanism in partially stabilized zirconia by which stress at a crack tip transforms tetragonal to monoclinic, and the accompanying volume expansion closes the crack and raises toughness.

Weibull modulus

The parameter m of the Weibull distribution that expresses how small the scatter in strength is. The larger it is, the smaller the scatter: about 5–20 for ceramics and several tens or more for metals.

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Crystallinity

The fraction of a crystalline polymer occupied by crystalline regions. It is determined from density, the heat of fusion by DSC, XRD and so on; higher crystallinity raises density and modulus but lowers transparency.

Glass transition temperature

The temperature at which molecular or atomic motion in an amorphous substance or the amorphous regions of a polymer freezes, switching between the glassy and rubbery (supercooled liquid) states. Written Tg.

Rule of mixtures

Expressions that estimate the properties of a composite from the properties and volume fractions of its constituents. Along the fibers, the isostrain form E = VfEf + VmEm applies; perpendicular to them, the isostress form is used as an approximation.

Thermosetting resin

A resin that forms a three-dimensional network by a curing reaction and does not melt when heated after curing. Examples include epoxy and phenolic resins.

Viscoelasticity

Behavior that combines properties of an elastic solid and of a viscous fluid. In polymers it appears as stress relaxation and creep and depends on time and temperature.

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Coercivity

The strength of the reverse magnetic field needed to bring the magnetization (or flux density) of a magnetized material back to zero. Materials with small coercivity are soft magnetic, and those with large coercivity hard magnetic.

Curie temperature

The temperature at which a ferromagnet (or ferroelectric) loses its spontaneous magnetization (or polarization); above it the material is paramagnetic. About 770 °C for iron and about 358 °C for nickel.

Indirect-bandgap semiconductor

A semiconductor whose conduction band minimum and valence band maximum occur at different crystal momenta. Radiative recombination requires a phonon, so emission efficiency is low. Silicon and germanium are examples.

Matthiessen's rule

The empirical rule that the resistivity of a metal is the sum of a temperature-dependent component due to lattice vibrations and a temperature-independent component due to impurities and defects.

Soft magnetic material

A magnetic material with small coercivity and low hysteresis loss, such as electrical steel, ferrites and amorphous alloys, used for transformer and motor cores.

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Brass

An alloy of copper with zinc. 70/30 brass, with about 30% Zn, is single-phase α and highly ductile, while 60/40 brass, with about 40% Zn, contains the β phase and is stronger.

Columnar grains

In the solidification of castings, elongated grains that grow inside the surface chill zone in the direction opposite to heat flow. Equiaxed grains form in the center.

Recovery

The process, preceding recrystallization when a cold-worked metal is heated, in which dislocations annihilate and rearrange and internal stresses and electrical resistivity decrease. Hardness changes little.

Recrystallization

The phenomenon in which new strain-free grains nucleate and grow when a metal storing deformation strain is heated. Strength decreases and ductility is restored.

Solid-solution strengthening

A strengthening method in which lattice strain created by solute atoms dissolved in the matrix obstructs dislocation motion and raises the strength of a metal. There are interstitial and substitutional types.

Stainless steel

An alloy steel containing roughly 11% Cr or more, made rust-resistant by a passive surface film. By microstructure it is divided into austenitic, ferritic, martensitic and other grades.

Titanium alloy

An alloy with a density about 60% that of steel, excellent specific strength and corrosion resistance. Depending on the proportions of the HCP α phase and BCC β phase, it is classified as α, α+β or β type.

Work hardening

The increase in the stress needed for deformation as plastic deformation multiplies dislocations, which become entangled with each other. Strength rises but ductility falls. Also called strain hardening.

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Layered rock salt structure

A structure in which Li layers and transition-metal layers alternate within close-packed oxygen. LiCoO₂ and LiNiO₂-based cathodes take this structure, and Li⁺ moves two-dimensionally between the layers.

Olivine structure

The structure of the mineral olivine, taken by the cathode LiFePO₄. Strong covalent bonds in PO₄ make it thermally stable, but Li⁺ diffusion is one-dimensional and electronic conductivity is low.

Polymer electrolyte fuel cell

A fuel cell whose electrolyte is a polymer membrane with sulfonic acid groups that conducts protons when hydrated. Abbreviated PEFC (also PEMFC); it is humidified to keep the membrane from drying and operates at about 80 °C.

Shockley–Queisser limit

The upper limit on the theoretical efficiency of a single-junction solar cell. Balancing the transmission of light below the band gap against thermalization losses, it reaches a maximum of about 33% at about 1.34 eV under terrestrial sunlight.

Solid electrolyte

A material that conducts ions while remaining solid but conducts almost no electrons. Examples include sulfide and oxide electrolytes for all-solid-state batteries and stabilized zirconia for fuel cells.

Spinel structure

A structure of composition AB₂O₄ in which cations occupy tetrahedral and octahedral sites in cubic close-packed oxygen. The cathode LiMn₂O₄ has three-dimensional Li⁺ pathways.

Theoretical capacity

The maximum charge an electrode material can store, expressed per unit mass. It is calculated as Q = nF/(3.6M) mAh/g; for graphite it is 372 mAh/g.

Thermoelectric figure of merit

The dimensionless value ZT = S²σT/κ that expresses the conversion performance of a thermoelectric material. It is larger the higher the Seebeck coefficient and electrical conductivity and the lower the thermal conductivity.

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Ceramic matrix composite

A composite (CMC) with a ceramic matrix such as SiC reinforced by ceramic fibers. A weak interface lets fibers pull out, giving a material that does not fail suddenly.

CFRP (carbon-fiber-reinforced plastic)

A composite of carbon fibers bound with epoxy or another resin. With low density and high modulus and strength, it excels in specific stiffness and is used in aircraft, automobiles and sporting goods.

Critical fiber length

The length needed for the stress at the middle of a short fiber to reach the fiber's tensile strength through interfacial shear. It is given by lc = σf·d/(2τc); fibers shorter than this pull out.

Delamination

Damage in which the resin or interface between plies of a laminate cracks and the plies separate. It occurs because the through-thickness strength is low, and when caused internally by impact it is hard to detect from outside.

GFRP (glass-fiber-reinforced plastic)

A composite of glass fibers bound with resin. It is less stiff than CFRP but inexpensive, electrically insulating and transparent to radio waves, and is used for boat hulls, bathtubs, printed circuit boards and more.

Metal matrix composite

A composite (MMC) with a metal matrix such as aluminum reinforced by SiC particles or fibers. It can raise stiffness and wear resistance and lower thermal expansion.

Quasi-isotropic laminate

A laminate, such as [0/±45/90]ₛ, stacked from plies whose fiber directions are divided at equal angles. The in-plane Young's modulus is nearly equal in all directions, but the through-thickness direction remains weak.

Silane coupling agent

A compound with, in a single molecule, a group that bonds to inorganic materials and a group that reacts with resin. It is used to treat the surface of glass fibers, improving interfacial adhesion and water resistance.

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BET method

A method that physically adsorbs a gas such as nitrogen onto a powder at low temperature, fits the BET equation to the adsorption isotherm, and obtains the specific surface area from the monolayer capacity.

Bottom-up synthesis

Methods of making nanomaterials by assembling atoms and molecules through nucleation and growth, such as liquid-phase reduction and thermal decomposition, the sol-gel method and CVD. The counterpart of top-down methods, which break down larger materials.

Carbon nanotube

A carbon material formed by rolling graphene into a tube about 1 nm to several tens of nanometers in diameter. Depending on the rolling direction (the chiral indices) it can be metallic or semiconducting, and its strength along the axis is extremely high.

Graphene

A single atomic layer of carbon atoms arranged in a honeycomb lattice by sp² bonds. Its band gap is essentially zero, its electron mobility is high, and its theoretical specific surface area counting both sides is about 2630 m²/g.

Melting point depression of nanoparticles

The lowering of the melting point of nanoparticles below that of the bulk due to the surface energy contribution. The depression is roughly inversely proportional to particle size and becomes pronounced for particles a few nanometers across.

Quantum dot

A semiconductor nanocrystal a few nanometers across that confines electrons and holes in three dimensions. The confinement energy is roughly inversely proportional to the square of the size, so the emission wavelength can be tuned by size.

Specific surface area

The surface area per unit mass of a powder or porous body, in m²/g. For spherical particles S = 6/(ρd), increasing in inverse proportion to particle size.

Zeta potential

The potential at the slipping plane outside the layer that moves with a particle in a liquid. The larger its absolute value, the stronger the electrostatic repulsion between particles and the more stable the dispersion. It is nearly zero at the isoelectric point.

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Domain wall

The transition layer at the boundary between neighboring domains, across which the direction of the magnetic moments rotates gradually. Its thickness is set by the balance between exchange and anisotropy energies.

Eddy-current loss

The loss due to Joule heating by eddy currents induced in a magnetic material when the flux changes under AC. It is proportional to the square of thickness and frequency and inversely proportional to resistivity.

Ferrimagnetism

Magnetism in which the moments of two antiparallel sublattices differ in size, leaving a spontaneous magnetization equal to the difference. Ferrites such as magnetite are typical examples.

Magnetic domain

A small region inside a ferromagnet or ferrimagnet in which the magnetization points in one direction. The material splits into many domains to lower the magnetostatic energy of its surface poles.

Magnetocrystalline anisotropy

The property that the ease of magnetization depends on the crystal direction. In iron, <100> is the easy axis. A large value raises coercivity, and a small one raises permeability.

Maximum energy product

The value (BH)max at which the magnitude of the product of flux density B and field H is greatest on the demagnetization curve of a permanent magnet. In kJ/m³, it measures a magnet's strength.

Saturation magnetization

The magnetization when a strong field aligns all the magnetic moments in the same direction. For iron it is about 1.7×10⁶ A/m (about 2.2 T as µ₀Ms), and it decreases as the temperature rises.

Superparamagnetism

The state of very small ferromagnetic particles in which the barrier to reversal, KV, is small compared with the thermal energy, so the magnetization reverses thermally and the coercivity is almost zero.

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Biocompatibility

The ability of a material to perform the required function in a specific application with an appropriate host response. It is evaluated including not only the material but also its shape, surface condition and location of use.

Biodegradable polymer

A polymer broken down in the body or the environment by hydrolysis or the action of microorganisms. Polylactic acid and polyglycolic acid are used in absorbable sutures and bone fixation devices.

Bone cement

A material made by mixing PMMA powder with liquid methyl methacrylate and polymerizing it in the body to fix artificial joints to bone. It fixes them not by adhesion but by filling the gap and interlocking mechanically.

Hydroxyapatite

A calcium phosphate with the formula Ca₁₀(PO₄)₆(OH)₂. Close to the mineral component of bones and teeth, it is used as a bioactive ceramic that bonds directly to bone. Its Ca/P ratio is 1.67.

Osseointegration

A state in which living bone and the implant surface are in direct contact without intervening fibrous tissue and can transfer load. It was discovered with titanium dental implants.

Stress shielding

A phenomenon in which an implant far stiffer than bone carries most of the load, the mechanical stimulus to the surrounding bone falls, and the bone is resorbed and thins.

Superelasticity

The property, above the reverse transformation finish temperature, of recovering large strains of several percent on unloading through stress-induced martensitic transformation and its reverse. Ni-Ti alloys are the typical example.

β titanium alloy

A titanium alloy containing large amounts of β-stabilizing elements such as Nb, Ta and Mo, so that it has the BCC β phase even at room temperature. Its low Young's modulus reduces stress shielding in medical use.

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Amorphous silicon

Silicon without long-range periodicity. a-Si:H, with its dangling bonds terminated by hydrogen, is used in thin-film transistors and thin-film solar cells.

Chemically strengthened glass

Glass strengthened by exchanging Na⁺ in its surface layer for larger K⁺ in a molten salt, introducing large compressive stress in the surface layer. It can be used even for thin sheets.

Metallic glass

An amorphous alloy solidified from a metallic melt without crystallizing. With no dislocations, it has high strength and a large elastic strain limit. Thick pieces are called bulk metallic glasses.

Network former

An oxide such as SiO₂, B₂O₃ or P₂O₅ whose cations form oxygen polyhedra that share corners, building a glass network even on its own.

Network modifier

An oxide such as Na₂O, K₂O or CaO that breaks bridges in a glass network to create non-bridging oxygens, with its cations occupying interstices in the network. It lowers the viscosity.

Non-bridging oxygen

An oxygen in a glass network bonded to only one network-forming cation and not linked to a neighboring polyhedron. It increases when modifying oxides are added.

Reduced glass transition temperature

The glass transition temperature Tg divided by the liquidus temperature Tl, Trg = Tg/Tl. The larger it is, the more readily a melt forms glass, with about 2/3 or more taken as a guideline.

Tempered glass

Glass strengthened by quenching a heated sheet with air so that compressive stress remains at the surface and tensile stress inside. When it breaks, it shatters into small granules.

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Critical nucleus radius

The nucleus radius above which growth becomes the more stable path in nucleation. For a spherical nucleus, r* = −2γ/ΔGv, which becomes smaller as the undercooling increases.

Ostwald ripening

Coarsening in which small particles dissolve and disappear while large particles grow. The driving force is the curvature-dependent difference in solubility (the Gibbs–Thomson effect).

Quantum size effect

The effect by which energy levels become discrete and the band gap widens when particles or films become as small as the spatial extent of electron waves. It determines the emission color of quantum dots.

Stranski–Krastanov growth

A thin-film growth mode in which, after layer-by-layer growth of a few atomic layers, three-dimensional islands grow to relax the strain from lattice mismatch. It is used to make quantum dots.

Thermal stress

Stress arising from a difference in thermal expansion. For a thin film on a substrate it is estimated as σ = EΔαΔT/(1 − ν); if the film's expansion coefficient is larger, the film is in tension after cooling.

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Bragg's law

The condition 2d sinθ = nλ for diffraction to reinforce from crystal planes with spacing d. It is the basic equation for finding interplanar spacings from XRD peak angles.

EDS (energy-dispersive X-ray spectroscopy)

A method of elemental analysis that measures the energies of characteristic X-rays excited by an electron beam with a semiconductor detector. It measures all elements simultaneously in a short time, but its resolution is lower than that of WDS.

Extinction rules

Rules by which diffraction from certain indices cancels out and disappears because of the arrangement of atoms. In BCC, only planes with h + k + l even diffract; in FCC, only planes whose h, k and l are all even or all odd.

Scherrer equation

The equation D = Kλ/(β cosθ) for estimating crystallite size from the broadening of XRD peaks, where β is the full width at half maximum in radians and K is about 0.9.

SEM (scanning electron microscope)

A microscope that scans a finely focused electron beam across a specimen surface and detects the secondary and backscattered electrons emitted, to observe surface shape and differences in composition.

SIMS (secondary ion mass spectrometry)

A method that mass-analyzes secondary ions ejected while the specimen is sputtered by primary ions. It can measure depth profiles of trace elements such as dopants with ppm to ppb sensitivity.

XPS (X-ray photoelectron spectroscopy)

An analytical method that determines the elements in the top few nanometers of a surface and their chemical bonding state (oxidation state and so on) from the binding energies of photoelectrons emitted by X-rays.

XRD (X-ray diffraction)

An analytical method that shines X-rays on a crystal and uses the angles and intensities of the diffracted X-rays to examine crystalline phases, lattice parameters, crystallite size, strain, texture and more.

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Faraday's law of electrolysis

The law that the amount of substance changed by an electrode reaction is proportional to the charge passed. The mass dissolved or deposited is m = ItM/(nF).

Galvanic corrosion

Accelerated corrosion of the more active metal, acting as the anode, when metals of different potential are in contact in an electrolyte. Also called dissimilar-metal corrosion.

Local cell

On the surface of a single metal, anodic and cathodic regions formed by inclusions, strain, oxygen concentration differences and the like, through which corrosion proceeds as in a battery.

Passivity

A state in which a dense oxide film a few nanometers thick forms on a metal surface and dissolution of a metal that should thermodynamically dissolve almost stops.

Pitting corrosion

Localized corrosion in which chloride ions or similar species locally break down the passive film and small pits are dug deeper. It is a problem for stainless steels and aluminum.

Sacrificial anode

An anode of zinc, aluminum alloy, magnesium or another metal more active than the metal to be protected, connected electrically so that it dissolves first and protects the metal as the cathode.

Standard electrode potential

The equilibrium potential of an electrode reaction, such as that between a metal and its ions, under standard conditions, relative to the standard hydrogen electrode at 0 V. The more negative it is, the more easily the metal is oxidized.

Stress corrosion cracking

Crack growth at stresses below the yield stress when a susceptible material under tensile stress is exposed to a specific corrosive environment.

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Ashby chart (materials selection chart)

A chart that plots two properties, such as Young's modulus and density, on log–log axes and shows the range of each material family. Lines of constant performance index are straight, and the chart is used to compare candidates.

Life cycle assessment

A method (LCA) for quantitatively evaluating energy consumption and environmental impact at each stage: material production, product manufacture, use, and disposal or recycling.

Material index (performance index)

The combination of material properties to be maximized in materials selection: E/ρ for a stiffness-limited tie, √E/ρ for a beam, ∛E/ρ for a plate, and σf/ρ for a strength-limited tie.

Pareto optimality

A state in which improving any one of several objectives necessarily worsens another. For competing objectives, candidates are chosen from the Pareto front using an exchange constant.

Specific stiffness

Young's modulus divided by density, E/ρ, also called specific modulus. Steel, aluminum alloys and titanium alloys are all roughly the same, at about 25 GPa/(g/cm³).

Tramp elements

Elements such as copper and tin that get mixed into steel scrap, are hard to remove by refining, and accumulate in steel with each recycling. They cause quality problems such as surface cracking during hot working.

Yield before fracture

The condition in which, even with a crack present, the whole component yields first and sudden brittle fracture does not occur. The allowable crack size is proportional to (K_IC/σy)², so K_IC/σy serves as the performance index.

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Energy release rate

The elastic energy released when a crack advances by a unit area. Written G, it equals K²/E in plane stress, and the crack advances when it reaches the critical value G_c.

Fatigue striations

Fine lines seen on a fracture surface where a fatigue crack has advanced. Their spacing corresponds roughly to the crack growth per cycle, and they are observed with an electron microscope.

Griffith theory

The theory that fracture proceeds when the elastic energy released as a crack extends exceeds the energy of the new surfaces. The fracture stress is given by √(2Eγs/(πa)).

Miner's rule

The rule that adds up damage at different stress amplitudes as the sum of the ratios n/N of applied cycles to life, and regards fatigue failure as occurring when the sum reaches 1.

Modified Goodman diagram

A diagram expressing the effect of mean stress. It joins the fully reversed fatigue limit and the tensile strength with a straight line, taking σa = σw(1 − σm/σB) as a guide to the allowable stress amplitude.

Paris law

The empirical law da/dN = C(ΔK)ᵐ, stating that the fatigue crack growth rate is proportional to a power of the stress intensity factor range. It is used to estimate crack growth life.

Stress concentration factor

The number Kt giving how many times the average stress the maximum stress at a hole or notch root is. For an elliptical hole it is 1 + 2√(a/ρ), and for a circular hole it is 3.

Stress intensity factor

A quantity expressing the strength of the stress field at a crack tip. Given by K = Yσ√(πa), it depends on both the stress and the crack length, and the crack grows unstably when it reaches a critical value.

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Abrasive wear

Wear in which hard particles or hard asperities on the counterface scratch and cut material from a softer surface. It drops greatly when the surface is made harder than the particles.

Adhesive wear

Wear in which metals bond at the real contact spots and, as sliding shears the junctions, material transfers to the counterface or detaches. It causes seizure.

Archard wear equation

The equation V = KWL/H, stating that wear volume V is proportional to the normal load W and sliding distance L and inversely proportional to hardness H. K is the wear coefficient, which varies widely with the wear mechanism.

Carburizing

A treatment in which low-carbon steel is held in a carbon-bearing atmosphere in the austenite region to raise the carbon content of the surface layer. Quenching then turns the surface into hard martensite.

Electroless nickel plating

Plating in which nickel is deposited autocatalytically by a reducing agent without a power supply. The deposit contains phosphorus and forms a uniform thickness even on parts of complex shape.

Nitriding

A treatment in which steel is held in a nitrogen-bearing atmosphere below the A₁ transformation temperature to form hard nitrides in the surface layer. No quenching is needed and distortion is small.

Real area of contact

The area where asperities on two surfaces actually touch. When the asperities deform plastically it equals the load divided by the hardness, and it is far smaller than the apparent contact area.

Stribeck curve

A curve plotting the friction coefficient of a plain bearing or similar contact against the bearing characteristic number, viscosity × speed ÷ pressure. It shows the transitions among boundary, mixed and hydrodynamic lubrication.

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Deformation mechanism map

A map with normalized stress and homologous temperature as axes, showing the fields of the mechanism that deforms fastest, such as dislocation glide, power-law creep and diffusion creep.

Diffusion creep

Creep that proceeds as grains elongate by atomic diffusion, with a rate proportional to stress. It includes Nabarro–Herring creep by lattice diffusion and Coble creep by grain boundary diffusion.

Larson–Miller parameter

The value P = T(C + log₁₀t_r) that combines the temperature and time of creep rupture. Taken as constant at a given stress, it is used to estimate long lives from short tests.

Nickel-based superalloy

A heat-resistant alloy with a large amount of the L1₂ ordered phase γ' (Ni₃Al) coherently precipitated in an FCC Ni matrix. Used for turbine blades, it retains strength up to temperatures close to its melting point.

Parabolic rate law

The relation x² = k_p t, in which the square of the oxide scale thickness increases in proportion to time. It holds when diffusion of ions through a dense scale controls the growth rate.

Pilling–Bedworth ratio

The ratio of the volume of an oxide to the volume of metal used to form it. A guide by which values below 1 tend to give cracked scales and values of about 1 to 2 tend to give protective ones.

Power-law creep

Creep in which the steady-state creep rate is proportional to the stress raised to the power n (n is about 3 to 8). It arises from dislocation glide combined with recovery by climb, and dominates at high stresses.

Thermal barrier coating

A ceramic coating of low thermal conductivity applied to the surface of high-temperature components. It consists of a zirconia top coat and a bond coat, and greatly lowers the metal temperature.

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CALPHAD method

A method that models the Gibbs energy of each phase as a function of temperature and composition and calculates multicomponent phase diagrams and phase fractions from a database fitted to experimental and other data.

Density functional theory

A theory that uses the fact that the ground-state energy is determined by the electron density, solving the Kohn–Sham equations to obtain the electronic states and energy of a material. The core of first-principles calculation.

Finite element method

A numerical method that divides a body into small elements and solves simultaneous equations with nodal displacements or similar as unknowns to find approximate distributions of stress or temperature.

Interatomic potential

A function that gives the energy and forces from the arrangement of atoms. Types include the Lennard-Jones form, the embedded atom method for metals, potentials for covalent bonds and machine-learning potentials.

Materials informatics

An approach that analyzes materials data with machine learning and other methods to help predict properties and choose which materials to try next. Combined with computation and experiment, it speeds up materials development.

Molecular dynamics

A method that numerically integrates Newton's equations of motion for many atoms, using forces obtained from interatomic potentials, to calculate atomic motion over time.

Monte Carlo method

A method that finds answers by repeating probabilistic trials using random numbers. In materials it includes equilibrium calculations by the Metropolis method and kinetic Monte Carlo for following diffusion.

Phase-field method

A method that calculates the time evolution of microstructure in the direction that lowers the free energy, treating an order parameter for the phase or crystal orientation as varying smoothly across interfaces. Used for solidification and precipitation.