Alloy

A material combining a metal with one or more other chemical elements, while retaining metallic properties.

A binary alloy is a metallic material whose specified alloy system has two elemental components. “Binary” counts components, not phases: one composition may form a single solid solution, while another or a different temperature can produce two coexisting phases.

If an overall component fraction $x_0$ lies between equilibrium phase compositions $x_{\alpha }$ and $x_{\beta }$, conservation of material gives the phase fractionThe fractions must use a consistent mass- or mole-based convention. A binary phase diagram therefore relates composition and temperature to equilibrium phase assemblages; it does not say that every alloy consists of separate pure-metal grains.

Elinvar names a family of alloys designed to have a small temperature coefficient of elastic stiffness over a useful operating range. This addresses a different problem from Invar: low thermal expansion does not automatically imply temperature-independent Young's modulus.^[ref]

For a simple elastic oscillator, $f\propto \sqrt{k/m}$, so a small stiffness change gives $\Delta f/f\simeq \frac{1}{2}\Delta k/k$ at fixed mass. An alloy with suitably compensated stiffness can reduce thermal drift in a mechanical frequency standard. Its composition, heat treatment and operating range still matter; the name does not mean exact invariance at every temperature.

An alloy involving mercury.

Formation of an amalgam. The historical report in The Seats and Causes of Diseases Investigated by Anatomy by Giovanni Battista Morgagni invokes it as a supposed way of reducing a swallowed silver coin; this does not establish therapeutic efficacy or safety. ^[ref]

An iron-based alloy with more carbon than ordinary steel, suitable for casting but with properties strongly dependent on composition and microstructure.

An alloy developed to sustain mechanical load at high temperatures while resisting creep and environmental attack.

A high-temperature alloy based on a nickel-rich disordered $\gamma$ matrix, commonly strengthened by ordered ${\gamma }^{\prime }$ precipitates and substitutional solutes.

A turbine blade cast as one crystal to remove high-temperature grain boundary sliding and grain-boundary cavitation pathways. This does not eliminate dislocations or all sources of creep.

The ordered $L{1}_2$ phase based on $\mathrm{N}{\mathrm{i}}_3\mathrm{Al}$ in many nickel-based superalloys. A matrix translation $a⟨110⟩/2$ disrupts its order and can create an antiphase boundary.

An alloy based on zirconium. Low neutron absorption and corrosion behaviour motivate nuclear fuel cladding applications; irradiation growth, creep and hydrogen uptake remain constraints.

A family of zirconium-based alloys developed for nuclear applications. Specific alloy and heat treatment determine corrosion, hydrogen uptake and irradiation response.

Enrichment of one component at a material surface relative to its bulk composition. Surface free energies, adsorbates, elastic strain and the energetic cost of changing bulk bonding jointly determine equilibrium enrichment.

Preferential occupation of distinct crystal sublattices by different chemical elements. Favourable unlike-neighbour bonding can stabilize a periodic alloy arrangement despite its lower configurational entropy than a random alloy.

For a stoichiometric $A_{3}B$ alloy with one corner sublattice and three equivalent face sublattices, let $p_c$ and $p_f$ be the respective occupation probabilities of species $B$. Define $\rho =(4p_c-1)/3$. Conservation of composition, $p_c+3p_f=1$, gives $p_c=(1+3\rho )/4$ and $p_f=(1-\rho )/4$. Thus the random alloy has $\rho =0$ and the fully ordered corner-$B$ pattern has $\rho =1$. The coherent superlattice reflection amplitude is $\rho (f_B-f_A)$, so its wave intensity scales as ${\rho }^2$, while the equal-parity fundamental amplitude $f_B+3f_A$ is composition-fixed. The definition assumes equivalent face sublattices; endpoint normalization alone does not uniquely specify an arbitrary order coordinate.

Heat treatment that develops a fine dispersion of a new solid phase in an alloy, impeding dislocation motion. It is distinct from precipitation from a liquid chemical solution. A solid solution may first be formed at high temperature, quenched to retain supersaturation, and then aged to promote solid-state precipitation.

For one spherical particle per representative volume $L^3$, a volume fraction $f$ implies $d=L(6f/\pi {)}^{1/3}$. A mean nearest-neighbor distance in a random population does not determine this number density exactly, and an atomic thermodynamic phase fraction requires a molar-volume conversion before it is used as $f$.

A dislocation unable to shear an obstacle can bow around it and leave a loop. Balancing the Peach-Koehler force against the tension of a curved dislocation gives the critical scale $\Delta \tau \simeq 2T_{\ell }/(b\ell )$, where $\ell$ is the free obstacle span on the slip plane. Centre pitch and free span are not interchangeable when particle size is appreciable.

An obstacle calculation produces a resolved shear-stress increment. A single crystal needs its Schmid factor, while a polycrystal needs a deformation-geometry or Taylor factor. The relation $\Delta \sigma =M\Delta \tau$ therefore requires an explicit orientation assumption rather than a universal tensile prefactor.

Resistance to dislocation motion caused by the energetic cost of disrupting chemical order, for example creating an antiphase boundary in a gamma prime phase precipitate.

A new solid phase formed within an existing solid matrix. Its morphology reflects anisotropic interfacial energy, coherency strain and growth kinetics.

Evolution toward larger characteristic precipitate sizes, often by diffusional growth of larger particles at the expense of smaller ones. The associated changes of spacing and shape can alter strengthening.

The shape of a solid-state precipitate. Thin plates can result when broad faces have much lower interfacial energy than edge regions.

An aluminium scandium alloy contains scandium added to aluminium, often in a relatively small proportion. Scandium-containing precipitates and changes in grain structure can influence strength and stability.

The strengthening effect depends on microstructure and processing, not simply on adding the masses of two pure metals. It provides an example of how a minor alloying element can strongly alter dislocation motion and grain evolution.

Bronze usually denotes a copper-based alloy containing tin, with the term also used for certain related copper alloys. Its composition is not one fixed stoichiometric formula.

Tin content, other alloying elements, and processing change phase structure and mechanical behavior. Bronze therefore illustrates the difference between an alloy family and a single pure chemical compound.

Manganin is a copper-manganese-nickel alloy valued for a small temperature dependence of electrical resistance over a useful operating range. It is used in precision resistance components.

Its benefit concerns stability of resistance, not perfect temperature independence under all conditions. Alloy composition, mechanical strain, and thermal history can affect its electrical properties.

Steel is an iron-based alloy family in which carbon and other alloying elements control structure and properties. It is not a single compound with one fixed carbon content.

Cooling and heat treatment change the distribution of phases and microstructural features. The same overall elemental composition can therefore give very different strength, hardness, and ductility depending on how the material was processed.

A steel with an austenitic, face-centered cubic matrix in the specified condition. Alloying and temperature determine its stability.

A stainless steel with an austenitic matrix. Some grades are used in nuclear components, where void swelling and helium embrittlement can limit performance.

A chromium–nickel–molybdenum stainless-steel grade. Annealed and cold-worked conditions can have different irradiation microstructures.

A chromium-bearing steel whose protective surface film can confer corrosion resistance. Composition, microstructure and environment determine whether that protection persists.

Steel microstructure describes the spatial arrangement of phases, grains, defects, and precipitates in a steel. Ferrite, austenite, cementite-containing mixtures, and martensitic structures are important examples.

These features influence dislocation motion and fracture, connecting thermal processing with mechanical performance. Overall carbon percentage alone cannot specify a steel's microstructure or uniquely determine its properties.

A nitric-acid/alcohol metallographic etchant. In pearlitic steel it can preferentially remove ferrite, leaving cementite standing higher. In an atomic force microscopy height image, darker then means lower surface height, not an optical reflectivity or atomic-number contrast.

Heating quenched steel below the austenitizing range to adjust its microstructure and relieve stresses. Carbon redistribution and carbide formation can improve toughness at a cost in hardness.

A microstructure in which carbon redistribution and carbide formation reduce the supersaturation of a martensitic matrix. Plate or lath morphology can remain while local strain and thermodynamic phase composition evolve. The term describes a material state, not a universal guarantee of a particular toughness.

A chart of the time needed to reach specified transformation fractions after cooling to, and holding at, a fixed temperature. Its curves are not themselves continuous-cooling histories; estimating a critical cooling rate from their nose is an approximation.

A product of a displacive transformation. In carbon steel, rapid cooling can trap carbon in a distorted iron lattice, producing high hardness and low as-quenched toughness.

A martensitic variant is one of the lattice deformations corresponding to the low-temperature crystal phase. The parent crystal's discrete symmetries generate different variants. In a nonlinear elasticity model each representative $U_i$ supplies a hyperelastic energy well $SO(3)U_i$. A representative need not itself be a symmetric stretch tensor; multiplication by a proper rotation leaves the same well.

Deformation twinning joins differently oriented crystal variants across a coherent interface. In a piecewise affine nonlinear elasticity model the two deformation gradients must differ by $a\otimes N$, where $N$ is the reference interface normal. The Hadamard jump condition gives this requirement from continuity along every interface tangent. Compatible alternating layers can then make a mixture of variants whose macroscopic shape differs from either variant alone.

A twin plane is a compatible planar interface between differently oriented crystal variants. In a piecewise homogeneous elastic deformation its reference normal is the $N$ in a rank-one connection between the two variant deformation gradients. Continuity of the deformation holds along this plane even though its derivative changes. Other material planes crossing the interface can kink after deformation.

Let $B=\mathrm{diag}(b,a,a)$, with $a,b>0$, $a\ne b$, and $A=R\mathrm{diag}(a,b,a)$ be a twin-related gradient with $\cos \theta =2ab/(a^2+b^2)$, $\sin \theta =\kappa (b^2-a^2)/(a^2+b^2)$, $\kappa =\pm 1$. Their jump is $(b^2-a^2)(-b,\kappa a,0)\otimes (1,\kappa ,0)/(a^2+b^2)$.

A plane through the origin with normal $p=(p_1,p_2,0)$ is spanned by $e_3$ and $t=(-p_2,p_1,0)$. Both gradients map $e_3$ to the same direction, so the two image half-planes are coplanar exactly when $At$ and $Bt$ are parallel in their transverse section. Direct calculation givesIts nonzero prefactor makes planarity equivalent to $p\parallel (1,\kappa ,0)$, the twin normal. On that plane the two affine maps agree, proving sufficiency as well. The restriction on the third normal component matters; this statement is not a classification of every possible material plane.

A lamellar two-phase microconstituent of ferrite and cementite, rather than a single thermodynamic phase. Shorter diffusion distances at greater undercooling generally produce finer lamellae before diffusional transformation is bypassed.

The proportions of ferrite and cementite within the two-phase pearlite microstructure. A lever rule on a weight-percent-carbon diagram gives mass fractions; converting those to volume fractions requires the phase densities. Proeutectoid phases outside pearlite must be treated separately.

Cementite is iron carbide, $\mathrm{F}{\mathrm{e}}_3\mathrm{C}$, a hard phase important in many steel microstructures. It can occur with ferrite in organized mixtures such as pearlite.

The amount, size, and distribution of cementite affect mechanical behavior because a carbide particle interacts differently with deformation than the surrounding iron-rich phase. Chemical composition and spatial arrangement must therefore be considered together.

The face-centred cubic iron-rich solid phase of steel. Its transformation products depend on composition and cooling history.

The body-centred cubic iron-rich solid phase of ordinary low-temperature steel, with low equilibrium carbon solubility.

A nickel–iron alloy with unusually small thermal expansion over a limited temperature range. Composition and treatment matter; its name does not mean every specimen has zero expansion. The Guillaume thermal expansion experiment explains how the effect was measured.^[ref]