Codex @codex  0

An alloying element is a chemical element deliberately included in an alloy to control its properties or processing behaviour. In steel, carbon changes the phases and transformations available during heat treatment; other additions can modify corrosion, hardenability or high-temperature behaviour.

The effect depends on how an element is incorporated. Atoms dissolved in a solid solution can hinder dislocation motion, while an element concentrated in a secondary phase can affect strength through the size and distribution of particles. Thus a bulk composition does not uniquely determine mechanical strength: processing controls the microstructure through which the composition acts.^[ref]

A semiconductor solid solution whose composition changes its band gap.

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.

A group of silicate minerals with several cation positions that permit extensive solid solutions. Pyrope is the magnesian aluminium-bearing endmember relevant to a simple iron–magnesium exchange model.

Lead zirconate titanate is an oxide solid solution commonly written $\mathrm{Pb}(\mathrm{Z}{\mathrm{r}}_{\mathrm{x}}\mathrm{T}{\mathrm{i}}_{1-\mathrm{x}}){\mathrm{O}}_3$. Its perovskite structure can support switchable electric polarization and a strong piezoelectricity response.

Changing the zirconium-to-titanium ratio changes the competing crystal structures and the response to an applied field or stress. Composition, domain configuration, and processing therefore matter when using the material as a transducer.

A specified limiting composition used to describe a solid solution in a mineral. Its thermodynamic activity depends on the chosen standard state and activity model. For example, pyrope is a magnesian garnet endmember, while phlogopite is a magnesian biotite endmember.

Mineralogy studies the composition, structure and properties of minerals. A chemical analysis identifies which elements are present, while X-ray diffraction constrains their periodic atomic arrangement. These measurements answer different questions: substances with the same overall composition can have different crystal structures.

Microscopy and physical properties provide complementary evidence. Mineral assemblages and textures help reconstruct rock formation, deformation and fluid interaction. Identification must allow for solid solutions, in which composition varies within one structural family, and for alteration that changes only part of a grain.

For $N$ distinguishable lattice sites occupied by $N_i$ mutually indistinguishable atoms of each species, the number of configurations isUsing Stirling's approximation,For one mole, $N=N_A$ and $k_B{N}_A=R$, soEquiatomic configurational entropy follows when the composition has $X_i=1/n$, givingThe reference is the unmixed configurational arrangement, and the model assumes random site occupation without short-range order. It counts configurational entropy, not all vibrational, electronic or magnetic entropy. A large number of elements does not by itself guarantee a stable single solid solution: competing thermodynamic phases and the enthalpy term also enter the Gibbs free energy.

The nickel-rich $\gamma$ matrix is a disordered substitutional solid solution on a face-centered cubic lattice. The ordered ${\gamma }^{\prime }$ phase has the L12 structure, approximately $\mathrm{N}{\mathrm{i}}_3\mathrm{Al}$: aluminium occupies cube corners and nickel occupies face centres. Its occupied-site geometry is often called ordered FCC, but its chemically labelled Bravais lattice is primitive cubic, with a four-atom basis. A face-centre translation exchanges chemical sublattices and is not a symmetry of the ordered crystal.

Each Al atom has twelve nearest-neighbour Ni atoms at Euclidean distance $a/\sqrt{2}$. Each Ni atom has twelve nearest neighbours too, but these are four Al and eight Ni. The chemical distinction matters for slip. In disordered $\gamma$, the shortest perfect Burgers vector isFor the ordered primitive cubic translation lattice, the shortest order-preserving perfect vector isThis does not imply that $⟨100⟩$ slip must dominate. A vector must lie in a favourable glide plane and have an accessible core structure and activation stress. Matrix dislocations commonly glide on $\{111\}⟨110⟩$ systems. A single $a⟨110⟩/2$ passage through ${\gamma }^{\prime }$ leaves an antiphase boundary; a second matching passage restores order, giving total vector $a⟨110⟩$. Such a superdislocation has a longer total vector than $a⟨100⟩$, yet its constituent dislocations can move on the favourable close-packed planes and interact with the matrix. Paired motion balances line and antiphase-boundary energies, so the shortest abstract lattice translation alone does not select the active slip system.^[ref]

Pearlite is a microstructural arrangement of two phases, ferrite and cementite, rather than a single phase. Ferrite is an iron-rich solid solution; cementite is the carbide $\mathrm{F}{\mathrm{e}}_3\mathrm{C}$. A pearlite colony contains alternating lamellae of these constituents formed by transformation of austenite.

A thermodynamic phase has a specified crystal structure and composition range with locally homogeneous properties on the appropriate scale. The word pearlite instead describes how distinct phases are arranged. Its lamellar spacing and orientation can change while the identities of its two phases remain the same.

Synroc immobilises waste ions in selected durable crystalline hosts, rather than trying to put the whole inventory into one universal site. The underlying philosophy is that minerals retaining analogous elements over geological times suggest useful crystal structures for engineered containment. These natural analogues motivate the choice; their survival does not prove that every synthetic composition, damaged microstructure or groundwater environment will behave identically. This was the rationale of the original mineral-analogue proposal.^[ref]

A representative Synroc-C assemblage includes zirconolite, $\mathrm{CaZrT}{\mathrm{i}}_2{\mathrm{O}}_7$, as an actinide host; a hollandite waste-form phase, represented by $\mathrm{BaA}{\mathrm{l}}_2\mathrm{T}{\mathrm{i}}_6{\mathrm{O}}_{16}$, whose tunnels accommodate large cations such as caesium; and a perovskite waste-form phase, $\mathrm{CaTi}{\mathrm{O}}_3$, which can accept strontium on calcium sites and other constituents with suitable charge compensation in a crystal. Titanium-oxide phases provide additional accommodation and composition flexibility. The actual phases are solid solutions, not simply pure end-member minerals mixed with an inert waste powder.^[ref]

Manufacture combines a characterised waste feed with selected oxide-forming precursors, converts the mixture to a suitable powder or calcination product, and consolidates it while forming the host phases. hot pressing and hot isostatic pressing are consolidation approaches; the latter uses pressure acting approximately equally in all directions. The objective is a dense ceramic with the intended phase assemblage and low connected porosity, contained in an appropriate radioactive waste package. Verify density and phase composition, use microscopy to find segregated constituents or pores, and test leaching of the actual product. Successful densification alone does not establish radionuclide retention.^[ref]

The magnesian biotite mineral endmember. Iron substitution on its magnesium-bearing positions produces a solid solution requiring an activity model when used in chemical equilibrium calculations.

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.

A secondary phase is a distinguishable material phase present alongside a principal matrix phase. It can differ in chemical composition, crystal structure or both. Particles of a secondary phase within an alloy are therefore different from atoms simply dissolved in a solid solution.

Their effects depend on size, distribution and interface properties. Fine particles can obstruct dislocation motion and increase mechanical strength, while coarse or brittle regions can assist crack initiation. Heat treatment can change a secondary phase's amount and morphology, explaining why overall composition alone does not determine an alloy's behaviour.

A solid solution is a solid phase whose composition can vary as components share one crystal structure. In a substitutional solid solution, atoms replace host atoms on lattice sites; interstitial solutions place smaller atoms between them.

This is distinct from a macroscopic mixture of separate solid phases. Composition-dependent lattice distortion can affect strength and transport, linking atomic placement with the properties of an alloy or mineral.

A boundary giving the equilibrium limit of one solid solution against coexistence with another solid phase. Moving along a solvus during cooling changes equilibrium solid compositions even after all liquid has disappeared.

A family of mineral-analogue ceramic waste forms. Different titanate phases accept different waste ions by solid solution; phase assemblage is tailored to the waste inventory.

A solid solution adjoining a pure-component end of a composition phase diagram. Its solute content can be small but need not be zero. A phase label such as (Bi) therefore does not by itself mean exactly pure bismuth.

An approximate linear interpolation of a substitutional solid solution's lattice parameter with atomic composition. Converting the inferred atomic fraction to mass fraction requires molar masses. Ordering, nonideal mixing, strain and multiple phases can invalidate a simple two-endpoint interpolation.