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For the upper core-shell precursor, first reduce a precursor of metal A to make seeds; then introduce and reduce a precursor of B under conditions favouring heterogeneous deposition on those seeds rather than independent nucleation. Control added quantity, reduction rate and surface ligands to build a shell.

For the lower disordered-alloy precursor, reduce both metal precursors together so both metals enter the growing particles. Match their effective reduction rates by precursor chemistry, temperature, complexation or controlled feeding; otherwise sequential reduction can produce segregation instead of co-incorporation. Quenching or sufficiently mild growth can retain a disordered alloy before the later anneal. These routes need not initially produce equilibrium atomic arrangements.^[ref]

A faceted, approximately equiaxed crystal is indicated. A truncated octahedron bounded by low-energy $\{111\}$ and $\{100\}$ facets is a plausible three-dimensional shape for an fcc metal particle; the hexagonal section alone does not uniquely distinguish it from other faceted polyhedra.

The Wulff construction minimizes ${\sum }_i{\gamma }_i{A}_i$ at fixed particle volume. Place a plane with normal ${\hat{\mathbf{n}}}_i$ a distance $h_i=C{\gamma }_i$ from a common centre and take the inner envelope. Low-surface-energy orientations survive as large facets. Annealing permits diffusion toward this equilibrium morphology, provided the time is sufficient. For a supported or strained alloy, substrate adhesion and elastic energy modify this simple free-particle construction.

Void swelling is generally favored by an intermediate irradiation temperature window. The balance involves defect mobility, stable nucleation, absorption at defect sinks and thermal emission; a larger vacancy population alone does not guarantee a larger void.

At low temperature, vacancy migration is slow. Self-interstitials may migrate and form dislocation loops, and small clusters can cause considerable irradiation hardening, while vacancies cannot readily feed large growing cavities. Defects retained in the matrix can evolve during later heating.

At intermediate temperature, vacancies can migrate far enough to reach stable cavities. Interstitial bias and the competition among defect sinks sustain a net vacancy flux into these cavities. Once the incubation period has produced suitable nuclei and sink populations, substantial void swelling can develop.

At high temperature, the thermal equilibrium vacancy population and vacancy emission from small cavities rise. A small void's curvature further favors emission, so maintaining stable nuclei becomes harder. Recovery changes the dislocation population, and recombination, gas transport and evolving precipitates also change the flux balance. The irradiation-driven vacancy supersaturation can fall, suppressing void nucleation and net swelling. Existing cavities may still coarsen, and gas bubbles, material creep and other damage can remain important.

Thus low-temperature defect retention, intermediate-temperature cavity growth and high-temperature recovery/emission are different regimes. The boundaries depend on alloy composition, initial microstructure, gas production, accumulated displacements per atom and displacement dose rate. No alloy-independent peak temperature can be inferred from the paper's data.

Irradiation softening occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones. It is particularly plausible in an initially hardened alloy, rather than an initially soft annealed reference.

In a material strengthened by cold working, the starting dislocation density is high. Irradiation-generated point defects can assist dislocation climb, rearrangement and annihilation, reducing the contribution of work hardening. A schematic estimate iswhere $\mu$ is the shear modulus, $b$ the magnitude of the Burgers vector, ${\rho }_d$ the dislocation density, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in $\Delta {\sigma }_{\mathrm{irr}}$.

In a material strengthened by precipitation hardening, ballistic mixing can dissolve or disorder the original obstacles. Radiation-enhanced diffusion can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: irradiation can instead create new strengthening precipitates.

The required conditions therefore include an appropriate initial microstructure, enough displacement dose to modify it, and a temperature and displacement dose rate at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same temperature to separate ordinary thermal aging from an irradiation effect.

A drop in yield strength or hardness need not restore ductility: cavities, helium embrittlement or localization of dislocation glide can coexist with softening. Conversely, an initially annealed steel may show strong irradiation hardening under the same exposure conditions.

Assume a homogeneous Fe–Cr–Ni alloy, normal incidence, independent scattering events and the stated effective scattering cross-sections. Neglect absorption, other constituents and changes in neutron energy within the thin sheet. The atomic fractions are not supplied; take $x_{\mathrm{Fe}}=0.70$, $x_{\mathrm{Cr}}=0.20$, $x_{\mathrm{Ni}}=0.10$ as an explicit representative assumption, not a composition measured or specified in the paper.

The conventional cell of a face-centered cubic lattice containsatoms. The number density is thereforeFor a mixture, the scattering probability per unit path length is ${\Sigma }_s={\sum }_j{n}_j{\sigma }_j=n{\bar{\sigma }}_s$, whereThus ${\Sigma }_s=27.751{\mathrm{m}}^{-1}$. For thickness $t=10^{-3}\mathrm{m}$, the unscattered fraction $U$ satisfies $dU/dz=-{\Sigma }_{s}U$ with $U(0)=1$. The fraction undergoing at least one neutron scattering event isThe thin-sheet approximation gives $P_s\simeq {\Sigma }_{s}t=2.78\%$, consistent to the accuracy of the assumed composition. A simple iron-dominated estimate ${\bar{\sigma }}_s\simeq 3.2$ barns gives essentially the same about $3\%$ scattered conclusion.

For any other assumed composition, use the displayed weighted formula; mass fractions must first be converted to atomic fractions. Since the supplied elemental cross-sections span $2.8$–$4.1$ barns, any mixture of these three elements at the stated number density gives approximately $2.39$–$3.48\%$. This is a bound within the idealized mixture model, not a claim that every such composition is stable austenite.

Physical metallurgy connects the internal structure of metals and alloys to their properties and the processes used to change them. It studies crystal structures, crystal defects, phases and their transformations, including changes caused by deformation and heat treatment.

A controlled comparison heats samples of the same steel and cools them differently, then measures hardness and examines their microstructures. Differences in properties can then be related to phase formation and transformation history rather than to a change in overall chemical composition. This is why selecting an alloy and selecting its thermal/mechanical processing are coupled design decisions.^[ref]

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.

An iron–manganese–carbon alloy historically used to adjust steel composition.

Steelmaking produces steel by controlling the carbon content, other alloying elements and unwanted constituents of iron. A blast furnace first produces carbon-rich pig iron; a basic oxygen furnace then refines the molten material by oxidation and composition adjustment. An electric arc furnace instead supplies heat electrically to melt a charge that can include recycled steel, direct reduced iron and pig iron.^[ref]

The distinction between iron extraction and steelmaking matters: converting an iron oxide to metallic iron and adjusting an existing iron-based alloy to the required composition are different tasks. The Bessemer process is an important historical example of refining pig iron by an air blast; modern basic oxygen steelmaking uses an oxygen supply rather than ordinary air.

Vanadium is the chemical element with atomic number 23 and symbol $\mathrm{V}$. It is a transition metal. It supports several oxidation states, producing differently colored ions in solution. Vanadium-containing alloys strengthen steel, while vanadium oxides participate in oxidation catalysis; the same element therefore plays distinct structural and chemical roles.^[ref]