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A feature that absorbs mobile point defects, such as a free surface, grain boundary, dislocation or cavity. Capture efficiency and relative preference for defect types are as important as visible size or number.

Motion of an edge component perpendicular to its glide plane by absorbing or emitting point defects. Unlike conservative dislocation glide, it changes the extra-plane content locally and is coupled to defect transport. Irradiation can drive climb by creating nonequilibrium vacancies and self-interstitials.

An interface between crystalline regions with different orientations. Its structure affects transport, mechanical response and absorption of mobile point defects.

Journal of Nuclear Materials 306, 61–72. Simulation study using empirical potentials; a disordered cascade core and surrounding point defects are distinguished.

The actual ionic radii need not equal the limiting ratio, and electronic charge distributions are not rigid sphere boundaries. In the same unlike-contact hard-sphere model, put $q=r_a/r_c$ and use $a=4(r_a+r_c)/\sqrt{3}$ to getA cation somewhat larger relative to the anion than the limiting size opens gaps between the anions. Starting from $q=1.366$ and reducing $q$ modestly reduces this packing fraction; thus a lower value is expected for that departure from the ideal contact construction. The formula is not monotonic for all imaginable ratios, so no universal inequality should be inferred without specifying radii. Coordination-dependent ionic radii, polarizability, nonionic contributions to bonding, thermal expansion and point defects also limit the model. No numerical real-crystal packing fraction is determined by the supplied data alone.

helium changes cavity stability and ductility; void swelling changes bulk volume and component dimensions. These effects interact, but a helium bubble and a vacancy-rich void are not interchangeable descriptions.

neutron reactions produce helium from alloy constituents and impurities. For example, capture by boron-10 can produce helium through ${}^{10}\mathrm{B}+n⟶{}^7\mathrm{Li}+{}^4\mathrm{He}$; the production per displacement dose depends on composition and neutron spectrum. Retained helium has low solubility and is trapped at defects or in bubbles. Bubble nucleation and growth at grain boundaries can assist intergranular cavitation, lowering tensile ductility and creep-rupture resistance, particularly when temperature permits the relevant transport. This is important even before a large bulk void swelling is measurable. A primary study linked high-temperature ductility loss to observed bubbles and grain-boundary weakening in irradiated stainless steel.^[ref]

displacement damage continuously creates vacancies and self-interstitials. Their different capture efficiencies at dislocations and other sinks can leave a vacancy supersaturation available to cavities. A stable cavity grows when its net vacancy uptake exceeds vacancy emission and interstitial absorption. helium can help stabilise small nuclei, but the later volume increase is not simply the volume of gas inserted into an unchanged matrix. Changing helium content can also change cavity number, size and competition for point defects; a universal proportionality between helium concentration and void swelling is not justified.

For nuclear fuel cladding, void swelling can enlarge the diameter, alter the fuel–nuclear fuel cladding gap, reduce clearances and distort reactor coolant channels or nearby structures. Nonuniform void swelling generates additional stresses. Bubble-assisted embrittlement and stress-dependent creep then affect the ability of the wall to contain the fuel and internal pressure. The relevant measurements combine density or volume change, dimensional strain, cavity microscopy and mechanical tests. Pressurised-tube experiments explicitly separated void swelling, creep, plastic strain and precipitation strain; void swelling itself was approximately isotropic in that study.^[ref]

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.

Irradiation creep adds stress-directed, time-dependent strain driven by the irradiation-generated defect population. It can be appreciable where ordinary thermal material creep would be slow, because irradiation maintains mobile point defects far above their equilibrium populations.

Absorption or emission of vacancies and self-interstitials permits dislocation climb. Applied stress can make differently oriented dislocations or dislocation loops absorb defects at different rates: stress-induced preferential absorption then produces a directional strain. Climb can also allow a pinned dislocation to bypass an obstacle and continue dislocation glide, providing a second route to strain.

A useful small-strain empirical form, over a limited range of conditions, isfor constant stress $\sigma$ and approximately constant irradiation-creep compliance $B$. Here $d$ is the accumulated displacements per atom and $\dot{d}$ the displacement dose rate; $B$ is measured per unit stress and per unit dpa. This relation explains why creep can scale approximately with both stress and neutron flux when the damage spectrum is fixed. It is not a constitutive law valid at every dose or temperature.

The total strain can also include thermal material creep, void swelling, irradiation growth and changes due to precipitation or recovery. Stress-free swelling is not itself irradiation creep. Experiments on pressurized type316 tubes separated these contributions and found that correcting stress-enhanced swelling materially affected comparisons between annealed and specimens strengthened by cold working.^[ref]

At sufficiently high temperature, thermal material creep can dominate. Changes in microstructure caused by irradiation hardening, softening, bubbles and cavities can either alter the creep rate or shorten rupture life. Thus enhanced defect-driven creep is the central effect, while the net rate and lifetime remain material- and history-dependent.

A parent initially at rest emits an alpha particle and a recoiling heavy daughter. momentum conservation gives equal and opposite momenta, so their nonrelativistic kinetic energies satisfyHere $Q$ is the kinetic energy available to this branch; excitation of the daughter reduces it and may be followed by photon emission. For an illustrative $Q=5$ MeV, $m_{\alpha }=4\mathrm{u}$ and $M_d=236\mathrm{u}$, the energies are $4.917$ MeV in the alpha particle and $83.3$ keV in the daughter. The heavy daughter receives much less energy, but that does not imply much less atomic damage.

The fast alpha particle loses most of its energy through electronic stopping: ionization and electronic excitation along a relatively long path. It also undergoes nuclear collisions, particularly towards the end of its range, and can produce displacement damage. The slower, heavy, highly charged recoil couples strongly to surrounding nuclei and generates a compact displacement cascade. Successive knock-on atoms create vacancies, interstitial defects and clusters. Some Frenkel pairs recombine as the cascade relaxes; the initial collision count is therefore not the number of defects that remain.

A quantitative illustration comes from brannerite rather than an assumed universal ceramic. Simulations in the primary natural-mineral study used a $4.5$ MeV alpha particle and an $80$ keV daughter recoil. The corresponding ranges were about $13$ micrometres and $23$ nanometres. At the study's assumed $50$ eV threshold displacement energy, its tabulated results give roughly $560$–$571$ recoil atomic displacements and $91$–$100$ alpha particle atomic displacements per radioactive decay. The numbers depend strongly on the displacement threshold and material, but the shorter recoil path contains the dominant and much denser ballistic radiation damage.^[ref]

In a susceptible ceramic, cascade cores can accumulate into an amorphous fraction; defects and associated relaxation can also change volume, thermal conductivity and mechanical response. molecular dynamics simulations of zirconolite found a strongly disordered core surrounded by more isolated point defects, supporting this distinction between local cascade damage and an entirely transformed specimen.^[ref]

The alpha particle eventually becomes a helium atom after slowing and charge exchange. helium accumulation can have later microstructural effects distinct from the initial knock-on cascade. Material-dependent recombination and annealing limit surviving disorder; a change in diffraction or radiation-induced swelling is not automatically radiation-induced amorphization, and radiation-induced amorphization is not automatically dissolution or release of the contained radionuclide.

An energetic neutron can collide with a lattice atom and create a primary knock-on atom. That recoil transfers energy to other atoms in a displacement cascade. Some atoms leave their normal lattice sites, creating Frenkel pairs: a vacancy and an extra atom at an interstitial position.

Many nearby defects recombine during the cascade and its thermal relaxation. The surviving point defects are therefore fewer than a simple count of all displacement events. Some defects are already clustered within the cascade; others migrate and aggregate later.

A collection of vacancies can collapse into a platelet bounded by a vacancy-type dislocation loop. An aggregation of self-interstitial atoms can create an extra atomic platelet bounded by an interstitial-type dislocation loop. The boundary is a line defect because a circuit around it has a nonzero Burgers vector. The allowed Burgers vectors and habit planes depend on the material's crystal structure and fault energies.

Loops can grow by absorbing mobile point defects, shrink by emitting or absorbing the opposite defect type, and interact with existing dislocations. Some remain faulted, while suitable loops can unfault or become part of a larger dislocation network. Repeated cascades and subsequent defect transport therefore create a population of extended defects even in material with a low initial dislocation density.

This describes the main displacement-damage mechanism. Ionizing energy deposited in a material does not automatically create the same defect population as a neutron recoil cascade; recoil spectrum, displacement thresholds and material response matter.

The resulting dislocation density reflects competing production, growth and recovery rates. The irradiation spectrum and displacement dose rate set the supply of recoil cascades and surviving point defects. Cascade structure controls the fraction born as isolated defects or clusters; equal nominal displacements per atom can therefore give different defect populations.

Temperature sets vacancy and interstitial mobilities and the rates of thermal emission and recovery. A simple radiation damage rate theory model illustrates the competition using number densities $c_i,c_v$:Here $G$ is the surviving mobile-pair production rate per volume, $K_{\mathrm{rec}}$ is the recombination coefficient, $D_i,D_v$ are diffusion coefficients, and $k_i^2,k_v^2$ are sink strengths. The model omits explicit cluster-size populations and thermal-equilibrium emission; those must be added for a quantitative description of a particular exposure.

The initial dislocation density, grain size, free surfaces, precipitates and existing cavities all change sink strengths. Dislocations can have an interstitial bias, so their capture rates for the two defect types differ. Solutes and transmutation gases alter defect binding and mobility. Crystal structure, elastic anisotropy and applied stress affect which loop orientations survive and grow.

For a number density $N_{\ell }$ of circular loops of radius $R$, their contribution to line length per volume isThus loop nucleation and loop growth both increase dislocation density, while shrinkage, annihilation and absorption at other sinks can decrease it. A change in loop count alone does not determine the change in total line density.

Schematically, ${\dot{\rho }}_d$ is a production-and-growth contribution minus recovery and annihilation. An initial rise followed by approximate saturation is possible when these balance, but the saturation value and approach rate depend on the evolving microstructure. There is no universal dislocation density fixed by dose alone.

Transport accelerated by irradiation-maintained populations of mobile point defects. It can change precipitation, segregation and recovery. Its consequences depend on defect production, recombination and defect sinks, rather than simply on the nominal displacement dose.

An irradiation creep mechanism in which applied stress makes differently oriented dislocations or dislocation loops absorb point defects at different rates. The resulting directional strain is distinct from stress-free void swelling.