# Precipitation hardening **Precipitation hardening**, also called age hardening or particle hardening, is the strengthening of an [[Alloy|alloy]] by a dispersion of fine second-phase particles grown out of a [[Supersaturation|supersaturated]] [[Solid_solution|solid solution]]. The treatment has three steps: a solution treatment that dissolves the alloying element into a single phase, a [[Quenching|quench]] that traps it there, and an ageing hold at a lower temperature during which the trapped atoms come back out as particles. Those particles obstruct the [[Dislocation|dislocations]] that carry [[Slip_(materials_science)|slip]], and the alloy's [[Yield_(engineering)|yield strength]] can reach several times that of the same metal in the annealed state. In the microsim below the reader watches one glide plane, seeded with particles of radius *r* and mean spacing *λ*, while a single logarithmic control — the ageing time — grows both. Early on, when the particles are small and coherent, a dislocation cuts straight through them and the strength increment rises roughly as `d(tau) ~ r^(1/2)`. Once the particles are large enough to resist cutting, the dislocation bows between them instead and leaves a loop behind, the Orowan mechanism, whose increment `d(tau) = G·b/lambda` *falls* as the spacing opens. The alloy is strongest where the two curves cross, and past that point it is over-aged: the under-aged, peak-aged and over-aged arms of the classic ageing curve, with [[Aluminium_alloy|2024 and 7075 aluminium]] presets. On the [[Materials_science|Materials science]] flagship this article serves the *Precipitation hardening* section of Part VIII, Industry, as the [[Aluminium|aluminium]]-placed sibling of the [[Dislocation|dislocation]] sim whose glide plane it reuses; [[Work_hardening|work hardening]] is the same obstacle argument with other dislocations as the obstacles. ## Kinetics versus thermodynamics Which particles form is a question for [[Thermodynamics|thermodynamics]]; which particles actually appear in a given hold is a question for kinetics, and the two answers differ. A [[Phase_diagram|phase diagram]] says only that below the solvus line the equilibrium state of the alloy is two phases, and names the equilibrium precipitate. It says nothing about how long the alloy takes to get there, and in a well-designed age-hardening alloy the answer is: much longer than the treatment.[^callister-precip] What forms instead is a sequence of metastable phases, each easier to nucleate than the last because each fits the parent lattice better. In aluminium–copper the sequence begins with [[Guinier–Preston_zone|Guinier–Preston zones]] — copper-rich platelets one or two atoms thick, fully coherent with the matrix, identified by X-ray diffraction in 1938 in independent papers by André Guinier and George Dawson Preston[^guinier1938][^preston1938] — and passes through θ″ and θ′ before reaching the equilibrium θ (Al₂Cu), which is incoherent and, by the time it appears, coarse and weak.[^callister-precip] Peak strength belongs to the middle of that sequence, not to its end. The effect itself was found empirically long before any of that structure was known, when Alfred Wilm observed that a quenched aluminium–copper–magnesium alloy hardened on standing at room temperature; the alloy became Duralumin.[^wilm1906] The rate is set by [[Diffusion|diffusion]], so ageing obeys an [[Arrhenius_equation|Arrhenius]] temperature dependence: a hold that takes days at room temperature takes hours at 120 °C and minutes at 190 °C, and the peak that is reached is lower the hotter the hold, because the particles that grow fast also coarsen fast.[^callister-precip] That trade — reach the peak sooner, reach a lower peak — is why ageing schedules are quoted as a temperature *and* a time, and why the sim's control is time on a logarithmic axis at a fixed ageing temperature. ## Alloy design An alloy can be precipitation hardened only if its phase diagram has the right shape: an appreciable solid solubility at high temperature that falls steeply as the temperature drops, so that a quench from the single-phase field leaves a large supersaturation to precipitate.[^callister-precip] Aluminium–copper is the textbook case, with the solvus running from about 5.6 % copper at the eutectic temperature down to almost nothing at room temperature. A [[Eutectic_system|eutectic system]] whose solvus is nearly vertical offers nothing to precipitate; a system with no solubility at all offers nothing to dissolve. Beyond that, the designer wants a precipitate that is coherent or semi-coherent with the matrix, so that it nucleates readily and carries a strain field the dislocations feel; that is thermally stable at the service temperature, so the part does not over-age in use; and that is present at a high enough volume fraction to give the spacing the Orowan equation needs. These pull in different directions. Coherence raises the nucleation rate but limits the particle to a small size before it loses coherence; a large volume fraction of a stable phase gives strength at temperature but needs an alloying addition that may harm [[Corrosion|corrosion]] resistance, weldability or toughness. The result is that precipitation-hardening alloys are narrow families rather than a general technique. Aluminium's 2xxx (Al–Cu), 6xxx (Al–Mg–Si) and 7xxx (Al–Zn–Mg) series, the nickel-base [[Superalloy|superalloys]], the maraging steels, the precipitation-hardening stainless steels and beryllium [[Copper|copper]] between them cover nearly all industrial use.[^callister-alloys] ## Types of hardening Particle hardening is one of four routes to a higher yield stress in a metal, and the four are usually combined. [[Grain_boundary|Grain-boundary]] strengthening raises the stress by shortening the slip distance; [[Solid_solution_strengthening|solid-solution strengthening]] raises it by scattering dislocations off individual solute atoms; [[Work_hardening|work hardening]] raises it by tangling dislocations with one another; and precipitation hardening raises it by inserting discrete particles in the glide plane.[^callister-strength] Within particle hardening itself the pair's distinction is between *shearable* and *non-shearable* particles, which is exactly the sim's crossover. Small, coherent particles are shearable: the dislocation passes through, and the resistance comes from the work of creating new interface, from the difference in shear modulus across the boundary, from the coherency strain field, and — in an ordered precipitate — from the anti-phase boundary the dislocation leaves inside the particle. Every one of those contributions grows with particle size, which is why the under-aged arm rises. Large or incoherent particles are non-shearable. The dislocation cannot enter, so it bows between neighbours until the two arms meet and pinch off, leaving an Orowan loop around each particle and moving on. The resistance now depends only on how far apart the obstacles are, and coarsening moves them apart. The same non-shearable mechanism describes dispersion-strengthened alloys, in which stable oxide particles are mixed in mechanically rather than precipitated, and which therefore do not over-age. ## Theory A dislocation gliding on its plane meets the particles that intersect that plane. The strength increment is the extra shear stress needed to get past them, and the whole subject is the calculation of that stress for the two ways of getting past. For a shearable particle the dislocation must do work inside it. The most transparent contribution is the interface created: a dislocation of [[Burgers_vector|Burgers vector]] *b* cutting a particle of radius *r* offsets its two halves and makes new interface of area of order `2·r·b`, at an energy cost proportional to the interfacial energy. Summing over the particles a dislocation line meets, at a fixed volume fraction, gives an increment that rises as the square root of the radius, `d(tau) ~ r^(1/2)` — the sim's under-aged arm. Coherency strain and modulus mismatch give increments with the same qualitative size dependence, which is why one exponent stands for the whole group. For a non-shearable particle the argument is geometric and due to Egon Orowan.[^orowan1948] A dislocation line has a line tension of order `G·b²/2`, so bowing it to a radius of curvature *R* costs a stress of about `G·b/(2R)`. To pass between obstacles a distance *λ* apart the line must bow to a radius of about `lambda/2`, so the stress required is of order `d(tau) = G·b/lambda`. That is the sim's over-aged arm, and it is the same line-tension argument that governs the [[Frank–Read_source|Frank–Read source]]. More complete treatments replace the constant with a logarithmic factor in `r/b` and correct for the character of the dislocation, but they do not change the `1/lambda` dependence.[^orowan1948][^callister-strength] ## Governing equations The sim computes both increments and takes the smaller, because a dislocation will do whatever is easiest: `d(tau) = min( C·r^(1/2) , G·b/lambda )`. For the aluminium presets it uses `G = 26 GPa` and `b = 0.286 nm`, so `G·b = 7.44 N/m`, and converts shear to tensile stress with a Taylor factor of 3, the usual value for a face-centred cubic polycrystal.[^callister-strength] It also assumes that ageing coarsens the structure at constant volume fraction, so that the spacing stays proportional to the radius; the sim uses `lambda = 10·r`, an ILLUSTRATIVE geometric factor standing for a volume fraction of a few percent rather than a measured one, and it fixes `C` so that the two curves cross at `r = 5 nm`. With those choices the ageing curve reads as follows (all values derived on the page from the constants above): | particle radius *r* | spacing *λ* | cutting Δτ | Orowan Δτ | governing Δτ | tensile Δσ = 3Δτ | condition | |---|---|---|---|---|---|---| | 1 nm | 10 nm | 67 MPa | 744 MPa | 67 MPa | 200 MPa | under-aged | | 2 nm | 20 nm | 94 MPa | 372 MPa | 94 MPa | 282 MPa | under-aged | | 5 nm | 50 nm | 149 MPa | 149 MPa | 149 MPa | 446 MPa | peak-aged | | 10 nm | 100 nm | 210 MPa | 74 MPa | 74 MPa | 223 MPa | over-aged | | 20 nm | 200 nm | 297 MPa | 37 MPa | 37 MPa | 112 MPa | over-aged | The shape is the point. Strength rises as the square root of radius on the way up and falls as its inverse on the way down, so the peak is sharp on the over-aged side and forgiving on the under-aged side: doubling the ageing time past the peak costs more than halving it short of the peak. Heat-treaters exploit that asymmetry, and the T6 and T7 tempers of the aluminium alloys are respectively the peak and a deliberately over-aged condition chosen for better [[Corrosion|stress-corrosion]] resistance at some cost in strength. ## Other Considerations Three qualifications belong with the equations. First, the increment computed here adds to a base strength the alloy already has from solid solution, grain size and prior deformation; the sim shows the increment alone, not the yield stress. On the shop floor the whole treatment is one entry in a furnace schedule alongside annealing, normalizing and the quench-and-temper route for steels, and it is bought by holding a named temperature for a named time.[^virasak-ch6] Second, over-ageing happens in service as well as in the furnace. A precipitation-hardened part held near its ageing temperature keeps coarsening by [[Ostwald_ripening|Ostwald ripening]], which is why the 2xxx and 7xxx aluminium alloys are not used much above about 150 °C, and why [[Creep_(deformation)|creep]]-resistant alloys need a precipitate that coarsens slowly. Third, heat undoes the treatment locally. [[Welding|Welding]] a T6 aluminium extrusion leaves a soft band beside the weld where the alloy has been solution-treated, over-aged, or both, and design codes derate the joint accordingly. The same mechanism gives natural ageing its nuisance value: an alloy quenched and left at room temperature hardens on its own over days, so rivets in the 2xxx alloys were once refrigerated between quench and driving. Shearable particles have one further liability. Because each dislocation that cuts a particle makes it a slightly easier target for the next, slip concentrates onto a few planes rather than spreading, which coarsens the slip step at the surface and is unhelpful for [[Fatigue_(material)|fatigue]] and for stress-corrosion cracking. Over-aged, non-shearable structures spread slip more evenly, which is part of why a T7 temper survives a corrosive environment better than a T6. ## Computational discovery of new alloys The design problem stated above — find a phase that nucleates readily, stays fine, and sits at a useful volume fraction — is now attacked computationally. Assessed thermodynamic databases of the CALPHAD type predict which phases are stable in a candidate composition and at what temperature the solvus lies; coupling them to a diffusion model predicts how fast the particles nucleate, grow and coarsen; and first-principles calculation supplies the interfacial energies and lattice misfits the kinetic model needs. The output is a predicted ageing curve for a composition that has never been cast.[^callister-phase] The strength model at the end of that chain is the one above. Because `d(tau)` depends on radius and spacing rather than on chemistry directly, a kinetic simulation that predicts the particle-size distribution can be converted straight into a predicted peak strength and a predicted time to reach it, which is what makes the whole pipeline worth running. Screening then reduces to searching composition space for the alloy whose predicted peak is highest and whose predicted coarsening at the service temperature is slowest. Additive processes have widened the search. Because a powder-bed melt pool solidifies and cools far faster than a casting, [[Selective_laser_melting|laser powder-bed fusion]] can hold more solute in solution than conventional processing, and the post-build heat treatment rather than the casting practice sets the final precipitate structure; *Additive Manufacturing Essentials* surveys the alloy families available to additive processes in its AM Materials chapter and treats post-processing among the supporting processes.[^ame-ch3][^ame-ch2] ## Examples of precipitation hardening materials The aluminium alloys are the largest family. The 2xxx series (Al–Cu, with magnesium) reaches its strength through the GP-zone-to-θ′ sequence above and is the traditional airframe skin alloy; the 7xxx series (Al–Zn–Mg, with copper) precipitates the η′ and η phases and is stronger still, at some cost in corrosion resistance; the 6xxx series (Al–Mg–Si) precipitates β″ and is the extrusion alloy of architectural and automotive practice. Handbook values for the peak-aged tempers put 2024 at roughly 325 MPa yield and 470 MPa [[Ultimate_tensile_strength|tensile strength]], and 7075 at roughly 505 MPa and 570 MPa, against about 100 MPa and 180 MPa for the same metal annealed.[^callister-alloys] The nickel-base [[Superalloy|superalloys]] are the high-temperature case. They precipitate the ordered γ′ phase, Ni₃(Al,Ti), which is coherent with the matrix, resists coarsening, and is present at volume fractions far higher than anything achievable in aluminium — high enough in a single-crystal [[Jet_engine|turbine]] blade that the matrix is the minority constituent by volume. That is what lets a blade carry load at a large fraction of its melting temperature.[^callister-alloys] Among ferrous alloys, the maraging steels take a soft iron–nickel martensite and age it to precipitate intermetallics containing [[Molybdenum|molybdenum]], [[Titanium|titanium]] and [[Cobalt|cobalt]], reaching yield strengths well above those of conventional [[Carbon_steel|carbon steels]] while keeping good toughness; the precipitation-hardening [[Stainless_steel|stainless steels]] such as 17-4 PH add a copper-rich precipitate to a corrosion-resistant matrix. Beryllium copper is the non-ferrous spring alloy, combining high strength with the conductivity of a copper base.[^callister-alloys] ## See also - [[Aluminium_alloy]] - [[Aluminium]] - [[Guinier–Preston_zone]] - [[Superalloy]] - [[Work_hardening]] - [[Solid_solution_strengthening]] - [[Nucleation]] - [[Heat_treating]] ## References [^orowan1948]: Orowan, E. (1948). Discussion contribution, in *Symposium on Internal Stresses in Metals and Alloys*. London: Institute of Metals. (Pages to pin against the symposium volume; no DOI asserted.) [^wilm1906]: Wilm, Alfred. The discovery that a quenched aluminium–copper–magnesium alloy hardens on standing, made at Neubabelsberg and published in the following years; the alloy was commercialized as Duralumin. (Exact date, publication venue and patent record all to pin; no DOI asserted.) [^guinier1938]: Guinier, André (1938). On the structure of age-hardened aluminium–copper alloys. *Nature* 142. (Article title as printed, pages and DOI to pin against the journal record.) [^preston1938]: Preston, George Dawson (1938). On the structure of age-hardened aluminium–copper alloys. *Nature* 142. (Article title as printed, pages and DOI to pin against the journal record.) [^virasak-ch6]: Virasak, LamNgeun (2019). *Manufacturing Processes 4-5* (Portal Book 094). Chapter 6, Heat Treating, pp. 147–150 — annealing, normalizing, hardening and tempering as furnace operations. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 [^callister-precip]: Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Hoboken: Wiley. Chapter 11, Applications and Processing of Metal Alloys — precipitation hardening: the solution-treatment, quench and ageing sequence, the aluminium–copper solvus, the GP-zone → θ″ → θ′ → θ sequence, and the effect of ageing temperature on the position and height of the strength peak. Not a Portal Book; pages to pin. [^callister-alloys]: Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Chapter 11 — tables of composition, mechanical properties and typical applications for the wrought and heat-treatable aluminium alloys, for the superalloys, and for the maraging and precipitation-hardening stainless steels. The 2024, 7075 and annealed-aluminium values quoted here are the handbook figures of that table. Not a Portal Book; table page to pin. [^callister-strength]: Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Chapter 7, Dislocations and Strengthening Mechanisms — grain-size, solid-solution and strain-hardening mechanisms, the Taylor factor for a face-centred cubic polycrystal, and the shear-modulus and Burgers-vector values used for aluminium. Not a Portal Book; page to pin. [^callister-phase]: Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Chapter 9, Phase Diagrams, and Chapter 10, Phase Transformations — the solvus, the distinction between equilibrium and metastable products, and the diffusion-controlled kinetics of nucleation, growth and coarsening. Not a Portal Book; pages to pin. [^ame-ch3]: Barnes, John; Simpson, Timothy (2025). *Additive Manufacturing Essentials* (Portal Book 110). Chapter 3, AM Materials, pp. 49–74 (page to pin). https://open.umn.edu/opentextbooks/textbooks/additive-manufacturing-essentials [^ame-ch2]: Barnes, John; Simpson, Timothy (2025). *Additive Manufacturing Essentials* (Portal Book 110). Chapter 2, Core AM Technologies and Supporting Processes, pp. 25–48 (page to pin). https://open.umn.edu/opentextbooks/textbooks/additive-manufacturing-essentials ## Further reading - Barnes, John; Simpson, Timothy (2025). *Additive Manufacturing Essentials*. Portal Book 110. Chapters 2 and 3. https://open.umn.edu/opentextbooks/textbooks/additive-manufacturing-essentials - Virasak, LamNgeun (2019). *Manufacturing Processes 4-5*. Portal Book 094. Chapter 6, Heat Treating, pp. 147–150 — the shop-floor version of solution treatment, quench and temper. https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5 - Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Wiley. Chapters 7, 9, 10 and 11. Not a Portal Book. - Orowan, E. (1948). Discussion, *Symposium on Internal Stresses in Metals and Alloys*. Institute of Metals. Not a Portal Book. ## External links - [*Additive Manufacturing Essentials*](https://open.umn.edu/opentextbooks/textbooks/additive-manufacturing-essentials), Open Textbook Library — Portal Book 110, open access - [*Manufacturing Processes 4-5*](https://open.umn.edu/opentextbooks/textbooks/manufacturing-processes-4-5), Open Textbook Library — Portal Book 094, open access - For alloy-specification and standards links, see the external links of the Wikipedia pair at the pinned revision below; none is reproduced here unverified. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Precipitation_hardening.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Precipitation hardening* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Precipitation_hardening.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Precipitation_hardening.html" data-title="Precipitation hardening"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Precipitation_hardening) : [Wikitube](https://en.wikitube.io/wiki/Precipitation_hardening) · pinned revision [1368446392](https://en.wikipedia.org/w/index.php?oldid=1368446392) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M53 · sim pending (matter/Precipitation_hardening).*