# Eutectic system A **eutectic system** is a mixture of two or more components that freezes, at one particular composition, at a single temperature lower than the melting point of any of them. The name is from the Greek for "easily melted", and the fact is counter-intuitive: mixing two solids that each melt high can give an [[Alloy|alloy]] that melts low. [[Lead|Lead]] melts at 327 °C and [[Tin|tin]] at 232 °C, but a mixture of 61.9 % tin by weight melts and freezes at 183 °C, 49 °C below tin and 144 °C below lead.[^melting-points] That single number is why [[Solder|solder]] exists. In the microsim below the reader sets the composition and cools it. On the Pb–Sn preset the liquid is tracked down the liquidus until it reaches the eutectic temperature `T_E` = 183 °C, where the remaining liquid freezes at once into an alternating lamellar structure of tin-rich and lead-rich [[Phase_(matter)|phases]]; the lamellar spacing shrinks as the undercooling grows, following the ILLUSTRATIVE display law `λ ≈ C/ΔT`. Away from 61.9 % tin the readout names the primary phase that came out first and gives its fraction by the [[Lever_rule|lever rule]], so the reader sees the hypoeutectic and hypereutectic structures as well as the eutectic one. On the [[Materials_science]] flagship this page serves Part V, Fundamentals › Thermodynamics, in the shared section *Eutectics*: it is where the [[Phase_diagram|phase diagram]] earns its keep, turning a thermodynamic surface into a prediction about what a cooled casting will actually look like. ## Eutectic phase transition The eutectic point is an invariant one, and the [[Phase_rule|phase rule]] [[Josiah_Willard_Gibbs|Gibbs]] published in the 1870s says why.[^gibbs1876] With the pressure fixed, the number of degrees of freedom in a system of `C` components and `P` phases is `F = C − P + 1`. At the eutectic of a binary alloy three phases coexist — the liquid and the two solids — so `F = 2 − 3 + 1 = 0`: neither the temperature nor any composition can be varied while the three remain together. The system is pinned, exactly as a one-component triple point is pinned in the diagrams of the Portal Book's phase chapter.[^atomsfirst-10-4] The transformation itself is `L → α + β`, and because it is invariant, it runs at constant temperature. Latent heat comes out while the temperature holds, so a cooling curve through a eutectic composition shows a flat arrest exactly like the melting of a pure substance — which is the practical test for a eutectic and the reason eutectic solders are prized: they have no pasty range in which the joint is neither liquid nor solid.[^latent-cn] Both solids grow together from the same liquid, and they must, because α is rich in one component and β in the other, so every advance of the α front rejects the atoms that β needs and vice versa. Growth therefore proceeds side by side with solute shuttling sideways between the two fronts across a distance of half the lamellar spacing. That coupling fixes the spacing. Fine lamellae shorten the diffusion distance but cost more interface; coarse lamellae are cheap in interface but slow to feed, and the structure grows at the spacing that balances the two, which Jackson and Hunt worked out in 1966 as `λ²·v` ≈ constant, equivalently `λ ∝ 1/ΔT`.[^jackson-hunt1966] The sim draws that inverse law with a fitted constant, marked ILLUSTRATIVE. At Pb–Sn's eutectic composition the two solids are not the pure elements. Tin dissolves in solid lead up to about 18.3 % by weight at 183 °C, and lead in solid tin up to about 2.2 %, so the lamellae are α at 18.3 % tin and β at 97.8 % tin.[^pbsn-cn] The lever rule then fixes the proportions: `(97.8 − 61.9)/(97.8 − 18.3)` = 45 % α and 55 % β by weight. ## Non-eutectic compositions Move the composition away from 61.9 % tin and the freezing stops being a single event. A hypoeutectic alloy — less tin than the eutectic — first crosses the liquidus and begins to deposit primary α, a lead-rich [[Solid_solution|solid solution]] that grows as dendrites into the melt. Every crystal of α is poorer in tin than the liquid it came from, so the liquid is enriched in tin as freezing proceeds and its composition slides down the liquidus toward the eutectic point. When it arrives there, whatever liquid remains freezes as eutectic lamellae between the dendrites already present. The arithmetic follows from the same three compositions. At a temperature just above 183 °C a 40 % tin alloy consists of primary α at 18.3 % tin and liquid at 61.9 %, so the primary fraction is `(61.9 − 40)/(61.9 − 18.3)` = 50 % — half the alloy is dendrites of soft lead-rich solid, and the other half becomes the fine two-phase eutectic. A hypereutectic 80 % tin alloy gives the mirror image, with `(80 − 61.9)/(97.8 − 61.9)` = 50 % primary β. The sim reads out exactly these two numbers, and its picture changes character as the reader crosses 61.9 %: coarse pale dendrites in a fine matrix on one side, coarse dark ones on the other. The practical difference is the freezing range. A eutectic alloy passes from liquid to solid at one temperature; a non-eutectic one is mushy over an interval, part solid and part liquid, and that interval is what a plumber's wiped joint exploits and what a printed-circuit assembler avoids. Slow freezing over a range also lets the last liquid, which is always of eutectic composition, collect in the spaces between dendrites, so a casting's final structure is a skeleton of primary phase with a low-melting film between the grains — which is why a slightly off-eutectic alloy can lose most of its strength just below its nominal solidus. ## Types Eutectic behaviour needs only two things: components that mix freely as liquids and separate as solids. That combination is so common that eutectics appear wherever mixtures freeze — in metals, in salt solutions, in rocks, in organic solids and in food. Frederick Guthrie, who named the effect in 1884 after studying salt solutions, was already clear that it was general and not a property of alloys.[^guthrie1884] What varies between systems is only the depth of the eutectic below the pure melting points, which is large when the two components dissolve poorly in one another as solids and shallow when they dissolve well, and the scale of the structure that results, which is set by how fast the heat is taken out rather than by the chemistry. ### Alloys The Pb–Sn system is the textbook case and was, for a century, the industrial one. Beyond solder, the aluminium–silicon system has its eutectic near 12.6 % [[Silicon|silicon]] at about 577 °C, which is why almost every [[Aluminium|aluminium]] casting alloy sits close to that composition: the eutectic flows well, fills thin sections and freezes without a long mushy range.[^pbsn-cn] [[Cast_iron|Cast iron]] is a eutectic alloy of [[Iron|iron]] and [[Carbon|carbon]] at about 4.3 % carbon, freezing near 1147 °C — some five hundred degrees below pure iron, which is what made iron castable long before it could be melted outright. Fusible alloys are the extreme case: multi-component eutectics of [[Bismuth|bismuth]], lead, tin and [[Cadmium|cadmium]] that melt below the boiling point of water and are used in sprinkler links and safety plugs. [[Pewter|Pewter]] and the low-melting [[Zinc|zinc]] die-casting alloys exploit the same principle, and [[Sodium|sodium]]–[[Potassium|potassium]] mixtures near their eutectic are liquid at room temperature. ### Others Salt and water form a eutectic at about 23.3 % [[Sodium_chloride|sodium chloride]] and −21.1 °C, the cryohydric point, which is both why salt melts [[Ice|ice]] on a road and the hard floor below which it cannot.[^pbsn-cn] The freezing-point depression that drives it is the [[Colligative_properties|colligative]] effect of the Portal Book's solutions chapter, pushed to the concentration where the solid salt itself starts to come out.[^atomsfirst-11] Rocks freeze the same way. A cooling granitic magma follows its liquidus until the residual melt reaches a eutectic-like minimum, and the last liquid crystallises as an intergrowth of quartz and feldspar whose interlocking texture is the [[Silicate_mineral|silicate]] version of solder's lamellae.[^earle-ch3] Pharmaceutical eutectics are used deliberately, mixing two drugs to obtain a liquid or low-melting phase at body temperature, and eutectic mixtures of salts and hydrogen-bond donors are used as low-melting solvents. ## Strengthening mechanisms A eutectic microstructure is a composite the material made for itself: two phases, one usually hard and one usually soft, interleaved on a scale of a micrometre or less, with a clean interface between them because they grew together from the same liquid. That last point is what distinguishes it from an artificial [[Composite_material|composite]], where the reinforcement has to be introduced, wetted and bonded. Here the two phases are in thermodynamic equilibrium with each other, so the interface is stable against the long exposures at temperature that would coarsen or dissolve an added phase. The price is that the composition is not free: a eutectic structure can only be had at one composition, and any deviation buys primary phase instead. ### Alloys The strength follows the spacing. A finer lamellar structure gives more interface per unit volume for [[Dislocation|dislocations]] to run into, and the flow stress rises roughly as `λ^(−1/2)`, the same inverse-square-root form the [[Grain_boundary|grain boundary]] page gets from pile-ups. Since `λ ∝ 1/ΔT`, faster cooling gives finer lamellae and a stronger casting — the reason a chilled mould produces a harder skin, and the reason the sim ties spacing to undercooling rather than to composition. Two things spoil it. A coarse eutectic with brittle plates is worse than either component alone, since the plates crack and the cracks run along the interfaces; and in hypereutectic alloys the primary phase can appear as large faceted crystals which behave as internal flaws. The industrial answer is modification: adding a few hundred parts per million of [[Sodium|sodium]] or strontium to an aluminium–silicon alloy changes the silicon from coarse plates to a fine fibrous form, roughly doubling the elongation without changing the composition in any way that shows on the phase diagram. The modifier works by interfering with the growth of one phase, which is [[Crystal_growth|crystal growth]] control rather than thermodynamics. ## Other critical points The eutectic is one member of a family of invariant reactions, all of them points where three phases meet on a binary diagram and the phase rule gives zero degrees of freedom. They differ only in which phases stand on which side of the arrow, and the four combinations — two phases from one, or one phase from two, with the parent either liquid or solid — exhaust the possibilities. The naming follows a simple rule: a reaction between a liquid and a solid takes a plain name, and the all-solid analogue takes the suffix *-oid*. Reading an unfamiliar binary diagram is largely a matter of finding these points and identifying which kind each one is, because they are where the [[Microstructure|microstructure]] of an alloy is decided. ### Eutectoid The eutectoid reaction has the same geometry with a solid parent: one solid phase decomposes into two others on cooling, `γ → α + β`. The example that matters is in steel, where [[Austenite|austenite]] of 0.76 % carbon transforms at 727 °C into ferrite and [[Cementite|cementite]] as the lamellar aggregate called [[Pearlite|pearlite]] — visibly the same alternating structure as a eutectic, produced by the same coupled growth, but with all three phases solid. Because diffusion in a solid is far slower than in a liquid, the eutectoid can be outrun by fast cooling, which is the whole of [[Heat_treating|heat treating]]. ### Peritectoid A peritectoid reaction runs two solids together into a third, `α + β → γ`, on cooling. It is the slowest of the family and the least often completed, because the product forms as a layer between the two reactants and then has to be crossed by diffusion for the reaction to continue. Peritectoid transformations are therefore common on equilibrium diagrams and rare in real microstructures. ### Peritectic In a peritectic reaction a liquid and a solid combine to give a different solid, `L + α → β`. The iron–carbon system has one at about 1495 °C, and it suffers from the same envelopment problem: the β layer separates the liquid from the α it must consume, so the reaction stalls and casting practice has to allow for the α that survives. Peritectics also drive fractional crystallisation in magmas, where an early mineral reacts with the melt instead of simply accumulating. ### "Bad solid solution" Two components whose atoms are similar in size, valence and structure can dissolve in one another in all proportions and give a continuous solid solution with no eutectic at all. As the mismatch grows, solid solubility falls at each end, the free-energy curve of the solid develops two minima instead of one, and the diagram is forced into the eutectic shape: the eutectic exists precisely because the solid solution is a bad one. The limiting cases are informative. Where solubility is very large the eutectic is shallow and the two-phase field narrow, and where it is near zero the lamellae are almost the pure components. Systems that are miscible when hot and unmix when cold, by nucleation or by [[Spinodal_decomposition|spinodal decomposition]], are the same competition resolved below the solidus rather than at it. ## Eutectic calculation The position of a eutectic can be estimated rather than measured. If the liquid is treated as an ideal solution and the solid that forms is taken to be pure, the equilibrium between them gives one liquidus for each component: `ln(x_A) = −(ΔH_fus,A/R)·(1/T − 1/T_m,A)` with `x_A` the mole fraction of A in the liquid, `T_m,A` its melting point and `ΔH_fus,A` its [[Enthalpy_of_fusion|enthalpy of fusion]]. Writing the same expression for B and requiring `x_A + x_B` = 1 gives two equations in two unknowns; their solution is the eutectic temperature and composition. Expanded near pure A, where `ln(1 − x_B) ≈ −x_B`, the expression collapses to the [[Colligative_properties|freezing-point depression]] `ΔT ≈ R·T_m²·x_B/ΔH_fus,A`, so each liquidus leaves its pure end as a straight line whose slope is set by that component's heat of fusion alone.[^atomsfirst-11][^atomsfirst-12] The two assumptions are where the estimate fails. Real liquids are not ideal, since unlike atoms attract or repel one another differently from like ones, and the resulting excess [[Gibbs_free_energy|free energy]] moves the liquidus in either direction. More seriously, the solids are not pure: Pb–Sn's 18.3 % and 2.2 % solubilities mean the model is solving the wrong problem, and its answer for that system is well above the measured 183 °C.[^pbsn-cn] The corrections are what [[Entropy_of_mixing|entropy of mixing]] and excess-enthalpy terms supply, and modern practice fits those terms to measurements for each binary system and then computes the multi-component diagram from the binaries.[^atomsfirst-12] Larry Kaufman and Harold Bernstein set that programme out in 1970, and it is why a five-element alloy's solidification can now be predicted from data that was never collected on it.[^kaufman1970] ## See also - [[Solder]] — the variant sim, the Pb–Sn assembly story - [[Tin]] — element variant - [[Lead]] — element variant - [[Pewter]] - [[Phase_diagram]] - [[Lever_rule]] - [[Heat_treating]] — where the eutectoid case is outrun - [[Cast_iron]] ## References [^atomsfirst-10-4]: Flowers, P.; Neth, E.; Robinson, W. et al. *Chemistry: Atoms First*, 2nd ed. (2019), OpenStax, Ch. 10 Liquids and Solids, §10.4 Phase Diagrams, pp. 502–508 (one-component phase diagrams, the triple point as an invariant point, the axes and conventions this page's binary diagram extends) (exact page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^atomsfirst-11]: Flowers, Neth & Robinson (2019), Ch. 11 Solutions and Colloids, pp. 545–596 (colligative properties; freezing-point depression of a solvent by a dissolved solute) (page to pin). [^atomsfirst-12]: Flowers, Neth & Robinson (2019), Ch. 12 Thermodynamics, pp. 597–622 (Gibbs free energy, entropy of mixing, and the condition for two phases to coexist) (page to pin). [^earle-ch3]: Earle, Steven. *Physical Geology* (2015), BCcampus Open Education, Ch. 3 Intrusive Igneous Rocks, pp. 67–92 (fractional crystallisation of a cooling magma, the residual melt, and the intergrowth textures of the last liquid to freeze) (page to pin). https://open.umn.edu/opentextbooks/textbooks/physical-geology [^jackson-hunt1966]: Jackson, K. A.; Hunt, J. D. (1966). "Lamellar and Rod Eutectic Growth." *Transactions of the Metallurgical Society of AIME* 236: 1129–1142 (volume and pages to pin; no DOI asserted). [^gibbs1876]: Gibbs, J. Willard (1876–1878). "On the Equilibrium of Heterogeneous Substances." *Transactions of the Connecticut Academy of Arts and Sciences* 3: 108–248 and 343–524 (the phase rule; pages to pin). [^guthrie1884]: Guthrie, Frederick (1884). "On Eutexia." *The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science* (series 5) 17 (104) (volume, issue and pages to pin; the paper that named the effect). [^kaufman1970]: Kaufman, Larry; Bernstein, Harold (1970). *Computer Calculation of Phase Diagrams, with Special Reference to Refractory Metals*. New York: Academic Press (the CALPHAD programme; chapter and page to pin). [^pbsn-cn]: *Citation needed.* The binary-system constants used on this page — Pb–Sn eutectic at 61.9 wt% Sn and 183 °C with maximum solid solubilities of 18.3 wt% Sn in α and 2.2 wt% Pb in β; Al–Si near 12.6 wt% Si at about 577 °C; Fe–C at about 4.3 wt% C near 1147 °C; H₂O–NaCl at 23.3 wt% and −21.1 °C; the Fe–C peritectic near 1495 °C — are the M26 sim row's Pb–Sn preset together with standard handbook values. No Portal Book carries a binary phase diagram. Every lever-rule figure computed here (45 % α / 55 % β at the eutectic; 50 % primary α at 40 wt% Sn; 50 % primary β at 80 wt% Sn) inherits that status, as does the statement that the ideal-solution estimate lands above 183 °C. A published Pb–Sn assessed diagram with its boundary compositions should be pinned first, since the rest follows arithmetically from it. [^latent-cn]: *Citation needed.* The thermal-arrest test — a eutectic composition showing a flat plateau on its cooling curve while a non-eutectic one shows a break followed by a slope — is standard practice, but no Portal Book carries a cooling-curve figure; an experimental methods text or a solidification text should be pinned here. [^melting-points]: Melting points quoted in the lead and in *Types*: lead 327 °C, tin 232 °C, pure iron about 1538 °C. These are standard element data; a periodic-table reference or the Portal Books' element tables should be pinned (values and source to pin). ### Bibliography - Gibbs, J. Willard (1876–1878). "On the Equilibrium of Heterogeneous Substances." *Transactions of the Connecticut Academy of Arts and Sciences* 3 — the phase rule that makes the eutectic invariant. - Guthrie, Frederick (1884). "On Eutexia." *Philosophical Magazine* (series 5) 17 — the paper that named the effect. - Jackson, K. A.; Hunt, J. D. (1966). "Lamellar and Rod Eutectic Growth." *Transactions of the Metallurgical Society of AIME* 236: 1129–1142 — the coupled-growth analysis behind the sim's spacing law. - Kaufman, Larry; Bernstein, Harold (1970). *Computer Calculation of Phase Diagrams*. New York: Academic Press — the origin of computed multi-component diagrams. ## Further reading - Flowers, P.; Neth, E.; Robinson, W. et al. *Chemistry: Atoms First*, 2nd ed. (2019), OpenStax — Ch. 10 §10.4 for the phase-diagram apparatus, Ch. 11 for freezing-point depression, Ch. 12 for the free-energy argument behind a two-phase field. - Earle, Steven. *Physical Geology* (2015), BCcampus — Ch. 3, for the same freezing sequence written about magma. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Eutectic_system.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Eutectic system* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Eutectic_system.html" data-title="Eutectic system"></div> *Built from `MICROSIM_GUIDE/specs/sims/Eutectic_system.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Eutectic_system) : [Wikitube](https://en.wikitube.io/wiki/Eutectic_system) · pinned revision [1368687256](https://en.wikipedia.org/w/index.php?oldid=1368687256) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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