When a Compound Won't Melt Straight
Guide 3 handed you the eutectic: a liquid that on cooling splits into two solids at once, L becoming S1 + S2, with the liquidus and solidus fencing the fields and the lever rule counting how much of each phase is present. But that whole tour quietly assumed one thing — that every solid, when you heat it, melts into a liquid of its very own composition. A pure element does this, and so does a well-behaved compound: we call it congruent melting. A congruent-melting compound is a gift, because it behaves like a pure component in its own right — its liquidus rises to a neat peak directly above its own composition, and it simply chops the binary diagram into two independent eutectic sub-diagrams, each read exactly as you already know how. Spinel, MgAl2O4, melts congruently near 2105 degrees C and does just that to the MgO-Al2O3 join.
Now the twist. Some compounds refuse to melt into a liquid like themselves. Heat them and they do not liquefy so much as decompose: the crystal falls apart into a different solid plus a liquid whose composition is nowhere near the compound's own. This is incongruent melting, and it happens whenever a compound's would-be liquidus peak is buried beneath the primary field of a neighbouring phase — the compound never gets the chance to melt on its own terms, because a different crystal is more stable at that temperature. The compound's vertical composition line, drawn upward, does not run into clear liquid at all; it runs into a two-phase field of solid-plus-liquid. That single geometric fact is the whole story of this guide.
The Peritectic Reaction
Read incongruent melting backwards — cool instead of heat — and you get the peritectic reaction. Where a eutectic is a liquid dividing into two solids, a peritectic is the opposite kind of meeting: a liquid and an already-existing crystal react with each other to build a single new phase. On cooling it reads L + A -> C, the liquid and the primary solid A consuming one another to grow the compound C. The name is a picture: peri means 'around', because the new crystal C tends to nucleate as a shell that grows around the older A crystals it is feeding on. Heat that same compound and the reaction simply runs the other way, C -> A + L — which is exactly the incongruent melting we just defined.
T
Tm(A) *
|\
| \_____ L (all liquid)
A+L | \______
| * P (peritectic point)
Tp - + - - - - - - - - - - - - - - - - peritectic isotherm
| A + C | C + L
+------------ + ----------------------
A C composition (fraction B) ->
COOL: L(P) + A --> C HEAT: C --> A + L(P)The geometry in that sketch is the tell. For a congruent compound, the vertical composition line would spear straight up through a liquidus maximum into pure liquid. For an incongruent one, the compound's line is offset from its liquid: the peritectic liquid P sits to the B-rich side of the compound C, so C's line runs up into the A + L field instead. That offset — liquid on one side, primary crystal on the other, compound stranded between them — is what you scan a diagram for. See a horizontal isotherm whose liquid endpoint does not sit over the compound beneath it, and you are looking at a peritectic, not a eutectic.
Tracing a Cooling Path
Let us actually cool a melt and watch the reaction fire. Put numbers on the sketch: solid A at 0 wt% B, compound C at 40 wt% B, peritectic liquid P at 60 wt% B, all meeting on the peritectic isotherm at temperature Tp. Take a melt whose overall composition is exactly the compound, 40 wt% B. As it cools, the A-liquidus is on top, so primary A crystallizes first and the leftover liquid drifts to the right, growing richer in B, until it reaches P at Tp. Now three phases stand together — A, C, and liquid P — and the lever rule tells us how much of each we have just before they react.
- Bulk = the compound (40 wt% B). Just above Tp the mix is solid A + liquid P: fraction liquid = (40 - 0)/(60 - 0) = 2/3, fraction A = (60 - 40)/60 = 1/3. The peritectic then fires, L + A -> C, and because the bulk is exactly C it eats up ALL the liquid and ALL the A: the result is 100% compound. A tidy 1/3 A + 2/3 liquid welds into a single pure phase.
- Bulk to the LEFT of C (say 30 wt% B). Above Tp: fraction A = (60 - 30)/60 = 1/2, fraction liquid = 1/2. The reaction runs until the liquid is used up, and A is left over. Read the leftovers with the lever rule between A (0) and C (40): fraction C = (30 - 0)/40 = 3/4, fraction A = 1/4. Final microstructure: 75% compound plus 25% surviving primary A.
- Bulk to the RIGHT of C (say 50 wt% B). Above Tp: fraction A = (60 - 50)/60 = 1/6, fraction liquid = 5/6. Now A runs out first, and liquid survives; the leftover liquid keeps crystallizing C as it cools further toward the eutectic between C and B. Which reactant is left standing — primary A, or excess liquid — is decided purely by which side of the compound your bulk composition sits on.
The Ceramist's Peritectics
This is not a textbook curiosity — it sits at the heart of firing. Take potassium feldspar. Orthoclase, KAlSi3O8, melts incongruently near 1150 degrees C: on heating it decomposes to leucite (KAlSi2O6) plus a silica-rich liquid, and on cooling that same isotherm is the peritectic leucite + liquid -> feldspar. Leucite on its own melts congruently far higher, near 1686 degrees C. That modest 1150-degree first-melting temperature is precisely why potassium feldspar is the flux of the pottery world: it yields a sticky, glass-forming liquid many hundreds of degrees below the melting points of the quartz and clay around it, and that liquid is what cements a porcelain body together.
Now the ceramist's headline case. In the Al2O3-SiO2 system, mullite (3Al2O3·2SiO2) — the needle-like phase that gives fired porcelain and high-alumina refractories their strength and creep resistance — is classically drawn melting incongruently near 1828 degrees C into corundum (alumina) plus a silica-rich liquid. But here is an honest complication worth carrying: whether mullite melts congruently or incongruently was fought over for more than half a century, from Bowen and Greig's 1924 incongruent diagram to later congruent-melting results by Aksay and Pask, and the answer turns out to depend delicately on stable-versus-metastable equilibrium and on tiny impurity levels. The modern stable diagram is usually taken as incongruent — but the long fight is a reminder that a phase diagram is hard-won experimental data, not a law handed down. Guide 5 reads this whole system in full.
Even the rock-forming silicates play the same game. In the MgO-SiO2 system, enstatite (MgSiO3) melts incongruently near 1557 degrees C into forsterite (Mg2SiO4) plus liquid — the very reaction Bowen and Andersen measured back in 1914. The shape is always the same: a compound whose vertical composition line runs up into a neighbour's primary field rather than into clear liquid. Once your eye catches that offset, you can predict on sight which crystal will appear first from a cooling melt and which reaction will fire when the temperature drops onto the isotherm — a genuinely useful piece of forecasting, done from the picture alone.
Putting It to Work: Flux, Glass, and Refractories
Here is the payoff that ties eutectics and peritectics together for a potter. The first drop of liquid in any body appears not at any pure phase's melting point but at the lowest invariant point its composition can reach — a eutectic or a peritectic, whichever comes first on cooling. Add a flux such as feldspar and you deliberately introduce a low invariant (feldspar's own roughly 1150-degree incongruent melt, plus eutectics it forms with quartz and clay), so a wetting liquid appears far below alumina's 2054 degrees C or silica's 1713 degrees C. That early liquid is what drives liquid-phase sintering: it wicks into the pores by capillarity, pulls the grains together, and densifies the body at a temperature the kiln can actually reach. A small flux addition slashing the firing temperature is just this — buying a low invariant point.
The same map even estimates the glass in a fired body. Because the firing liquid freezes to a glassy grain-boundary phase on cooling, the lever rule read at the firing temperature gives a first, honest guess of how much glass a body will end up holding — a porcelain soaked near 1300 degrees C can be well over half glass by the diagram. But carry the caution loudly: a phase diagram shows equilibrium only. A real firing quenches metastable glass that never crystallized, leaves grains of undissolved quartz, and freezes the cored, half-finished peritectic crystals from the last section. The diagram is the target the body is aiming at, not a photograph of the microstructure you actually pull from the kiln.
Turn the whole logic around and you get the recipe for a refractory. Something that must stay solid and load-bearing inside a furnace wants its composition to sit far from any low eutectic or peritectic — the exact opposite of a flux. A near-pure silica brick softens only up near its own high melting range; but let a little alumina and a trace of alkali sneak in, and the composition slides toward low-melting joins where a liquid appears early and the brick slumps and creeps under load. So the ceramist reads one and the same map two opposite ways: chase the lowest invariant point to fire cheaply with a strong glassy bond, or flee from it to stay stubbornly refractory. Incongruent melting and the peritectic are not fine print on that map — they are two of the roads it draws.