Phase Equilibria, Microstructural Synthesis, and Transformation Kinetics in Steels and Lead-Tin Alloys

Vocabulary practice flashcards covering phase diagrams, invariant reactions, equilibrium and non-equilibrium microstructures, morphological sketching rules, and quantitative lever rule calculations in the Fe-Fe3C and Pb-Sn alloy systems.

Austenite ($\gamma$)

A face-centred cubic ($\text{FCC}$) solid solution of carbon in iron that is stable above $727\,^{\circ}\text{C}$, non-magnetic, and can dissolve up to $2.14\,\text{wt\% C}$ at $1147\,^{\circ}\text{C}$ due to its larger interstitial octahedral voids.

Ferrite ($\alpha$)

A body-centred cubic ($\text{BCC}$) solid solution of carbon in iron with an extremely low maximum carbon solubility of $0.022\,\text{wt\% C}$ at $727\,^{\circ}\text{C}$. It is soft, ductile, and magnetic at room temperature.

Cementite ($Fe_3C$)

An extremely hard, brittle intermetallic iron carbide compound possessing an orthorhombic crystal lattice and a fixed stoichiometric carbon content of $6.67\,\text{wt\% C}$.

Pearlite

A two-phase lamellar microstructural constituent consisting of alternating plates of ferrite and cementite that forms at $727\,^{\circ}\text{C}$ upon slow cooling of austenite containing $0.77\,\text{wt\% C}$.

Eutectoid Invariant Reaction

An invariant, solid-state phase transformation occurring at $727\,^{\circ}\text{C}$ and $0.77\,\text{wt\% C}$ in the iron-carbon system where solid austenite decomposes isothermally into two solid phases: $\gamma\,(0.77\,\text{wt\% C}) \rightarrow \alpha\,(0.022\,\text{wt\% C}) + Fe_3C\,(6.67\,\text{wt\% C})$.

$A_1$ Line

The horizontal eutectoid isotherm at $727\,^{\circ}\text{C}$ in the iron-carbon phase diagram, spanning from $0.022\,\text{wt\% C}$ to $6.67\,\text{wt\% C}$, below which austenite cannot exist under equilibrium conditions.

$A_3$ Line

The upper critical boundary on the iron-carbon diagram below which austenite begins transforming into proeutectoid ferrite during the equilibrium cooling of hypoeutectoid steels.

$A_{cm}$ Line

The solvus line on the iron-carbon diagram defining the maximum carbon solubility limit in austenite before proeutectoid cementite begins precipitating along prior austenite grain boundaries.

Proeutectoid Ferrite

The primary ferrite phase that nucleates along prior austenite grain boundaries upon cooling between the $A_3$ and $A_1$ temperatures in hypoeutectoid steels ($< 0.77\,\text{wt\% C}$) prior to the eutectoid reaction.

Proeutectoid Cementite

The primary cementite phase that precipitates along prior austenite grain boundaries upon cooling between the $A_{cm}$ and $A_1$ lines in hypereutectoid steels ($> 0.77\,\text{wt\% C}$), forming a continuous, brittle intergranular network.

Hypoeutectoid Steel

A steel containing less than $0.77\,\text{wt\% C}$ (such as $0.35\,\text{wt\% C}$ or $0.40\,\text{wt\% C}$) whose room-temperature equilibrium microstructure consists of white equiaxed proeutectoid ferrite grains and striped pearlite colonies.

Hypereutectoid Steel

A steel containing between $0.77\,\text{wt\% C}$ and $2.14\,\text{wt\% C}$ (such as $1.20\,\text{wt\% C}$ tool steel) whose room-temperature equilibrium microstructure consists of central pearlite colonies surrounded by a continuous, brittle proeutectoid cementite network.

Grain Boundary Allotriomorph

A solid crystal morphology (such as proeutectoid ferrite) that nucleates heterogeneously along solid-state prior grain boundaries and whose external contours conform to the surrounding matrix grains rather than displaying faceted crystal faces.

Liquidus Line

The boundary on an equilibrium phase diagram above which an alloy is completely in a liquid state and below which solid crystals first begin to nucleate upon cooling.

Solidus Line

The boundary on an equilibrium phase diagram below which an alloy is completely solid and above which melting begins.

Solvus Line

The boundary on a phase diagram that dictates the temperature-dependent solid-state solubility limit of a solute dissolved within a terminal solid solution lattice.

Eutectic Invariant Reaction

An invariant, three-phase transformation where a liquid phase of fixed composition solidifies isothermally directly into two distinct solid phases without an intervening mushy zone, occurring in the $\text{Pb-Sn}$ system at $183\,^{\circ}\text{C}$ and $61.9\,\text{wt\% Sn}$.

Alpha ($\alpha$) Phase (Pb-Sn)

A terminal solid solution of tin dissolved in face-centred cubic ($\text{FCC}$) lead, with a maximum solubility of $18.3\,\text{wt\% Sn}$ at $183\,^{\circ}\text{C}$, dropping to approximately $2\,\text{wt\% Sn}$ at $20\,^{\circ}\text{C}$.

Beta ($\beta$) Phase (Pb-Sn)

A terminal solid solution of lead dissolved in body-centred tetragonal ($\text{BCT}$) tin, with a maximum lead solubility of $2.2\,\text{wt\% Pb}$ ($97.8\,\text{wt\% Sn}$) at $183\,^{\circ}\text{C}$.

Lamellar Morphology

A regular, striped microstructural arrangement of alternating thin parallel plates of two solid phases, formed because short atomic diffusion paths minimise the lateral transport distances required for solute redistribution during invariant cooling.

Dendrite

A primary solid crystal displaying a tree-like, branched morphology that nucleates and grows freely into an undercooled liquid during non-faceted solidification (such as primary $\alpha$ in hypoeutectic $\text{Pb-Sn}$).

Eutectic Colony

A distinct grain-like region of a eutectic constituent consisting of parallel alternating lamellae oriented in a uniform direction, separated by boundary lines from adjacent colonies with differing plate angles.

Hypoeutectic Alloy (Pb-Sn)

A lead-tin alloy containing less than $61.9\,\text{wt\% Sn}$ (e.g., $30\,\text{wt\% Sn}$ or $40\,\text{wt\% Sn}$) that solidifies rounded primary $\alpha$ dendrites prior to the transformation of the remaining liquid into a lamellar eutectic matrix at $183\,^{\circ}\text{C}$.

Hypereutectic Alloy (Pb-Sn)

A lead-tin alloy containing more than $61.9\,\text{wt\% Sn}$ (e.g., $85\,\text{wt\% Sn}$) that solidifies angular, faceted primary $\beta$ crystals before the remaining liquid freezes into a lamellar eutectic matrix at $183\,^{\circ}\text{C}$.

Reverse Lever Rule

A quantitative mathematical method that determines the mass fraction of a phase or constituent along a tie-line by dividing the length of the opposite lever arm by the total tie-line length ($W_{\alpha} = \frac{C_{\beta} - C_0}{C_{\beta} - C_{\alpha}}$).

Phase vs Constituent Distinction

A phase is a chemically uniform, structurally homogeneous state of matter ($\alpha$, $\beta$, $\gamma$, $Fe_3C$), whereas a constituent is an identifiable microstructural arrangement of phases (such as pearlite, primary $\alpha$ dendrites, or proeutectoid cementite networks).

Secondary Beta ($\beta$) Precipitates

Microscopic particles of tin-rich $\beta$ phase that nucleate and precipitate inside primary $\alpha$ dendrites upon cooling below the solvus line due to the decline in solid solubility of tin in lead from $18.3\,\text{wt\%}$ at $183\,^{\circ}\text{C}$ to $2\,\text{wt\%}$ at $20\,^{\circ}\text{C}$.

Martensite

A hard, brittle non-equilibrium phase featuring needle-like laths formed by a diffusionless, athermal shear transformation of austenite quenched past the $M_s$ temperature, trapping carbon in a heavily strained Body-Centred Tetragonal ($\text{BCT}$) lattice ($\sim 65\,\text{HRC}$).

Bainite

A non-equilibrium microstructural constituent formed at intermediate cooling rates (temperatures between $250\,^{\circ}\text{C}$ and $550\,^{\circ}\text{C}$) consisting of feathery or acicular aggregates of ferrite and fine cementite particles.

Upper Bainite

A morphology of bainite formed between $350\,^{\circ}\text{C}$ and $550\,^{\circ}\text{C}$ characterised by feathery ferrite laths with cementite particles precipitated predominantly along the lath boundaries.

Lower Bainite

A morphology of bainite formed between $250\,^{\circ}\text{C}$ and $350\,^{\circ}\text{C}$ characterised by acicular plate-like ferrite containing exceptionally fine, internal carbide precipitates oriented inside the plates.

Hardness Transformation Spectrum

The progressive increase in plain carbon steel hardness resulting from increasing cooling rates: coarse pearlite from slow furnace cooling ($\sim 15\,\text{HRC}$), fine pearlite from air cooling ($\sim 30\,\text{HRC}$), bainite from isothermal holding ($\sim 45\,\text{HRC}$), and martensite from rapid water quenching ($\sim 65\,\text{HRC}$).