10.1 Fe-Fe3C System, Crystal Lattices, c/a Ratio & Interstitial Solubility

10.1 Iron-Carbon Equilibrium Diagram & Equilibrium Phase Transformations

Quick Answer: The iron-carbon phase diagram forms the thermodynamic foundation of steel welding metallurgy. While the stable system represents iron and graphite, structural steels operate according to the metastable iron-cementite ($\text{Fe}-\text{Fe}_3\text{C}$) diagram. Pure iron exhibits three allotropes: Body-Centered Cubic (BCC) $\alpha$-ferrite, Face-Centered Cubic (FCC) $\gamma$-austenite, and BCC $\delta$-ferrite. Austenite dissolves up to $2.14\text{ wt}%$ carbon at $1148^\circ\text{C}$ due to its spacious octahedral interstitial sites, whereas ferrite dissolves a maximum of only $0.022\text{ wt}%$ carbon at $727^\circ\text{C}$. Three invariant reactions govern phase changes: peritectic ($1495^\circ\text{C}$, $0.17%\text{ C}$), eutectic ($1148^\circ\text{C}$, $4.30%\text{ C}$), and eutectoid ($727^\circ\text{C}$, $0.77%\text{ C}$). Alloying elements modify these boundaries: austenite stabilizers (Ni, Mn, C, N) expand the $\gamma$-phase field, whereas ferrite stabilizers (Cr, Mo, Si, V, Ti) contract it, closing the $\gamma$-loop above critical concentrations.

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The Fe-Fe3C Metastable vs. Fe-C Stable System

In steel welding metallurgy, thermodynamic equilibrium phase relationships are described by the binary iron-carbon system. Two distinct phase diagrams exist:

1. The Stable Iron-Graphite System ($\text{Fe}-\text{C}$): In this system, elemental carbon precipitates as hexagonal graphite. Graphite represents the true thermodynamic minimum in Gibbs free energy ($\Delta G < 0$). However, graphite nucleation kinetics in solid steel are exceedingly sluggish, requiring extremely slow cooling rates (on the order of degrees per hour) or prolonged isothermal holding at elevated temperatures ($>650^\circ\text{C}$) in the presence of strong graphitizing elements such as silicon (e.g., in grey cast irons).
2. The Metastable Iron-Iron Carbide System ($\text{Fe}-\text{Fe}_3\text{C}$): Under all practical arc welding, thermomechanical processing, and conventional heat-treating thermal cycles, carbon precipitates as the metastable intermetallic compound cementite ($\text{Fe}_3\text{C}$, or iron carbide). Because the free energy difference between cementite and graphite is small (approximately $3\text{ to }5\text{ kJ/mol}$), and the kinetic barrier to nucleating cementite is vastly lower than that of graphite, the metastable $\text{Fe}-\text{Fe}_3\text{C}$ system governs the microstructural evolution of carbon and low-alloy structural steels.

                               TEMPERATURE vs. PHASE STABILITY

    Liquid (L)
        |   [1538°C Melting Point]
        v
    Delta (δ) Ferrite (BCC, a = 0.293 nm) ----> Peritectic Reaction at 1495°C (0.17% C)
        |   [1394°C A4 Transition]
        v
    Gamma (γ) Austenite (FCC, a = 0.358 nm) --> Eutectic Reaction at 1148°C (4.30% C)
        |   [912°C A3 Transition]
        v
    Alpha (α) Ferrite (BCC, a = 0.286 nm) ----> Eutectoid Reaction at 727°C (0.77% C)
        |   [770°C A2 Curie Temperature (Magnetic Transition, No Phase Change)]
        v
    Room Temperature Equilibrium Microstructure (α-Ferrite + Fe3C Cementite / Pearlite)

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Crystal Structure, Lattice Parameters, c/a Ratio & Interstitial Sites

AWS B5.16 Clause 8.3.4 opens the metallurgy body of knowledge with crystal structure of metals (FCC, BCC, HCP, unit cells, lattice parameter, c/a ratio, atom positions, interstitial positions). Every solubility limit and transformation temperature discussed above ultimately traces back to these lattices.

The Three Engineering Lattices

Lattice parameter is the edge length of the unit cell. For iron, alpha-ferrite measures $a \approx 0.2866\text{ nm}$ at room temperature while gamma-austenite measures $a \approx 0.3647\text{ nm}$ near $912^\circ\text{C}$. The austenite cell is larger overall, yet austenite is the denser structure because it holds four atoms instead of two — the reason the volume contracts about 1% on heating through the $\text{A}_3$ transformation and expands on the reverse transformation, and the reason martensite formation expands a weldment and generates compressive transformation strain.

Atom positions are expressed in fractional cell coordinates: BCC has atoms at $(0,0,0)$ and the body centre $(\tfrac12,\tfrac12,\tfrac12)$; FCC adds face centres at $(\tfrac12,\tfrac12,0)$ and equivalents; HCP places the basal atoms at $(0,0,0)$ with the interior atom at $(\tfrac13,\tfrac23,\tfrac12)$.

The c/a Ratio

HCP metals are described by two lattice parameters — the basal edge $a$ and the prism height $c$. The c/a ratio for ideal hard-sphere stacking is

$\left(\frac{c}{a}\right)_{\text{ideal}} = \sqrt{\frac{8}{3}} = 1.633$

Real metals deviate, and the deviation predicts deformation behaviour that matters directly to weld ductility:

That single number explains why alpha-titanium weldments tolerate strain while zinc-rich coatings simply crack or vaporize.

Interstitial Positions and Why Carbon Behaves as It Does

Carbon, nitrogen, hydrogen, boron and oxygen dissolve interstitially, occupying the voids between iron atoms. The two void types have fixed radius ratios:

• Octahedral site: accommodates a sphere with $r/R = 0.414$ in an FCC lattice.
• Tetrahedral site: accommodates $r/R = 0.225$ in FCC, $0.291$ in BCC.

FCC austenite has larger, more symmetric octahedral holes and dissolves up to 2.11 wt% C at $1148^\circ\text{C}$. BCC ferrite, despite being the more open structure by packing factor, has small, distorted octahedral sites and dissolves only 0.022 wt% C at $727^\circ\text{C}$ — a factor of roughly 100 lower. This single ratio drives the entire discipline: it is why rapid cooling traps carbon in a supersaturated body-centred-tetragonal martensite, why the tetragonality $c/a$ of martensite rises with carbon content, and why hydrogen — small enough to hop between tetrahedral sites — diffuses orders of magnitude faster in ferrite than in austenite, which is the metallurgical basis of austenitic buttering layers for hydrogen control.

The Monotectic Reaction

Clause 8.3.4 lists four invariant reactions; the three iron-carbon reactions were covered above, and the fourth is the monotectic:

$L_1 \xrightarrow{\text{cooling}} S + L_2$

A single liquid decomposes into a solid plus a second, immiscible liquid of different composition. The classic system is copper-lead, which has a monotectic near $955^\circ\text{C}$ where a copper-rich liquid decomposes into FCC copper plus a lead-rich liquid; the liquid-lead phase persists to low temperature and is the basis of leaded bearing bronzes.

Monotectics matter to a welding engineer because the residual low-melting liquid is precisely what causes liquid metal embrittlement and hot shortness. Leaded free-machining steels, leaded brasses and leaded bronzes all retain a discrete lead-rich liquid phase far below the solidus of the matrix; welding them wets the grain boundaries ahead of the arc and produces intergranular cracking that no preheat or filler-metal change will fix. The correct engineering answer is a substitution — specify a bismuth-free, lead-free free-machining grade, or join by a solid-state or brazing process that never melts the matrix.

Exam Trap: Confusing monotectic with eutectic. Both start from a single liquid. A eutectic produces two solids ($L \rightarrow S_1 + S_2$). A monotectic produces one solid and one liquid ($L_1 \rightarrow S + L_2$). Any answer that describes a monotectic as yielding two solid phases is wrong.

Crystallographic Allotropes of Iron & Interstitial Solubility

Pure iron displays allotropy, transitioning between distinct crystallographic space groups as a function of temperature under atmospheric pressure:

1. Alpha Ferrite ($\alpha$)

• Crystal Structure: Body-Centered Cubic (BCC), space group $Im\bar{3}m$.
• Stability Range: Ambient temperature up to $912^\circ\text{C}$ ($1185\text{ K}$).
• Lattice Parameter: $a \approx 0.2866\text{ nm}$ ($2.866\text{ \AA}$) at $20^\circ\text{C}$.
• Interstitial Carbon Solubility: Maximum of $0.022\text{ wt}%$ ($0.10\text{ at}%$) at $727^\circ\text{C}$, dropping to less than $0.008\text{ wt}%$ at room temperature.
• Lattice Geometry Rationale: In the BCC unit cell, the octahedral interstitial sites (located at unit cell face centers $[\frac{1}{2}, \frac{1}{2}, 0]$ and edge centers $[0, 0, \frac{1}{2}]$) are non-spherical and highly constrained. The radius of the largest sphere that fits into an octahedral site without lattice distortion is $r_o = 0.155 R_{\text{Fe}} \approx 0.019\text{ nm}$. The tetrahedral site radius is $r_t = 0.291 R_{\text{Fe}} \approx 0.036\text{ nm}$. Although the tetrahedral site is geometrically larger, carbon atoms ($r_{\text{C}} \approx 0.077\text{ nm}$) preferentially occupy the octahedral sites because displacement of only two nearest-neighbor iron atoms along the $\langle 100 \rangle$ direction accommodates the carbon atom, producing severe tetragonal strain. This pronounced elastic strain field severely restricts carbon solid solubility in $\alpha$-ferrite.

2. Gamma Austenite ($\gamma$)

• Crystal Structure: Face-Centered Cubic (FCC), space group $Fm\bar{3}m$.
• Stability Range: $912^\circ\text{C}$ to $1394^\circ\text{C}$ ($1185\text{ to }1667\text{ K}$).
• Lattice Parameter: $a \approx 0.3585\text{ nm}$ ($3.585\text{ \AA}$) at $912^\circ\text{C}$.
• Interstitial Carbon Solubility: Maximum of $2.14\text{ wt}%$ ($9.2\text{ at}%$) at $1148^\circ\text{C}$, decreasing to $0.77\text{ wt}%$ at the eutectoid temperature ($727^\circ\text{C}$).
• Lattice Geometry Rationale: The FCC lattice possesses symmetric, spherical octahedral interstitial sites located at the center of the unit cell $[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}]$ and at the midpoints of all 12 cube edges. The octahedral radius is $r_o = 0.414 R_{\text{Fe}} \approx 0.053\text{ nm}$, surrounded by six equidistant iron atoms. Accommodating a carbon atom ($0.077\text{ nm}$) requires modest isotropic lattice expansion, allowing austenite to dissolve nearly $100\times$ more carbon than ferrite.

3. Delta Ferrite ($\delta$)

• Crystal Structure: Body-Centered Cubic (BCC), identical crystallographic symmetry to $\alpha$-ferrite.
• Stability Range: $1394^\circ\text{C}$ up to the congruent melting point of pure iron at $1538^\circ\text{C}$ ($1667\text{ to }1811\text{ K}$).
• Lattice Parameter: $a \approx 0.293\text{ nm}$ at $1400^\circ\text{C}$ due to thermal lattice expansion.
• Interstitial Carbon Solubility: Maximum of $0.09\text{ wt}%$ at $1495^\circ\text{C}$. The expanded lattice enables higher interstitial solubility than $\alpha$-ferrite, but it remains far lower than that of $\gamma$-austenite.

4. Cementite ($\text{Fe}_3\text{C}$)

• Crystal Structure: Complex Orthorhombic, space group $Pnma$, containing 12 iron atoms and 4 carbon atoms per unit cell ($a = 0.509\text{ nm}$, $b = 0.674\text{ nm}$, $c = 0.452\text{ nm}$).
• Stoichiometry: Fixed carbon concentration of $6.70\text{ wt}%$ ($25.0\text{ at}%$).
• Mechanical Characteristics: Extremely hard ($>800\text{ to }1000\text{ HV}$) and brittle, with negligible room-temperature tensile ductility. Acts as the primary strengthening constituent in pearlitic and bainitic microstructures.

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