Epsilon Carbide in Steels

ε-carbide and η-carbide are transient phases that typically emerge during the tempering of martensite or the formation of lower bainite in steels. These sources examine the crystal structures of these carbides, noting that ε-carbide possesses a hexagonal arrangement where carbon atoms occupy specific octahedral interstices.

Although cementite is the more stable end-product, alloying elements like silicon can delay its precipitation, thereby appearing to enhance the presence of transition carbides. First-principles calculations suggest this enhancement is likely kinetic rather than thermodynamic, as silicon-induced lattice contractions improve coherency with the surrounding martensite.

Furthermore, the mechanical properties of ε-carbide indicate it is significantly more brittle and stiff than both iron and cementite. These findings are critical for optimising the microstructure and performance of high-strength, silicon-rich alloy steels.

High-strength steel design relies on these insights to prevent embrittlement while maintaining structural integrity. Dedicated studies also highlight the rare homogeneous precipitation of these carbides within austenite.

ε-carbide is a transition iron carbide with a chemical formula between Fe₂C and Fe₃C. It has a hexagonal close-packed arrangement of iron atoms with carbon atoms located in the octahedral interstices.

The space group of ε-carbide is P6₃22. The lattice parameters (Fig. 1) are a = 0.4767 nm and c = 0.4353 nm. The illustrated cell contains six iron atoms and a full complement of carbon atoms. To achieve a composition Fe_2.4C the site labelled C1 would on average need to be partially occupied.

There is some confusion in the literature, where the space group of ε-carbide is taken to be that for hexagonal iron, i.e., P6₃/mmc. This is illustrated as the smaller unit cell defined by the dashed lines in Fig. 1, with a_h = 0.2752 nm. Here a = √3 a_h.

Further Illustrations of Structure

$Electron diffraction [001]$

Electron diffraction pattern, [001] zone axis

$Electron diffraction [010]$

Electron diffraction pattern, [010] zone axis

$Electron diffraction [100]$

Electron diffraction pattern, [100] zone axis

$Electron diffraction [110]$

Electron diffraction pattern, [110] zone axis. Note that [100], [110], and [010] are crystallographically equivalent.

$Electron diffraction [101]$

Electron diffraction pattern, [101] zone axis

$Electron diffraction [011]$

Electron diffraction pattern, [011] zone axis

$Electron diffraction [111]$

Electron diffraction pattern, [111] zone axis

Publications on ε-carbide

Part 1: Short-answer quiz

1. Why is a single variant of carbide typically observed in lower bainite, whereas multiple variants may appear during the tempering of martensite? The variant that forms in lower bainite is likely selected because it is best suited to relieve the elastic strains associated with the austenite to lower bainite transformation. While multiple variants are theoretically possible, standard micrographs of tempered martensite also frequently show a single dominant variant, suggesting that strain relief and stress play critical roles in variant selection.

2. Describe the chemical composition and atomic arrangement of ε-carbide. ε-carbide is a transition iron carbide with a chemical formula ranging between Fe₂C and Fe₃C, often specifically identified as Fe_2.4C. Its structure consists of a hexagonal close-packed (hcp) arrangement of iron atoms, with carbon atoms situated within the octahedral interstices.

3. What is the difference between the P6₃22 and P6₃/mmc space groups in the context of ε-carbide? The P6₃22 space group describes an ordered structure where carbon atoms occupy specific sub-lattices of octahedral sites to maximise their separation. The P6₃/mmc space group represents a higher-symmetry arrangement where carbon atoms are distributed randomly, making the structure consistent with that of hexagonal iron.

4. How does the presence of silicon affect the precipitation of cementite and ε-carbide? Silicon retards cementite precipitation due to its low solubility in that phase. This suppression allows ε-carbide to become more prominent. Additionally, silicon may enhance kinetics by contracting the c-axis of the carbide, improving lattice coherency with the surrounding martensite.

5. What is "microsyntactic intergrowth" as it relates to transition carbides? It refers to a state where cementite and χ-carbide (Hägg carbide) exist as interpenetrating layers only a few interplanar spacings thick, resulting in a nonstoichiometric overall composition often expressed as Fe_2n+1C_n.

6. Compare the mechanical properties of ε-carbide to those of cementite based on their elastic moduli. ε-carbide is predicted to be more brittle than cementite because its ratio of shear modulus to bulk modulus (G/B) is approximately 0.48, significantly higher than cementite's 0.33. Its Young’s modulus also exceeds that of iron.

7. Under what specific conditions does ε-carbide precipitate directly in austenite? Homogeneous precipitation of ε-carbide in austenite has been observed in high-carbon cast iron, forming as fine, coherent particles in at least three variants of the orientation relationship.

8. Define η-carbide and its occurrence in steel microstructures. η-carbide is an orthorhombic transition carbide (Fe₂C). It is typically associated with the tempering of martensite and has also been confirmed in the lower bainite of grey cast iron.

9. How does the partitioning of substitutional solutes like chromium differ between bainite and pearlite? In pearlite, chromium partitions into cementite during growth. In bainite, the partition coefficient is close to unity, meaning solute concentration in the carbide is nearly identical to the surrounding ferrite.

10. Why is ε-carbide generally observed only as very fine particles? The transformation from BCC ferrite to hexagonal ε-carbide involves large positive principal distortions. Particles must remain very small (platelets) to minimise the associated strain energy.

Part 2: Essay questions

Analytical Comparison: Compare the mechanisms of carbide precipitation in lower bainitic ferrite and tempered martensite.
Thermodynamics vs. Kinetics: Why does silicon-enhanced ε-carbide precipitation appear to be a kinetic rather than a thermodynamic effect?
Structural Transitions: Describe the sequence from carbon clusters to ε-carbide and finally to cementite.
Crystallographic Modelling: Explain the significance of the Jack orientation relationship in identifying carbide phases.
Phase Stability: Analyze the factors influencing the dissolution of mixed χ/cementite particles.

Part 3: Glossary of terms

Term	Definition
ε-Carbide	A hexagonal transition iron carbide (Fe_2.4C) with space group P6₃22.
η-Carbide	An orthorhombic transition iron carbide (Fe₂C) found in tempered martensite.
χ-Carbide (Hägg)	A metastable transition carbide (Fe₅C₂) forming microsyntactic intergrowths.
Bainite	A microstructural product consisting of ferrite and carbides (upper or lower).
Cementite	The equilibrium iron carbide (Fe₃C); more stable than transition carbides.
Invariant-Plane Strain	A type of strain relief observed in freshly formed bainite plates.
Jack Orientation	A specific orientation relationship between transition carbides and the matrix.
Microsyntactic Intergrowth	Interpenetration of carbide layers at the scale of a few interplanar spacings.
Octahedral Interstices	Spaces in a crystal lattice where smaller carbon atoms reside.

Epsilon Carbide

H. K. D. H. Bhadeshia and Jae Hoon Jang

Further Illustrations of Structure

Publications on ε-carbide

Study guide

Part 1: Short-answer quiz

Part 2: Essay questions

Part 3: Glossary of terms