Molybdenum Carbide in Tempered Martensite

Crystal Structure of Mo₂C

Molybdenum carbide (Mo₂C) can occur in many crystalline forms, but that which precipitates in steels has a close-packed hexagonal crystal structure of metal atoms, with the carbon atoms located in one half of the available octahedral interstices (but the carbon atom locations are assumed). The lattice parameters assumed for the diagrams below are a = 0.3007 nm and c = 0.4729 nm.

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Projection of four unit cells. The numbers indicate the fractional coordinates along the z-axis. The black atoms are carbon and the blue molybdenum.	Two molybdenum and one carbon atom per unit cell.
	As the projection along the z-axis, but with most of the atoms removed to show carbon in an octahedral interstice.
Carbon in an octahedral interstice.	Movie, structure rotated about z-axis Movie, structure rotated about y-axis Movie, structure rotated about x-axis Movie, octahedral interstice Crystalmaker file Crystalmaker file Crystalmaker file

Molybdenum carbide needles in tempered martensite

The following micrographs are taken from thin foil samples using a transmission electron microscope.

Molybdenum Carbide in Tempered Martensite

Tempered martensite in Fe-Mo-C alloy.	Tempered martensite in Fe-Mo-C alloy.	Tempered martensite in Fe-Mo-C alloy.
Tempered martensite in Fe-Mo-C alloy.	Tempered martensite in Fe-Mo-C alloy.	Tempered martensite in Fe-Mo-C alloy.
Molybdenum carbide precipitation.	Molybdenum carbide precipitation.	Molybdenum carbide precipitation.

Study guide: carbides in steels and transformations

Crystallography, morphology, and thermodynamic properties of molybdenum carbides.

Part I: Short-Answer Quiz

Instructions: Answer the following ten questions in 2–3 sentences.

What is the basic metal atom arrangement and carbon distribution in the hexagonal model of Mo₂C that precipitates in steels?
Why was neutron diffraction necessary to correctly identify the orthorhombic structure of Mo₂C?
In the context of lattice parameters, how do the hexagonal (a_h, c_h) and orthorhombic (a, b, c) representations of Mo₂C relate to one another?
How does the growth morphology of Mo₂C in a ferrite matrix differ from its shape in unconstrained environments like catalysis?
What determines the specific needle-like growth direction of Mo₂C within a ferrite crystal?
Regarding M₇C₃ carbides, what does recent research suggest about the nature of the streaks previously identified as stacking defects?
What is the primary industrial motivation for adding large concentrations of aluminium to steel alloys?
How do manganese and carbon contribute to the physical properties of low-density Fe-Mn-Al-C alloys?
Why has the orientation relationship between molybdenum carbide and austenite never been experimentally measured at typical steel compositions?

Part II: Answer Key

Metal atom and carbon distribution: The molybdenum atoms form a close-packed hexagonal crystal structure. The carbon atoms are located in one-half of the available octahedral interstices, though their specific locations are often assumed in traditional hexagonal models.
Neutron diffraction vs. X-ray: Carbon atoms have very weak X-ray scattering power compared to molybdenum, making their positions difficult to verify with X-ray diffraction. Neutron diffraction is superior for this task because the scattering powers of carbon and molybdenum atoms are similar, allowing for the identification of the true orthorhombic symmetry (space group Pbcn).
Lattice relationships: The hexagonal and orthorhombic representations share identical relative metal atom positions. The basis relationship is defined as a → c_h, b → 2a_h, and c → √3a_h, with the orthorhombic parameters measured as a = 0.4724 nm, b = 0.6004 nm, and c = 0.5199 nm.
Growth morphology: In a ferrite matrix, Mo₂C precipitates as thin needles to minimise strain energy. When synthesised for catalysis or formed via vapour deposition without matrix constraints, the particles approximate spheroids, faceted plates, or faceted platelets.
Needle growth direction: The needles grow along the ⟨100⟩α directions of the ferrite. This specific orientation occurs because the distortion (misfit) along the [100]α ≈ [010]_O direction is small compared to orthogonal directions, effectively limiting growth in high-distortion dimensions to minimise strain.
Streaks in M₇C₃: Recent crystallographic studies suggest these streaks are not stacking defects, but rather represent the coexistence of two crystallographic variants of the carbide. Each variant is approximately 5–10 nm thick, and the structure is best indexed as hexagonal with space group P6₃mc.
Aluminium additions: The main goal of adding aluminium is to reduce the density of the steel by increasing the lattice parameter of pure iron and reducing the average atomic mass. Additionally, aluminium has long been recognised for enhancing the oxidation resistance of the alloy.
Manganese and carbon roles: Manganese and carbon are added to increase the thermodynamic stability of the austenite phase, which aluminium typically destabilises. Furthermore, since both are lighter than iron, they contribute to the overall reduction of the alloy's density (e.g., down to approximately 6.8 g cm⁻³).
Austenite orientation measurement: At typical steel compositions, molybdenum carbide is not thermodynamically stable when in a mixture with austenite alone. Consequently, direct observations of precipitation in austenite are unavailable, and the orientation relationship must be assumed or inferred from other interfaces.

Part III: Essay Format Questions

Crystallographic Evolution of Mo₂C: Discuss the transition from the hexagonal close-packed model to the orthorhombic Pbcn model for molybdenum carbide. Explain the roles of X-ray and neutron diffraction in this transition.
Strain Energy and Precipitate Morphology: Analyse the relationship between lattice fit and the physical shape of Mo₂C precipitates. Compare the needle growth observed in tempered martensite with the shapes observed in unconstrained environments.
Design Challenges of Low-Density Steels: Evaluate the metallurgical trade-offs involved in creating Fe-Mn-Al-C alloys. Discuss how aluminium, manganese, and carbon interact to influence phase stability.
The Crystallography of M₇C₃ and Mo₂C in High-Alloy Systems: Compare the recent findings regarding M₇C₃ "stacking defects" with the structural complexities of Mo₂C.
Orientation Relationships in Ferrite Matrices: Explain the mathematical and crystallographic basis for the orientation relationship between ferrite (α) and Mo₂C. Detail the significance of the correspondence matrix.

Part IV: Glossary of Key Terms

Mo₂C: Molybdenum carbide; in steels, it precipitates as orthorhombic needles (space group Pbcn) within a ferrite matrix.
Ferrite (α): The body-centered cubic (BCC) phase of iron; serves as the matrix for Mo₂C needle precipitation in tempered martensite.
Lattice Parameters: The physical dimensions of the unit cell in a crystal lattice (e.g., a, b, c for orthorhombic; a, c for hexagonal).
Neutron Diffraction: A form of crystallographic study particularly useful for locating light atoms like carbon in the presence of heavy atoms like molybdenum.
Octahedral Interstice: The "holes" or spaces within a close-packed crystal structure where smaller atoms, such as carbon, are situated.
Orientation Relationship (OR): The specific geometric alignment between the crystal lattices of two different phases.
Strain Energy: The energy stored in a material due to the deformation of its lattice; in precipitation, it is minimised by selecting specific growth shapes.
Tempered Martensite: A microstructure formed by heating martensite to allow for the precipitation of carbides, which increases toughness.