Crystallography of iron

The crystallographic properties and diffraction analysis of various iron phases, specifically focusing on austenite and ferrite, is addressed. This includes the use of X-ray and electron diffraction to identify complex structures and the spatial relationships between iron and cementite precipitates. The documentation details the following microstructural and experimental characteristics:

Overall, the material serves as a technical guide for understanding the atomic arrangements and phase identification in steel through precise crystallographic characterisation.

Structure and diffraction

Complex diffraction patterns from multiple phases

The following details the analysis of complicated electron diffraction patterns containing ferrite, cementite and austenite. A computer programme was utilised to assist in this characterisation.

Ferrite and cementite
The ferrite zone is first identified from the ratio of, and angle between, two of the reciprocal lattice vectors. With a knowledge of the lattice parameter of the ferrite, this then allows the camera constant to be calculated. The next step is to calculate the d-spacings of the spots associated with cementite using the camera constant, and similarly analyse the pattern for cementite. The pattern was recorded by Lucy Fielding.

Ferrite and cementite (Bagaryatski orientation)
The cementite exhibits a Bagaryatski orientation relative to the ferrite matrix, with [001]_cementite parallel to [211]_ferrite and [100]_cementite parallel to [0 −1 1]_ferrite. This can be interpreted as an indication that the cementite precipitated directly from the ferrite. The pattern was recorded by Lucy Fielding.

Two ferrite crystals and one cementite precipitate
Diffraction characterisation recorded by Lucy Fielding.

Three ferrite crystals
Notice also the distinct spots arising from double diffraction mechanisms. The pattern was recorded by Ed Pickering.

Two ferrite crystals in twin orientation and one cementite precipitate
The twin patterns are related, for example, by a rotation of 180° about [1 2 −1]. This axis-angle pair can be represented in 24 crystallographically equivalent ways due to cubic symmetry constraints. The pattern was recorded by Lucy Fielding.

Diffraction pattern of ferrite and γ-Fe₂O₃
Obtained from a thin foil sample of steel. The oxide forms on the surface and makes a significant contribution to the overall pattern when the foil thickness is reduced during preparation. Also available are the calculated electron diffraction pattern, crystal structure and d-spacings for the iron oxide. The pattern was recorded by Pei Yan.

Interstices

Video presentations

Structure of austenite
Structure of ferrite
Carbon in octahedral interstice of austenite
Carbon in another equivalent octahedral interstice of austenite
Carbon atom in tetrahedral interstice of austenite
Carbon in octahedral interstice of ferrite
Carbon in an irregular tetrahedral interstice of ferrite
Carbon in tetrahedral interstice of ferrite

Atom models of austenite and ferrite

The following models have kindly been provided by Andrew Fairbank, who engineered them for teaching purposes. They are reproduced with permission.

Face-centred cubic, body-centred cubic and body-centred tetragonal arrangements of iron atoms.	Face-centred cubic, body-centred cubic and body-centred tetragonal arrangements of iron atoms.
Body-centred cubic and face-centred cubic (alternatively, cubic close-packed) arrangements of iron atoms.	Carbon atom in an octahedral interstice in austenite.
Carbon atom in an octahedral interstice in austenite, with the face-centering iron atom replaced into position.	Carbon atom in an octahedral interstice in austenite.
Carbon atom in an octahedral interstice in ferrite.	Carbon atom in an octahedral interstice in ferrite.
Carbon atom in an octahedral interstice in ferrite.
Possible position of a carbon atom in a tetrahedral interstice in ferrite. Carbon preferred configurations tracks to the octahedral interstices in ferrite.	Possible position of a carbon atom in a tetrahedral interstice in ferrite.
Possible position of a carbon atom in a tetrahedral interstice in ferrite. The strain energy is greater when carbon is in a tetrahedral interstice, because the expansion is isotropic, unlike the octahedral case where the strain is tetragonal.	Possible position of a carbon atom in a tetrahedral interstice in ferrite.
Chromium atom substituted into ferrite.	Chromium atom substituted into ferrite.
Silicon atom substituted into ferrite.	Atomic radii. It has been assumed in the preceding figures that iron has an atomic radius of 124 pm for all crystal structures.