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A steel with an austenitic, face-centered cubic matrix in the specified condition. Alloying and temperature determine its stability.

A body-centered cubic lattice consists of the points of a cubic lattice together with their body centers. Its reciprocal lattice is face-centered cubic.

Crystal packing describes how constituents are arranged and make contact within a crystal. It includes both the repeated geometry and, for molecular crystals, the orientations and intermolecular contacts of the molecules. Composition alone does not determine this arrangement: the same substance can have different crystal polymorphs with different packing.

A useful geometric model replaces constituents by equal hard spheres. Hexagonal close packing and face-centered cubic packing put each sphere next to twelve nearest neighbours but arrange successive close-packed layers differently. Their local contact geometry can therefore agree while their longer-range order differs. Real molecular shapes and directional intermolecular forces supply further constraints. Packing affects mass density, available slip geometry and directional response, making diffraction a way to connect structural measurements with macroscopic properties rather than merely assign a repeating pattern.

Edgar Bain was an American materials scientist who studied transformations in steel. His 1924 paper The Nature of Martensite by Edgar Bain examined how the structure of martensite relates to its parent austenite, connecting the mechanical behaviour of hardened steel with changes in crystal structure.^[ref]

The Bain path expresses a geometric connection between face-centered cubic and body-centred cubic structures through a tetragonal deformation. It helps make a structural transformation concrete: changing the relative lengths along different axes can map one lattice geometry to another. Such a geometric path by itself does not specify the complete chemical kinetics or every observed feature of a transformation in real steel; those also depend on chemical composition and microstructural constraints.

Close packing of triangular layers with ABAB stacking. Its nearest-layer geometry agrees with face-centered cubic stacking, but the further-layer registry differs.

A face-centered cubic cell has atoms at its corners and face centers. The $(111)$ plane intercepts the three positive cubic axes at $(a_0,0,0)$, $(0,a_0,0)$ and $(0,0,a_0)$; it is a close-packed triangular layer. Close-packed directions are the $⟨110⟩$ family, with the in-plane members satisfying $u+v+w=0$.

Nearest neighbors touch along a face diagonal: $4r=\sqrt{2}{a}_0$. HenceThe body diagonal is not the touching direction for this crystal structure.

Close-packed layers occupy one of three lateral registries, conventionally A, B and C. Hexagonal close packing has ABAB stacking, while face-centered cubic stacking is ABCABC. On a bulk-terminated (111) terrace the two kinds of threefold hollow differ by subsurface registry: an hcp hollow places an atom above a second-layer atom, while an fcc hollow continues the ABC sequence.

Compressing the top Au layer makes its registry drift relative to the unreconstructed layers. Parts of the cell occupy fcc hollows, others hcp hollows, and transition strips pass through less favorable bridge-like positions. Those registry changes are associated with partial-dislocation/domain boundaries. Varying local coordination and repulsion from the substrate cause vertical relaxation, producing the observed corrugation rather than an entirely flat shifted sheet.