The crystal structure of a metal — the three-dimensional arrangement of its atoms
in a repeating lattice — determines virtually every property it possesses: ductility, strength,
magnetic behaviour, thermal expansion, slip systems, response to heat treatment, and carbon
solubility. Understanding the three principal crystal structures — BCC (body-centred
cubic), FCC (face-centred cubic), and HCP (hexagonal close-packed) —
is the starting point for all of physical metallurgy and is essential for understanding why iron
can be hardened by heat treatment, why aluminium is more formable than titanium, and why
austenitic stainless steels remain tough at cryogenic temperatures.
KEY TAKEAWAYS
- BCC metals: 2 atoms/cell, APF 0.68, coordination number 8. Examples: α-Fe, W, Cr, Mo. Show DBTT at low temperatures.
- FCC metals: 4 atoms/cell, APF 0.74, coordination number 12. Examples: γ-Fe (austenite), Al, Cu, Ni. No DBTT — ductile to cryogenic temperatures.
- HCP metals: 6 atoms/cell, APF 0.74, coordination number 12. Examples: Ti(α), Mg, Zn, Co. Limited ductility due to only 3 easy basal slip systems.
- Iron undergoes allotropic transformation: BCC (α-Fe, ferrite) ↔ FCC (γ-Fe, austenite) at 912°C. This is the physical basis of all steel heat treatment.
- FCC austenite dissolves 2.14%C; BCC ferrite dissolves only 0.022%C — the 100:1 difference drives all carbide precipitation in steel.
- APF = 0.74 for FCC and HCP is the maximum possible for identical hard spheres — these are the two close-packed structures.
- Coordination number = number of nearest neighbours: 12 (FCC/HCP) vs 8 (BCC) — explains why BCC metals are slightly less dense.
Body-Centred Cubic (BCC)
BCC is one of the most common metallic crystal structures. Atoms occupy the 8 corners of a cube, plus one atom at the geometric centre of the cube. Each corner atom is shared between 8 adjacent unit cells (contributing 8 × 1/8 = 1), plus the body-centre atom = 2 atoms per unit cell.
| BCC Property | Value | Engineering Implication |
|---|---|---|
| Atoms per unit cell | 2 | Low packing density relative to FCC/HCP |
| Atomic Packing Factor (APF) | 0.68 (68%) | Less efficiently packed than FCC/HCP |
| Coordination number | 8 | Each atom has 8 nearest neighbours |
| Lattice parameter–radius | a = 4r/√3 | Close-packed along body diagonal [111] |
| Close-packed direction | ⟨111⟩ (body diagonal) | Slip direction for BCC metals |
| Slip systems | 12 primary ({110}⟨111⟩) | No truly close-packed plane → DBTT |
| Ductile-to-Brittle Transition | Yes — significant | BCC steels must be Charpy-tested at design temperature |
| Carbon solubility (in α-Fe) | 0.022%C max at 727°C | Very limited — BCC interstitial sites too small |
Key BCC engineering metals: α-iron (steel ferrite, below 912°C), tungsten (W, 3422°C melting point), chromium (Cr), molybdenum (Mo), vanadium (V), niobium (Nb), β-titanium (above 882°C), tantalum (Ta).
The DBTT in BCC metals: BCC metals have no close-packed plane, so dislocation motion requires overcoming a higher Peierls-Nabarro stress. At low temperatures, this barrier increases sharply — dislocations become pinned and the metal fractures in a brittle manner (cleavage) rather than deforming plastically. This is why structural steels must be impact-tested at their minimum design temperature, and why ferritic stainless steels cannot be used for cryogenic service.
Face-Centred Cubic (FCC)
FCC atoms sit at the 8 corners of the cube and at the centre of each of the 6 faces. Face-centre atoms are shared between 2 cells (6 × 1/2 = 3); with 8 corner atoms (8 × 1/8 = 1): 4 atoms per unit cell. FCC is a true close-packed structure — atoms touch along face diagonals.
| FCC Property | Value | Engineering Implication |
|---|---|---|
| Atoms per unit cell | 4 | Higher density than BCC |
| APF | 0.74 (74%) | Maximum for identical spheres (with HCP) |
| Coordination number | 12 | 6 in same layer + 3 above + 3 below |
| Lattice parameter–radius | a = 2√2·r | Close-packed along face diagonal [110] |
| Close-packed plane | {111} (octahedral) | 4 independent {111} planes in FCC |
| Slip systems | 12 ({111}⟨110⟩) | 4 planes × 3 directions = 12 systems |
| DBTT | None | Remains ductile from cryogenic to melting point |
| Stacking sequence | ABCABC | 3-layer repeat; contrast HCP = ABABAB |
| Carbon solubility (in γ-Fe) | 2.14%C max at 1147°C | High — large FCC octahedral holes |
Key FCC engineering metals: γ-iron (austenite, 912–1394°C), all austenitic stainless steels (304, 316, 310), aluminium (Al), copper (Cu), nickel (Ni), gold (Au), silver (Ag), lead (Pb), cobalt (above 417°C).
Why FCC is preferred for cryogenic and formability applications: The 12 slip systems on genuinely close-packed 111 planes mean FCC metals can accommodate shape change in any direction without cracking, and they maintain this ductility to cryogenic temperatures. This is why 304L/316L austenitic stainless steel is specified for LNG storage tanks (−165°C), and why aluminium, copper, and nickel alloys dominate applications requiring both high formability and low-temperature toughness.
Hexagonal Close-Packed (HCP)
HCP achieves the same maximum packing (APF = 0.74) as FCC but with a different stacking sequence (ABABAB instead of ABCABC). The unit cell is a hexagonal prism with 6 atoms: atoms at 12 hexagonal corners (shared by 6 cells each = 12/6 = 2), 2 atoms at top and bottom face centres (shared by 2 cells = 1 total), plus 3 atoms fully interior = 6 atoms per unit cell.
| HCP Property | Value | Comparison with FCC |
|---|---|---|
| Atoms per unit cell | 6 | vs 4 for FCC |
| APF | 0.74 (ideal c/a = 1.633) | Same as FCC |
| Coordination number | 12 | Same as FCC |
| Easy slip plane | {0001} basal plane (1 plane only) | vs 4 slip planes in FCC |
| Easy slip directions | ⟨11̄20⟩ (3 in basal plane) | = 3 slip systems only (basal) |
| Stacking | ABABAB | vs ABCABC for FCC |
| Ideal c/a ratio | 1.633 | Mg: 1.624; Ti: 1.587; Zn: 1.856 |
| Ductility | Low at room temperature (Mg) | FCC >> HCP for most alloys |
Key HCP metals: α-titanium (Ti below 882°C, c/a = 1.587), magnesium (Mg), zinc (Zn), cobalt (Co at room temperature), α-zirconium (Zr), beryllium (Be).
Why HCP ductility is limited: With only 3 easy slip systems in the basal plane, HCP polycrystals cannot satisfy the Von Mises criterion of 5 independent slip systems required for homogeneous deformation. Grains oriented with the c-axis perpendicular to the applied stress cannot deform easily — they crack or require high stresses to activate non-basal slip. Titanium is more formable than magnesium at room temperature because its c/a ratio (1.587, below ideal) makes prismatic slip more accessible, providing the additional independent systems needed.
Iron’s Allotropic Transformation — The Key to All Steel Heat Treatment
Iron’s ability to change crystal structure with temperature makes steel the most versatile structural material on Earth:
γ-Fe (FCC) ←——→ δ-Fe (BCC, delta ferrite) at 1394°C (A4)
On heating through 912°C: BCC → FCC
→ Crystal expands (FCC octahedral holes larger)
→ Carbon solubility jumps from 0.022%C to up to 2.14%C
→ Carbides dissolve into austenite solid solution
On cooling through 912°C: FCC → BCC
→ Carbon cannot fit in small BCC holes
→ Either: diffuses out → ferrite + cementite (pearlite) [SLOW COOLING]
→ Or: trapped in distorted BCT lattice → MARTENSITE [FAST COOLING]
| Property | BCC (α-Fe, ferrite) | FCC (γ-Fe, austenite) | Martensite (BCT) |
|---|---|---|---|
| Structure | Body-centred cubic | Face-centred cubic | Body-centred tetragonal (elongated BCC) |
| Stability range | Room temp to 912°C | 912°C to 1394°C | Metastable (forms below Ms, ~230°C for 0.8%C) |
| C solubility | 0.022%C (0.022 wt%) | 2.14%C max | Up to ~0.8%C in supersaturated BCT |
| Hardness (0.4%C) | ~130 HV (ferrite in steel) | ~200 HV (austenite) | ~500–580 HV (as-quenched) |
| Density | 7.87 g/cm³ | 7.63 g/cm³ (less dense) | ~7.75 g/cm³ |
| Magnetic | Yes (ferromagnetic <770°C) | No (paramagnetic) | Yes (ferromagnetic) |
Frequently Asked Questions
Q: Why does FCC iron (austenite) dissolve 100 times more carbon than BCC iron (ferrite)?
A: The critical factor is the size of the interstitial holes where carbon atoms fit. In BCC ferrite, the largest interstitial site (octahedral void) has a radius of only 0.019 nm — far smaller than carbon’s atomic radius of 0.077 nm. Forcing carbon into this site creates extreme lattice distortion, limiting solubility to just 0.022%C. In FCC austenite, the equivalent octahedral void is much larger (radius 0.052 nm), creating less distortion and allowing up to 2.14%C. This fundamental geometric difference — driven entirely by the crystal structure switch from BCC to FCC — is why steel can be hardened by quenching: heating dissolves all the carbon into austenite, then rapid cooling traps it in the BCC lattice as distorted martensite.
Q: Why do FCC metals have no ductile-to-brittle transition temperature?
A: The ductile-to-brittle transition in BCC metals arises because dislocation motion in BCC requires overcoming the Peierls-Nabarro stress — the lattice resistance to dislocation glide between successive equilibrium positions. In BCC, this resistance increases sharply at low temperatures because the dislocation core is narrow (atomically sharp) due to the non-close-packed structure. FCC dislocations have wide, spread-out cores (due to the close-packed {111} planes and lower stacking fault energy compared to BCC), meaning the Peierls stress is inherently lower and barely temperature-dependent. FCC metals therefore maintain their plastic flow mechanism — dislocation glide on {111} planes — right down to absolute zero.
Q: What determines whether titanium is alpha (HCP) or beta (BCC) at room temperature?
A: Pure titanium is HCP (α-phase) below 882°C. Adding beta-stabilising elements — V, Mo, Nb, Fe, Cr — lowers the β-transus temperature. If enough beta stabiliser is added (e.g. Ti-10V-2Fe-3Al, or Ti-15V-3Cr-3Sn-3Al), the BCC β-phase is metastable at room temperature. Alpha-beta alloys (Ti-6Al-4V) have both phases at room temperature — the Al stabilises the HCP α-phase while V stabilises the BCC β-phase. The volume fraction of each phase (typically 90%α + 10%β in Ti-6Al-4V after annealing) controls the balance of properties: HCP α provides corrosion resistance and creep strength; BCC β provides higher fracture toughness and better cold formability.
References
- Callister, W.D. and Rethwisch, D.G., Materials Science and Engineering. 10th ed. Wiley, 2018. Chapters 3–4.
- Ashby, M.F. and Jones, D.R.H., Engineering Materials 1. 4th ed. Butterworth-Heinemann, 2012.
- Hull, D. and Bacon, D.J., Introduction to Dislocations. 5th ed. Butterworth-Heinemann, 2011.
Related:
Iron-Carbon Phase Diagram ·
Slip Systems in BCC, FCC and HCP ·
Dislocations in Metals ·
Ferrite in Steel
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