A student claims that BCC iron and FCC aluminum must have the same crystal structure because both belong to the cubic crystal system. What error is the student making?
AThey belong to different crystal systems — BCC is tetragonal, not cubic
BThey have the same crystal system but different Bravais lattices — the cubic system contains three distinct lattice types
CThey have the same lattice type, but BCC and FCC unit cells differ only in size
DBravais lattices apply only to non-cubic systems; cubic has just one lattice type
The cubic crystal system contains three Bravais lattices: primitive (P), body-centered (I/BCC), and face-centered (F/FCC). BCC iron and FCC aluminum share the same unit cell geometry (a = b = c, all 90° angles) but are genuinely distinct lattice types with different packing efficiencies, nearest-neighbor distances, and numbers of slip systems. The error is equating 'crystal system' (geometry) with 'Bravais lattice' (point arrangement).
Question 2 Multiple Choice
FCC metals like aluminum deform easily, while HCP metals like magnesium are more brittle. What property of the Bravais lattice most directly explains this difference?
AFCC has a larger unit cell volume, providing more space for dislocation movement
BFCC has 12 available slip systems while HCP has only 3, due to their different lattice point arrangements
CFCC and HCP belong to different crystal systems, and higher-symmetry systems are always more ductile
DHCP metals have higher melting points, which makes them harder to deform at room temperature
The number of slip systems — combinations of close-packed planes and directions along which dislocations can glide — depends directly on the Bravais lattice type, not merely the crystal system. FCC has 12 slip systems (4 {111} planes × 3 ⟨110⟩ directions), giving many pathways for plastic deformation. HCP has only 3 primary slip systems (basal plane), making deformation geometrically restricted and the metal more brittle. This is why Bravais lattice classification matters for predicting mechanical behavior.
Question 3 True / False
There are 7 Bravais lattices, one corresponding to each of the 7 crystal systems.
TTrue
FFalse
Answer: False
There are 14 Bravais lattices distributed unevenly across the 7 crystal systems. Some systems have only one (triclinic has just primitive P), while others have multiple — the cubic system alone has three (P, I, F). Bravais proved in 1848 that exactly 14 distinct periodic point arrangements are possible in three dimensions. If each system had exactly one lattice, the 14 would collapse to 7.
Question 4 True / False
A cubic crystal is isotropic in properties such as elastic stiffness and thermal expansion — meaning these properties are the same in any measurement direction.
TTrue
FFalse
Answer: True
The cubic crystal system has the highest symmetry of all seven systems, with three mutually perpendicular four-fold rotation axes. This symmetry equates all three principal directions, making scalar and second-rank tensor properties (like thermal expansion) and even elastic stiffness the same regardless of direction. Lower-symmetry systems (orthorhombic, monoclinic, triclinic) are anisotropic to varying degrees. Knowing the Bravais lattice immediately tells you whether a material's properties will be direction-dependent.
Question 5 Short Answer
Why are there 14 Bravais lattices rather than just 7 — one per crystal system?
Think about your answer, then reveal below.
Model answer: Because within a given crystal system, additional lattice points can be placed at body centers or face centers while preserving the system's symmetry, creating physically distinct arrangements. Each unique combination of cell geometry and lattice point positions that cannot be reduced to a simpler lattice counts as a separate Bravais lattice.
The 7 crystal systems describe the shape of the unit cell (constraints on edge lengths and angles). But a box of a given shape can have lattice points only at corners (primitive), or also at the body center, or at face centers. Each combination that yields a genuinely distinct periodic arrangement — meaning it cannot be re-described as a simpler lattice — counts as a separate Bravais lattice. Not all centering operations are symmetry-consistent with every system, which is why some systems have one lattice and others have three, giving a total of 14.