Copper and aluminum are highly ductile, while zinc and magnesium are comparatively brittle at room temperature. Which crystal structure explanation best accounts for this difference?
ACopper and aluminum have smaller unit cells, allowing atoms to rearrange more easily under stress
BFCC metals have 12 close-packed slip systems, while hexagonal metals have fewer, restricting dislocation movement
CZinc and magnesium have triclinic crystal structures that create directional covalent bonds resisting deformation
DBCC metals like zinc have lower atomic packing efficiency than FCC metals
Face-centered cubic metals (Cu, Al, Au) have 12 distinct {111}<110> slip systems, giving dislocations many paths to move — hence high ductility. Hexagonal close-packed metals (Zn, Mg) have only a few active slip planes at room temperature, limiting dislocation glide and resulting in lower ductility. Zinc is hexagonal, not triclinic or BCC — option D contains a factual error about zinc's structure.
Question 2 Multiple Choice
A crystallographer finds a new mineral whose unit cell has equal edge lengths and equal inter-edge angles, but the angles are not 90°. Which Bravais lattice system does this belong to?
ACubic, because all edge lengths are equal
BTetragonal, because the angles deviate from 90°
CRhombohedral (trigonal), because all lengths are equal but angles are not 90°
DMonoclinic, because one angle differs from the others
The rhombohedral (trigonal) system is defined by a = b = c and α = β = γ ≠ 90°. Cubic also has equal lengths but requires all angles to be exactly 90°. Tetragonal has two equal lengths (a = b ≠ c) with right angles. Monoclinic has all lengths different and exactly one non-right angle. The angle constraint is what distinguishes rhombohedral from cubic.
Question 3 True / False
A body-centered cubic unit cell has lattice points primarily at the eight corners of the cube.
TTrue
FFalse
Answer: False
A BCC cell has lattice points at all eight corners plus one additional point at the geometric center of the cube — hence 'body-centered.' The primitive cubic cell has corner points only. This central atom is a full lattice point equivalent to any corner atom; it is not an atom of a different type or a defect.
Question 4 True / False
The seven crystal systems and fourteen Bravais lattices together form a complete classification — every periodic crystalline arrangement in three dimensions belongs to exactly one of these fourteen categories.
TTrue
FFalse
Answer: True
This completeness is mathematically proven, not just empirically observed. By systematically applying all possible symmetry constraints to the six unit cell parameters (a, b, c, α, β, γ) and all valid centering types, exactly 14 distinct translational symmetries arise. No valid periodic arrangement falls outside this classification, and none of the 14 is redundant.
Question 5 Short Answer
Why do face-centered cubic metals like copper tend to be more ductile than body-centered cubic metals like iron at room temperature? Explain in terms of crystal structure and slip systems.
Think about your answer, then reveal below.
Model answer: FCC metals have atoms packed densely along {111} planes in <110> directions, producing 12 independent slip systems. With many available slip planes and directions, dislocations can move and multiply easily under stress, allowing large plastic deformation before fracture. BCC metals have fewer close-packed planes, so fewer slip systems are active at room temperature, requiring higher shear stress to move dislocations and resulting in higher strength but lower ductility.
The number of slip systems directly controls how easily a crystal can deform plastically by dislocation glide. More slip systems mean more paths for dislocations to travel without encountering barriers, giving the material flexibility to deform rather than crack. This is why FCC metals are the workhorses of forming and drawing operations in manufacturing.