A crystal structure (HCP) formed by stacking close-packed planes in an ABAB… sequence. The coordination number is 12 and the ideal c/a is about 1.633. Examples include Mg, Ti and Zn.
Japanese name: 六方最密構造
Hexagonal close-packed appears in 1 practice question across 1 topic, including Crystal structures and Miller indices.
HCP is the structure obtained by stacking close-packed planes in the sequence ABAB…. The hexagonal prism usually drawn contains a net 6 atoms: 12 × 1/6 at the corners, 2 × 1/2 at the centers of the top and bottom faces and 3 inside. The unit cell of the lattice (a prism with a rhombic base) contains 2 atoms. When hard spheres touch ideally, c/a is √(8/3) ≈ 1.633, with a coordination number of 12 and a packing factor of about 0.74, the same close packing as FCC. Mg, Ti, Zr, Zn, Co and Be have this structure at room temperature.
The c/a ratios of real HCP metals deviate from the ideal value: they are large for Zn (about 1.86) and Cd (about 1.89), nearly ideal for Mg (about 1.62), and small for Ti and Zr (about 1.59) and Be (about 1.57). In metals with large c/a, the basal planes are widely spaced and basal slip dominates. In Ti and Zr, whose c/a is below the ideal value, prismatic slip occurs readily. Even within HCP, which slip systems operate changes the ease of deformation and the textures that develop, so c/a is an important guide.
For a polycrystal to change shape freely, five independent slip systems are needed. Basal slip in HCP, {0001}<11-20>, has only three systems, only two of them independent, and it cannot accommodate deformation along the c axis. Unless pyramidal slip with a c-axis component or deformation twinning operates, deformation becomes incompatible at grain boundaries and cracks form easily. This is why magnesium alloy sheet is hard to press at room temperature and is often formed warm, and why titanium is not as easy to cold work as FCC metals.
Because HCP crystals have low symmetry, the Young's modulus, thermal expansion coefficient and ease of slip differ between the c-axis direction and directions perpendicular to it. Rolled sheet readily develops a texture with the basal planes aligned with the sheet surface, so strength and formability vary with direction in the sheet. In the zirconium alloys used for nuclear fuel cladding tubes, texture is controlled so that precipitated hydrides are aligned in an orientation that resists cracking. For HCP metal parts, properties must be considered together with how the crystal orientations are aligned.
Answer: A. c/a ≈ 1.633, and its packing factor is about 0.74, the same as FCC
HCP stacks close-packed planes in an ABAB… sequence, and when hard spheres touch ideally, c/a = √(8/3) ≈ 1.633. The coordination number is 12 and the packing factor is about 0.74, the same close packing as FCC, which stacks ABCABC…. About 0.68 is the packing factor of BCC, and 1.414 (√2) is the ratio of the face diagonal to the edge in FCC, not the c/a of HCP. Real HCP metals deviate from the ideal c/a: about 1.62 for Mg, about 1.59 for Ti and about 1.86 for Zn. Because they have few slip systems, HCP metals tend to be less ductile at room temperature than FCC metals.
Three spheres in the lower layer and one above them touch to form a regular tetrahedron, whose height is √(2/3) times the interatomic distance a. Since c is twice this height, c/a = 2√(2/3) = √(8/3) ≈ 1.633.
The primitive unit cell with a rhombic base contains 2. Counted in the hexagonal prism, there are 12 × 1/6 at the corners + 2 × 1/2 at the face centers + 3 inside = 6, equivalent to three primitive cells.
Both are made by stacking close-packed planes, but the stacking is ABAB… in HCP and ABCABC… in FCC. A single stacking error creates an HCP-like sequence inside FCC, so some metals, such as cobalt, switch between HCP and FCC, at about 420 °C in its case.
Atomic packing factor Body-centered cubic Face-centered cubic Miller indices