A crystal structure (BCC) with atoms at the corners and the center of the cube. The unit cell contains 2 atoms; the coordination number is 8 and the packing factor about 0.68. Examples include α-iron, Cr and W.
Japanese name: 体心立方格子
Body-centered cubic appears in 1 practice question across 1 topic, including Crystal structures and Miller indices.
In BCC the corner atoms and the body-center atom touch along the body diagonal, so the nearest-neighbor distance is √3a/2; for α-iron (a = 0.2866 nm) it is about 0.248 nm. Besides the 8 nearest neighbors, there are 6 second-nearest neighbors at distance a, only about 1.15 times farther away. α-iron, Cr, Mo, W, V, Nb, Ta and high-temperature β-titanium are BCC, and a notable feature is that many high-melting metals such as W, Mo, Nb and Ta are included.
BCC has no truly close-packed plane. The slip direction is fixed as the close-packed <111> direction, but besides {110}, the {112} and {123} planes also act as slip planes. On the other hand, the core of a screw dislocation spreads out three-dimensionally, so the stress needed to move dislocations (the Peierls stress) is large and rises sharply as temperature falls. BCC metals therefore show a large increase in yield stress at low temperature and become prone to brittle cleavage fracture. This is why ferritic steels show a distinct ductile-to-brittle transition.
BCC has a packing factor of about 0.68, lower than FCC, and a larger total volume of interstitial space, but that space is divided among many small sites. In the hard-sphere model, the sphere that fits has a radius about 0.29 times (tetrahedral site) or 0.15 times (octahedral site) that of the host atom. This is why the maximum solubility of carbon in α-iron is as small as about 0.022 wt%. Carbon and nitrogen distort the lattice asymmetrically, so they strengthen it strongly, and they gather at dislocations, causing yield-point phenomena and strain aging.
Pure iron is BCC α-iron below 912 °C, FCC γ-iron from 912 to 1394 °C, and BCC δ-iron again from 1394 °C up to its melting point of 1538 °C. In the BCC-to-FCC transformation the volume per atom decreases by about 1%, so the transformation point can be found by dilatometry. In XRD, only planes with h + k + l even diffract in BCC, so peaks appear in the order (110), (200), (211)…. This sequence differs from FCC's (111), (200), (220)…, so the crystal structure can be identified from the indices of the peaks.
Answer: A. 2
Each corner atom is shared by 8 unit cells, so it contributes 1/8, while the body-center atom belongs entirely to that cell. The net number of atoms is therefore 8 × 1/8 + 1 = 2. Nine comes from counting each corner atom as a whole atom without considering sharing, and 4 is the value for FCC (corners 8 × 1/8 + face centers 6 × 1/2 = 4). The number of atoms per unit cell n goes straight into the density calculation ρ = nM/(N_A a³), so you need to know it reliably for each structure. SC has 1, and the hexagonal-prism cell of HCP has 6.
The close-packed direction is the body diagonal <111>, and the most densely packed plane is {110}. However, the planar packing fraction of {110} is about 0.83, lower than that of the FCC {111} plane (about 0.91), so it is not a truly close-packed plane.
The stress needed to move screw dislocations rises sharply at low temperature, so the stress reaches the cleavage fracture stress before the metal yields. This appears in the Charpy impact test as a temperature range where the absorbed energy drops sharply.
No. The ions at the corners and the body center are different species, so a translation to the body center does not bring the structure into coincidence, and the Bravais lattice is simple cubic. A structure is BCC only when the corner and body-center sites hold the same atoms.
Atomic packing factor Face-centered cubic Hexagonal close-packed Miller indices