Chemistry · Ch 6 — Solid State
Body Centered Cubic Unit Cell (BCC)
Body Centered Cubic Unit Cell (BCC)
In the body-centred cubic (bcc) unit cell, an identical particle occupies every corner, AND one additional atom sits exactly at the body centre of the cube. The corner atoms do not touch one another, but every one of them touches the central atom -- so each atom in the structure is surrounded by 8 nearest neighbours, giving the bcc arrangement a coordination number of 8. Unlike a corner atom, the body-centre atom belongs entirely and exclusively to its own unit cell -- it is not shared with any neighbouring cell.
Counting atoms per cell: the 8 corner atoms each contribute 1/8 (as in the simple cubic case), and the 1 body-centre atom contributes a full 1:
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What this figure shows. A cube of edge a labelled at its 8 vertices A-H, with a sphere of radius r at every corner and one larger sphere of radius r at the exact body centre; a dashed line runs along the leading body diagonal, marked 2r across the central sphere and annotated a and root-2 a on the visible face diagonal -- setting up the geometry used later (6.6.4) to derive the body-diagonal relation root-3 a = 4r. The figure makes visually clear that the 8 corner spheres do NOT touch one another directly (there is visible space between them along every edge and face diagonal), while every one of them DOES touch the central sphere -- which is exactly why the body-centre atom's coordina …