Chemistry · Ch 6 — Solid State
Primitive (or) Simple Cubic Unit Cell (SC)
Primitive (or) Simple Cubic Unit Cell (SC)
In the simple (primitive) cubic unit cell, an identical atom, ion or molecule occupies every one of the cube's 8 corners. Neighbouring corner atoms touch each other along the edges of the cube, but they do NOT touch along the face or body diagonals -- so from the touching-along-the-edge relation, the edge length a is exactly twice the atomic radius r (a = 2r). Each atom has exactly 6 nearest neighbours (the 6 atoms one edge-length away along +x, -x, +y, -y, +z, -z), so the coordination number of a simple cubic arrangement is 6.
To count how many whole atoms belong to one unit cell, note that a corner atom is shared among the 8 unit cells that meet at that corner, so it contributes only 1/8 of itself to any single cell. With Nc = 8 corner atoms: …
What this figure shows. A cube outline of edge length a with a sphere of radius r drawn at each of its 8 corners; adjacent corner spheres visibly touch each other along the cube's edges (the r, r, a labelling shows the edge equals two radii) but a corner sphere does not reach the sphere on the far diagonal corner. Because the spheres touch ONLY along the edge and nowhere else, the edge length a is exactly twice the atomic radius r (a = 2r), which is the single relation this figure sets up and which Section 6.6.3 later uses to derive the …