Atoms at the corners of a cube with coordination number 6 and packing efficiency 52 percent.
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The simple cubic lattice has atoms at the eight corners of a cube, giving one atom per unit cell because each corner atom contributes 1/8. Each atom touches six nearest neighbours along the cube edges, so its coordination number is six. The atoms touch along the edge, so the edge length equals twice the atomic radius, a = 2r. Its packing efficiency is π/6, about 52.4 percent, which makes it the least efficient of the common cubic packings. Simple cubic structures are rare among elemental metals, with polonium being the best-known example.
Key ideas: Relationships: a = 2r, volume a^3 = 8 r^3, and packing efficiency = (4/3)pi r^3 / (8 r^3) = pi/6 = 0.524. The cell has 1 atom, so density = M / (NA a^3). The nearest neighbours are 6 at distance a; second neighbours at a sqrt(2).
Common mistakes and connections: Students confuse the simple cubic cell with the CsCl structure, which has two ion types and is a simple cubic arrangement of one ion with the other in the centre. Another error is believing that many metals pack this way; only polonium does. The large void in the centre of the cell is not an atom. Related to bcc, fcc and packing efficiency.
Simple cubic: one atom per cell (8 corners x 1/8), coordination number 6 and 52% packing efficiency; polonium is the rare example. The interactive lesson shows this as a live animation or chart.
Polonium adopts a simple cubic structure, which is unusual for an element.
Atoms at the corners of a cube with coordination number 6 and packing efficiency 52 percent.
Simple Cubic Lattice is a intermediate topic in States of Matter & Solutions. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in States of Matter & Solutions first: Crystalline Solids, Amorphous Solids, Unit Cell.
The next topics in States of Matter & Solutions are Body-Centered Cubic and Face-Centered Cubic.
Yes. The interactive lesson includes a self-check question on Simple Cubic Lattice, and the States of Matter & Solutions quiz draws on every topic in this area.
Simple Cubic Lattice is topic 58 of 109 in States of Matter & Solutions.