Allotropy

Core Structural Trends: $$\begin{aligned} \text{Carbon Allotropes} &\implies \text{Diamond (crystalline } sp^3\text{), Graphite (layered } sp^2\text{), Fullerenes (cage structures)} \\ \text{Phosphorus Allotropes} &\implies \text{White (reactive discrete } P_4 \text{ tetrahedra), Red (polymeric chains), Black (layered sheets)} \\ \text{Sulfur Allotropes} &\implies \text{Rhombic (stable puckered } S_8 \text{ rings), Monoclinic (puckered } S_8 \text{ needle-like crystals)} \end{aligned}$$

Concept: The property of certain chemical elements to exist in two or more different physical forms in the same state, differing drastically in their crystal structures and bonding modes.

Notation:

• $$\text{Diamond}$$ = Extremely hard insulator;
• $$\text{Graphite}$$ = Thermodynamically stable conductor;
• $$\text{White P}$$ = Highly unstable and chemiluminescent due to a severe $$60^\circ$$ bond angle strain.