Solid State

A crystalline solid has its particles arranged in a regular, repeating three-dimensional pattern, and almost everything else about it follows from that. It has a definite geometric shape, and its interfacial angles are constant however the crystal was grown and remain characteristic even when it is ground to a fine powder. It has a sharp melting point. It breaks along definite cleavage planes set at a characteristic angle. And it is anisotropic: a measured property such as electrical conductance, thermal conductance or refractive index changes with the direction through the crystal, while molar mass does not, because molar mass belongs to the substance rather than to a direction in the lattice. An amorphous solid has none of this, because its particles are jumbled with no long-range order: it has no sharp melting point, no definite heat of fusion, no cleavage planes, and it is isotropic. Glass, plastic, rubber, charcoal, coke, cement, concrete and ceramics are the amorphous set, while sugar, glucose, alum, copper and rhombic sulphur are crystalline.

Three terms sit close together here and papers set them against one another on purpose. Isomorphism is when two different compounds crystallise in the same geometric form, because their ions match in ratio and size: $\text{Ag}_2\text{SO}_4$ and $\text{Na}_2\text{SO}_4$ are isomorphs, as are $\text{NaNO}_3$ and $\text{CaCO}_3$, both trigonal, while $\text{AgNO}_3$ and $\text{KNO}_3$ are the recorded non-isomorphic pair because their structures do not match. Polymorphism is when one compound can take more than one crystal structure, as calcium carbonate does in calcite, which is trigonal, and aragonite, which is orthorhombic. Allotropy is the same idea restricted to a pure element, and it is the correct word when one element appears in two forms, carbon as diamond and graphite being the standard case.

Transition temperature ties the allotropes together. It is the temperature at which two crystalline forms of the same substance coexist in dynamic equilibrium, and just above or below it only one form can exist; for sulphur the change between the rhombic and monoclinic forms sits at $95.5^\circ\text{C}$. An amorphous solid may still hold small islands where the particles are orderly, but there is no long-range order joining those islands, which is why it softens across a range of temperature instead of melting at a point, and why it has no definite heat of fusion.