Classification of Solids

A crystalline solid is defined by its unit cell — the smallest repeating structural unit of the lattice. Common unit-cell geometries include simple cubic, body-centred cubic (BCC), face-centred cubic (FCC), and hexagonal close-packed (HCP). X-ray diffraction (XRD) exploits the regular spacing (d) between lattice planes, described by Bragg's Law (nλ = 2d sinθ), to identify crystalline structures. Amorphous solids such as silica glass (SiO₂) contain the same local bonding as their crystalline counterparts (SiO₄ tetrahedra) but lack the periodic repetition; XRD of amorphous materials produces a broad hump rather than sharp diffraction peaks.

In molecular solids, discrete covalently bonded molecules occupy the lattice points. The forces holding the lattice together are intermolecular forces (IMFs): London dispersion forces, dipole–dipole interactions, and hydrogen bonds. These are much weaker than covalent or ionic bonds, so molecular solids typically have low melting points (often below 300 °C), are soft, and are non-conductors of electricity in any state. Examples include ice (H₂O, held by hydrogen bonds, m.p. 0 °C), iodine (I₂, held by dispersion forces, m.p. 114 °C), and naphthalene (C₁₀H₈, m.p. 80 °C). The stronger the IMF, the higher the melting point — a direct application of periodic trends.

Ionic solids consist of cations and anions arranged in a lattice stabilised by electrostatic attraction. The lattice energy (U) — the energy released when gaseous ions combine to form one mole of ionic solid — is large and positive (endothermic to break), explaining the high melting points of ionic compounds: NaCl m.p. 801 °C, MgO m.p. 2852 °C. Lattice energy increases with increasing ionic charge and decreasing ionic radius, as described by the Born–Landé equation. Ionic solids are hard and brittle (displacement of planes lines up like charges, causing repulsion and cleavage), are non-conductors in the solid state (ions are fixed), but conduct electricity when molten or dissolved in water because ions become free to move.

Metallic solids are composed of metal cations (kernels) surrounded by a 'sea' of delocalised electrons — the free-electron model (or more rigorously, described by band theory). This delocalisation is responsible for the characteristic properties of metals: high electrical and thermal conductivity, metallic lustre, malleability, and ductility. Melting points vary widely: mercury (Hg) is liquid at room temperature (m.p. −39 °C) while tungsten (W) has a m.p. of 3422 °C, reflecting differences in the number of valence electrons contributing to the metallic bond. Alloys such as steel (Fe–C) and brass (Cu–Zn) are also metallic solids with tuned properties.

In covalent network solids (also called giant covalent or atomic solids), every atom is linked to its neighbours by covalent bonds that extend throughout the entire crystal as one enormous macromolecule. Breaking any part of the structure requires breaking covalent bonds, giving these solids exceptionally high melting points and hardness. Diamond (C, each carbon sp³-hybridised, bonded to 4 others) is the hardest natural substance (Mohs 10) and a poor electrical conductor because all electrons are localised in σ-bonds. Graphite (C, sp²-hybridised layers with delocalised π electrons) is an unusual covalent solid that conducts electricity within layers. Silicon dioxide (SiO₂) and silicon carbide (SiC) are other key examples used in ceramics and semiconductors.

• n — Order of reflection (dimensionless (integer)): Integer (1, 2, 3, …) representing the order of the diffraction maximum
• \lambda — Wavelength of X-rays (m (or Å)): Wavelength of the incident X-radiation used to probe the crystal
• d — Interplanar spacing (m (or Å)): Distance between adjacent parallel planes of atoms in the crystal lattice
• \theta — Glancing angle (degrees (°)): Angle between the incident X-ray beam and the crystal lattice plane surface

Problem. X-rays of wavelength 1.54 Å are reflected from the (200) planes of a NaCl crystal. The first-order reflection (n = 1) is observed at a glancing angle of 15.9°. Calculate the interplanar spacing d and identify what this reveals about the NaCl unit cell.

Answer. Interplanar spacing d = 2.81 Å; unit cell parameter a ≈ 5.62 Å, consistent with the FCC ionic lattice of NaCl.

• Intermolecular Forces — Molecular solids are held together by IMFs (London dispersion, dipole–dipole, and hydrogen bonds); understanding these forces explains the variation in melting points within the molecular solid class.
• Ionic Bonding and Lattice Energy — Lattice energy determines the stability and melting point of ionic solids; the Born–Haber cycle quantifies this using Hess's Law and is central to explaining ionic solid properties.
• Metallic Bonding and Band Theory — Band theory extends the simple electron-sea model to explain conductivity, semiconduction (Si, Ge), and the insulating nature of diamond — directly linking to metallic and covalent solid behaviour.
• Unit Cells and Crystal Systems — The geometry of unit cells (cubic, hexagonal, etc.) determines packing efficiency and density calculations, fundamental to describing any crystalline solid at the microscopic level.
• Periodic Trends: Atomic Radius and Ionisation Energy — Ionic radius and charge directly influence lattice energy; atomic size affects packing in metallic and molecular solids, linking periodic table trends to solid-state properties.