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Solid state chemistry studies the structure, bonding, and properties of crystalline and amorphous solids. Crystal structures are described by unit cells and space groups; bonding ranges from ionic (NaCl) to covalent (diamond) to metallic (copper). Band theory extends molecular orbital theory to infinite arrays of atoms, explaining why some solids are metals, some are semiconductors, and some are insulators. Defects in crystal lattices — vacancies, interstitials, substitutions — profoundly affect properties like conductivity, color, and catalytic activity.
Molecular orbital theory works beautifully for discrete molecules with a countable number of atoms. But what happens when you bring together 10²³ atoms in a solid? The orbitals do not disappear — they multiply. When N atoms combine, each atomic orbital produces N molecular orbitals, so closely spaced in energy that they form a continuous band. Band theory is simply MO theory applied to infinite periodic arrays, and it provides the framework for understanding the electrical, optical, and thermal properties of solids.
Consider metallic sodium. Each atom contributes its 3s orbital. In a solid with N sodium atoms, these N orbitals produce a band of N energy levels. Since each Na contributes one electron, the band is half-filled. Electrons at the top of the occupied levels can easily move into nearby empty levels when an electric field is applied — this is metallic conduction. Now consider diamond: each carbon contributes four orbitals that hybridize and form bonding and antibonding bands (the valence and conduction bands). All bonding levels are filled, all antibonding levels are empty, and the gap between them is 5.5 eV — far too large for thermal excitation. Diamond is an insulator. Silicon has the same structure but a gap of only 1.1 eV, allowing some thermal excitation: a semiconductor.
Crystal structures describe how atoms pack in three dimensions. The simplest ionic structures — rock salt (NaCl), cesium chloride (CsCl), zinc blende (ZnS), fluorite (CaF₂) — are determined primarily by the radius ratio of the cation to the anion, which dictates the coordination number that maximizes electrostatic attraction while avoiding ion-ion repulsion. The rock salt structure (coordination number 6 for both ions) is adopted by hundreds of binary compounds. The perovskite structure (ABX₃, with A in a 12-coordinate site and B in a 6-coordinate octahedral site) is important for understanding materials from calcium titanate to high-temperature superconductors.
Real crystals are never perfect. Point defects — missing atoms (vacancies), extra atoms (interstitials), and foreign atoms (substitutions) — profoundly affect properties. Vacancies in ionic crystals allow ion migration, enabling solid-state ionic conduction. Color centers (electrons trapped at anion vacancies) give crystals like NaCl their characteristic colors when irradiated. Doping semiconductors with controlled impurities creates the p-type and n-type materials that form the basis of transistors and solar cells. In catalysis, surface defects provide the active sites where reactions occur. The chemistry of defects is often more important than the chemistry of the perfect crystal — a lesson that extends throughout materials science.