5.1: The Solid State of Matter Some substances form crystalline solids consisting of particles in a very organized structure; others form amorphous (noncrystalline) solids with an internal structure that is not ordered. The main types of crystalline solids are ionic solids, metallic solids, covalent network solids, and molecular solids. The properties of the different kinds of crystalline solids are due to the types of particles of which they consist, the arrangements of the particles, and the strengths of the attractions bet 5.2: Lattice Structures in Metallic Solids The structures of crystalline metals and simple ionic compounds can be described in terms of packing of spheres. Metal atoms can pack in hexagonal closest-packed structures, cubic closest-packed structures, body-centered structures, and simple cubic structures. The anions in simple ionic structures commonly adopt one of these structures, and the cations occupy the spaces remaining between the anions. 5.3: Lattice Structures in Ionic Solids Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size. Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite charge 5.4: Alloys and Crystal Defects Alloys are mixtures of metals or a mixture of a metal and another element. An alloy may be a solid solution of metal elements (a homogeneous mixture) or a mixture of metallic phases (a heterogeneous mixture of two or more solutions). In a crystalline solid, the atoms, ions, or molecules are arranged in a definite repeating pattern, but occasional defects may occur in the pattern. Several types of defects are known. 5.5: Ionic Lattices 5.5.1: Structure - Rock Salt (NaCl) 5.5.2: Structure - Caesium Chloride (CsCl) 5.5.3: Structure - Zinc Blende (ZnS) 5.5.4: Structure - Fluorite and Antifluorite 5.5.5: Structure - β-Cristobalite (SiO₂) 5.5.6: Spinel, Perovskite, and Rutile Structures 5.6: Work Hardening, Alloying, and Annealing 5.7: Properties of Unit Cells The size of a cubic unit cell is describe by the length of the side of the unit cell and by the volume of the unit cell. The length of the side of the unit cell depends on the radius of the atoms contained in the unit cell and on the arrangement of the atoms in the unit cell (the structure of the unit cell). Likewise, the mass of a unit cell and density of a crystalline solid also depend on the unit cell structure. 5.8: Enthalpy of Hydration The formation of a solution involves the interaction of solute with solvent molecules. Many different liquids can be used as solvents for liquid solutions, and water is the most commonly used solvent. When water is used as the solvent, the dissolving process is called hydration. 5.9: Enthalpy of Solution This page looks at the relationship between enthalpies of solution, hydration enthalpies and lattice enthalpies. 5.10: Lattice Energy - The Born-Haber cycle Ionic solids tend to be very stable compounds. The enthalpies of formation of the ionic molecules cannot alone account for this stability. These compounds have an additional stability due to the lattice energy of the solid structure. However, lattice energy cannot be directly measured. The Born-Haber cycle allows us to understand and determine the lattice energies of ionic solids. 5.11: Lattice Energy - Madelung Constants For simplicity, let us consider the ionic solids as a collection of positive and negative ions. In this simple view, appropriate number of cations and anions come together to form a solid. The positive ions experience both attraction and repulsion from ions of opposite charge and ions of the same charge. The Madelung constant is a geometrical factor that depends on the arrangement of ions in the solid. 5.12: Basic Science of Nanomaterials Nanomaterials describe materials of which a single unit is sized (in at least one dimension) between 1 and 1000 nanometers, but is usually 1—100 nm. Nanomaterials research takes a materials science-based approach to nanotechnology, leveraging advances in materials metrology and synthesis which have been developed in support of microfabrication research. Materials with structure at the nanoscale often have unique optical, electronic, or mechanical properties. 5.12.1: Prelude to Basic Science of Nanomaterials 5.12.2: Physics and Length Scales- Cavity Laser, Coulomb Blockade, Nanoscale Magnets 5.12.3: Semiconductor Quantum Dots 5.12.4: Synthesis of Semiconductor Nanocrystals 5.12.5: Surface Energy 5.12.6: Nanoscale Metal Particles 5.12.7: Applications of Nanomaterials 5.12.8: Discussion Questions 5.12.9: Problems 5.12.10: References 5.13: Bonding in Metals and Semicondoctors 5.13A: Electrical Conductivity and Resistivity 5.13B: Band Theory of Metals and Insulators 5.13C: The Fermi Level 5.13D: Band Theory of Semiconductors 5.14: Bonding in Metals Bonding in metals and semiconductors can be described using band theory, in which a set of molecular orbitals is generated that extends throughout the solid. The primary learning objective of this Module is to describe the electrical properties of solid using band theory. 5.15: Bonding in Metals, Semiconductors and Insulators – Band Structure