Summary
Highlights
Solids have definite shape and volume, strong intermolecular forces, and are incompressible. They are classified into crystalline and amorphous solids. Crystalline solids have a regular arrangement, long-range order, sharp melting points, and are anisotropic. Amorphous solids have irregular arrangements, short-range order, range melting points, and are isotropic. Glass is an example of a 'supercooled liquid' due to its ability to flow over time.
Crystalline solids are categorized into ionic, metallic, covalent, and molecular solids based on their bonding. Ionic solids (e.g., NaCl) have high melting points, are brittle, insulators in solid state, and conductors in molten state. Metallic solids (e.g., iron) have a 'sea of delocalized electrons,' high melting points, are malleable, ductile, and good conductors. Covalent solids (e.g., diamond) have high melting points, are hard, and are poor conductors or semiconductors. Molecular solids (e.g., sugar) have low melting points, are soft, and are insulators.
Solids are composed of constituent particles forming a crystal lattice, the regular 3D arrangement. The smallest repeating part of a crystal lattice is called a unit cell. Lattice points represent individual atoms, ions, or molecules. Unit cells are classified into primitive (particles only at corners) and non-primitive (particles at corners and other positions like body-centered, face-centered, or edge-centered).
The contribution of an atom refers to the fraction of an atom's volume inside a unit cell. For example, an atom at a corner contributes 1/8 to a unit cell, a body-centered atom contributes 1, an edge-centered atom contributes 1/4, and a face-centered atom contributes 1/2. A trick is introduced to easily remember these contributions and use them to calculate the total number of atoms in different unit cell types (SCC, BCC, FCC, ECC).
Using the contribution trick, the number of atoms in different unit cells can be calculated: SCC has 1 atom, BCC has 2 atoms, FCC has 4 atoms, and ECC has 4 atoms. This method can also be applied to determine the chemical formula of a unit cell given the positions of different atoms (e.g., A at corners, B at edges, C at faces).
Each unit cell is defined by six parameters: three edge lengths (a, b, c) and three interfacial angles (alpha, beta, gamma). A mnemonic 'C Tom There' is used to remember the seven crystal systems: Cubic, Tetragonal, Orthorhombic, Monoclinic, Triclinic, Hexagonal, and Rhombohedral, along with their characteristic edge lengths and angles.
Closed packing refers to arranging spheres (constituent particles) to maximize space occupancy and minimize empty space. Coordination number is the number of touching spheres. Types include 1D (coordination number 2), 2D (Square Close Packing - SCP with coordination number 4, AAA arrangement; Hexagonal Close Packing - HCP with coordination number 6, ABA arrangement), and 3D (Cubic Close Packing - CCP with AAA arrangement and HCP with ABA arrangement). HCP generally has higher efficiency than SCP.
Voids are empty spaces between spheres. Two main types are tetrahedral voids (formed by four spheres) and octahedral voids (formed by six spheres). The number of octahedral voids in a unit cell equals 'n' (number of atoms), and tetrahedral voids equal '2n'. Finally, the density of a unit cell is calculated using the formula: density = (Z * M) / (a^3 * Na), where Z is the number of atoms, M is the molar mass, a is the edge length, and Na is Avogadro's constant. It's crucial to convert picometer to centimeter and remember the unit for density is g/cm³.