Crystalline and Amorphous Solids: Structure, Classification, and Properties

Solids: A Brief Introduction

General Properties of Solids

Solids are one of the fundamental states of matter, characterized by closely packed particles that vibrate but do not move freely. This arrangement results in solids retaining their shape and volume, making them incompressible and preventing them from flowing.

• Particles in solids are fixed in position, though they may vibrate.

• Close packing of particles leads to incompressibility.

• Solids retain their shape and volume due to the inability of particles to move around.

Types of Solids

• Crystalline solids: Particles arranged in an orderly, repeating pattern.

• Amorphous solids: Particles do not follow a regular pattern.

Crystalline solids can be analyzed using X-ray crystallography to determine atomic arrangement. This technique is not useful for amorphous solids.

Crystalline Solids: Structure and Unit Cells

Crystal Lattice and Unit Cell

The arrangement of particles in a crystalline solid is called the crystal lattice. The smallest repeating unit that shows the pattern of arrangement is the unit cell.

• Unit cells are repeated over and over to give crystal structure.

• Common types: Simple cubic, Body-centered cubic (bcc), Face-centered cubic (fcc).

Simple Cubic Unit Cell

• Atoms at each corner.

• Each corner atom is shared by 8 unit cells: $8 imes rac{1}{8} = 1$ atom per unit cell.

Body-Centered Cubic Unit Cell (bcc)

• Atoms at each corner plus one atom in the center.

• Each corner atom: $8 imes rac{1}{8} = 1$ atom; center atom: $1$atom; total: $2$ atoms per unit cell.

Face-Centered Cubic Unit Cell (fcc)

• Atoms at each corner plus atoms on each face.

• Corner atoms: $8 imes rac{1}{8} = 1$ atom; face atoms: $6 imes rac{1}{2} = 3$ atoms; total: $4$ atoms per unit cell.

Unit Cells: Coordination Number and Packing Efficiency

The coordination number is the number of other atoms each atom is in contact with. Higher coordination numbers mean more interaction and stronger attractive forces.

Unit Cell Type	Coordination Number	Packing Efficiency
Simple cubic	6	52%
Body-centered cubic	8	68%
Face-centered cubic	12	74%

Closest-Packed Structures

Arrangement of Atoms in Layers

• First layer (A): Atoms as close together as possible.

• Second layer (B): Atoms placed over the holes in the first layer (A-B pattern).

• Third layer: Two choices:

  • Atoms over holes not directly above A atoms (ABC pattern) – face-centered cubic (cubic closest packed).

  • Atoms placed in holes directly above A atoms (ABA pattern) – hexagonal closest packed (hcp).

Calculations Involving Unit Cells

Examples

• Calculate packing efficiency for simple cubic and face-centered cubic cells.

• Calculate length, mass, and density of unit cells (e.g., copper and barium).

Classifying Crystalline Solids

Types of Crystalline Solids

Crystalline solids are classified by their particles and the forces holding them together:

• Atomic solids: Made of atoms; can be nonbonding, metallic, or network covalent.

  • Nonbonding atomic solids: Held by dispersion forces (e.g., noble gases).

  • Metallic solids: Held by metallic bonds.

  • Network covalent solids: Held by covalent bonds (e.g., diamond).

• Molecular solids: Made up of molecules held by intermolecular forces (IMFs).

• Ionic solids: Made up of ions held by strong electrostatic forces.

Types of Crystalline Solids (Summary Table)

Type	Particles	Forces	Examples
Atomic	Atoms	Dispersion, metallic, covalent	He, Cu, Diamond
Molecular	Molecules	IMFs (dispersion, dipole, H-bonding)	H2O, CO2
Ionic	Ions	Electrostatic	NaCl, K2O

Molecular Solids

Molecular solids are made up of molecules held together by weak intermolecular forces (IMFs) such as dispersion, dipole-dipole, and hydrogen bonding. They have relatively low melting points.

• Example: H2O (0°C), P4 (44°C)

Ionic Solids and Crystal Lattice Energy

Ionic solids are held together by strong attractions between ions. Lattice energy measures the strength of ionic bonds and depends on the size and charge of ions.

• High melting points

• Conduct electricity in liquid state, not in solid state

Compound	Lattice Energy (kJ/mol)	Bond Strength
LiCl	-861	Stronger
NaCl	-786	Strong
KCl	-715	Moderate
CsCl	-657	Weaker

Atomic Solids

• Nonbonding atomic solids: Noble gases at very low temperatures, held by dispersion forces.

• Metallic atomic solids: Metal atoms release their electrons, forming a "sea" of electrons.

• Network covalent atomic solids: Atoms held by covalent bonds (e.g., diamond, graphite).

Network Covalent Solids

Graphite

• Carbon atoms in sheets held by covalent bonds.

• Sheets held together by dispersion forces.

• Good electrical conductor (parallel to sheets), thermal insulator.

Diamond

• Each carbon atom bonded tetrahedrally to four others.

• Very high melting point, very hard, electrical insulator, thermal conductor, chemically nonreactive.

Polymers

Polymers are very large molecules made by repeated linking of small molecules called monomers.

• Natural polymers: Found in living organisms (starch, proteins, DNA).

• Synthetic polymers: Made in labs (plastics, Styrofoam, nylon rope, Plexiglas).

Examples of Polymers

• PVC (Polyvinyl chloride): Used in pipes and cables.

• Nylon: Monomers are H2N(CH2)6NH2 and HOOC(CH2)4COOH.

Practice Problems

• Identify solids as molecular, ionic, or atomic; specify dominant attractive force (nonbonding, metallic, or network).

• Determine which solid has the lowest and highest melting point.

Additional info: These notes cover key concepts from Chapter 13: Liquids, Solids & Intermolecular Forces, focusing on the structure, classification, and properties of solids, including crystalline and amorphous solids, unit cells, packing efficiency, and types of crystalline solids.