Solids: Structure, Properties, and Classification (Chapter 13 Study Notes)

Solids

Introduction

Solids are one of the fundamental states of matter, characterized by structural rigidity and resistance to changes in shape or volume. The study of solids in chemistry focuses on their atomic arrangement, bonding, and physical properties, which are crucial for understanding materials science and many chemical phenomena.

Crystallography

Definition and Importance

• Crystallography is the study of crystal structures and their properties.

• Crystalline solids have atoms, ions, or molecules arranged in a highly ordered, repeating pattern.

• Examples include minerals and salts, which display distinct geometric shapes.

Bragg's Law and X-ray Diffraction

Principles and Calculations

• Bragg's Law describes the condition for constructive interference of X-rays scattered by crystal planes.

• It is used to determine the spacing between atomic planes in a crystal.

Bragg's Law Equation:

$n\lambda = 2d \sin\theta$

• n: order of reflection (integer)

• λ: wavelength of incident X-rays

• d: distance between atomic planes

• θ: angle of incidence/reflection

Unit Cells

Types and Properties

• Unit cell: the smallest repeating unit in a crystal lattice.

• This course focuses on the cubic unit cell, where all edges are equal and all angles are 90°.

Common Cubic Unit Cells

• Simple Cubic (SC): atoms at corners only

• Body-Centered Cubic (BCC): atoms at corners and one in the center

• Face-Centered Cubic (FCC): atoms at corners and centers of each face

Terminology

• Coordination number: number of nearest neighbors to an atom in the lattice

• Packing efficiency: percentage of volume occupied by atoms in the unit cell

• Simple cubic, BCC, FCC, HCP (hexagonal closest packing), CCP (cubic closest packing)

Simple Cubic Structure

Arrangement and Calculation

• Atoms are located at the corners of the cube.

• Each corner atom is shared by eight unit cells, so only 1/8 of each atom belongs to one unit cell.

• Coordination number: 6

• Packing efficiency: 52%

Body-Centered Cubic (BCC) Structure

Arrangement and Calculation

• Atoms at each corner and one atom in the center of the cube.

• Corner atoms: 1/8 per unit cell; center atom: 1 per unit cell.

• Coordination number: 8

• Packing efficiency: 68%

Face-Centered Cubic (FCC) Structure

Arrangement and Calculation

• Atoms at each corner and at the center of each face.

• Corner atoms: 1/8 per unit cell; face atoms: 1/2 per unit cell.

• Coordination number: 12

• Packing efficiency: 74%

Summary Table: Cubic Unit Cells

Unit Cell Type	Atoms per Unit Cell	Coordination Number	Edge Length (a)	Packing Efficiency
Simple Cubic	1	6	$a = 2r$	52%
Body-Centered Cubic	2	8	$a = \frac{4r}{\sqrt{3}}$	68%
Face-Centered Cubic	4	12	$a = \frac{4r}{\sqrt{2}}$	74%

Classification of Crystalline Solids

Types and Properties

• Molecular solids: composed of molecules held together by intermolecular forces (e.g., ice, dry ice)

• Ionic solids: composed of ions held together by electrostatic forces (e.g., NaCl)

• Atomic solids: composed of atoms held together by covalent or metallic bonds (e.g., diamond, gold)

• Polymorphs: substances that can exist in more than one crystal structure

Metallic Bonding

Structure and Properties

• Metal atoms release their valence electrons, forming a "sea" of mobile electrons.

• Metal cations are fixed in position, surrounded by delocalized electrons.

• This structure explains properties such as electrical conductivity and malleability.

Ionic Solids: Sodium Chloride (NaCl)

Structure and Formula

• NaCl adopts the rock salt structure, with Cl- ions in a FCC arrangement.

• Na+ ions occupy octahedral holes between Cl- ions.

• Coordination number: 6 for both Na+ and Cl-

• Unit cell composition: Na+ in center and edges, Cl- on corners and faces.

• Na:Cl ratio is 1:1, so the formula is NaCl.

Silicates

Structure and Properties

• Silicates make up ~90% of Earth's crust.

• They have an extended network covalent structure.

• Each Si atom is bonded to four O atoms (tetrahedral geometry).

• Each O atom is bonded to two Si atoms and has two lone pairs.

• Example: Quartz (SiO2)

Semiconductors and Band Theory

Band Theory and Conductivity

• Band theory builds on molecular orbital theory, with orbitals delocalized over the entire crystal.

• Energy bands are formed: valence band (occupied) and conduction band (empty).

• The band gap is the energy difference between these bands.

Classification by Band Gap

• Conductor: No energy gap; electrons move freely.

• Semiconductor: Small energy gap; conductivity increases with temperature.

• Insulator: Large energy gap; poor conductivity.

Extrinsic Semiconductors

• Impurity atoms (dopants) are introduced to tune the band gap.

• n-type: dopant has more valence electrons than crystal atoms (e.g., Group 15 dopant in Group 14 crystal).

• p-type: dopant has fewer valence electrons than crystal atoms (e.g., Group 13 dopant in Group 14 crystal).

Fullerenes

Structure and Examples

• Fullerenes are molecular forms of carbon with cage-like structures (e.g., C60, C70).

• They have unique properties and applications in materials science and nanotechnology.

Summary of Atomic Contributions in Cubic Unit Cells

• 1/8 of each atom on a corner

• 1/4 of each atom on an edge

• 1/2 of each atom on a face

• 1 of each atom in the body

Homework and Further Study

• Read Chapter 13.1 – 13.9

• Complete Mastering Chemistry Assignment 3

Additional info: These notes expand on the provided slides and handwritten content, adding definitions, equations, and academic context for clarity and completeness.