Chapter 5: Imperfections in Solids

Introduction to Defects in Solids

All crystalline solids contain various types of defects, which are deviations from the ideal arrangement of atoms. These imperfections play a crucial role in determining the physical properties of materials, such as strength, conductivity, and ductility.

• Types of Defects: Defects can be classified based on their dimensionality and nature.

• Desirability of Defects: While some defects may be undesirable, many are intentionally introduced to enhance material properties.

Impurities in Solids

Role and Nature of Impurities

Impurities are foreign atoms or molecules present in a solid. It is nearly impossible to create a perfectly pure solid, and in most cases, pure metals are not desirable for engineering applications. The addition of impurity atoms can improve specific characteristics of materials, such as strength or corrosion resistance.

• Alloys: Alloys are mixtures of metals with impurity atoms added to improve properties (e.g., iron-carbon alloy).

• Intentional Impurities: Impurity atoms are often added deliberately to tailor the material's behavior.

Classification of Defects

Main Types of Defects

Defects in solids are categorized by their dimensionality and atomic involvement.

• Point Defects: Associated with one or two atomic positions. Examples include vacancy (missing atom) and self-interstitial (extra atom in a lattice site).

• Impurity Defects: Can be substitutional (impurity replaces host atom) or interstitial (impurity occupies space between host atoms).

• Line Defects: One-dimensional defects such as dislocations.

• Surface/Planar Defects: Two-dimensional defects like grain boundaries.

Point Defects in Metals

Vacancy Defects

A vacancy defect occurs when a lattice site in the crystalline structure is unoccupied because an atom is missing. Vacancies are formed during solidification due to atomic vibrations and are a common type of point defect.

• Distortion: Vacancies cause distortion in the surrounding atomic planes.

• Formation: The number of vacancies increases with temperature.

Number of Vacancy Sites

Equilibrium Vacancy Concentration

The equilibrium number of vacancies in a solid at a given temperature can be calculated using the following equation:

• : Total number of atomic sites,

• : Avogadro's Number ( atoms/mol)

• : Density of the material

• : Atomic weight

• : Energy required for the formation of a vacancy

• : Absolute temperature (Kelvin)

• : Boltzmann's constant ( J/atom·K or eV/atom·K)

Key Insights from the Vacancy Equation

• Temperature Dependence: The number of vacancies increases exponentially with temperature.

• Atomic Vibration: Higher temperatures lead to greater atomic vibrations, facilitating vacancy formation.

• Experimental Measurement: is determined experimentally.

Estimating Vacancy Concentration

Example Calculation

To estimate the equilibrium number of vacancies in 1 m3 of copper (Cu) at 1000°C:

• Given: g/cm3, g/mol, eV/atom, atoms/mol, K, eV/atom·K

• Calculation: sites$ $N_v = (2.7 \times 10^{-4})(8.0 \times 10^{28}) = 2.2 \times 10^{25}

Other Point Defects in Metals

Interstitial Defects

An interstitial defect occurs when an extra atom is forced into a non-lattice site within the crystal structure. This can be a self-interstitial (host atom) or an impurity interstitial (foreign atom).

• Self-Interstitial: Host atom occupies an interstitial site.

• Impurity Interstitial: Foreign atom occupies an interstitial site.

Solid Solutions

Formation and Types

A solid solution is formed when impurity atoms are added to a host material, resulting in a homogeneous mixture at the atomic level. The host is called the solvent, and the added element is the solute.

• Substitutional Solid Solution: Solute atoms replace host atoms in the lattice (e.g., Cu in Ni).

• Interstitial Solid Solution: Solute atoms occupy interstitial sites (e.g., C in Fe).

Rothery Rules for Substitutional Solid Solutions

The extent to which a solute dissolves in a solvent for substitutional solid solutions is governed by the following factors:

• Atomic Size Factor: Difference in atomic radii should be less than 15%.

• Crystal Structure: Both elements must have the same crystal structure.

• Electronegativity: The electronegativity values should be similar.

• Valency: The valency of the solute and solvent should be similar.

Interstitial Solid Solutions

In interstitial solid solutions, impurity atoms fill the voids between host atoms. The impurity must be substantially smaller than the host atom, and the concentration is typically less than 10% of the host atoms (e.g., C in Fe).

• Example: Carbon atoms in iron (steel) form an interstitial solid solution, with carbon's atomic radius (0.071 nm) much smaller than iron's (0.124 nm).

Summary Table: Types of Point Defects

Review Questions

• Vacancy defect: A point defect in which an atom is missing from a lattice site.

• Self-Interstitial defect: A defect where a host atom occupies an interstitial site.

• Solid solution: Formed when solute atoms are added to a host material, resulting in a compositionally homogeneous structure with no new phases.

• Factors for substitutional impurity solubility: Atomic radii, crystal structure, valency, and electronegativity.

• Interstitial impurity concentration: Should be less than 10% of host atoms.

Additional info: These notes expand on the brief points in the original slides, providing definitions, equations, and examples for clarity and completeness.