Fundamental Concepts in Materials Engineering: Atomic Structure, Bonding, and Crystal Structures

Atomic Structure and Electron Configurations

Valence Electrons and Electron Configurations

Understanding the arrangement of electrons in atoms is essential for predicting chemical behavior and bonding. The electron configuration describes the distribution of electrons among the atomic orbitals.

• Valence electrons: Electrons in unfilled shells; most available for bonding and determine chemical properties.

• Filled shells: More stable; atoms tend to achieve filled shells through bonding.

• Example (Carbon, atomic number 6): $1s^2\ 2s^2\ 2p^2$ — the four electrons in the second shell (2s and 2p) are valence electrons.

• Example (Iron, atomic number 26): $1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 3d^6\ 4s^2$ — the electrons in 3d and 4s are considered valence electrons.

Additional info: Electron configurations are written in order of increasing energy, and the arrangement affects bonding and material properties.

Electronegativity

Definition and Trends

Electronegativity is a measure of an atom's ability to attract electrons in a chemical bond. It influences the type of bonding and the properties of compounds.

• Range: 0.9 (lowest, e.g., Cs) to 4.1 (highest, e.g., F).

• High electronegativity: Tendency to acquire electrons (e.g., nonmetals like F, O, N).

• Low electronegativity: Tendency to lose electrons (e.g., metals like Na, K).

• Periodic trend: Electronegativity increases across a period (left to right) and decreases down a group (top to bottom).

Example: In the periodic table, fluorine (F) has the highest electronegativity, while cesium (Cs) has one of the lowest.

Atomic Bonding

Types of Atomic Bonding

Atoms can exist in gas, liquid, or solid states, held together by interatomic forces. The nature of these forces determines the physical properties of materials.

• Interatomic forces: Attractive and repulsive forces between atoms, dependent on temperature and pressure.

• Physical properties: Explained by the strength and type of interatomic forces.

Primary and Secondary Bonds

• Primary Bonds:

  • Ionic Bonding: Occurs between metals and nonmetals; involves electron transfer and formation of cations and anions. Requires large difference in electronegativity. Example: NaCl, MgO.

  • Covalent Bonding: Occurs between atoms with similar electronegativity; involves sharing of electrons, typically in s and p orbitals. Example: H2, diamond (C).

  • Metallic Bonding: Valence electrons are delocalized and form a 'sea of electrons' around positive metal ions (cores). Example: Cu, Fe, Al.

• Secondary (Van der Waals) Bonds:

  • Arise from interactions between dipoles (permanent or induced).

  • Weaker than primary bonds; important in polymers and molecular solids.

  • Special case: Hydrogen bonding (N, O, or F bonded to H).

Bonding Energy and Material Properties

The minimum in the energy vs. interatomic distance ($E$ vs $r$) curve represents several key material parameters:

• Melting Temperature ($T_m$): Higher bond energy generally means higher melting temperature.

• Equilibrium Interatomic Spacing ($r_0$): The distance at which attractive and repulsive forces balance.

• Thermal Expansion Coefficient ($\alpha$): Related to the asymmetry of the $E$ vs $r$ curve.

• Bonding Energy ($E_0$): Depth of the energy well; stronger bonds have larger $E_0$.

• Stiffness (Elastic Modulus): Related to the slope of the $E$ vs $r$ curve near $r_0$.

Equation: The net energy between two atoms as a function of distance $r$ is given by: $E(r) = E_A(r) + E_R(r)$ where $E_A$ is the attractive energy and $E_R$ is the repulsive energy.

Structure of Materials

Length Scales and Structural Hierarchy

Material structure can be described at different length scales, from subatomic to macro:

• Subatomic: Particles smaller than atoms (quarks, electrons).

• Atomic: Arrangement of atoms; determines chemical properties.

• Micro: Features visible under electron or probe microscopy (grain boundaries, defects).

• Meso: Intermediate structures (composites, clusters).

• Macro: Bulk properties and visible features.

Techniques: Particle accelerators, probe microscopy (AFM), electron microscopy, light microscopy are used to study structures at different scales.

Crystalline and Noncrystalline Solids

Atomic Arrangement

Solids can be classified based on the periodicity of atomic packing:

• Crystalline solids: Atoms are arranged in periodic, three-dimensional arrays. Typical of metals, many ceramics, and some polymers.

• Noncrystalline (amorphous) solids: Atoms lack long-range periodic packing. Occurs in complex structures or rapid cooling.

Example: Crystalline SiO2 vs. noncrystalline SiO2.

Metallic Crystal Structures

Dense Packing and Unit Cells

Metals tend to pack atoms densely to minimize empty space and lower bond energy. The arrangement is described using unit cells and lattices.

• Lattice: Array of points coinciding with atom positions.

• Unit cell: Smallest repeating entity representing the symmetry of the crystal structure.

• Lattice parameters: Dimensions and angles defining the unit cell.

Types of Cubic Crystal Structures

• Simple Cubic (SC):

  • Low packing density; rare (only polonium).

  • Atoms at cube corners.

  • Coordination number: 6.

  • Atomic Packing Factor (APF): $0.52$

  • Number of atoms/unit cell: 1

• Body-Centered Cubic (BCC):

  • Atoms at cube corners and one at the center.

  • Coordination number: 8.

  • APF: $0.68$

  • Number of atoms/unit cell: 2

  • Examples: Cr, W, Fe, Ta, Mo

• Face-Centered Cubic (FCC):

  • Atoms at cube corners and centers of each face.

  • Coordination number: 12.

  • APF: $0.74$

  • Number of atoms/unit cell: 4

  • Examples: Al, Cu, Au, Pb, Ni, Pt, Ag

Atomic Packing Factor (APF)

APF is the fraction of volume in a unit cell occupied by atoms, assuming hard spheres.

• Formula: $\text{APF} = \frac{\text{Volume of atoms in unit cell}}{\text{Volume of unit cell}}$

• SC: $0.52$

• BCC: $0.68$

• FCC: $0.74$

Summary Tables

Bonding Types and Properties

Bond Type	Bond Energy	Directionality	Examples
Ionic	Large	Nondirectional	Ceramics (NaCl, MgO)
Covalent	Variable (large in diamond)	Directional	Diamond, polymers
Metallic	Variable (large in tungsten)	Nondirectional	Metals (Cu, Fe, Al)
Van der Waals	Smallest	Directional	Polymers, molecular solids

Primary Bonds in Materials

Material Type	Bonding	Bond Energy	Melting Temp ($T_m$)	Elastic Modulus ($E$)	Thermal Expansion ($\alpha$)
Ceramics	Ionic & Covalent	Large	High	Large	Small
Metals	Metallic	Variable	Moderate	Moderate	Moderate
Polymers	Covalent & Secondary	Small	Low	Small	Large

Additional info: These tables summarize how bonding type affects key material properties such as melting temperature, stiffness, and thermal expansion.