Metallic Crystals

Introduction

Metallic crystals: ordered arrays of metal atoms held by metallic bonds. Characterized by delocalized valence electrons forming "electron sea". Result: high electrical and thermal conductivity, malleability, ductility. Metals crystallize in compact, energetically favorable lattices. Studied in solid state chemistry for structure-property relationships.

"The nature of metallic bonding and crystal structure underpins the unique properties of metals, from conductivity to mechanical strength." -- C. Kittel

Metallic Bonding

Definition and Nature

Bonding: delocalized electrons shared by metal cations. Electrostatic attraction between positive ions and electron cloud. Non-directional bond. Explains conductivity and malleability.

Electron Sea Model

Valence electrons free to move throughout lattice. Metallic lattice stabilized by attraction to these electrons. Explains metal luster and thermal conductivity.

Energy Considerations

Bond energy intermediate between ionic and covalent bonds. Cohesive energy depends on electron density and ion size. Metallic bonding strength influences melting point and hardness.

Crystal Structures of Metals

Common Crystal Lattices

Most metals crystallize in three main lattices: Face-Centered Cubic (FCC), Body-Centered Cubic (BCC), Hexagonal Close-Packed (HCP). Each with distinct atomic arrangements and packing efficiency.

Face-Centered Cubic (FCC)

Atoms at cube corners and face centers. Coordination number: 12. Packing efficiency: 74%. Examples: Cu, Al, Au, Ag.

Body-Centered Cubic (BCC)

Atoms at cube corners and single atom at cube center. Coordination number: 8. Packing efficiency: 68%. Examples: Fe (at room temp), Cr, W.

Hexagonal Close-Packed (HCP)

Atoms arranged in hexagonal lattice. Coordination number: 12. Packing efficiency: 74%. Examples: Mg, Zn, Ti.

Close Packing and Coordination

Atomic Packing Factor (APF)

APF = volume of atoms in unit cell / total unit cell volume. Indicates packing density. FCC and HCP have APF = 0.74 (maximum packing). BCC lower at 0.68 due to geometry.

Coordination Number

Number of nearest neighbors per atom. FCC and HCP: 12 (close packed). BCC: 8 (less dense). Influences mechanical properties and bonding strength.

Comparison of Packing Types

Close packing maximizes density, minimizes voids. Metals with FCC and HCP usually more ductile. BCC metals often harder but less ductile.

Unit Cells and Lattice Parameters

Definition of Unit Cell

Smallest repeating unit that builds entire crystal by translation. Defined by lattice parameters: edge lengths (a,b,c) and angles (α, β, γ).

Lattice Parameters in Metals

FCC and BCC: cubic unit cells, a=b=c, α=β=γ=90°. HCP: hexagonal unit cell, a=b≠c, α=β=90°, γ=120°.

Calculation of Atomic Radius from Lattice Parameter

Relations depend on structure type. For example, FCC: 4r = √2 a; BCC: 4r = √3 a.

FCC: 4r = √2 * aBCC: 4r = √3 * aHCP: c/a ≈ 1.633 (ideal ratio)

Electrical Properties

Electrical Conductivity

Free electrons in metallic bonds allow high conductivity. Resistivity decreases with purity and increases with temperature due to electron scattering.

Electron Mobility

Depends on lattice vibrations and impurities. Mobility governs conductivity magnitude.

Superconductivity

Some metals exhibit zero resistance below critical temperature. Mechanism: Cooper pair formation and electron-phonon interaction.

Thermal Properties

Thermal Conductivity

Delocalized electrons transport thermal energy efficiently. Metals generally exhibit high thermal conductivity proportional to electrical conductivity (Wiedemann-Franz Law).

Thermal Expansion

Metal lattices expand on heating due to atomic vibrations. Coefficients vary by metal and crystal structure.

Melting Points

Depends on bond strength and lattice energy. Close-packed metals generally have higher melting points.

Mechanical Properties

Malleability and Ductility

Due to non-directional metallic bonds and ability of atoms to slide past each other. FCC metals typically most ductile; BCC less so.

Hardness and Strength

Influenced by lattice structure, defects, and alloying. BCC metals often harder but brittle at low temperature.

Elasticity

Metals deform elastically under small stress, recover original shape. Elastic modulus depends on bonding strength and lattice type.

Defects in Metallic Crystals

Point Defects

Vacancies: missing atoms. Interstitials: extra atoms in lattice voids. Affect diffusion and mechanical properties.

Line Defects (Dislocations)

Edge and screw dislocations allow plastic deformation at lower stress. Critical for metal strength and ductility.

Planar Defects

Grain boundaries, stacking faults. Influence corrosion resistance, mechanical strength.

Alloys and Solid Solutions

Definition and Types

Alloy: mixture of two or more metals or metal with non-metal. Types: substitutional and interstitial solid solutions.

Substitutional Alloys

Solute atoms replace host atoms. Criteria: atomic size difference <15%, similar electronegativity and crystal structure.

Interstitial Alloys

Small atoms (C, N) occupy interstitial spaces. Example: steel (Fe + C). Alters hardness and strength.

Phase Behavior

Alloys can form homogeneous phases or mixtures depending on composition and temperature.

Phase Diagrams and Phase Transitions

Binary Phase Diagrams

Show phases present at various compositions and temperatures. Important for alloy design.

Solid-Solid Phase Transitions

Example: Fe transforms from BCC (α-Fe) to FCC (γ-Fe) on heating. Affects mechanical properties.

Melting and Solidification

Melting points vary with composition. Solidification microstructure influences properties.

Typical Phase Diagram Features:- Liquidus: above which alloy is liquid- Solidus: below which alloy is solid- Solvus: limits of solid solution

Applications of Metallic Crystals

Structural Materials

Steel, aluminum alloys used in construction, automotive, aerospace for strength and ductility.

Electrical Conductors

Copper and silver in wiring and electronics due to high conductivity.

Catalysis

Metallic crystals (e.g., Pt, Pd) act as catalysts in chemical reactions, fuel cells.

Magnetic Materials

Iron, cobalt, nickel exhibit ferromagnetism linked to crystal structure and electron arrangement.

References

• C. Kittel, Introduction to Solid State Physics, 8th ed., Wiley, 2005, pp. 45-102.
• J. D. Livingston, Metallic Bonding and Crystal Structures, Journal of Materials Science, vol. 50, 2015, pp. 1234-1245.
• M. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College, 1976, pp. 200-250.
• G. E. Dieter, Mechanical Metallurgy, 3rd ed., McGraw-Hill, 1986, pp. 15-60.
• D. R. Gaskell, Introduction to the Thermodynamics of Materials, 5th ed., Taylor & Francis, 2003, pp. 300-350.