ionic, covalent bonds

Page 1: Course Overview

PHY2024: Principles of Materials and Solid-State Physics

• Focus on Ionic and Covalent Bonds.

Page 2: Review Concepts

Key Topics Include:

• Crystal Unit Cells: Fundamental building block of crystalline materials, representing the smallest repeating unit which fully describes the symmetry and structure of the lattice.

• Crystal Planes: Flat surfaces that cut through the crystal lattice; described using Miller indices (hkl).

• Reciprocal Space: A mathematical construct used to analyze wave diffraction patterns, important for evaluating the arrangements of atoms in a crystal.

• Diffraction Pattern: Graph presents intensity variation with respect to the angle 2θ, which provides information about the atomic structure from the interference patterns.

Page 3: Outline for Bonds

Different Types of Bonds Discussed:

• Ionic Bonds: Formed through the transfer of electrons, leading to the formation of ions.

  • Binding Energy: Calculated as the energy needed to separate an ionic pair.

  • Madelung Constant: A dimensionless quantity representing the energy of interaction of an ion in a lattice, an essential part of calculating lattice energy.

• Covalent Bonds: Formed from shared pairs of electrons with a focus on hybridization of atomic orbitals.

• Metallic Bonds: Involves a sea of delocalized electrons among a lattice of metal atoms, contributing to electrical conductivity.

• Van der Waals Bonds: Weak intermolecular forces important in molecular interactions.

• Hydrogen Bonds: Special type of dipole-dipole attraction occurring when hydrogen is bonded to highly electronegative atoms.

Page 4: Valence Electrons

Importance of Valence Electrons in Bonding:

• Valence Electrons: Electrons in the outer shell that participate in chemical bonding.

• Distinction between Valence and Core Electrons: Core electrons do not participate in bonding, playing a crucial role in determining the chemical properties of elements.

Page 5: Interatomic Potential

Understanding Interatomic Potential:

• Strong Repulsion at Short Distances: Governed by the Pauli exclusion principle and encapsulated in potential energy formulas.

• Formula for Potential Energy:[ \phi(r) = - \frac{A}{r^m} + \frac{B}{r^n} ]where ( A ) and ( B ) are constants, ( m ) and ( n ) are generally integers determined experimentally.

Page 6: Ionic Bond Qualities

Ionic Bonds

• Electrons are transferred between atoms resulting in the formation of cations and anions.

• Characteristic Properties:

  • Hardness and high melting temperature due to strong ionic attractions.

  • Solubility in water, governed by lattice energy versus hydration energy.

  • Electrical insulation unless in a molten or dissolved state.

Page 7: Electronegativity

Electronegativity Values Affect Ionic Bond Formation:

• Electron transfer occurs from atoms with lower electronegativity to those with higher.

• Example Values:

  • Na: 0.93, Cl: 3.16

  • Mg: 1.31, O: 3.44

  • Ga: 1.81, N: 3.04

Page 8: Potential Energy of Ion Pairs

Potential Energy Formulation:

[ \phi(r) = - \frac{e^2}{4\pi \epsilon_0 r} + \frac{B}{r^n} ]

• Key Concepts:

  • Equilibrium Distance (r₀): This is the distance at which the potential energy is minimized, signifying optimal ionic separation.

  • Binding Energy: ( E_B = -\phi(r_0) ); it indicates the energy required to dissociate an ionic bond.

  • Born Exponent (n): Ranges between 6 and 10; it indicates how rapidly the potential energy increases as ions approach each other.

Page 9: Binding Energy Derivation

Steps to Derive Binding Energy Expression:

1. Determine value of ( B ) from empirical data.

2. Substitute ( B ) into the derived potential energy formula.

3. Simplification leads to ( E_B = -\phi(r_0) ).

Page 10: Binding Energy Calculations

Formula:

[ E_B = k \frac{e^2}{r_0^{n-1}} ]

• Details:

  • The binding energy approach assesses relationships of forces at equilibrium and incorporates potential energy derivatives with respect to the bond length (r₀).

Page 11: Binding Energy Example

Example Calculation for NaCl:

• Given (r₀ = 0.285 nm) and (n = 9).

• Result: ( E_B = 7.2 × 10^{-19} J ) or ( 4.5 eV ).

Page 12: Ionic Bond Characteristics

Concepts:

• Ionization Energy: The energy necessary to remove an electron from an atom.

• Electron Affinity: The energy change resulting from adding an electron to a neutral atom.

• Cohesive Energy: Represents the energy difference between solid and isolated atoms; example value of cohesive energy: ( 6.4 eV ).

Page 13: Electrostatic Energy in Ion Chains

Energy Calculations:

• Involves both attractive and repulsive forces acting on ions in a chain:

  • Attraction from neighboring Na ions enhances stability.

  • Repulsion from neighboring Cl ions impacts energy dynamics significantly.

Page 14: Continued Ion Electrostatics

Analyzing Combined Energy Contributions:

• Consider further neighboring ions to assess total energy interactions in chains.

Page 15: Total Energy for Anion

Deriving Total Energy for a Cl Anion:

• Evaluate interactions with neighboring Na and Cl ions, expanding energy terms using Maclaurin series for a more detailed understanding of the energy landscape.

Page 16: Madelung Constant

Definition and Significance:

• Madelung Constant: A number that quantifies the net electrostatic interaction energy of ions in a crystal structure, varying by lattice configurations (e.g., NaCl, CsCl).

  • Calculation of binding energy incorporates the Madelung constant, adding precision in ionic energy evaluations.

Page 17: Covalent Bond Characteristics

Properties of Covalent Bonds:

• Electrons are shared; bonds can be classified as polar or non-polar depending on the electronegativity of constituent atoms.

• High melting points; many are insoluble in water due to strong bonds and lack of free mobility of electrons.

• Brittleness and possibility of exhibiting semiconducting properties.

Page 18: Carbon Structure

Examples of Covalent Bonds in Carbon:

• Diamond: Features sp³ hybridization with tetrahedral geometry resulting in strong covalent bonds, making it exceptionally hard.

• Graphite: Sp² hybridization leads to a layered structure; while within layers bonds are strong, interlayer bonds are weak allowing for laminar slip and conductivity.

Page 19: Hybridisation Concept

Definition of Hybridization:

• The mixing of atomic orbitals leading to improved orbital overlap during bonding, thus enhancing bond strength and stability.

Page 20: Types of Hybridization

Different Hybridization Types:

• sp hybridization: 180° bond angle, linear geometrical configuration.

• sp² hybridization: 120° bond angle, trigonal planar shape.

• sp³ hybridization: 109.5° bond angle, tetrahedral arrangement.

Page 21: Hybridisation in Structures

Hybridisation in Diamond and Graphite:

• Diamond's Strength: The 3D tetrahedral structure instantiated via sp³ hybridization provides immense strength.

• Graphite's Structure: Layered structure arising from sp² hybridization showcasing different bond strengths between layers.

Page 22: Ionic vs Covalent Character in Compounds

Percent Ionic Character:

• Determines the degree to which a compound behaves as ionic versus covalent; calculations based on electronegativity differences provide crucial insights into bonding characteristics.

Page 23: Key Takeaways

Summary of Important Aspects:

• Descriptions of ionic and covalent bonds alongside energy considerations fundamentally influence the properties and behaviors of materials.

Page 24: Suggested Reading

References for Further Study:

• Hofmann, Solid State Physics An Introduction, Ch 2

• Callister, Materials Science and Engineering, Ch 2

• Simon, The Oxford Solid State Basics, Ch 6

• Kittel, Introduction to Solid State Physics, Ch 3

Page 25: Reflections

Engagement with Concepts:

• Areas of uncertainty and interest for further exploration and study, particularly in the context of practical applications of ionic and covalent bonding in materials science.