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Materials Science Fundamentals: The Atom and Bonding

I. The Atom

  • Structure of the Atom:

    • Composed of a central nucleus containing protons (positively charged) and neutrons (no charge).

    • Electrons (negatively charged) orbit the nucleus.

  • Atomic Number (Z): Number of protons in the nucleus. It is the primary factor determining an element's chemical behavior.

  • Mass Number (A): Total number of protons and neutrons in the nucleus.

  • Atomic Weight: The mass of an atom, typically expressed in atomic mass units (amu).

  • Models of the Atom:

    • Bohr Model (a): Depicts electrons orbiting the nucleus in distinct, fixed energy levels or shells. It is a simplified model.

    • Wave-Mechanical Model (b): A more accurate model that describes electrons existing in probability distributions called orbitals rather than precise orbits. The probability of finding an electron is highest close to the nucleus and decreases with distance.

  • Atomic Orbitals (Subshells): Regions of space around the nucleus where electrons are most likely to be found.

    • s-orbitals: Spherical in shape (e.g., 1s, 2s, 3s). They can contain nodes (regions of zero electron probability).

    • p-orbitals: Dumbbell-shaped, oriented along the x, y, and z axes (Px, Py, P_z).

    • d-orbitals: More complex shapes, typically five per shell.

  • Shell/Subshell Options (Electron Configuration):

    • 1st Shell: 1s

    • 2nd Shell: 2s, 2p

    • 3rd Shell: 3s, 3p, 3d

    • 4th Shell: 4s, 4p, 4d, 4f

    • 5th Shell: 5s, 5p, 5d, 5f

    • 6th Shell: 6s, 6p, 6d, 6f

    • 7th Shell: 7s, 7p, 7d, 7f

  • Relative Energy of Electrons: Electrons fill orbitals from the lowest energy level to the highest. The general order is 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p, etc. (Refer to the elaborate energy diagram for exact order and overlaps).

  • Ground State: The lowest energy state that an atom's electrons can occupy.

  • Valence Electrons: The electrons in the outermost shell of an atom. These electrons are primarily involved in chemical bonding and largely determine an element's chemical properties.

  • Pauli Exclusion Principle: States that no two electrons in the same atom can have an identical set of four quantum numbers. This means each atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.

  • Quantum Numbers: A set of four numbers that describe the state of an electron in an atom.

    • Principal Quantum Number (n):

      • Defines the electron shell and its main energy level.

      • Values: 1, 2, 3, 4, …

      • Shell designations: K for n=1, L for n=2, M for n=3, N for n=4, etc.

    • Subsidiary (Angular Momentum) Quantum Number (l):

      • Defines the shape of the electron subshell (orbital type).

      • Values: 0, 1, 2, …, n-1

      • Corresponding orbital types: l=0 (s-orbital), l=1 (p-orbital), l=2 (d-orbital), l=3 (f-orbital).

    • Magnetic Quantum Number (m_l):

      • Defines the orientation of the orbital in space.

      • Values: -l, …, 0, …, +l

    • Spin Quantum Number (m_s):

      • Describes the intrinsic angular momentum (spin) of an electron.

      • Values: +1/2 or -1/2

  • Electron Configuration Filling Trick: A mnemonic (e.g., diagonal rule) can be used to remember the order in which subshells are filled: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

  • Periodic Table and Electronic Structure:

    • The periodic table organizes elements by increasing atomic number and electron configuration.

    • s-block: Elements where the outermost s-subshell is being filled (Groups 1 and 2).

    • p-block: Elements where the outermost p-subshell is being filled (Groups 13-18).

    • d-block (Transition Metals): Elements where (n-1)d subshells are being filled.

    • f-block (Inner Transition Metals): Elements where (n-2)f subshells are being filled.

    • This arrangement allows for the identification of valence electronic structure and prediction of chemical behavior.

  • Families of Elements: The periodic table categorizes elements into families with similar properties (e.g., alkali metals, halogens, noble gases, transition metals).

  • Electronegativity:

    • Definition: The relative electron-attracting power of an atom in a chemical bond.

    • Periodic Trend: Generally increases from left to right across a period and decreases from top to bottom down a group.

II. Bonding

  • Structure Determines Properties: The fundamental idea in materials science is that the micro- and macro-structure of a material directly dictates its properties.

    • Protons & Electrons: Determine the properties of an individual atom (mass, charge, stability).

    • Atom Valence Structure & Bonding Type: Influence the atomic arrangement, leading to specific electrical, magnetic, and crystal structures.

    • Atomic Arrangement: Ultimately determines the material's deformation properties (strength, hardness, stiffness, thermal expansion).

  • Bond Energy: The energy required to separate two atoms. It can be represented by the integral of the attractive force (F) over the interatomic separation (r): W = E = ext{integral of } F dr.

    • The bond energy is the depth of the potential energy well at the equilibrium interatomic separation (r_0).

Primary Bond Types

Occur due to strong interatomic forces and achieve stable electron configurations.

  • 1. Ionic Primary Bonding:

    • Mechanism: Involves the complete transfer of electrons from a metal (electropositive) to a non-metal (electronegative) atom. This creates oppositely charged ions (cations and anions) that are held together by strong electrostatic attraction.

    • Characteristics: Occurs between elements with a large difference in electronegativity.

    • Properties:

      • Highly specific (often directional due to charge interaction).

      • Electrically insulating (electrons are localized).

      • Generally hard, brittle, and possess high melting temperatures.

  • 2. Covalent Primary Bonding:

    • Mechanism: Involves the sharing of valence electrons between atoms, typically between two non-metal atoms with similar electronegativities. Each shared pair of electrons constitutes one covalent bond.

    • Properties:

      • Highly specific and directional (electrons are localized in specific bonds).

      • Electrically insulating (unless conjugated systems are present).

      • Fairly stiff and strong, on average.

      • High melting temperatures.

  • 3. Mixed Primary Bonding:

    • Most chemical bonds exhibit both ionic and covalent characteristics to some degree, meaning electrons are shared but not necessarily equally. The degree of ionic or covalent character depends on the electronegativity difference between the bonded atoms.

    • Only atoms with perfectly equal electronegativities will form a purely covalent (nonpolar) bond.

  • 4. Metallic Primary Bonding:

    • Mechanism: Characterized by a 'sea' or 'cloud' of delocalized valence electrons that are shared among all positively charged metallic ion cores within the lattice. The attraction between the delocalized electrons and the positive ion cores holds the metal together.

    • Properties:

      • Non-specific bonding scheme (non-directional, allows for atom shifting).

      • Loosely bound electrons are easily influenced, leading to high electrical and thermal conductivity.

      • Opaque to most electromagnetic radiation (free electrons absorb light).

Secondary Bonding (Van der Waals Forces)

Weaker intermolecular forces that arise from temporary or permanent charge imbalances (dipoles).

  • 1. Fluctuating Induced Dipole Bonds (London Dispersion Forces):

    • Mechanism: Even in non-polar molecules, temporary, instantaneous fluctuations in electron distribution can create a very short-lived dipole moment. This temporary dipole can then induce a temporary dipole in a neighboring atom, leading to a weak, short-lived attractive force.

    • These bonds are present in all types of molecules, but are the only intermolecular forces in non-polar molecules.

  • 2. Polar Molecule-Induced Dipole Bonds:

    • Mechanism: A molecule that possesses a permanent dipole (a polar molecule due to uneven electron distribution from electronegativity differences) can induce a temporary dipole in a neighboring non-polar molecule. This results in an attraction between the permanent and induced dipoles.

  • 3. Permanent Dipole Bonds (Dipole-Dipole Interactions):

    • Mechanism: Occur between two molecules that both have permanent dipole moments. The partially positive end of one polar molecule is attracted to the partially negative end of a neighboring polar molecule.

    • Example: Permanent dipoles in water (H_2O) molecules lead to attractions.

  • Special Case: Hydrogen Bonding:

    • A particularly strong type of permanent dipole-dipole interaction.

    • Conditions: Occurs when a hydrogen atom (which becomes significantly positive due to its low electronegativity) is covalently bonded to a highly electronegative and small atom: Oxygen (H-O), Fluorine (H-F), or Nitrogen (H-N).

    • Reasons for its exceptional strength:

      • a) Large Electronegativity Difference: The high electronegativity of O, F, or N pulls electron density away from hydrogen, leaving it with a substantial partial positive charge.

      • b) Small Atomic Size: The small size of O, F, and N atoms allows for a very close approach of the involved atoms, concentrating the charge and enabling a strong electrostatic attraction with the partially positive hydrogen of an adjacent molecule.

Comprehension Self-Test Objectives

  • Be able to determine the valence electron configuration for any given element (e.g., Zr (Atomic Number 40)).

  • Identify the most probable primary bond type between two elements (e.g., Cu-Zn).

  • Compare the electronegativity values of different elements (e.g., Bromine (Br) vs. Strontium (Sr)).

  • Predict which primary bond types allow for easy shifting of atoms within their bonding scheme (e.g., metallic bonds).

  • Identify which bonding schemes are likely to produce materials that are electrically and/or thermally insulating (e.g., ionic, covalent, secondary bonds).