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PS204 - Solid State Physics (2022) - Coggle Diagram
PS204 - Solid State Physics (2022)
Ionic/Covalent Bonding
Ionic Bonding:
Nature:
Transfer of electrons from one atom to another, resulting in the formation of ions.
Characteristics:
Electronegativity difference between atoms.
Formation of cations (positively charged) and anions (negatively charged).
Force:
Electrostatic attraction between oppositely charged ions.
Examples:
Sodium chloride (NaCl), potassium iodide (KI).
Covalent Bonding:
Nature:
Sharing of electron pairs between atoms.
Characteristics:
Similar electronegativity between atoms.
Formation of molecules or covalent networks.
Force:
Sharing of electrons leads to a stable electron configuration for both atoms.
Examples:
Hydrogen (H2), water (H2O), methane (CH4).
Key Differences:
Ionic Bonding:
Transfer of electrons.
Forms ions.
Typically between a metal and a non-metal.
Covalent Bonding:
Sharing of electrons.
Forms molecules or covalent networks.
Typically between non-metal atoms.
General Principle of X-ray Diffraction Analysis
X-ray Incident on Crystal:
Directed onto a crystalline solid.
Interaction with Crystal:
X-rays interact with electron cloud and nuclei of atoms in crystal lattice.
Scattering occurs due to wave interference.
Diffraction Pattern Formation:
Incident X-rays interfere constructively or destructively after scattering.
Results in a diffraction pattern.
Analysis of Diffraction Pattern:
Reveals information about arrangement of atoms in crystal.
Peaks correspond to specific crystallographic planes.
Examples
Broadband Radiation:
Example: Powder X-ray Diffraction (PXRD).
Principle: Uses a range of X-ray wavelengths.
Application: Identifying crystalline phases, determining crystal structure.
Monochromatic Radiation:
Example: Single Crystal X-ray Diffraction (SCXRD).
Principle: Uses a single X-ray wavelength.
Application: Determining precise atomic positions, molecular structures.
Models
Classical Dulong-Petit Model:
Predicts a constant molar specific heat capacity (Cv) for crystals at high temperatures.
Assumes each vibrational mode in the crystal lattice contributes kT/2 to the heat capacity, based on equipartition theorem.
Agrees well with experimental data at high temperatures but fails at low temperatures.
Einstein Model:
Treats atoms as independent harmonic oscillators.
Assumes all oscillators have the same frequency (Einstein frequency) and contribute equally to heat capacity.
Accurate at low temperatures but overestimates heat capacity at high temperatures.
Debye Model:
Treats atoms as part of a continuous elastic medium.
Considers the vibrational modes of the entire crystal lattice.
Introduces a characteristic frequency (Debye frequency) that varies with temperature.
Accurate at both low and high temperatures, capturing the temperature dependence of heat capacity.
Main Difference:
Classical Model: Predicts a constant heat capacity regardless of temperature.
Einstein and Debye Models: Account for temperature dependence of heat capacity due to varying vibrational modes.
Agreement:
Einstein and Debye models agree with the classical model at high temperatures when thermal energy is large enough to excite all vibrational modes.
Classical Drude Model vs. Quantum Mechanical Free Electron (Sommerfeld) Model:
Drude Model:
Classical model based on classical mechanics.
Assumes free electrons moving through a lattice of positively charged ions.
Electrons experience collisions with ions, leading to resistivity.
Sommerfeld Model:
Quantum mechanical model incorporating principles of quantum mechanics.
Treats electrons as quantum mechanical particles with wave-like properties.
Accounts for electron energy levels and quantization effects.
Improvements of Sommerfeld Model over Drude Model:
Quantum Mechanical Effects:
Sommerfeld model considers the wave-like nature of electrons.
Accounts for quantization of electron energy levels and Fermi-Dirac statistics.
Specific Improvements:
Energy Levels: Sommerfeld model includes discrete energy levels for electrons, unlike the continuous energy spectrum in the Drude model.
Temperature Dependence: Sommerfeld model explains temperature dependence of conductivity, including behavior at low temperatures (approaching absolute zero).
Magnetic Effects: Sommerfeld model can describe magnetoresistance and other magnetic phenomena due to its quantum mechanical foundation.