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PS204 - Solid State Physics - Coggle Diagram
PS204 - Solid State Physics
General Principle of X-ray Diffraction Analysis:
X-ray Incident on Crystal:
X-rays directed onto a crystalline solid.
Interaction with Crystal:
X-rays interact with the electron cloud of atoms in the crystal.
Electrons in the atoms scatter X-rays.
Diffraction Pattern Formation:
Incident X-rays interfere constructively or destructively after scattering.
Results in a diffraction pattern.
Analysis of Diffraction Pattern:
Diffraction pattern reveals information about the arrangement of atoms in the crystal.
Peaks in the pattern correspond to specific crystallographic planes.
Relative Size of X-ray Wavelength and Interatomic Distances:
X-ray wavelength is typically similar to or smaller than interatomic distances in solids.
Allows for diffraction to occur due to the wave nature of X-rays.
Small wavelength enables resolution of atomic positions and crystal structure details.
Physics Behind Electron and Neutron Diffraction Studies:
Wave-particle Duality:
Both electrons and neutrons exhibit wave-like behavior, described by quantum mechanics.
Scattering by Crystal:
Electrons and neutrons interact with the electron cloud and nuclei of atoms in a crystal.
Scattering occurs due to wave interference.
Diffraction Pattern Formation:
Wave-like nature causes electrons and neutrons to diffract when interacting with crystal lattice.
Resultant diffraction pattern provides information about the crystal's structure.
Fundamental Feature from Quantum Mechanics:
Wave Function:
Wave function determines the diffraction pattern observed in electron and neutron diffraction studies.
Quantum mechanics predicts the behavior of particles with wave-like properties, such as electrons and neutrons.
Describes the probability amplitude of finding a particle at a certain position.
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.
Quantum Mechanical Features:
Wave-Particle Duality: Treats electrons as both particles and waves, crucial for understanding their behavior in a crystalline lattice.
Quantization: Incorporates quantization of energy levels, especially near absolute zero and at very small length scales.
Fermi-Dirac Statistics: Accounts for the distribution of electrons among energy levels at finite temperatures, essential for describing conductivity in metals accurately.
Improvements of Sommerfeld Model over Drude Model:
Specific Improvements:
Magnetic Effects: Sommerfeld model can describe magnetoresistance and other magnetic phenomena due to its quantum mechanical foundation.
Temperature Dependence: Sommerfeld model explains temperature dependence of conductivity, including behavior at low temperatures (approaching absolute zero).
Energy Levels: Sommerfeld model includes discrete energy levels for electrons, unlike the continuous energy spectrum in the Drude model.
Quantum Mechanical Effects:
Accounts for quantization of electron energy levels and Fermi-Dirac statistics.
Sommerfeld model considers the wave-like nature of electrons.
Superconductivity Phenomenon:
Complete absence of electrical resistance in certain materials when cooled below a critical temperature.
Key Features:
Zero Resistance:
Electric current flows without any loss of energy.
Critical Temperature (Tc):
Temperature below which a material becomes superconducting.
Above Tc, the material behaves like a normal conductor.
Meissner Effect:
Expulsion of magnetic field from the interior of a superconductor when it transitions to the superconducting state.
Magnetic field lines are pushed out, resulting in zero magnetic flux inside the superconductor.
Effects on Sample Resistivity:
Resistivity drops abruptly to zero below the critical temperature.
At temperatures above Tc, resistivity returns to normal levels characteristic of the material.
Significance:
Offers potentially revolutionary applications in power transmission, magnetic levitation, and sensitive instrumentation.
Allows for lossless transmission and storage of electrical energy.
Type I Superconductors:
Characteristics:
Exhibit a single critical temperature (Tc).
Expel magnetic field completely below Tc (Meissner effect).
Have a sharp transition from normal to superconducting state.
Magnetic Field Response:
Magnetic field penetration leads to complete expulsion (perfect diamagnetism).
Examples:
Pure metals like lead, aluminum.
Type II Superconductors:
Characteristics:
Characteristics:
Exhibit two critical magnetic fields (Hc1 and Hc2).
Tend to allow partial penetration of magnetic field below Hc1.
Can exist in a mixed state, with both normal and superconducting regions.
Magnetic Field Response:
Magnetic flux penetrates in the form of quantized vortices.
Examples:
High-temperature superconductors, such as yttrium barium copper oxide (YBCO).