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PS204 - Solid State Physics (2022R) - Coggle Diagram
PS204 - Solid State Physics (2022R)
General Features of Bonding in Solids
Attractive Forces:
Hold atoms together in a solid.
Ionic Bonds:
Attraction: Electrostatic attraction between oppositely charged ions.
Nature: Typically occurs between a metal and a non-metal, where one atom loses electrons (cation) and another gains electrons (anion).
Covalent Bonds:
Attraction: Sharing of electron pairs between atoms.
Nature: Typically occurs between non-metal atoms, where electrons are shared to achieve a stable electron configuration.
Repulsive Forces
Act to keep atoms apart due to electron-electron repulsion and Pauli exclusion principle.
Equilibrium Separation:
The distance at which attractive and repulsive forces balance out, determining the stable atomic arrangement in a solid.
Binding Energy
Energy required to separate atoms from each other completely, indicating the strength of the bond.
Physical Processes:
Van der Waals Forces:
Dominant interaction between closed outer shell atoms.
Weak attractive forces between atoms due to temporary fluctuations in electron distributions.
London Dispersion Forces:
Type of Van der Waals force.
Arises from temporary fluctuations in electron distribution.
Induces temporary dipoles in neighboring atoms.
Close Packing:
Atoms arrange themselves in a close-packed structure to maximize Van der Waals interactions.
In solid argon, atoms pack closely to maximize these weak forces, resulting in a stable solid structure.
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.
Thermal Expansion
Vibrational Motion:
Atoms in a solid lattice are constantly in motion, vibrating about their equilibrium positions.
These vibrations are due to the thermal energy present in the solid, causing atoms to oscillate back and forth.
Increased Temperature:
When the temperature of the solid increases, the average kinetic energy of the atoms also increases.
This leads to an increase in the amplitude of the atomic vibrations.
Effect on Lattice Structure:
As the atoms vibrate with greater amplitude, they tend to push against their neighboring atoms.
This results in a slight increase in the average separation between atoms in the lattice.
Expansion Phenomenon:
The increase in average atomic separation leads to an expansion of the overall solid volume.
This expansion is observed as an increase in the dimensions of the solid in all directions.
Magnetic Ordering Behaviour
Exchange Interaction:
Definition:
Arises due to the overlap of electron wave functions and the Pauli exclusion principle.
Quantum mechanical effect describing the interaction between neighboring magnetic moments in a material.
Concept:
Electrons in adjacent atoms or ions influence each other's spins.
Leads to alignment or anti-alignment of neighboring magnetic moments depending on the strength and sign of the exchange interaction.
Context of Ferromagnetism
Definition:
Exchange interaction is a quantum mechanical effect that influences the alignment of magnetic moments in ferromagnetic materials.
It arises due to the interaction of the spin and orbital angular momentum of electrons in adjacent atoms or ions.
Mechanism:
In ferromagnetic materials, adjacent atoms have aligned magnetic moments due to the exchange interaction.
When atoms are close together, the exchange interaction leads to a lower energy state when the magnetic moments of neighboring atoms are parallel (aligned in the same direction).
This alignment is favored energetically, leading to the formation of magnetic domains with aligned magnetic moments.
Contribution to Ferromagnetism:
The exchange interaction is responsible for the spontaneous magnetization observed in ferromagnetic materials at low temperatures.
It promotes the alignment of magnetic moments, resulting in a net magnetic moment even in the absence of an external magnetic field.
Role in Magnetic Domains:
Exchange interaction also plays a crucial role in the formation and stability of magnetic domains in ferromagnetic materials.
Within each domain, the exchange interaction aligns the magnetic moments, while the boundaries between domains, known as domain walls, involve a reorientation of magnetic moments to minimize the exchange energy.
Types
Ferromagnetic:
Definition: Adjacent magnetic moments align parallel to each other.
Result: Strong net magnetization even in the absence of an external magnetic field.
Example: Iron, cobalt, nickel.
Antiferromagnetic:
Definition: Adjacent magnetic moments align antiparallel to each other.
Result: Net magnetic moment is zero, but there is magnetic ordering.
Example: Manganese oxide (MnO).
Ferrimagnetic:
Definition: Similar to antiferromagnetic, but with unequal magnitudes of magnetic moments.
Result: Net magnetic moment exists due to unequal cancellation of moments.
Example: Magnetite (Fe3O4).