Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate ↓


Solid state physics


Solid state physics is the study of how atoms are arranged in solids and what properties those solids exhibit as a result of their atomic arrangement. This fundamental field of physics attempts to explain how the macroscopic properties of a solid arise from its microscopic components. Many modern technological advances, such as semiconductors, lasers, and magnetic materials, are based on the principles of solid state physics.

Structure of solids

One of the first things to understand about solids is their structure. When atoms come together to form solids, they often arrange themselves in an orderly pattern called a crystal lattice.

A crystal lattice can be thought of as a three-dimensional arrangement of atoms, ions, or molecules that occurs in a repeating pattern. The smallest repeating unit, often called a parallelepiped, is known as a unit cell. Some common types of unit cells are as follows:

  • Cube: All sides of a cube are equal, and all angles are 90 degrees.
  • Quadrilateral: Two sides are equal, and the angles are 90 degrees.
  • Orthorhombic: All sides are unequal, but the angles are 90 degrees.
Cube

Binding forces in solids

The type of chemical bond that holds the lattice together can significantly affect the properties of a solid. There are several types of bond:

  • Ionic bond: attraction between positive and negative ions. Example: sodium chloride (NaCl).
  • Covalent bonding: shared pairs of electrons between atoms. Example: diamond.
  • Metallic bond: Electrons are free to move around in a "sea of electrons." Example: copper.
  • Van der Waals force: Weak force due to permanent or induced dipoles. Example: graphite.

Thermal properties of solids

Since temperature affects the vibration of atoms, it significantly affects the thermal expansion, heat capacity, and other thermal properties of solids.

The specific heat of a solid is related to the energy needed to raise its temperature. An important model for describing the specific heat of solids is the Dulong-Petit law. It approximates the molar heat capacity of many solids as 3R, where R is the ideal gas constant.

Electrical and magnetic properties

Solids are classified into conductors, insulators, and semiconductors based on their electrical conductivity. This classification relies heavily on the electronic band structure, which describes the energy levels that electrons are allowed to occupy in a solid.

Ohm's law is important in understanding electrical conduction:

V = IR

This equation relates voltage V, current I, and resistance R

Band theory of solids

Band theory explains the nature of electrical conductors, insulators and semiconductors. According to this theory, the electron energy levels in a solid are not clearly defined like those in an atom but are spread over continuous bands.

  • Conduction band: The higher energy band in which electrons are free to conduct electricity.
  • Valence band: Energy band filled with valence electrons.
  • Band gap: The difference in energy between the conduction band and the valence band. Large band gaps are characteristic of insulators, small or no gaps are characteristic of conductors, and intermediate band gaps are characteristic of semiconductors.
band gap conduction band valence band

Semiconductors

Semiconductors have had a significant impact on modern technology. They have electrical conductivity between metals and insulators. Their conductivity can be controlled by adding impurities through a process called doping.

  • N-type: Extra electrons are added to the structure. This is usually done by adding elements such as phosphorus or arsenic.
  • p-type: holes (absence of electrons) are formed by adding elements such as boron or gallium.

Magnetic properties of solids

The magnetic properties of solids are determined by the magnetic moments of the atoms and the order of these moments. There are different types of magnetic order:

  • Diamagnetism: All electron spins are paired, and the solid is weakly repelled by a magnetic field.
  • Paramagnetism: A solid material is weakly attracted to a magnetic field due to some unpaired electron spins.
  • Ferromagnetism: The spins are aligned parallel in a large domain, creating a strong net magnetic field. Example: Iron.
  • Antiferromagnetism: adjacent spins are aligned antiparallel, cancelling each other out. Example: manganese oxide.

Superconductivity

Finally, superconductivity is a phenomenon in which a material exhibits zero electrical resistance below a certain critical temperature. This allows the free and unhindered flow of electrons.

Josephson effect: Quantum mechanical phenomenon in which current can flow between two superconductors separated by a thin insulating layer.


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Solid state physics

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