Solid State Physics

Solid State Physics

1. Unit cell(Bravais lattice)

   • in 2D
     • 1.Oblique
     • 2.Rectangular
     • 3.Centered Rectangular
     • 4.Hexagonal
     • 5.Square
   • In 3D
     • 1.Simple cubic
     • 2.FCC
     • 3.BCC
     • 4.Tetragonnal
     • 5.Orthorhombic
     • 6.Hexagonal
     • 7.monoclinic
     • 8.Triclinic

2. Crystal Structures

   • Packing Factor
     • P.F=volume of the atom/volume of the cell
     • P.F=volume of the atom/volume of the cell
   • Simple cubic(NaCl)
     • packing factor=0.52
   • BCC structure(CsCl)
     • packing factor=0.68
   • FCC structure(Pervoskite)
     • packing factor=0.74

3. Crystal Planes and Miler Indices

4. Diffraction patterns

   • X-Ray Diffraction
     • 2*dsin(theeta)=n*lamda
   • Electron Diffraction
   • Neutron Diffraction

5. Lattice vibrations and Phonons

   • Phonons
     • In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids
   • Inter-atomic Potential
   • cohesive Energy of ionic Crystals
   • Cohesive Energy of Van der waals solids

6. Thermal Properties of Solids

   • Classical Theory
     • Dulong–Petit law in modern terms is that, regardless of the nature of the substance or crystal, the specific heat capacity c of a solid substance (measured in joule per kelvin per kilogram) is equal to 3R/M, whereR is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole). Thus, the heat capacity per mole of many solids is 3R.
   • Einstein's Theory
     • The Einstein solid is a model of a solid based on two assumptions: Each atom in the lattice is an independent 3D quantum harmonic oscillatorAll atoms oscillate with the same frequency (contrast with the Debye model) While the assumption that a solid has independent oscillations is very accurate, these oscillations are sound waves or phonons, collective modes involving many atoms. In the Einstein model, each atom oscillates independently
   • Debye Theory
     • In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid.It treats the vibrations of theatomic lattice (heat) as phonons in a box, in contrast to the Einstein model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low temperature dependence of the heat capacity, which is proportional to  – the Debye T^3 law. Just like the Einstein model, it also recovers the Dulong–Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures

7. Models of electrons in Solids

   • Classical Free electron Theory
     • The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). The model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions. The two most significant results of the Drude model are an electronic equation of motion,
   • Quantum Free electron Theory
     • This has a Quantum approach As in the Drude model, valence electrons are assumed to be completely detached from their ions (forming an electron gas). As in an ideal gas, electron-electron interactions are completely neglected. The electrostatic fields in metals are weak because of the screening effect. The crystal lattice is not explicitly taken into account. A quantum-mechanical justification is given by Bloch's Theorem: an unbound electron moves in a periodic potential as a free electron in vacuum, except for the electron mass m becoming aneffective mass m* which may deviate considerably from m (one can even use negative effective mass to describe conduction by electron holes). Effective masses can be derived from band structure computations. While the static lattice does not hinder the motion of the electrons, electrons can be scattered by impurities and by phonons; these two interactions determine electrical and thermal conductivity
   • Band Theory of Solids
     • A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically. An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties

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