Solid State Physics: Crystal Structures, Phonons and Bands

solid state physics

1. structural Properties of physics

   • Crystal structures and inter atomic-bonding
     • Importance of solid state matter
     • Crystal structures
     • Crystal planes and Miller Indices
       • Miller indices form a notation system in crystallography for planes incrystal (Bravais) lattices. In particular, a family of lattice planes is determined by three integers h,k, and ℓ, the Miller indices. They are written (hkℓ), and each index denotes a plane orthogonal to a direction (h, k, ℓ) in the basis of thereciprocal lattice vectors. By convention, negative integers are written with a bar, as in 3 for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller index 100 represents a plane orthogonal to direction h; index 010 represents a plane orthogonal to direction k, and index 001 represents a plane orthogonal to ℓ.
   • Diffraction method and Crystal Structure Determination
     • Experimental method of X-ray diffraction
     • Electron Diffraction
       • Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interferencepattern. This phenomenon is commonly known as the wave–particle duality, which states that a particle of matter (in this case the incident electron) can be described as a wave. For this reason, an electron can be regarded as a wave much like sound or water waves. This technique is similar to X-ray and neutron diffraction. Electron diffraction is most frequently used in solid state physics and chemistry to study the crystal structure of solids. Experiments are usually performed in a transmission electron microscope (TEM), or a scanning electron microscope (SEM) as electron backscatter diffraction. In these instruments, electrons are accelerated by an electrostatic potential in order to gain the desired energy and determine their wavelength before they interact with the sample to be studied. The periodic structure of a crystalline solid acts as a diffraction grating, scattering the electrons in a predictable manner. Working back from the observed diffraction pattern, it may be possible to deduce the structure of the crystal producing the diffraction pattern. However, the technique is limited by the phase problem. Apart from the study of crystals i.e. electron crystallography, electron diffraction is also a useful technique to study the short range order of amorphous solids, and the geometry of gaseous molecules.
     • Neutron Diffraction
   • Lattice Vibration and Phonons
     • Bonding in solids
       • Solids can be classified according to the nature of the bonding between their atomic or molecular components. The traditional classification distinguishes four kinds of bonding:[1] Covalent bonding, which forms network covalent solids (sometimes called simply "covalent solids")Ionic bonding, which forms ionic solidsMetallic bonding, which forms metallic solidsWeak intermolecular bonding, which forms molecular solids (sometimes anomalously called "covalent solids") Typical members of these classes have distinctive electron distributions, [2] thermodynamic, electronic, and mechanical properties. In particular, the binding energies of these interactions vary widely. Bonding in solids can be of mixed or intermediate kinds, however, hence not all solids have the typical properties of a particular class, and some can be described as intermediate forms.
     • Cohesive energy of ionic crystal
     • Model inter atomic potential
   • Thermal Properties of Solids
     • Classical Theory
     • Einstein's Theory
     • 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.[1] 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 T3law. 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.

2. Electrical properties of solids

   • Models of Electrons in solids
     • Classical free electron theory of metals
     • Quantum free electron theory
     • Band theory of solids