Osm Physics by Ashish

Nanoscale Dimensions and Properties 1.3.3 How nanoscale dimensions affect properties Many properties are continuously modified as a function of system size. Often these are extrinsic properties, such as resistance, which depend on the exact size and shape of the specimen. Other properties depend critically on the microstructure of the material; for example, the Hall–Petch equation for yield strength, σ, of a material as a function of average grain size (d) is given by \[ \sigma = k(d)^{-1/2} + \sigma_0 \] where k and σ 0 are constants. Intrinsic materials properties, such as resistivity, should be independent of specimen size, however, even many of the intrinsic properties of matter at the nanoscale are not necessarily predictable from those observed at larger scales. As discussed above this is because totally new phenomena can emerge, such as: Quantum size confinement leading to changes in electronic structure The presence of wave-like transp...

Effects of the Nanometre Length Scale When the size of a material is reduced to the nanometre scale (1–100 nm) , its physical and electronic properties change significantly. These changes mainly occur due to quantum confinement effects , which influence the energy band structure and atomic arrangement of the material.  At very small dimensions, electrons are confined within a limited space. This confinement alters the density of electronic states and changes the behaviour of electrons compared with those in bulk materials. Changes to the System Total Energy According to the free electron model , the energy of electronic states is inversely proportional to the square of the system dimension (1/L²), where L represents the size of the system . As the system size decreases, the spacing between energy levels increases. In bulk materials, atoms form closely spaced molecular orbitals and energy bands , but when the number of atoms decreases in nanoscale systems, these energy levels beco...

Electronic Conduction in Solids Electronic Conduction in Solids 1. Introduction Electronic conduction refers to the movement of electrons through a solid material when an external electric field or voltage is applied. The ability of a material to conduct electricity depends mainly on its electronic band structure and the availability of empty energy states for electrons to move into. In crystalline solids, electrons occupy specific energy bands that arise from the interaction of atomic orbitals in the periodic crystal lattice. 2. Allowed Energy States In a crystal lattice, electrons are described using wave vectors (k-values). The allowed k-values extend up to the edges of the Brillouin zone . Each allowed k-state can contain two electrons. The two electrons must have opposite spin (spin-up and spin-down). If a crystal contains N unit cells, each energy band contains 2N states . In three-dimensional crystals, the total number of states...

Free Electron Model and Energy Bands Free Electron Model and Energy Bands Free Electron Model An alternative approach to understanding the electronic band structure of solids is to consider electron waves in a periodic crystalline potential. The Drude–Lorentz free electron model treats a metallic solid as a lattice of positive ions surrounded by free electrons. This model explains:High electrical conductivity, High thermal conductivity, Optical reflectivity, Ductility and, Alloy formation In a more accurate description electrons are treated quantum mechanically. Here the free valence electrons are assumed to be constrained within a potential well which essentially stops them from leaving the metal (the ‘particle-in-a-box’ model). Particle in a Box Model Electrons are assumed to move inside a potential well (particle-in-a-box model). Allowed wavelengths: \[ \lambda_n = \frac{2L}{n} \] Wave vector: \[ k_n = \frac{2\pi}{\lambda} \] \[ k_n = \fr...

  Restoring Force  Definition:  A restoring force is the force that acts to bring a displaced system back to its equilibrium position. It is directly proportional to the displacement. Where k is constant and Negative sign presenting that restoring force is opposite to displacement.   2.     2. Damping Force Definition: A damping force is the resistive force that opposes the motion of an oscillating body. It reduces the amplitude of oscillation with time. Origin: friction, air resistance, viscous drag, etc. It is directly proportional to the velocity. Where λ is damping constant and negative sign → damping force always acts opposite to velocity.   3.      3. Equation of Motion for Damped Oscillator

Dispersion Relation in Bands  

Optical Fibre, Optics, Total internal reflection, Types of fibres, Step and Gradient optical fibre