Physics of Advanced Materials (DBATU Sem

Cheatsheet Content

1. Crystal Structure & Defects Q: Define crystal lattice, unit cell, and basis. A: Crystal lattice is a periodic arrangement of points in space. Unit cell is the smallest repeating unit of the lattice. Basis is the atom or group of atoms associated with each lattice point. Q: Explain Bravais lattices and common crystal systems. A: There are 14 Bravais lattices, which are distinct lattice types that fill space. Common crystal systems include cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic. Q: What are Miller Indices? How are they determined? A: Miller Indices $(hkl)$ are a notation system for crystallographic planes and directions. To determine: find intercepts, take reciprocals, clear fractions. Q: Differentiate between point, line, and surface defects in crystals. A: Point defects (vacancies, interstitials, impurities) are localized to a single lattice site. Line defects (dislocations) are one-dimensional. Surface defects (grain boundaries, free surfaces) are two-dimensional. Q: Explain Schottky and Frenkel defects with examples. A: Schottky defect : a pair of cation and anion vacancies to maintain charge neutrality (e.g., NaCl). Frenkel defect : an ion leaves its lattice site and occupies an interstitial position (e.g., AgBr). 2. Electrical Properties of Materials Q: What is the band theory of solids? Explain conductors, semiconductors, and insulators. A: Band theory describes electron energy levels in solids forming bands. Conductors have overlapping valence and conduction bands. Semiconductors have a small band gap. Insulators have a large band gap. Q: Define intrinsic and extrinsic semiconductors. Explain n-type and p-type doping. A: Intrinsic : pure semiconductor (e.g., Si, Ge). Extrinsic : doped semiconductor. n-type : doped with donor impurities (e.g., P in Si), increasing electron concentration. p-type : doped with acceptor impurities (e.g., B in Si), increasing hole concentration. Q: What is Hall Effect? How is it used to determine carrier concentration and mobility? A: The development of a transverse voltage (Hall voltage) across a current-carrying conductor placed in a magnetic field. It helps determine the sign and concentration of charge carriers and their mobility. Q: Explain superconductivity and its key properties (Meissner effect, critical temperature). A: Superconductivity is a phenomenon where certain materials exhibit zero electrical resistance and expel magnetic fields ( Meissner effect ) below a characteristic critical temperature ($T_c$) . Q: Differentiate between Type-I and Type-II superconductors. A: Type-I : Sharp transition to superconductivity, complete Meissner effect, single critical magnetic field ($H_c$). Type-II : Gradual transition, two critical fields ($H_{c1}$, $H_{c2}$), partial flux penetration in mixed state. 3. Magnetic Properties of Materials Q: Define magnetic susceptibility, permeability, and magnetization. A: Magnetic susceptibility ($\chi$) : degree of magnetization of a material in response to an applied magnetic field. Permeability ($\mu$) : measure of the material's ability to support the formation of a magnetic field within itself. Magnetization ($\vec{M}$) : magnetic moment per unit volume. Q: Explain diamagnetism, paramagnetism, and ferromagnetism. Give examples. A: Diamagnetism : weakly repelled by magnetic fields (e.g., Cu, water). Paramagnetism : weakly attracted (e.g., Al, Pt). Ferromagnetism : strongly attracted, retains magnetization (e.g., Fe, Ni, Co). Q: What is magnetic hysteresis? Differentiate between hard and soft magnetic materials. A: Hysteresis is the lagging of magnetization behind the applied magnetic field. Hard magnetic materials have large coercivity and retentivity (permanent magnets). Soft magnetic materials have small coercivity and retentivity (transformers). Q: What are magnetic domains? How do they explain ferromagnetism? A: Regions within a ferromagnetic material where magnetic moments are aligned. In an unmagnetized state, domains are randomly oriented. Applied field causes domain growth and rotation, leading to net magnetization. 4. Dielectric & Optical Properties Q: Define dielectric constant, dielectric loss, and dielectric strength. A: Dielectric constant ($\epsilon_r$) : ratio of permittivity of material to permittivity of free space. Dielectric loss : energy dissipated as heat in a dielectric material under AC field. Dielectric strength : maximum electric field a material can withstand without breakdown. Q: Explain different types of polarization in dielectrics (electronic, ionic, orientational, space charge). A: Electronic : displacement of electron clouds. Ionic : displacement of ions. Orientational : alignment of permanent dipoles. Space charge : accumulation of charges at interfaces. Q: What are ferroelectric materials? Give examples and applications. A: Materials exhibiting spontaneous electric polarization that can be reversed by an external electric field (e.g., BaTiO$_3$). Used in capacitors, memory devices, sensors. Q: Explain the principle of stimulated emission and population inversion in lasers. A: Stimulated emission : an excited electron is stimulated to emit a photon identical to the incident photon. Population inversion : more electrons in an excited state than in a lower energy state, necessary for laser action. Q: Describe the working of a Ruby laser. A: A three-level solid-state laser. Cr$^{3+}$ ions in Al$_2$O$_3$ crystal are pumped by flash lamp, achieving population inversion. Red light ($\approx 694.3 \text{ nm}$) is emitted via stimulated emission. 5. Nanomaterials Q: What are nanomaterials? Explain the concept of quantum confinement. A: Materials with at least one dimension in the nanoscale (1-100 nm). Quantum confinement : when material dimensions become comparable to electron wavelength, energy levels become discrete, altering properties. Q: Discuss the unique properties of nanomaterials compared to bulk materials. A: Increased surface area to volume ratio, quantum confinement effects, altered optical (e.g., color), electrical (e.g., conductivity), mechanical (e.g., strength), and catalytic properties. Q: What are quantum dots? List their applications. A: Semiconductor nanocrystals that exhibit quantum confinement in all three dimensions. Applications: LEDs, solar cells, biosensors, medical imaging. Q: Explain the synthesis methods for nanomaterials (top-down vs. bottom-up). A: Top-down : bulk material is reduced in size (e.g., milling, lithography). Bottom-up : atoms/molecules are assembled into larger structures (e.g., sol-gel, chemical vapor deposition). Q: What are carbon nanotubes (CNTs)? Describe their properties and applications. A: Cylindrical nanostructures of carbon atoms with exceptional strength, high thermal and electrical conductivity. Applications: composites, electronics, sensors, drug delivery.