PHYSMET

• Crystal imperfections


  Defects in the regular geometrical arrangement of the atoms in a crystalline solid

  
• Perfect crystal


  • An idealization, there is no such thing in nature
• Defects


  • May be the results of crystal deformation, rapid cooling from high temperature, or high energy radiation striking the solid
• Defects


  • Influence the mechanical, electrical, and optical behavior of the crystal
• Types of crystal imperfections

  • Point defects
  • Line defects
  • Surface defects
  • Volume defects

  
• Point defects


  Lattice errors at isolated points, due to imperfect packing of atoms during crystallization or vibrations of atoms at high temperatures

  
• Equilibrium concentration of point defects


  n = N * exp(-Ed/kbT), where n is number of defects, N is number of atomic sites per mole, Ed is free energy required to form defects, kb is Boltzmann's constant, and T is absolute temperature
• Vacancies


  Simplest point defect, missing atom or vacant atomic site
• Frenkel defect


  Cation leaving its normal position and moving into an interstitial site
• Schottky defect


  Removing one cation and one anion from the interior of the crystal and placing them both at an external surface

  
• Compositional defects


  Impurity atoms during crystallization, occurring as substitutional or interstitial impurities
• Electronic defects


  Errors in charge distribution in solids, necessary for electrical conductivity and related phenomena
• Line imperfections/dislocations


  1. D defects around which some of the atoms are misaligned, responsible for ductility in materials

  
• Edge dislocations


  Vertical plane in the crystal doesn't extend from top to bottom, causing compression above and tension below the slip plane
• Screw dislocations


  Formed by shear stress, upper region of crystal shifted one atomic distance relative to bottom portion
• Burgers vector


  Magnitude and direction of lattice distortion associated with a dislocation, perpendicular to dislocation line in edge dislocations and parallel in screw dislocations
• Surface imperfections


  1. D defects arising from a change in the stacking of atomic planes on or across a boundary
• External surface imperfections


  Boundary where bonds do not extend beyond, surface atoms have higher energy
• Internal surface imperfections


  Grain boundaries, tilt boundaries, twin boundaries, stacking faults

  
• Grain boundaries


  Separate crystals/grains of different orientation in a polycrystalline material, region of imperfect atomic packing

  
• High angle grain boundaries


  Orientation difference between neighboring grains is more than 10-15 degrees

  
• Interfaces


  Boundary between 2 crystals with different crystalline arrangements or compositions
• Tilt boundaries


  Low angle boundary with orientation difference less than 10 degrees, composed of edge dislocations
• Twin boundaries


  Atomic arrangement on one side is a mirror reflection of the other side, occur in pairs
• Stacking defects


  Fault arising from stacking one atomic plane out of sequence on another, while the lattice on either side is perfect
• Volume imperfections


  1. D imperfections like cracks and large vacancies/voids
• Technically important properties like mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength, and semiconductor conduction are greatly affected by crystal imperfections
• Why should we study crystal imperfections? To understand their influence on the properties of crystalline solids
• Diffusion


  The process by which atoms move in a material. Many reactions in solids and liquids are diffusion dependent.

  
• Diffusion in solids


  • Atoms are not fixed at their position but constantly move (oscillate)
  • Diffusion is difficult in solids due to bonding and requires time, external energy to mobilize the atoms

  
• Diffusion couple


  • Joining bars of two different metals together so that there is intimate contact between the two faces, then heating and cooling to observe interdiffusion
• Interdiffusion


  The process whereby atoms of one metal diffuse into another
• Self-diffusion


  Atoms within one material exchanging positions
• Diffusion mechanism: Vacancy diffusion

  1. Atom interchanges from a normal lattice position to an adjacent vacant lattice site or vacancy

  2. Diffusing atoms and vacancies exchange positions, so diffusion of atoms in one direction corresponds to motion of vacancies in the opposite direction
• Diffusion mechanism: Interstitial diffusion


  1. Atoms migrate from an interstitial position to a neighboring one that is empty

  2. Found for interdiffusion of impurities like hydrogen, carbon, nitrogen, oxygen which have atoms small enough to fit into interstitial positions

  
• Factors influencing diffusion


  • Diffusion mechanism (substitutional vs interstitial)
  • Temperature
  • Type of crystal structure of the host lattice
  • Type of crystal imperfections (faster along grain boundaries and dislocation lines)
  • Excess vacancies
  • Concentration of diffusing species

  
• Steady-state diffusion


  Diffusion that takes place at a constant rate, where the number of moles of particles crossing a given interface is constant with time

  
• Steady-state diffusion


  1. dc/dx = constant

  2. dc/dt = 0

  
• Fick's first law


  Diffusive flux is directly proportional to the existing concentration gradient
• Unsteady-state (non-steady state) diffusion

  Diffusion where the rate is a function of time, so the rate of change of concentration with distance (dc/dx) varies with time and the change of concentration with time (dc/dt) is not zero