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 or large vacancies/voids where clusters of atoms are missing
• Technically important properties like mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength, and semiconductor conduction are greatly affected by crystal imperfections
• 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 mechanisms


  1. Vacancy diffusion

  2. Interstitial diffusion

  
• Vacancy diffusion

  • Involves the interchange of an atom from a normal lattice position to an adjacent vacant lattice site or vacancy
  • Diffusing atoms and vacancies exchange positions, so diffusion of atoms in one direction corresponds to motion of vacancies in the opposite direction
• Interstitial diffusion

  • Atoms migrate from an interstitial position to a neighboring one that is empty
  • Found for interdiffusion of impurities like hydrogen, carbon, nitrogen, and oxygen which have atoms small enough to fit into interstitial positions
  • Host or substitutional impurity atoms rarely form interstitials and do not normally diffuse via this mechanism

  
• Interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, since the interstitial atoms are smaller and more mobile

  
• There are more empty interstitial positions than vacancies, so the probability of interstitial atomic movement is greater than for vacancy diffusion

  
• Factors that influence diffusion

  • Diffusion mechanism (substitutional vs interstitial)
  • Temperature
  • Type of crystal structure of the host lattice
  • Type of crystal imperfections (diffusion 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

  
• Unsteady-state (non-steady state) diffusion


  Diffusion where the rate is a function of time, so the rate of change of concentration with distance varies with time