ch4

• All crystalline solids contain vacancies, and it is not possible to create such a material that is free of these defects
• Vacancy


  Vacant lattice site, one normally occupied but from which an atom is missing
• Self-interstitial


  An atom from the crystal that is crowded into an interstitial site - a small void space that under ordinary circumstances is not occupied
• Boltzmann's constant


  1.38 × 10^-23 J/atom·K, or 8.62 × 10^-5 eV/atom·K
• For most metals, the fraction of vacancies N𝜐/N just below the melting temperature is on the order of 10^-4
• Self-interstitials exist in very small concentrations that are significantly lower than for vacancies
• Even with relatively sophisticated techniques, it is difficult to refine metals to a purity in excess of 99.9999%
• Alloy


  A metal consisting of two or more elements
• Solid solution


  Forms when, as the solute atoms are added to the host material, the crystal structure is maintained and no new structures are formed
• Substitutional solid solution


  Solute or impurity atoms replace or substitute for the host atoms
• Interstitial solid solution


  Impurity atoms fill the voids or interstices among the host atoms
• Hume-Rothery rules for substitutional solid solubility

  • Atomic size factor
  • Crystal structure
  • Electronegativity factor
  • Valences
• Tetrahedral interstitial site


  Coordination number of 4, formed by straight lines drawn from the centers of the surrounding host atoms
• Octahedral interstitial site


  Coordination number of 6, formed by joining the centers of the surrounding host atoms
• Metallic materials have relatively high atomic packing factors, which means that interstitial positions are relatively small
• The maximum allowable concentration of interstitial impurity atoms is low (less than 10%)
• Interstitial solid solution


  When added to iron, the maximum concentration of carbon is about 2%. The atomic radius of the carbon atom is much less than that of iron: 0.071 nm versus 0.124 nm.
• Other octahedral and tetrahedral interstices are located at positions within the unit cell that are equivalent to these representative ones.
• Locations of tetrahedral and octahedral interstitial sites within (a) FCC and (b) BCC unit cells

  • Octahedral
  • Tetrahedral
• Computation of Radius of BCC Interstitial Site

  1. Atom just touches the two adjacent host atoms, which are corner atoms of the unit cell

  2. Unit cell edge length = 2R + 2r

  3. r = (2/√3 - 1)R = 0.155R
• Composition


  The relative content of a specific element or constituent in an alloy
• Weight percent (wt%)


  The weight of a particular element relative to the total alloy weight
• Atom percent (at%)


  The number of moles of an element in relation to the total moles of the elements in the alloy
• Computation of weight percent (for a two-element alloy)

  C1 = m1 / (m1 + m2) x 100
• Computation of atom percent (for a two-element alloy)

  C'1 = nm1 / (nm1 + nm2) x 100
• Conversion of weight percent to atom percent (for a two-element alloy)


  C'1 = (C1A2) / (C1A2 + C2A1) x 100

  C'2 = (C2A1) / (C1A2 + C2A1) x 100
• Conversion of atom percent to weight percent (for a two-element alloy)

  C1 = (C'1A1) / (C'1A1 + C'2A2) x 100

  C2 = (C'2A2) / (C'1A1 + C'2A2) x 100
• Conversion of weight percent to mass per unit volume (for a two-element alloy)


  C"1 = (C1 / (C1/ρ1 + C2/ρ2)) x 103

  C"2 = (C2 / (C1/ρ1 + C2/ρ2)) x 103
• Computation of density (for a two-element metal alloy)

  ρave = 100 / (C1/ρ1 + C2/ρ2)

  ρave = (C'1A1 + C'2A2) / (C'1A1/ρ1 + C'2A2/ρ2)
• Computation of atomic weight (for a two-element metal alloy)

  Aave = 100 / (C1/A1 + C2/A2)

  Aave = (C'1A1 + C'2A2) / 100
• Equations 4.9 and 4.11 are not always exact as they assume total alloy volume is exactly equal to the sum of the volumes of the individual elements, which is normally not the case for most alloys.
• Burgers vector


  The same at all points along its line for a dislocation, points in a close-packed crystallographic direction and is of magnitude equal to the interatomic spacing
• The permanent deformation of most crystalline materials is by the motion of dislocations
• The Burgers vector is an element of the theory that has been developed to explain this type of deformation
• Dislocations can be observed in crystalline materials using electron-microscopic techniques
• Virtually all crystalline materials contain some dislocations that were introduced during solidification, during plastic deformation, and as a consequence of thermal stresses that result from rapid cooling
• Dislocations are involved in the plastic deformation of crystalline materials, both metals and ceramics
• Dislocations have also been observed in polymeric materials
• Interfacial defects


  Boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations
• Types of interfacial defects

  • External surfaces
  • Grain boundaries
  • Phase boundaries
  • Twin boundaries
  • Stacking faults
  • Ferromagnetic domain walls