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(solution) 1. Intrinsic crystal A is fcc and has a vacancy content given by


1. Intrinsic crystal A is fcc and has a vacancy content given by cv = 10 exp(?120/RT), withenergies in kJ/mole. Suppose that a second crystal of A contains 1 at.% of impurity elementB, where the A-vacancy binding energy is 16 kJ/mole with impurities. Assuming ?S = 0 forthe complexes, what is the total vacancy concentration in the impure crystal at 1000K?


relevant information 

  • "Measurements of Equilibrium Vacancy Concentrations in Aluminum." R. O. Simmons and R. W. Balluffi,Phys. Rev.117, 52 (1960):doi:10.1103/PhysRev.117.52
  • "Measurements of the High-Temperature Electrical Resistance of Aluminum: Resistivity of Lattice Vacancies." R. O. Simmons and R. W. Balluffi,Phys. Rev.117, 62 (1960):doi:10.1103/PhysRev.117.62
  • Warning: a long review. Should be skimmed to get a feel for what has been done, and worth skimming the list of papers that cite it: "Investigation of Thermal Equilibrium Vacancies in Metals by Positron Annihilation." H. E. Schaefer,phys. stat. sol. (a)102, 47 (1987):doi:10.1002/pssa.2211020104
  • "Breakdown of the Arrhenius Law in Describing Vacancy Formation Energies: The Importance of Local Anharmonicity Revealed by Ab initio Thermodynamics." A. Glensk, B. Grabowski, T. Hickel, and J. Neugebauer,Phys. Rev. X4, 011018 (2014):doi:10.1103/PhysRevX.4.011018

 


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