A perfect crystal has N lattice sites. To model defects in a crystal we introduce M...

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A perfect crystal has N lattice sites. To model defects in a crystal we introduce M interstitial locations. An energy A is required to remove an atom from a lattice site and place it at an interstitial location, when the number of displaced atoms n is much smaller than N and M. a. How many ways are there of removing n atoms from N sites? b. How many ways are there of placing n atoms on M interstitial locations? c. Use the microcanonical ensemble to calculate the entropy as a function of the total energy E, and define the temperature. d. Show that the average number of displaced atoms n at temperature T is given by: n² (N-n)(M-n) and obtain n for A<<kT, and A >> kT. = e-A/kT e. Use this model for defects in a solid to find the defect concentration at T = 1,000 and 300 K. Set N = M and A = 1 eV. A perfect crystal has N lattice sites. To model defects in a crystal we introduce M interstitial locations. An energy A is required to remove an atom from a lattice site and place it at an interstitial location, when the number of displaced atoms n is much smaller than N and M. a. How many ways are there of removing n atoms from N sites? b. How many ways are there of placing n atoms on M interstitial locations? c. Use the microcanonical ensemble to calculate the entropy as a function of the total energy E, and define the temperature. d. Show that the average number of displaced atoms n at temperature T is given by: n² (N-n)(M-n) and obtain n for A<<kT, and A >> kT. = e-A/kT e. Use this model for defects in a solid to find the defect concentration at T = 1,000 and 300 K. Set N = M and A = 1 eV.

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The problem describes a model for defects in a crystal The crystal has N lattice sites and M interstitial locations An energy A is required to remove an atom from a lattice site and place it at an int... View the full answer