lecture13-14 - Thermodynamic Properties of Point Defects...

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The enthalpy (energy for constant volume) change by removing an atom inside a crystal and placing it on the surface is called the formation enthalpy (energy) of a vacancy, H ( E ). The formation entropy, S, consists of two parts: vibrational entropy, S v , and configuration entropy, S c . The vibrational entropy of a vacancy can be estimated as = i i i k S ω ' v ln Boltzmann constant Vibration frequencies of atoms in a crystal with a vacancy Vibration frequencies of atoms in a perfect crystal metals in ~ v k S Thermodynamic Properties of Point Defects To calculate S c , consider a crystal with N lattice sites and n vacancies () ! ! ! ln n n N N k S c = Number of possible configurations with ( N-n ) atoms and n vacancies The total free energy of a crystal with N lattice sites and n vacancies: () + + = ! ! ! ln v v n n N N k S n T H n G G p Free energy of perfect crystal Sterling approximation for large N : N N N N =
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lecture13-14 - Thermodynamic Properties of Point Defects...

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