Measurements of Equilibrium Vacancy Concentration in Bismuth

Precision measurements of macroscopic (dilatometric) thermal expansion Δ L / L 0 and microscopic (X-ray) thermal expansion Δ d / d 0 have been carried out on bismuth single crystals (99.9999%) along both a and c directions in the temperature range between 50° to 260°C. The equilibrium defect concentration was obtained as a function of temperature by assuming the primary defects to be monovacancies. The concentration of vacancies is 6.17×10 -4 at the melting point, and the formation energy and entropy of a monovacancy are 0.35 eV and 0.3 k , respectively. The ratios of the expansion arising exclusively from the creation of defects to the true thermal expansion of the ideal lattice without any thermal generation of vacancies are 2.0% and 0.53% at the melting point for the a and c directions, respectively.