Use of Thermal Expansion Measurements to Detect Lattice Vacancies near the Melting Point of Pure Lead and Aluminum

Abstract

Dilatometric and x-ray measurements of the thermal expansion of pure lead and aluminum have been carried out between room temperature and the melting point. For lead, the results obtained by the two techniques agree within experimental error, which is interpreted to imply that the vacancy concentration at the melting point is (in mole fraction) less than or equal to 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. For aluminum the dilatometric expansion appears to be slightly greater than the x-ray expansion. If this discrepancy is real, it corresponds to a vacancy concentration at the melting point of aluminum of about 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. The corresponding estimate for the formation energy, ${\ensuremath{\epsilon}}_{v}$, of a vacancy in lead is ${\ensuremath{\epsilon}}_{v}\ensuremath{\geqq}0.53$ ev, and in aluminum, ${\ensuremath{\epsilon}}_{v}=0.77$ ev.