About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Physical Review
Paper
Equilibrium defect concentration in crystalline sodium
Abstract
The thermal expansion of high-purity sodium crystals has been measured from -25°C up to the melting point by precision interferometric and x-ray techniques. Above 15°C the two expansion curves diverge in a manner indicating a predominance of vacancy-type defects. The difference at the melting point is equivalent to a net vacancy concentration of 7.5×10-4. Within experimental error, the divergence between the curves varies exponentially with reciprocal temperature and, if interpreted as due only to vacancies, yields a formation energy E1vf of 0.42±0.03 eV and a formation entropy: S1vf=(5.8±1.1)k (k is Boltzmann's constant). This value of E1vf accounts for almost all of the self-diffusion activation energy (0.45±0.01 eV) and therefore leads to a very low value for the vacancy migration energy E1vm. Both the high value of S1vf and the low value of E1vm are consistent with the existence of a large lattice relaxation around a vacancy. Other possible interpretations of the results are also considered, involving the presence of divacancies or interstitials in addition to the monovacancies. However, the totality of evidence available from the present and other work favors the interpretation that monovacancies are the dominant defect in sodium both in the present measurement and in self-diffusion. Discrepancies between the present results and previous work have been attributed to the irreversibility in the macroscopic expansion caused by an oxide coating. © 1966 The American Physical Society.