Vacancy Formation Volume Research Articles

Formation volume of vacancies in platinum quenched under high pressure

The effect of hydrostatic pressures up to 8 kbar on the electrical resistance quenched in platinum has been studied. The formation volume of vacancies ${V}^{F}$ was obtained under experimental conditions that minimized necessary corrections due to vacancy interactions and vacancy losses during the quench, as well as various uncertainties in the quench temperature. In particular, special care was taken to monitor the quench temperature accurately by using a specific calibration for the variation of resistance against pressure. The fractional measured value of ${V}^{F}$ at 800 \ifmmode^\circ\else\textdegree\fi{}C is 0.67 \ifmmode\pm\else\textpm\fi{} 0.03 atomic volume. Previously published results are reviewed and reanalyzed with the help of the new calibration data.

On the vacancy formation energy and volume of simple cubic metals

A derivation of the vacancy formation energy and volume is given within the framework of local pseudopotential theory. Numerical results are presented for the alkalis and for Al. The theory is based on the previous work of Ho (1971) but with some modifications and extensions. The differences are not numerically very significant in the alkalis but are critical in Al for which the authors obtain satisfactory results while Ho's theory failed.

Application of Pseudopotentials to the Calculation of Vacancy Formation Energy and Volume for Alkali Metals

Based on the pseudopotential formalism, a calculation for vacancy formation energy and formation volume in metals has been formulated. The calculation is carried out in three steps: First, the structural energy required to create the vacancy is calculated; then the latticestatics method is used to calculate the relaxed vacancy configuration and the energy; finally, the dilatation of the whole defect lattice is determined according to the equilibrium condition. When applying this calculation to alkali metals, it was found that (a) the contribution from the volume-dependent lattice energy to the vacancy formation energy is very large compared to that due to the relaxation around the vacancy. Therefore, such energy must be considered in calculating vacancy volume and energy. (b) The relaxed displacements near the vacancy are highly anisotropic and quite large but the related relaxation energy contributes only about 25% of the formation energy. A local potential and an optimized nonlocal potential were chosen as pseudopotentials in the calculation, both of which have corrections for the electron exchange and correlation interactions in the screening function. The results are in quantitative agreement with the available experimental data of alkali metals. Some general problems about defect calculations for metals are also discussed.

Atom Transport Under Varying Pressure * *

Abstract Study of the effect of hydrostatic pressure on the rate of diffusion-limited processes gives in­ formation regarding the intrinsic volume changes associated with formation and motion of defects. While there are basic problems associated with interpretation of the motional volume, such effects may be measured directly in some cases and subtracted to give unambiguous results for the defect formation volume. Experimentally, precise measurement of specimen temperature within a high-pressure environment poses the most severe practical constraint. Results are given for measurements to pressures of 7 kilobars of ionic conductivity in a series of pure and doped alkali halides: NaCl, KCl, NaBr, and KBr, all of which are predominantly cationic vacancy conductors. The activation volumes are found to be pressure dependent in the intrinsic regions. In all cases the Schottky pair vacancy formation volume is found to be larger than the molar volume, the ratio being largest for NaCl and smallest for KBr. Results are also given for the total activation volume for diffusion of Ti44 in beta-Ti, a case of "anomalous" bulk diffusion. The tracer penetration plots do not follow a perfect gaussian profile. However, if the penetration plots are fit to a single gaussian, the activation volume derived is consistent with that expected for a vacancy mechansm in bcc metals