The interfacial free energies of solid chromium, molybdenum and tungsten

Abstract

The average surface free energies, γ sv, of chromium, molybdenum, and tungsten have been measured at 0.6 to 0.8 of the absolute melting temperature, T M, by multiphase equilibrations with liquid tin or silver in tantalum-gettered argon. With grain-boundary groove angles measured by interferometry and stylus profile tracing, the respective values were 1700 ± 360, 1750 ± 390, and 1810 ± 630 ergs/cm 2. Similar values for molybdenum were obtained from an analysis of the kinetics of grain-boundary grooving. Ratios involving the high-angle grain boundary, solid-liquid, and solid- foreign metal vapor interfacial free energies and γ sv were consistent with theoretical considerations. The presence of surface active impurities was predicted on the basis of a positive temperature coefficient, dγ sv d T . Values of the order of +0.6 erg/cm 2/ °C were calculated from the temperature dependence of grain boundary groove angles from which it was found that the relative grain boundary free energy, γ ss γ sv decreased from ~0.5 at 0.5 T M to ~0.35 at 0.95 T M. In the case of molybdenum, grain boundary groove angles were insensitive to environments ranging from 10 −9 Torr residual pressure to 1.0 Torr of nitrogen. Indications of surface impurities during equilibration were given by Auger electron spectroscopy which revealed carbon and sulfur on molybdenum at 0.65 T M under ultra-high vacuum conditions. Adjusting the surface free energy values to the melting points and dividing by the surface tension of the corresponding liquid, γ lv, resulted in γ sv γ lv ratios above unity, as predicted by Skapski's broken bond model.