Estimation of surface tension of grain boundaries in allotropes of elements

Recently (Prokofjev in J Mater Sci 52:4265–4277, 2017. https://doi.org/10.1007/s10853-016-0681-2 ), the empirical expressions representing the surface tension of general-type high-angle grain boundaries in elemental solids as a function of their melting temperature and molar volume in the solid state at the melting temperature were proposed. In this paper, the application of the expressions to estimate the grain boundary surface tension in the allotropes of elemental solid, which do not melt but transform to the higher-temperature allotrope, is described. The parameters of the temperature dependences of grain boundary surface tension in allotropes of 22 elemental solids are presented.