Implicit size dependence of the valence electron concentration criterion in high-entropy alloys

RESUMO

The valence electron concentration (VEC) is the most widely used predictor of FCC against BCC stability in high-entropy alloys (HEAs), yet it is a compositional average carrying no information about atomic size. Using the macroscopic atom model, we show that the mixing enthalpy is almost size-blind, shifting by less than 6\% even when constituent volumes differ by a factor of 2, so that size can act only on the electron count. That action equals exactly the covariance of the atomic surface $V^{2/3}$ with the valence electron count, divided by its mean. This covariance is not free. Volume and valence are strongly anti-correlated across the elements used to build HEAs, so the size-corrected count is an affine rescaling of VEC over 265 characterized alloys and improves no prediction. VEC already encodes atomic size, which explains its success and locates its failure among large, electron-rich elements. Chemistry sets the enthalpy through one switch element.