An Observation Related to the Pressure Dependence of Ionic Radii

Abstract

Here it is shown that the crystal radii of ions are represented by a simple relation rcryst = rB3√(10 m)/N, where m and N are small integer numbers determined by the principal and orbital quantum numbers and valence, and rB is the Bohr radius. The relation holds to within 5%. This finding elucidates that despite their original definition crystal- and ionic radii are not classical but represent the limiting case of spherically symmetric spatial averages of the valence electron states and, therefore, are able to reflect changes in the valence electron configuration with pressure and temperature. The relation is used to show general pressure-effects on the radii, in particular the increase of bond coordination with pressure and metallization as limiting state. The pressure-effect is exemplified for the elements Mg and Si as major constituent cations in the Earth’s mantle, and for Ba as a large ionic lithophile element. It is found that at least to about 140 GPa the radii depend linearly on pressure. Further, if a generalization is permitted for just three elements, the pressure-dependence is lesser the higher the charge of the ion. The three elements exhibit a much weaker pressure-dependence than previously calculated non-bonding radii. For mantle geochemistry this finding implies that elements incompatible in the upper mantle remain so for the main lower mantle minerals bridgmanite and periclase and are hosted by davemaoite.