Empirical determination of bulk moduli of elemental substances by pseudopotential radius

The present paper proposes that bulk moduli B of elemental substances can be determined by the effective pseudopotential radius r(ps) through an empirical relation; B = Cr-ps(-m), where C and m are constants related to the bonding character. For the highly sp-bonded elemental substances, the powers m were determined to range from 3.1 to 3.4 and the values agree fairly well with the power (3.5) in the previous relation (B = kd(-3.5)) which was determined from the interatomic distance d. The value of the power in the relation (B = Cr-ps(-m)) corresponding to each bonding mode increases with the increase of the angular momentum quantum number l of elemental substance. It shows the maximum value (m = 6.70) for 5d transition metal and lanthanide elemental substances. Subsequently, the ratios of the sd hybridization to the sum of sd and sp hybridizations for transition and lanthanide elemental substances were evaluated from the dependence of the power on l and from the experimental and calculated bulk moduli of elemental substances, assuming that the contribution of d and f electrons to the chemical bond can be approximated by the sd hybridization (including f electron effects in lanthanide). The evaluation indicates that the ratios of the sd hybridization agree with the values determined by the interatomic distance within about 20% accuracy for late- and post-transition metal elements except for Mn and Hg, while the ratios are fairly high for some early-transition metals because of the increase in the effect of inner d shells on the bulk modulus. Further, within about 20% accuracy, except for Eu, Gd and Yb, the ratios of sd hybridization for lanthanide elements agree with the values determined by interatomic distances.