Homology of interatomic forces and Debye temperatures in transition metals

Using experimental data on the entropy S at intermediate temperatures, corrected for an electronic term to get the vibrational entropy, we obtain well-defined and accurate ``entropy Debye temperatures'' FTHETA=FTHETAS. From FTHETAS we define a quantity with the dimension of a force constant, kS==M(kBFTHETA/{})², where M is the atomic mass. Similarly, data on the low-temperature vibrational heat capacity and the elastic coefficients yield Debye temperatures FTHETAC and FTHETAᵉˡᵃˢ and corresponding force constants kC and kᵉˡᵃˢ. The ratios of kS for the 4d-5d pairs Zr,Hf, Nb,Ta, Mo,W, Tc,Re, Ru,Os, Rh,Ir, and Pd,Pt are remarkably constant, (kS{)}⁴ᵈ$/(${k}S)⁵ᵈ =0.76±{}0.01, in spite of varying crystal structures. Further, (kC{)}⁴ᵈ$/(${k}C)⁵ᵈ =0.70±{}0.07 and (k^elas)⁴ᵈ/(k^elas)⁵ᵈ =0.69±{}0.08. The corresponding force-constant ratios k³ᵈ/k⁴ᵈ vary more. This correlates with an approximately constant atomic-volume ratio Ω⁴ᵈ/Ω⁵ᵈ=0.99±{}0.02, while Ω³ᵈ/Ω⁴ᵈ=0.81±{}0.05 shows irregularities, mainly of magnetic origin. As a basis for our analysis, we review low-temperature Debye temperatures FTHETAᵉˡᵃˢ and FTHETAC and the bulk modulus B of the transition metals.