The starting point of the present article is a careful analysis of the physical meaning of the three deformation electron-charge-density maps for ${\mathrm{V}}_3$Si, ${\mathrm{V}}_3$Ge, and ${\mathrm{Cr}}_3$Si [previously presented by J.-L. Staudenmann et al., Phys. Rev. B 24, 6446 (1981)]. Based on the significant differences exhibited in these maps, it was shown that one can organize all the Debye temperatures at 0 K from specific-heat measurements into five collections which were called Debye classes. The findings here presented are not limited to $A15\mathrm{}$ alloys alone, but rather can be applied to any other family of compounds that satisfies the free-atom superposition principle and the small-amplitude vibration hypothesis. It is shown that deformation electron charge densities depend only weakly upon structure and that they are mainly related to physical properties. Furthermore, the use of deformation electron-charge density as a criterion in setting the starting point for the three main Debye classes is justified a posteriori. We point out that when one takes into account the consequences of the dielectric function, the static or bonding electron charge density can only be extracted with great difficulty from any experimental data. This certainly complicates any comparison between experimental and computed electron charge densities. It is shown that the deformation and total electron charge densities are the only well-defined inverse Fourier transforms. If the vibration amplitude of the valence-electron orbitals are non-negligible, the valence-electron charge density, in contrast to the deformation and total electron charge densities, has no simple interpretation. It has the same meaning, however, if the valence-electron orbitals are in a quasistatic configuration. Moreover, in the case of a non-negligible vibration amplitude for the valence-electron orbitals, the comparison between valence- and deformation-electron charge densities leads to a qualitative separation between dynamics and statics for the valence-electron orbitals. This observation is of fundamental importance in linking experimental electron charge densities and inelastic neutron scattering measurements.

• Received 2 July 1982

DOI:https://doi.org/10.1103/PhysRevB.27.4186