Evaluation of the Faintness Indices for All of the Zero-Wavenumber Vibrational Modes Whose Oversoftening Causes Ferroelectricity or Ferroelasticity

When the point group of the prototypic phase and the irreducible representation for the soft vibrational modes with zero wavenumber are specified at discretion, the ferroic species are determined and the faintness indices for ferroelectricity and ferroelasticity are evaluated. The results are shown together in a table, by surveying which it is found that with respect to the electric polarization components the faintness indices range from 1 to 6, and with respect to the mechanical strain components from 1 to 3. It is also found that of the 212 nonmagnetic ferroic species 48 are not generated by a zero-wavenumber vibrational mode or a set of degenerate zero-wavenumber vibrational modes.