Lattice Dynamicsof Ca₃Si₄ andCa₁₄Si₁₉ Compounds

The vibrational properties of Ca₃Si₄ and Ca₁₄Si₁₉ were studied by inelastic neutron scattering (INS) experiments as a function of temperature and by density functional theory (DFT) lattice dynamics calculations. The good agreement between the DFT calculations and INS experiments shows that the vibrational dynamics of both structures can be described by normal modes. Phonons of strong linear dispersion, which may be interpreted as acoustic modes, are observed up to about 10 meV in both compounds. Above 10 meV, phonons are progressively localized toward higher energies, taking on the maximum values of 50 meV in Ca₃Si₄ and 53 meV in Ca₁₄Si₁₉. Thereby, Ca contributes to phonons with high amplitudes below about 25 meV and Si dominates the vibrational properties above 25 meV. However, localization effects over an extended <i>Q</i> range in the phonon properties are observed already at energies of 10 and 6.5 meV in Ca₃Si₄ and Ca₁₄Si₁₉, respectively. Ca₁₄Si₁₉ shows in the phonon dispersion a strong anticrossing behavior due to equal symmetries of the low-energy localized and acoustic modes. We observe a weak relative shift of 2–4% of phonon energies upon heating to 540 K and estimate the contribution from thermal expansion to this anharmonic response to more than 50%.