Lattice dynamics and elasticity in thermoelectric Mg2Si1−xSnx

Lattice dynamics and elastic constants in ${\mathrm{Mg}}_2{\mathrm{Si}}_{1-x}{\mathrm{Sn}}_x$ were investigated using resonant ultrasound spectroscopy, Mössbauer spectroscopy, nuclear inelastic scattering, and inelastic x-ray scattering. Increasing the Sn content $x$ results in smaller elastic constants, lower Sn specific Debye temperature, lower speed of sound, and a softening of acoustic Sn specific phonons. However, close to band convergence at about $x=0.6$, the shear modulus is well below the expected value, which suggests a pronounced connection between band convergence and lattice dynamics in this system. Based on the determined speed of sound and average phonon group velocity, the importance of optical phonons for lattice thermal conductivity is discussed, as the significant reduction in both velocities would yield an implausibly low lattice thermal conductivity of only about 60% of the experimental value. Sn specific thermodynamic quantities calculated from the Sn specific density of phonon states substantiate the general softening of lattice vibrations upon substitution of Si by Sn. A major contribution to the vibrational entropy is thus due to Sn specific vibrational modes. The generalized density of phonon states in ${\mathrm{Mg}}_2{\mathrm{Si}}_{1-x}{\mathrm{Sn}}_x$ derived from inelastic x-ray scattering for one composition shows that vibrational modes related to lightweight Mg and Si set in above 12.5 meV, whereas Sn specific modes are concentrated around 11 meV.