Elastic properties of type-I clathrate K₈Zn₄Sn₄₂ determined by inelastic X-ray scattering

We measured the phonon dispersion at ambient conditions in single-crystal type-I clathrate K₈Zn₄Sn₄₂, a material with promising thermoelectric properties that has only recently been synthesized, using the high-energy resolution inelastic X-ray scattering (IXS) technique. From the sound velocities along high-symmetry directions, we extracted the elastic constants (C ₁₁, C ₁₂, C ₄₄ = 63.2, 19.1, 21.9 GPa, respectively). Experimental results agree with the predictions from first-principles calculations on the hypothetical, "guest-free", type-I clathrate Sn₄₆. The size of the crystal investigated was several orders of magnitude smaller than what is required for neutron and ultrasonic measurements. Due to this essential property, together with the high-energy resolution, high-momentum-transfer resolution, and the access to the strongest Bragg reflections, IXS is the technique of choice for measuring the full elastic constant tensor for microcrystals.