Phonon dispersion curves in the type-I crystalline and molten clathrate compound Eu₈Ga₁₆Ge₃₀

<jats:title>Abstract</jats:title> <jats:p>The dynamic structure factor <jats:inline-formula> <jats:tex-math><?CDATA $S(Q,E)$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cmacb0a5ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, where <jats:italic>Q</jats:italic> and <jats:italic>E</jats:italic> are momentum and energy transfer, respectively, has been measured for liquid Eu<jats:sub>8</jats:sub>Ga<jats:sub>16</jats:sub>Ge<jats:sub>30</jats:sub> (EGG), using inelastic x-ray scattering. The excitation energy of the longitudinal acoustic mode in the liquid was scaled to that in liquid Ba<jats:sub>8</jats:sub>Ga<jats:sub>16</jats:sub>Sn<jats:sub>30</jats:sub> (BGS) with the effective mass. This result means that the local structure in both liquids are similar. The longitudinal acoustic excitation energy of type-I clathrate compound EGG disperses faster than that in the liquid, suggesting that the interatomic force is weakened on melting. The lower energy excitation was observed in both liquid EGG and liquid BGS. In comparison with the longitudinal phonon dispersion in crystalline clathrate compound EGG obtained by density functional theory-based calculations, the lower energy in the liquid was found to be near the optical mode energy. The result indicates that the lower energy mode arises from the relative motion between Eu and (Ga, Ge) atoms.</jats:p>