Speed of sound in methane under conditions of planetary interiors

We present direct observations of acoustic waves in warm dense matter. We analyze wave-number- and energy-resolved x-ray spectra taken from warm dense methane created by laser heating a cryogenic liquid jet. X-ray diffraction and inelastic free-electron scattering yield sample conditions of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>0.3</a:mn><a:mo>±</a:mo><a:mn>0.1</a:mn></a:mrow></a:math> eV and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>0.8</b:mn><b:mo>±</b:mo><b:mn>0.1</b:mn></b:mrow></b:math> g/<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mi mathvariant="normal">cm</c:mi><c:mrow><c:mo>−</c:mo><c:mn>3</c:mn></c:mrow></c:msup></c:math>, corresponding to a pressure of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mo>∼</e:mo><e:mn>13</e:mn></e:math> GPa. Inelastic x-ray scattering was used to observe the collective oscillations of the ions. With a highly improved energy resolution of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mo>∼</f:mo><f:mn>50</f:mn></f:math> meV, we could clearly distinguish the Brillouin peaks from the quasielastic Rayleigh feature. Data at different wave numbers were utilized to derive a sound speed of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>5.9</g:mn><g:mo>±</g:mo><g:mn>0.5</g:mn></g:mrow></g:math> km/s, marking a high-temperature data point for methane and demonstrating consistency with Birch's law in this parameter regime.