Thermoelastic properties of liquid Fe‐C revealed by sound velocity and density measurements at high pressure

<jats:title>Abstract</jats:title><jats:p>Carbon is one of the possible light elements in the cores of the terrestrial planets. The <jats:italic>P</jats:italic> wave velocity (<jats:italic>V<jats:sub>P</jats:sub></jats:italic>) and density (<jats:italic>ρ</jats:italic>) are important factors for estimating the chemical composition and physical properties of the core. We simultaneously measured the <jats:italic>V<jats:sub>P</jats:sub></jats:italic> and <jats:italic>ρ</jats:italic> of Fe‐3.5 wt % C up to 3.4 GPa and 1850 K by using ultrasonic pulse‐echo method and X‐ray absorption methods. The <jats:italic>V<jats:sub>P</jats:sub></jats:italic> of liquid Fe‐3.5 wt % C decreased linearly with increasing temperature at constant pressure. The addition of carbon decreased the <jats:italic>V<jats:sub>P</jats:sub></jats:italic> of liquid Fe by about 2% at 3 GPa and 1700 K and decreased the Fe density by about 2% at 2 GPa and 1700 K. The bulk modulus of liquid Fe‐C and its pressure (<jats:italic>P</jats:italic>) and temperature (<jats:italic>T</jats:italic>) effects were precisely determined from directly measured <jats:italic>ρ</jats:italic> and <jats:italic>V<jats:sub>P</jats:sub></jats:italic> data to be <jats:italic>K</jats:italic><jats:sub>0,1700 K</jats:sub> = 83.9 GPa, d<jats:italic>K<jats:sub>T</jats:sub></jats:italic>/d<jats:italic>P</jats:italic> = 5.9(2), and d<jats:italic>K<jats:sub>T</jats:sub>/</jats:italic>d<jats:italic>T</jats:italic> = −0.063<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#jgrb51854-disp-0008"/> GPa/K. The addition of carbon did not affect the isothermal bulk modulus (<jats:italic>K<jats:sub>T</jats:sub></jats:italic>) of liquid Fe, but it decreased the d<jats:italic>K/</jats:italic>d<jats:italic>T</jats:italic> of liquid Fe. In the <jats:italic>ρ‐V<jats:sub>P</jats:sub></jats:italic> relationship, <jats:italic>V<jats:sub>P</jats:sub></jats:italic> increases linearly with <jats:italic>ρ</jats:italic> and can be approximated as <jats:italic>V<jats:sub>P</jats:sub></jats:italic> (m/s) = −6786(506) + 1537(71) × <jats:italic>ρ</jats:italic> (g/cm<jats:sup>3</jats:sup>), suggesting that Birch's law is valid for liquid Fe‐C at the present <jats:italic>P‐T</jats:italic> conditions. Our results imply that at the conditions of the lunar core, the elastic properties of an Fe‐C core are more affected by temperature than those of Fe‐S core.</jats:p>