Elastic properties of monoclinic $Gd_{5}(Si_{2}Ge_{2})$

$Gd_{5}(Si_{2}Ge_{2})$ is an alloy characterized by a giant magnetocaloric effect $(\Delta T/\Delta B \sim 8K/2T)$ and a colossal strain (up to 10,000ppm) that exist due to a magnetic- martensitic phase transition occurring close to the room temperature. Because of these unique properties, $Gd_{5}(Si_{2} Ge_{2})$ has a potential for energy efficient environmentally friendly refrigeration and actuation uses. We show the results of the first-ever ultrasonic study of a single crystal of this alloy. Sound speeds measured in a number of different geometries allowed us to determine the full elastic constant tensor for this material in the monoclinic phase. The anisotropy of elasticity of the crystal is demonstrated by the polar plots of the speed of sound, Young's modulus and linear compressibility in all three main crystallographic planes. The pure modes directions are determined. The bulk modulus is estimated at $2.58 \times 10^{11}~dynes/cm^{2}$ and the Debye temperature at 250 K. Work in Ames is supported by the US DOE. Work in NHMFL is supported by the In-House Research Program, NSF and State of Florida.