Cluster-induced crater formation
  Using molecular-dynamics simulation, we study the crater volumes induced by energetic impacts ($v= 1- 250$ km/s) of projectiles containing up to N=1000 atoms. We find that for Lennard-Jones bonded material the crater volume depends solely on the total impact energy $E$. Above a threshold $\Eth$, the volume rises linearly with $E$. Similar results are obtained for metallic materials. By scaling the impact energy $E$ to the target cohesive energy $U$, the crater volumes become independent of the target material. To a first approximation, the crater volume increases in proportion with the available scaled energy, $V=aE/U$. The proportionality factor $a$ is termed the cratering efficiency and assumes values of around 0.5. 
Christian Anders and Gerolf Ziegenhain and Steffen Zimmermann and   Herbert M. Urbassek