Calculate the concentration of vacancies (equilibrium fraction of lattice sites that are vacant, Nv/N) in silicon at the solid-liquid equilibrium temperature of 1683 K where single crystals of silicon are grown. The enthalpy of formation for vacancies in silicon is 2.3 eV/vacancy.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.