The melting temperature of zirconium is 1855 °C, the solid-liquid interfacial energy is 0.193 Jm-2 and the latent heat of fusion is 1.26 kJ/cm3.

(a) Calculate the critical radius and the homogeneous nucleation rate in liquid zirconium for undercoolings of 300, 320, 340, 360, 380, 400, 420, 440, 460, 480 and 500 K. Determine the nucleation temperature. (Hint: The concentration of liquid zirconium can be approximated by 1023 atoms/cm3 and the frequency factor by 1011s-1).

(b) Determine the undercooling for heterogeneous nucleation at a flat mould wall with wetting angles of 5, 10, 15, 20, 25, 30, 35, 40 and 45. Plot your results as undercooling vs. wetting angle