Pure titanium has two allotropic forms: β-Ti (high temperature) and α-Ti (low temperature). For equilibrium heating conditions, the low-temperature α phase transforms to the high-temperature β phase at 883 °C (1156K), a) Calculate the critical radius r* and the activation free energy ΔG* for a body-centered cubic beta phase nucleus in a superheated alpha titanium matrix at 1165 K. Assume a spherical nucleus (homogeneous nucleation), ΔGv(1165 K) = - 0.095 J/m3, and σsl = γ = 0.2 J/m2 . b) Given your answer in part (a), explain why nucleation of the β phase is unlikely to occur if you heat the titanium to 1165 K. What can you do to make nucleation more likely to occur?
Pure titanium has two allotropic forms: β-Ti (high temperature) and α-Ti (low temperature). For equilibrium heating conditions, the low-temperature α phase transforms to the high-temperature β phase at 883 °C (1156K), a) Calculate the critical radius r* and the activation free energy ΔG* for a body-centered cubic beta phase nucleus in a superheated alpha titanium matrix at 1165 K. Assume a spherical nucleus (homogeneous nucleation), ΔGv(1165 K) = - 0.095 J/m3, and σsl = γ = 0.2 J/m2 . b) Given your answer in part (a), explain why nucleation of the β phase is unlikely to occur if you heat the titanium to 1165 K. What can you do to make nucleation more likely to occur?
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. Pure titanium has two allotropic forms: β-Ti (high temperature) and α-Ti (low
temperature). For equilibrium heating conditions, the low-temperature α
phase transforms to the high-temperature β phase at 883 °C (1156K),
a) Calculate the critical radius r* and the activation free energy ΔG* for a
body-centered cubic beta phase nucleus in a superheated alpha titanium
matrix at 1165 K. Assume a spherical nucleus (homogeneous
nucleation),
ΔGv(1165 K) = - 0.095 J/m3, and σsl = γ = 0.2 J/m2 .
b) Given your answer in part (a), explain why nucleation of the β phase is
unlikely to occur if you heat the titanium to 1165 K. What can you do to
make nucleation more likely to occur?
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