Understanding Dendrite Formation in Solidification
During the solidification of a pure metal, heat is released at the liquid-solid interface (latent heat of fusion). Dendrites, which are tree-like crystal structures, form because of a temperature gradient in the liquid adjacent to the interface. The interface itself is at the melting temperature ($T_m$).
Analyzing the Temperature Gradient
For solidification to occur, the liquid must be slightly cooler than its equilibrium melting point. This phenomenon is related to supercooling:
- The interface temperature is the melting point, $T_m$.
- Solidification requires heat removal from the interface into the liquid.
- As heat moves into the liquid, the liquid just ahead of the interface must be at a temperature below $T_m$ for heat transfer to occur.
- Therefore, as we move from the interface into the liquid, the temperature must decrease.
This temperature decrease establishes the thermal condition necessary for crystal growth and the eventual formation of dendrites, especially under conditions where heat removal is directional.
Conclusion on Interface Temperature
The temperature from the interface into the liquid decreases, creating a thermal gradient that drives the solidification process.
Important Questions from Solidification Cooling Curve Analysis
- Critical value of the Gibbs energy of nucleation at equilibrium temperature is
- Which one of the following schematics represents the variation of the rate of nucleation of solid from a pure liquid metal as a function of undercooling ($\Delta T = T_m - T$, where $T_m$ and $T$ are the freezing temperature and the liquid temperature, respectively)?
A given volume of liquid is undercooled just below the melting temperature to form a spherical solid nucleus (consider homogeneous nucleation). The Gibbs free energy of solidification ($\Delta G_v$) is ($- 0.5 \times 10^8$) J/m$^3$. The solid-liquid interfacial energy ($\gamma$) is isotropic and its value is 0.1 J/m$^2$.
The critical nucleus size for a stable nucleus is __________ nm (answer in integer).
During solidification of a pure metal, the radius of critical nucleus at an undercooling of 10 K is ________ $\times 10^{-9} \text{ m}$ (answer rounded off to 1 decimal place).
Given: solid/liquid interface energy = $0.177 \text{ J} \cdot \text{m}^{-2}$,
melting point of the metal = 1356 K and
latent heat of fusion = $1.88 \times 10^9 \text{ J} \cdot \text{m}^{-3}$Consider homogeneous nucleation of a spherical solid in liquid. For a given undercooling, if surface energy of a nucleus increases by $20\%$, the corresponding increase (in percent) in the critical radius of the nucleus is: ___________(round off to nearest integer).
