2.4 Nucleation: Critical Radius

Interactive Graph
The volumetric Gibbs energy used in the calculation of the critical radius for growth of a nucleus changes as the temperature is increased (or decreased) above (or below) the equilibrium reaction temperature. Figure 2.06 will allow you to change the ΔGrxn value by changing the temperature beyond equilibrium |ΔT| (the overstepping value). Click on Figure 2.06 to open a larger version and move the |ΔT| slider to see this effect. There are also sliders to change how the ΔGrxn value changes with temperature and to change the interfacial Gibbs energy (σA). Because ΔGrxn for chemical reactions is commonly tabulated in molar units, the molar volume of the product phase is needed to convert the data to Gibbs energy per unit volume ΔGV. There is also a slider to change the molar volume.

As you increase the |ΔT| with its slider in Figure 2.06, you will see the ΔGV increase and the calculated critical radius decrease. Although the interfacial Gibbs energy does change with temperature, typically decreasing with increasing T and increasing with decreasing T, these changes are poorly known and believed to be small so they are not included in this model.

As an example, consider the kyanite = sillimanite reaction at a pressure of 0.6 GPa. You can see Gibbs energy data for this reaction here. The value of dΔGrxn/dΔT for this reaction is about -12 J/K/mole of Al2SiO5. The molar volume for sillimanite is about 50 cm3/mole of Al2SiO5. Using these values and an interfacial Gibbs energy of 0.015 J/m2, what is the ΔT required to have a critical nucleus with a radius of 1 nm? Use Figure 2.06 to answer the question, type your answer in the box.

What is the ΔT required (number only) in °C?:

Press "Enter" after you type in the number.