Activation free energy for nucleation

In summary, the activation free energy required for the formation of a stable nucleus in metals is different for a cube and a sphere due to the larger surface area of the cube, which requires more energy to create a stable nucleus. However, this difference is not solely attributed to surface area and a better understanding can be achieved by calculating the activation free energy using the differentiation of total energy and surface area energy with respect to cluster size.
  • #1
soul
62
0
Hi everyone,

Question

In metals, for homogeneous nucleation, activation free energy required for the formation of a stable nucleus are different when the nucleus are considered as a cube and considered as a sphere and the relation between them is energy for cube is almost double of the energy for the sphere. Why?

The answer I gave for this question is;

During the transformation, the total energy is used to create the surface, since the atoms on the surface aren't in equilibrium. For sphere and cube which have the same volume, the surface of the cube is greater than the other. Thus, more energy is needed to create a stable nucleus when its shape is cube.

This was our quiz question and I got zerofrom that! However, I still think that this answer is correct. Could you please tell me the faults and missimg parts that you think could be the answer?

Thank you.
 
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  • #2
The question isn't just asking why the activation free energy is larger, it's asking why it's almost twice as large (actually, 1.9 times). Your answer attributes this increase to surface area, but the surface area of a cube is only 24% larger than that of a sphere of identical volume. I trust that's why your answer was marked wrong.

A better answer would have been to show how the activation free energy is calculated (by differentiating the total volumetric and surface area energy with respect to cluster size). This approach yields the 1.9x figure.
 
  • #3




Your answer is generally correct. However, there are a few additional factors that could be considered in explaining the difference in activation free energy between a cube and a sphere in homogeneous nucleation in metals.

Firstly, the surface energy of a material is dependent on its crystal structure and orientation. In metals, the surface energy of a cube is higher than that of a sphere due to the presence of high energy facets on the cube's surface. This difference in surface energy contributes to the higher activation free energy required for the formation of a cube-shaped nucleus compared to a sphere-shaped nucleus.

Secondly, the shape of the nucleus also affects the number of atoms required for its formation. A cube has more edges and corners compared to a sphere, which translates to a larger number of atoms needed to form a stable nucleus. This increase in the number of atoms also contributes to the higher activation free energy for a cube-shaped nucleus.

Lastly, the shape of the nucleus can also affect the diffusion of atoms on its surface. In a cube-shaped nucleus, atoms have to travel a longer distance to reach the edges and corners, which can slow down the diffusion process and increase the activation free energy. In contrast, a sphere-shaped nucleus has a more uniform surface, allowing for easier diffusion of atoms and lower activation free energy.

In conclusion, the difference in activation free energy between a cube and a sphere in homogeneous nucleation in metals is primarily due to the difference in surface energy, the number of atoms required for formation, and the diffusion of atoms on the surface. It is important to consider all of these factors in understanding the energetics of nucleation in materials.
 

1. What is activation free energy for nucleation?

Activation free energy for nucleation is a measure of the energy required to initiate the formation of a new phase or particle in a system. It is a thermodynamic parameter that describes the energy barrier that must be overcome for nucleation to occur.

2. How is activation free energy for nucleation calculated?

The activation free energy for nucleation is calculated using the classical nucleation theory, which takes into account the system's thermodynamic properties, such as temperature, pressure, and chemical potential. It also considers the size and shape of the nucleating particle, as well as any interactions between the new phase and the existing phase.

3. What factors affect the activation free energy for nucleation?

The activation free energy for nucleation is affected by several factors, including temperature, pressure, chemical potential, and the properties of the nucleating particle. Other factors that can influence it include the presence of impurities or defects in the system, as well as any external forces or fields.

4. Why is activation free energy for nucleation important?

The activation free energy for nucleation is important because it determines the likelihood and rate at which new phases or particles will form in a system. It is a critical factor in many natural and industrial processes, such as crystal growth, precipitation, and phase transformations.

5. How can activation free energy for nucleation be controlled or manipulated?

The activation free energy for nucleation can be controlled or manipulated by adjusting the system's thermodynamic properties, such as temperature, pressure, and chemical potential. It can also be influenced by changing the size and shape of the nucleating particles or by adding impurities or external forces to the system. Understanding the factors that affect activation free energy for nucleation can help scientists develop strategies to control and optimize nucleation processes.

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