How Can I Determine ε and σ for Lennard Jones Potential in an FCC Structure?

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In summary, the task is to find the parametres ε and σ for a fcc structure with a net parametre of 4.46*10-10m and a potential energy/mol of -1.88kJ/mol. The equation used is Φ=-4ε[(σ/r)6-(σ/r)12]. One method to find the values is to use the derivative of Φ and set it equal to zero. This will provide an additional equation to solve for the parametres.
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Homework Statement


I have a fcc structure, the net parametre is 4.46*10-10m, the potential energy/mol is -1.88kJ/mol. My task is to find the parametres ε and σ of the potential.

Homework Equations



Φ=-4ε[(σ/r)6+(σ/r)12]

The Attempt at a Solution


I can find the value of r using the net paramentre; r=[(√2)/4]*a.
If I divide the potential energy/mol by 6.02*1023 I can find the potential energy/atom, but I still have only one equation with both of the parametres to determine.
I have to find another equation with one or both paramentres, but I don't know where to find it.

All sugestions are appreciated.
Thank you very much.
 
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You know that this distance r in your material is at a special point of the potential. Otherwise the distance would increase or decrease.
 
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Helpless guy said:

Homework Statement


I have a fcc structure, the net parametre is 4.46*10-10m, the potential energy/mol is -1.88kJ/mol. My task is to find the parametres ε and σ of the potential.

Homework Equations



Φ=-4ε[(σ/r)6+(σ/r)12]

There is a mistake in the formula. It should be Φ=-4ε[(σ/r)6-(σ/r)12]
Helpless guy said:

The Attempt at a Solution


I can find the value of r using the net paramentre; r=[(√2)/4]*a.
If I divide the potential energy/mol by 6.02*1023 I can find the potential energy/atom, but I still have only one equation with both of the parametres to determine.
I have to find another equation with one or both paramentres, but I don't know where to find it.

All sugestions are appreciated.
Thank you very much.
The neighbouring atoms are arranged at such distance from each other where the L-J potential is minimum. Find the derivative of Φ and make it equal to zero: this gives you an additional equation.
 
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Thank you so very much! It's a brilliant idea.
 

FAQ: How Can I Determine ε and σ for Lennard Jones Potential in an FCC Structure?

1. What is the Lennard Jones potential?

The Lennard Jones potential is a mathematical function that describes the potential energy between two neutral atoms or molecules as a function of their separation distance. It is commonly used in molecular simulations and is based on the principle that atoms or molecules are held together by both attractive and repulsive forces.

2. How is the Lennard Jones potential calculated?

The Lennard Jones potential is calculated using the following equation: V(r) = 4ε[(σ/r)^12 - (σ/r)^6], where r is the distance between the two atoms or molecules, ε is the depth of the potential well, and σ is the distance at which the potential is zero. The values of ε and σ depend on the specific atoms or molecules involved.

3. What is the significance of the Lennard Jones potential in molecular simulations?

The Lennard Jones potential is significant in molecular simulations because it accurately describes the interactions between atoms or molecules at a microscopic level. It allows for the prediction of properties such as boiling points, heat capacities, and diffusion coefficients, which are important in understanding the behavior of complex systems.

4. Are there any limitations to the Lennard Jones potential?

Yes, there are limitations to the Lennard Jones potential. It assumes spherically symmetric interactions between particles and does not account for more complex interactions, such as dipole-dipole or hydrogen bonding. Additionally, it is not suitable for describing interactions between charged particles.

5. Can the Lennard Jones potential be modified for different systems?

Yes, the Lennard Jones potential can be modified for different systems by adjusting the values of ε and σ to better represent the interactions between the specific atoms or molecules being studied. Additionally, modifications can be made to the equation to account for additional interactions, such as those mentioned in the previous question.

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