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

[Helpless guy]

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.

 

[mfb]

You know that this distance r in your material is at a special point of the potential. Otherwise the distance would increase or decrease.

 

[ehild]

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]

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.

 

[Helpless guy]

Thank you so very much! It's a brilliant idea.