Calculating force between atoms

[casmir]

Hi, can someone please tell me how to calculate force which is acting on one atom. Let's look at the crystal of manganese for example, manganese crystal is simple cube (as far I remember) so how can I calculate force acting on one of 8 atom in that crystal?

And one more question, it's often said that temperature is average kinetic energy of some object. So if It's known to me that some object have temperature of 300K and I know the mass of that object is it possible from this data to calculate kinetic energy of this object?

English isn't my native language so it might be that I'm bit unclear to you, so just warn me and I would try to be more clear.

 

[mfb]

Force from what, and on which parts?
The total average force is 0, as the atom does not accelerate away from its position.

And one more question, it's often said that temperature is average kinetic energy of some object.

Temperature is related to the average unordered kinetic energy. If you put an object on a moving train, it gains kinetic energy, but not temperature.

So if It's known to me that some object have temperature of 300K and I know the mass of that object is it possible from this data to calculate kinetic energy of this object?

You need to know the internal degrees of freedom of that material.

 

[casmir]

Force from what, and on which parts?
The total average force is 0, as the atom does not accelerate away from its position.

OK, I've set the question wrong, I want to know how to calculate each component of force acting upon each atom.

Temperature is related to the average unordered kinetic energy. If you put an object on a moving train, it gains kinetic energy, but not temperature.

Yeah i know that, but didn't know that term.

 

[Vanadium 50]

Oh, and manganese is not simple cubic. The only element that is simple cubic is polonium.

 

[casmir]

Oh, and manganese is not simple cubic. The only element that is simple cubic is polonium.

Thanks, but for this example let's take it is :)

 

[mfb]

OK, I've set the question wrong, I want to know how to calculate each component of force acting upon each atom.

Simple coulomb force. As approximation, you could consider both electrons and nuclei at the same position. The distance between atoms depends on the material and lattice structure.

Yeah i know that, but didn't know that term.

It depends on the material. For a simple cubic lattice, you have vibrations in 3 dimensions, with 6 degrees of freedom per atom and therefore an average of 3kT of energy per atom with the Boltzmann constant k. Electrons are more complicated and depend on the band structure - for an isolator, you can neglect them.

 

[casmir]

Simple coulomb force. As approximation, you could consider both electrons and nuclei at the same position. The distance between atoms depends on the material and lattice structure.

So for calculation I'm using just electrons from last orbital or all electrons?

It depends on the material. For a simple cubic lattice, you have vibrations in 3 dimensions, with 6 degrees of freedom per atom and therefore an average of 3kT of energy per atom with the Boltzmann constant k. Electrons are more complicated and depend on the band structure - for an isolator, you can neglect them.

OK, and if we are looking at just one crystal cube with 8 atoms and we know the temperature and mass of this cube how can we calculate energy of this crystal?

Thanks for your answers.

 

[mfb]

So for calculation I'm using just electrons from last orbital or all electrons?

You are looking for all particles you want to consider.

OK, and if we are looking at just one crystal cube with 8 atoms and we know the temperature and mass of this cube how can we calculate energy of this crystal?

The average energy of the crystal. The whole crystal has just 8 atoms? This is not sufficient to use the usual approximations of thermodynamics (large number of particles), you would need different concepts to analyze this cube.

 

[casmir]

The average energy of the crystal. The whole crystal has just 8 atoms? This is not sufficient to use the usual approximations of thermodynamics (large number of particles), you would need different concepts to analyze this cube.

I thought it would be more simple with just 8 atoms, but OK, let's say that this material has 16000000 atoms and we know the temperature and mass of this material, what is the average energy than?

 

[mfb]

~3kT per atom, with k=1.38*10^-23 J/K and T=300K this corresponds to 1.2*10^-20 J per atom. You can multiply that with the number of atoms to get a rough estimate of the total energy. You can divide it by the mass of a single atom to get the specific heat (J/kg).
Usually, this is an overestimation of the total thermal energy, a better calculation would use the Debye model.