I am confused by the entropy.

[dyc_2008]

dear all,

I substitute an atom in my system with alloying element.
In the OUTCAR, I find the energy of the system is lower than the un-substitute one.
Base on thermodynamics, G=H-TS, it is possible to achieve a lower energy if H and S increase simultaneously.
But, in VASP, the temperature is 0k, then TS=0. So entropy dose not contribute any effect in the equation G=H-TS.

please Somebody tell me how to explain this.
thank you so much.

[alex]

Dear dyc_2008,

could you clarify, if you are talking about the total energy of your doped system or energy differences between undoped and doped systems?

Thx,

alex

[dyc_2008]

dear alex,
differences between undoped and doped systems
thank you

[tlchan]

I don't think you should directly compare the total energies of the doped and undoped system. You can calculate the formation energy. For your case, the formation energy is the energy release to substitute a host atom by a dopant, where the dopant is extracted from a source, and the substituted host atom should go to a sink. Energy is required to extract the dopant from the source, and there is energy gain by depositing a host atom to the sink. The two energies correspond to the chemical potentials, which can be determined by the experimental conditions or your project.

As you mentioned, the total energies from VASP correspond to T = 0, so the contribution from entropy is not included. If you think entropy is important for your project, you have to separately add in the configurational entropy yourself.

[zzhlax]

What is "the configurational entropy"? Is it different from the entropy due to temperature?
thanks

[vistawanted]

Well, based on thermodynamics, G=H-TS, when T=0, G=H, especially when P=0, G=H=U=A, where A and U are Helmholtz Free Energy and internal energy, respectively.
In your system, we may only think about U, which was contributed by chemical bonding and configuration.
Then, all the substitutiaonal process has two steps, from un-sub one -> point defect one -> substituated one. Since doping element and replaced element, let us say element 1 was replaced by element 2, are definitely different, the chemical potential of them should be considered, too.
Therefore, the change of free energy, or internal energy, should be:
DeltaU = (Usub - U2) - (Uun - U1)
Where, Usub and Uun are the total energy of substituted and un-sub models, U2 and U1 are chemical potential of element 2 and 1, which should be obtained from their corresponding most stable phase.