I want to calculate the defect formation energy for different systems with defects (both for atomic vacancies and doping impurity) using VASP.
I have found some papers from Physical Review Letters and Physical Review B to calculate defect formation energy in different cases. But I am not getting how to calculate the chemical potential of individual atoms using VASP.
It seems you are not the first person confused with that. I also spent some time trying to understand where to get the correct chemical potentials.
The physically reasonable answer is: chemical potentials for each element depend on the conditions of the experiment. If you carry, say, crystal annealing in sodium vapour that increases the chemical potential for sodium. Quite logically and even trivially, sodium from sodium vapour easily enters your crystal, while in vacuum it does not.
So, the chemical potential for certain element depends on the chemical form in which that element is present in the experimental conditions, on its concentration and on the temperature.
This is why most people use total energies instead of honestly calculated chemical potentials. Take the most widespread chemical form of your element (say, O2 for oxygen, metallic sodium for Na) and calculate total energy per one atom. Use this value instead of chemical potential.
This is what I get thinking about this question and looking what other people do, but, may be, someone can provide better answer.
It seems you are not the first person confused with that. I also spent some time trying to understand where to get the correct chemical potentials.
The physically reasonable answer is: chemical potentials for each element depend on the conditions of the experiment. If you carry, say, crystal annealing in sodium vapour that increases the chemical potential for sodium. Quite logically and even trivially, sodium from sodium vapour easily enters your crystal, while in vacuum it does not.
So, the chemical potential for certain element depends on the chemical form in which that element is present in the experimental conditions, on its concentration and on the temperature.
This is why most people use total energies instead of honestly calculated chemical potentials. Take the most widespread chemical form of your element (say, O2 for oxygen, metallic sodium for Na) and calculate total energy per one atom. Use this value instead of chemical potential.
This is what I get thinking about this question and looking what other people do, but, may be, someone can provide better answer.
The "An Introduction to Applied Statistical Thermodynamics" book by Stanley Sandler (or any other statistical mechanics book) contains expressions for Gibbs free energies of an ideal gas (=chemical potential) that require knowledge of temperature, pressure, vibrational frequencies, principal moments of inertia, as well as the electronic energy of a given molecule, calculated directly from VASP. I believe "Atomic Simulation Environment" platform (ASE) has such expressions built-in and probably represents the most convenient way to calculate chemical potentials using VASP. See https://wiki.fysik.dtu.dk/ase/. Also, I suggest checking out the "ab initio thermodynamics" approach, pioneered by M. Scheffler in early 2000's, for example, Reuter and Scheffler, Physical Review B 65.3 (2001): 035406. They employ atomic chemical potentials to calculate relative stability of material phases as a function of reaction conditions.
Hi there,
I like the explanations of Gaussian Inc. very much:
http://gaussian.com/thermo
They provide a detailed and step by step description of how to calculate each contribution to the chemical potential. They use the analytical expressions as well as give examples which help you understanding.
Alex
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