Can any body clarify me, the diffusion coefficient calculated using the slope of mean square displacement(MSD) curve is the tracer diffusion coefficient or the chemical diffusion coefficient. I am trying to calculate the the activation energy and it is not in agreement with experiments. I have taken the calculated diffusivity from the MSD graph as the chemical diffusion coefficient.
The chemical diffusion coefficient is given by the following expression acording to Darken's theory:
Dchem= NA DB + NB DA where DA and DB are called intrinsic diffusivities, which may be obtained from the tracer diffusivities if one knows the chemical factor that is defined by {1 + dLn Gama A /dLn NA} where Gama is the chemical activity coefficient of species A, NA and NB are mole fractions that sums up to unity.
I am not very sure about your data acquisition system but no matter what is it you may get at most tracer diffusion coefficient.
Above equation also shows that the chemical diffusivity of an alloys system is controlled by the diffusivity of the minor species, which is also called solute and it has much smaller concentration in the system.
Note: If you wish to get more help from me you should give more detailed and concise information about the procedures adopted in your analysis.
I have run a MD simulation taking Buckingham potential as the short range potential with a set of parameter. Then I got the trajectory and from the trajectory i have calculated the MSD for O2- ion. Then I calculate the diffusivity D as D=MSD/6t where t is the time of evolution of the system. Now I am confused that whether I am calculating the tracer diffusion or the chemical diffusion. Please clarify me.
You are calculating the tracer diffusivity without the correlation correction and without the consideration that the final site should be vacant. Otherwise that would be interstitial type of diffusion. If one assumes that the vacancy mechanism is operating then the correlation between the tracer and vacancy enters into account as a factor, the value of which depends on the structure. SC= 0.653, BCC= 0.727, FCC= 0.781 and HCP(a)= 0.7812 and HCP(c)=0.7814 , Diamond= 1/2.
Probably you are making fundamental error in the calculation of the mean flight time THO (the inverse of the jump frequency) from one equilibrium position to another equilibrium position, which appears as t in your equation. This quantity depends on the potential barrier as well as the choice of the path, which takes you from one position to the other position, which should be vacant. Therefore you have to take into account the vacancy concentration (fraction) into account. That is very small and depends on the temperature as well. If you don't consider that there would be large deviation from experiment. At room temperature Nv = 10^-8 and near melting temperature 10^-4.
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