MD/MC simulation in VCSGC ensemble

[Alise9876]

Hi, I have a question about the VCSGC ensemble.
How should I set the chemical potential of the species in my system to fix the average fluctuations of their concentration on a specific value? For example, using 16 element General NEP, I have a CuZrAg alloy. I want to use the Monte Carlo VCSGC ensemble. What should I put for the Chemical Potential of Cu Zr Ag, so that their average concentration is Cu=40%, Zr=50%, and Ag=10%? I read Sadigh and Rahm papers in the references but couldn't figure this out.
thanks

[brucefan1983]

Thanks for the question. I think the expert Paul Erhart might have good comments or even existing tutorials on this. @erhart1

[erhart1]

Thanks for your question. In the VCSGC ensemble you do not control the chemical potential but rather the average constraint phi and the variance constraint kappa. The former approximately controls the composition whereas the latter controls the fluctuations. The implementation in GPUMD differs slightly from the common implementation used in, e.g., icet/mchammer, in so far that as phi spans a different range. To scan your composition over the entire range you should vary phi between approximately -2 and +2 (instead of about -2 to 0). This principle is illustrated in the figure below, which shows results for the Ti-Zr system on the BCC and HCP lattices. By varying phi with a "sufficiently strong" kappa (the recommended value of 200 should be fine for most cases), you can then vary the composition practically linearly by changing phi. You can then extract the derivative of the free energy and by integration over composition the free energy.