Dear all,
I am a PhD student using simulation package ATAT in a paper. The code is convenience and powerful, and the guide is easy to follow. However, I still have some questions. I am not senior in thermodynamics, thus the questions may be stupid. I will be appreciate it if any help.
The first question is the concentration in Monte Carlo simulation (emc2). I guess the concentration is the concentration of first element in lat.in (for example, 0 0 0 Cu,Al, then the concentration is Cu). However, this concentration ranges from -1 to 1, which makes me very confused. I noticed that the chemical potential is defined as mu(Cu)- mu(Al) [A van de Walle and M Asta, 2002 Modelling Simul. Mater. Sci. Eng. 10 521], so does it mean that concentration is xCu- xAl as well?
Follow the first question, the second question is that why mu(Cu)- mu(Al) is chosen as constraint of semi-grand canonical potential rather than mu(Cu) or mu(Al) only? Can anyone give me any hint or introduce some related literature to me?
The third question is that how can I make sure the starting point (T0 and mu0) is stable? For temperature the user guide suggested me to start form 0K where every ground phase will be stable, but I don’t understand how to confirm a corresponding chemical potential. It seems like the user guide plotted a convex hull and take the slope between energy and concentration of each neighbour ground state, and the slope is a bound stable chemical potential in 0K. Does it mean that the chemical potential will become more and more positive with selected ground phase contained more and more Al element?
Thank you very much!
Concentration is -1 for pure A, +1 for pure B.
To get physical concentration of B, just use (x+1)/2
The chemical potential is defined as the difference between the two sorts. IIUC (please someone correct me if wrong, I’m quite new to ATAT myself) this means that mu=0 means that the semi-grand-canonical potential has no preference for either species.
Concerning the 3rd question, if you have, for example, phases A, AB, and B, a input chemical potential of 0.5 stabilizes A, 1.5 stabilizes AB, 2.5 stabilizes B. The logic is that for convenience, in the input the chemical potential is normalised so that phase boundaries are at integer values.
Dear mbaeker,
Thank you very much!
You have solved most of my questions but I still feel confused about the third one. If I can input a chemical potential of a phase by only knowing the order it appears in convex hull, then does this chemical potential have a real physical meaning? You see for Al-Cu systems, M-NM-1-Mg will be stabilised by 0.5, and for Fe-C systems, M-NM-1-Fe will be stabilised by 0.5 as well, since both of them are the first phase appeared in their individual convex hull. However, they are different systems.
I noticed that you said the potential are ‘normalised’, also in guide the chemical potential is called ‘dimensionless’. So I think of concentration, which is also a constant for any phase consist of any element A and B only if the form of phase is AxBy, while x and y are constants. Nevertheless it still need a condition that the phase have same x and y, but for chemical potential I can find no condition to restrict (the only restrict I know is its appear order in gs_str.out file). Such a freedom make me very confused. What’s the relationship of such input chemical potential compared with the chemical potential of output files (the data right after temperature) ? Could you please tell some details?
Thank you!
ATAT uses two conventions for mu:
As an input variable, the phase boundaries are at mu=1, 2 etc.
These are converted by ATAT to the corresponding physical mu-value. You can simply run a single emc2-run to see which physical mu corresponds to which input-mu.
(At T=0, it should simply be the change in the energy if you replace one A-atom with B, IIUC).
Probably it would have been easier to give the input variable a different name…
PS: PLease note that I am an absolute newbie with ATAT, just having started looking at it, so I do not guarantee that I correct.