This is a general question on cluster methods:
For precipitations in alloys to grow, they need to be sufficiently large (nucleation barrier). This is usually explained by the fact that there is a (negative) volume energy and a (positive) surface energy so that for small radii, the surface energy is larger than the volume energy and the precipitate will shrink.
My question is: How is this implemented/reflected in Cluster expansion codes? In the simplest case of two atoms A and B, if E_BB is smaller than E_AB, even a cluster of two B atoms will be stable and there is no nucleation barrier. Do we need cluster terms with a large number of atoms to capture this effect? How large does this number have to be?
I’m grateful for any help or a reference where this is explained.
Thanks,
Martin.
Hi,
This is on the application of CE. But as a theory answering the configuration energetics, CE itself does not answer the question of nucleation barrier.
On the application, you need first to get the free energy (that means, including the configuration entropy) of clustered atoms, Bennett overlapping method is on this, you can google it (J Comput Phys 1976;22:245).
Then you got a curve of free-energy G versus number-of-clustered-atoms n. To obtain the so called volume energy and interracial energy (under the picture of classical nucleation), you should fit the curve to an empirical equation (Phys Rev B 1984;29:2689), and re-cast the equation as a function of n and n^2/3.
the process is treating a inhomogeneous system, and the energy error in fact should be larger than the CE cross-validation error.
Thanks a lot for the links, that is very helpful.