I Want to Understand What is this cluster expansion. Please provide me the material which explain cluster expansion from basics.
If you haven’t looked at the ‘original’ paper, I highly suggest looking into that first (it is the first reference in the sqs paper for the code).
The general idea is to build up your supercell, using smaller clusters. Each subcluster (or sub lattice) has its own weight in this build up process. With regards to the objective function the code minimizes, this is where mz_lida’s comment comes in. In the Ising model, the energy is minimized (naturally), as the atoms on the lattice obtain the same spin. In this similar sense, if you have a lattice containing two types of atoms, you can pick (for example) spin up (+1) and spin down(-1). Using these spin numbers, you can develop a correlation function which is used in the objective function. For example, if you had 1 atom of A type and 1 atom of B type, you can expect to have a correlation parameter of 0.
Hope that makes a bit more sense, I’m still trying to figure out the details as I personally find the papers I’ve read so far not too in depth.
Hi, I started to learn cluster expansion 3 weeks ago. I didn’t know anything about that. Now I have a good idea of what it is and am trying to learn ATAT code. This is what I finally did:
First I learned about the Ising model, for doing that I listened to 2 lectures in Youtube:
https://www.youtube.com/watch?v=3hh0lJZbUfo (from minute 35)
https://www.youtube.com/watch?v=AT4_S9vQJgc
After that this article explained the method very well:
Cluster expansion method for adsorption: Application to hydrogen chemisorption on graphene(by Sluiter and Kawazoe)
I hope that’ll help.
Lida
textbook level:
F. Ducastelle. Order and Phase Stability in Alloys
Some reviews of mine:
papers:
https://dx.doi.org/10.1007/s11837-013-0764-3
https://arxiv.org/abs/cond-mat/0106490
https://dx.doi.org/10.1103/RevModPhys.74.11
https://arxiv.org/abs/cond-mat/0201511
in books:
A. van de Walle.
First-principles alloy thermodynamics.
In P. Derosa and T. Cagin, editors, Multiscale Modeling: From Atoms to Devices. CRC press, 2010.
A. van de Walle and M. Asta.
First-principles modeling of phase equilibria.
In S. Yip, editor, Handbook of Materials Modeling, volume Part A. Springer, Dordrecht, the Netherlands, 2005.