Automating First-Principles Phase Diagram Calculations

By Axel van de Walle, Mark Asta, Gerbrand Ceder. 2002

871 citations recorded by the source corpus.

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented.

Subfields: Atmospheric Science, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/3e1d91b1f5245c6518ad47de4d0d8794e81e3848

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In Atmospheric Science

In Atomic and Molecular Physics, and Optics

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Citations in the corpus

AB Initio Atomistic Thermodynamics and Statistical Mechanics of Surface Properties and Functions (2004, background): “While there are some attempts to automatize this procedure (van de Walle and Ceder, 2002), it is probably fair to say that the actual implementation remains to date a delicate task.”
The Intercalation Phase Diagram of Mg in V2O5 from First-Principles (2015, positive): “54 The high-temperature phase diagram is then obtained with GMC calculations on supercells containing at least 1728 Mg/ Va sites (equivalent to a 12 × 6 × 6 supercell of the conventional unit cell) and for a minimum of 100 000 equilibration steps followed by 200 000 sampling steps.”
Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams (2002, background): “enabled the automation of cluster expansion construction [33], signifies that it is now possible for large community of researchers to employ first-principles calculations to augment and complete existing experimental thermodynamic databases without facing the steep learning curve that has tradition”
ElaStic: A tool for calculating second-order elastic constants from first principles (2013, methodology): “This can be done with the help of a cross-validation (CV) method [24–26].”