Source-linked AI summary
Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit
Axel van de Walle
TL;DR
ATAT needed broader capabilities for complex alloy systems and thermodynamic effects beyond configurational entropy. This paper presents practical extensions, including generalized cluster expansions and interfaces for atomistic calculations, and formally demonstrates the multicomponent multisublattice extension. The resulting toolkit covers these additions while continuing to evolve through new features.
Problem
ATAT required extensions beyond its earlier functionality to support multicomponent multisublattice alloys and nonconfigurational entropy sources.
Method
The paper provides a practical overview of ATAT’s new capabilities and formally develops the cluster expansion extensions for multicomponent multisublattice alloys.
Results
ATAT now supports multicomponent multisublattice systems, vibrational and electronic entropy, SQS generation, tensorial cluster expansions, multiple atomistic codes, and analysis utilities.
Takeaways & Limitations
The additions provide a practical toolkit for determining alloy thermodynamic properties across more complex compositions, sublattices, entropy sources, and computational workflows.
Takeaways & Limitations
The documented feature set is not exhaustive, and further additions depend partly on user interest and available funding.
Abstract
from arXiv · showhide
A number of new functionalities have been added to the Alloy Theoretic Automated Toolkit (ATAT) since it was last reviewed in this journal in 2002. ATAT can now handle multicomponent multisublattice alloy systems, nonconfigurational sources of entropy (e.g. vibrational and electronic entropy), Special Quasirandom Structures (SQS) generation, tensorial cluster expansion construction and includes interfaces for multiple atomistic or ab initio codes. This paper presents an overview of these features geared towards the practical use of the code. The extensions to the cluster expansion formalism needed to cover multicomponent multisublattice alloys are also formally demonstrated.
1 Introduction
This paper documents major ATAT additions since its previous review and provides a practical overview of their use. The extensions cover alloy complexity, entropy modeling, structure generation, cluster expansions, code interfaces, and analysis utilities.
- 1 Introduction: ATAT determines thermodynamic properties of solid-state alloys from first-principles calculations using cluster expansion models.The toolkit builds effective Hamiltonians that reproduce quantum-mechanical results and support efficient thermodynamic calculations.
- 1 Introduction: The paper describes new ATAT support for multicomponent multisublattice alloy systems.This extends the toolkit to more chemically and structurally diverse alloy systems.
- 1 Introduction: ATAT now includes vibrational and electronic entropy as nonconfigurational entropy sources.These additions broaden thermodynamic modeling beyond configurational contributions.
- 1 Introduction: The toolkit adds Special Quasirandom Structures generation and tensorial cluster expansion construction.These features support modeling disordered alloys and more general cluster-expansion quantities.
- 1 Introduction: ATAT provides interfaces for multiple atomistic or ab initio codes and new conversion and analysis utilities.The paper presents these additions as part of a practical user-oriented overview.
- 1 Introduction: The documented features are not exhaustive because ATAT continues to receive new additions.The paper directs readers to the distribution manual or website for up-to-date information.
2 Multicomponent multisublattice systems
ATAT extends cluster expansion methods and software support to alloys with multiple components and sublattices. The generalized formalism preserves a complete orthogonal cluster-function basis while distinguishing correlation, composition, and chemical-potential representations for practical calculations.
- Multicomponent multisublattice extensions: ATAT allows different lattice sites to host arbitrary, potentially different numbers of elements, including elements shared across sublattices.The sublattices may consist of symmetrically equivalent sites or not.
- Cluster expansion formalism: A configuration is represented by occupation variables σ_i, where each site i can host M_i components and σ_i ranges from 0 to M_i −1.This is the lattice-gas representation used by the generalized cluster expansion.
- Cluster expansion formalism: The generalized expansion uses cluster functions, symmetry multiplicities, and effective cluster interactions to represent configuration-dependent scalar quantities.Clusters are grouped by lattice-space-group symmetry, while multiplicities count equivalent clusters and coefficients are fitted ECIs.
- Cluster expansion formalism: Cluster functions form a complete orthogonal basis because their inner product is zero for differing clusters and one for identical clusters.The proof accommodates site-dependent M_i and mixed products of different single-site functions.
- Composition representations: Point correlations, nonredundant concentrations, and full concentrations serve different algorithmic roles in energy prediction, convex-hull construction, and user-facing output.These quantities are linearly related through constant matrices and vectors that may be rectangular and noninvertible.
- Software functionality: ATAT’s mmaps and memc2 tools extend cluster-expansion construction and hybrid canonical/grand-canonical Monte Carlo simulations to multicomponent systems.The matrix X also converts chemical potentials into shifts of effective cluster interactions for grand-canonical simulations.
3 Nonconfigurational sources of entropy
ATAT provides two approaches for calculating vibrational free energies: an accurate but computationally demanding force-constant fit and a faster stiffness-vs.-length scheme based on transferability. The fitfc workflow relaxes structures, generates perturbed geometries, and can include quasiharmonic thermal expansion through volume-dependent phonon frequencies.
- 3.1 Lattice vibrations: ATAT offers two techniques for calculating vibrational free energies: the fitfc force-constant method and the stiffness-vs.-length scheme.The latter is implemented in fitsvsl and svsl.
- 3.1.1 The fitfc code: The fitfc code fits a Born-von Kármán spring model to reaction forces from imposed atomic displacements in a supercell.The method is preferred for very accurate calculations because the spring interaction range can be increased as needed.
- 3.1.1 The fitfc code: The fitfc approach is computationally demanding when vibrational free energies are needed for many structures during cluster-expansion construction.
- 3.1 Lattice vibrations: The stiffness-vs.-length scheme reduces spring-constant calculations by exploiting transferability across structures after controlling for factors such as bond length or composition.Its accuracy is limited by transferability, which typically does not extend beyond nearest-neighbor springs.
- 3.1.1 The fitfc code: The fitfc workflow begins with relaxed and unrelaxed structures, then generates perturbed geometries using user-specified supercell separation, displacement, strain-level, and maximum-strain parameters.The unrelaxed structure determines neighbor shells and interatomic distances, while the relaxed geometry supplies the relaxed structure.
- 3.1.1 The fitfc code: Specifying multiple isotropic strain levels invokes a quasiharmonic model that accounts for thermal expansion through volume-dependent phonon frequencies.The code subsequently determines volume as a function of temperature by minimizing the free energy.
- 3.1.1 The fitfc code: Linear-response calculations would account for infinite-range interactions and are preferable in principle for ionic materials, but ATAT does not implement them.They must be performed within the ab initio code itself.
3. Each vol
This section describes how ATAT generates strained and perturbed structures, obtains ab initio reaction forces, fits force constants, and diagnoses unstable phonon modes.
- 3. Each vol: ATAT creates one directory per imposed strain and perturbation subdirectories containing ideal, relaxed, and perturbed structures.The workflow then invokes ab initio calculations for reaction forces and further relaxations as required.
- 3. Each vol: Opposite-sign perturbations can cancel third-order force-constant effects exactly in the fit.When symmetry already cancels these terms, ATAT generates only the positive perturbation.
- 3. Each vol: The ab initio code calculates reaction forces for each perturbation without allowing structural degrees of freedom to relax.These force.out files provide the data used by fitfc.
- 3. Each vol: fitfc -f -fr=... fits force constants and performs phonon calculations, with -fr controlling the included spring-interaction range.The range should generally not exceed half the earlier -er distance, and convergence should be checked as -fr increases.
- 3. Each vol: Unstable-mode messages can indicate mechanical instability, although some modes may be artifacts of the fitting procedure.ATAT can generate perturbations along unstable directions for additional ab initio force calculations.
8. The ab initio code should then be run in the subdirectory generated (named vol
This section documents ATAT’s outputs and the fitsvsl workflow for deriving transferable, length-dependent force constants from diverse structure calculations.
- 8. The ab initio code should then be run in the subdirectory generated (named vol: The output files include free energy, entropy, phonon density of states, force constants, and equation-of-state data.For example, fvib contains free energy, svib contains entropy, and vdos.out contains phonon density of states.
- 8. The ab initio code should then be run in the subdirectory generated (named vol: fitsvsl determines bond-stiffness versus bond-length relationships so svsl can predict vibrational properties across many similar structures.The approach is worthwhile when vibrational properties are needed for a large number of structures.
- 8. The ab initio code should then be run in the subdirectory generated (named vol: The fitting structures must be diverse enough to contain every chemical-bond type that svsl will encounter.For binary alloys, this typically requires structures including pure and mixed bonding environments.
- 8. The ab initio code should then be run in the subdirectory generated (named vol: fitsvsl uses force.out and corresponding structure files to create length-dependent force constants in slspring.out.Users should inspect the output because insufficient fitting data can leave parameters equal to zero.
- 8. The ab initio code should then be run in the subdirectory generated (named vol: The default stiffness-versus-length model is linear, while higher-order, direction-dependent, and composition-dependent alternatives are available.The -op, -dd, and -pc options control these model choices.
4 Special Quasirandom Structure generation
ATAT generates Special Quasirandom Structures by matching selected disordered-state correlations, then supports screening, parallel or stochastic search, and cluster-expansion use.
- 4 Special Quasirandom Structure generation: Cluster expansions are essential for nondilute configurational disorder, while fully random alloys can sometimes be approximated directly at sufficiently high temperatures.The random limit may be estimated from a small number of supercell ab initio calculations.
- 4 Special Quasirandom Structure generation: SQS generation begins with a lattice file and a composition-matching superstructure, followed by calculation of target pair and multibody correlations.The geometry of the composition structure is irrelevant provided its composition and superstructure constraints are correct.
- 4 Special Quasirandom Structure generation: gensqs -n=16 generates 16-atom SQS candidates, but it lists only structures with exactly the requested unit-cell size.If no candidates are produced, the correlation-matching range must be reduced.
- 4 Special Quasirandom Structure generation: Candidate SQS can be screened using additional, larger-radius correlations to distinguish and rank structures beyond the initial criteria.This is useful because candidates matching the specified correlations can still differ in untested correlations.
- 4 Special Quasirandom Structure generation: Parallel gensqs processes and stochastic sampling reduce the time required for exhaustive SQS generation.Atom-permutation sampling becomes increasingly advantageous away from equiatomic compositions.
- 4 Special Quasirandom Structure generation: SQS structures can be added to cluster-expansion training sets to ensure that disordered-state properties are reproduced.They are incorporated by placing the desired SQS in a str.out file and running an ab initio calculation.
5 The tensorial cluster expansion
ATAT extends cluster expansion from scalar properties to tensors by encoding tensor symmetries, generating generalized clusters, fitting structure-specific tensors, and expanding intensive quantities.
- 5 The tensorial cluster expansion: The tensor formalism follows the scalar cluster-expansion procedure while incorporating the tensor’s specified symmetry constraints.The paper presents this as a practical use of the generalized formalism.
- 5 The tensorial cluster expansion: A gcetensor.in file specifies the tensor rank and index permutations that leave the tensor invariant.For strain or stress, the tensor is symmetric; elastic constants require additional permutation symmetries.
- 5 The tensorial cluster expansion: The gce command generates symmetry-distinct clusters using syntax analogous to corrdump for scalar expansions.Pair, triplet, and higher-order cluster-radius limits can be supplied.
- 5 The tensorial cluster expansion: Each structure’s property tensor is calculated with application-dependent tools before the generalized cluster expansion is fitted.Examples include calculating static lattice strain or elastic constants from ab initio structures.
- 5 The tensorial cluster expansion: clusterexpand -pa -g strain or clusterexpand -pa -g elas performs the generalized expansion, with -pa indicating intensive quantities per atom.The -g option invokes the generalized cluster-expansion mode.
6 Interfaces with ab initio codes
ATAT provides interfaces to several ab initio and atomistic codes through a common runstruct framework. These interfaces standardize geometry and parameter inputs, execute calculations, record outputs, and support remote or pooled job execution.
- ATAT supports runstruct interfaces for VASP, GULP, and abinit, while PWscf is under development.
- Each interface reads ATAT-format geometry from str.out, or preferentially from hint.out when an externally supplied relaxed-geometry guess exists.
- Code-specific calculation parameters are separated into xxxx.wrap files, preserving interoperability among ATAT components.
- Interfaces run the selected ab initio or atomistic code and write energies, relaxed geometries, forces, stresses, and electronic density of states to standardized files when implemented.
- Remote execution is enabled through a command prefix, while pollmach dispatches waiting jobs across processors and manages batches of calculations.
- Calculation failures are recorded in an error file, providing a standard diagnostic output.
7 Utilities
ATAT includes utilities that expose core algorithms and support structure generation, defect construction, file conversion, fitting, neighbor analysis, and text parsing.
- corrdump finds symmetry operations, enumerates clusters, and calculates correlations, including those of the disordered state.
- genstr enumerates superstructures of a specified lattice, while pdef generates substitutional point-defect supercells.
- cellcvrt manipulates ATAT structure files, including coordinate conversion and supercell or subcell construction.
- lsfit performs least-squares fitting and nnshell identifies nearest-neighbor shells.
- Text parsing utilities include getvalue, getlines, and sspp, with further information available through each utility’s -h option.
8 Conclusion
The paper concludes by outlining prospective ATAT developments and noting that future priorities will depend partly on user interest and available funding.
- Planned work includes tighter integration between Monte Carlo outputs and thermodynamic databases such as Thermocalc and Pandat.
- Material-property optimization modules are proposed to exploit the tensorial cluster expansion.
- Further goals include more automated treatment of nonconfigurational free energy and improved electronic free-energy calculators.
- The direction of subsequent development will depend substantially on user-expressed interests and the funding obtained by the author.
A Correlation to concentration conversions
ATAT converts between point correlations and concentrations by selecting an independent structure set, constructing transformation matrices, and removing redundant rows.
- ATAT begins by enumerating structures in increasing unit-cell size and retaining non-colinear augmented point-correlation vectors until their number matches the vector dimension.
- For the retained structures, ATAT forms matrices A and B from concentration and augmented correlation vectors, with B square and invertible by construction.
- The resulting augmented transformation matrix yields X from its nonfinal columns and x0 from its final column.
- Removing colinear rows from X produces C, while the corresponding elements of x0 are removed to produce c0.