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CASM: A Clusters Approach to Statistical Mechanics

CASM (https://github.com/prisms-center/CASMcode) is an open source software package designed to perform first-principles statistical mechanical studies of multi-component crystalline solids. CASM interfaces with first-principles electronic structure codes, automates the construction and parameterization of effective Hamiltonians and subsequently builds highly optimized (kinetic) Monte Carlo codes to predict finite-temperature thermodynamic and kinetic properties. CASM uses group theoretic techniques that take full advantage of crystal symmetry in order to rigorously construct effective Hamiltonians for almost arbitrary degrees of freedom in crystalline solids. This includes cluster expansions for configurational disorder in multi-component solids and lattice-dynamical effective Hamiltonians for vibrational degrees of freedom involved in structural phase transitions.

This version of CASM supports:

  • Constructing, fitting, and evaluating cluster expansion effective Hamiltonians with:
    • Occupational degrees of freedom.
  • High-throughput calculations using:

CASM is updated frequently with support for new effective Hamiltonians, new interfaces for first-principles electronic structure codes, and new Monte Carlo methods. Collaboration is welcome and new features can be incorporated by forking the repository on GitHub, creating a new feature, and submitting pull requests. If you are interested in developing features that involve a significant time investment we encourage you to first contact the CASM development team at [email protected].

CASM is currently beta software with very active development. Our goal is that the casm program interface, including file input and output formats, is mostly stable and backwards compatiblity will be taken into account as new features are added (though some breaking changes may occur as we learn from experience). The CASM library libcasm is much less stable and we anticipate significant changes will be incorporated in the near future.

Citing CASM

CASM can be cited using the following four references:

  • [ref1] CASM, v0.1.0 (2015). Available from https://github.com/prisms-center/CASMcode. doi:[include doi here]
  • [ref2] J. C. Thomas, A. Van der Ven, Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles, Physical Review B, 88, 214111 (2013).
  • [ref3] B. Puchala, A. Van der Ven, Thermodynamics of the Zr-O system from first-principles calculations, Physical Review B, 88, 094108 (2013).
  • [ref4] A. Van der Ven, J. C. Thomas, Q. Xu, J. Bhattacharya “Linking the electronic structure of solids to their thermodynamic and kinetic properties”, Mathematics and Computers in Simulation, 80(7) 1393-1410 (2010).

As an example, CASM can be acknowledged in a publication with:

“We used the CASM code [ref1], which automates the construction and parameterization of effective Hamiltonians and implements these Hamiltonians in Monte Carlo simulations [ref2,ref3,ref4].”

Citing Algorithms

CASM utilizes a wide variety of algorithms, many of which were developed by the CASM development team, and some of which have yet to be published. Please cite CASM [ref1] if you implement a particular algorithm from CASM in other software.

CASM also relies on algorithms and methods that have been published in the literature. The cluster expansion for configurational degrees of freedom was rigorously formalized by Sanchez et al. [ref5, ref6]. The anharmonic potential cluster expansion as implemented in CASM was developed by Thomas et al. [ref2]. The local cluster expansion for diffusion barriers was introduced by Van der Ven et al. [ref7].

The algorithms in CASM that enumerate symmetrically distinct configurations rely on algebraic properties of principal ideal domains, which were brought to bear on the problem by Hart and Forcade [ref8]. The fitting of the interaction coefficients of a cluster expansion to first-principles data relies on a minimization of the cross-validation (CV) score, an approach introduced to cluster expansions by van de Walle et al. [ref9]. The approach of using a genetic algorithm to pick interaction coefficients that minimize the CV score was introduced by Hart et al. [ref10] while the depth first search approach is due to Puchala et al. [ref3]. The use of compressive sensing methods to parameterize a cluster expansion was introduced by Nelson et al. [ref11]. Convergence criteria for Monte Carlo sampling are due to van de Walle et al. [ref12].

  • [ref5]: J. Sanchez, F. Ducastelle and D. Gratias, Phys. A 128, 334–350 (1984).
  • [ref6]: D. deFontaine, in Solid State. Phys., ed. H. Ehrenreich and D. Turnbull, Academic Press, vol. 47, pp. 33–176 (1994).
  • [ref7]: A. Van der Ven, G. Ceder, M. Asta, and P. D. Tepesch, Phys. Rev. B 64, 184307 (2001).
  • [ref8]: G.L.W. Hart and R.W. Forcade, Phys. Rev. B 77, 224115 (2008).
  • [ref9]: A. van de Walle and G. Ceder, J. Phase Equilib. 23, 348 (2002).
  • [ref10]: G. L. W. Hart, V. Blum, M. J. Walorski, and A. Zunger, Nat. Mater. 4, 391 (2005).
  • [ref11]: L.J. Nelson, G.L.W. Hart, F. Zhou, and V. Ozoliņš, Phys. Rev. B 87, 035125 (2013).
  • [ref12]: A. van de Walle, M. Asta, Modell. Simul. Mater. Sci. Eng. 10, 521 (2002).

Developers and Contributors:

CASM is developed by the Van der Ven group, originally at the University of Michigan and currently at the University of California Santa Barbara.

Lead developers: John C. Thomas and Brian Puchala

Developers: John Goiri and Anirudh Natarajan.

Other contributors: Min-Hua Chen, Jonathon Bechtel, Max Radin, Elizabeth Decolvenaere and Anna Belak

Acknowledgements

The development of CASM was made possible with support from:

  • The U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award #DE-SC0008637 that funds the PRedictive Integrated Structural Materials Science (PRISMS) Center at University of Michigan.

  • The National Science Foundation under Awards DMR-1410242, DMR-1105672 and DMR-1436154.

Contact:

Contact the developers at [email protected].

The CASM development team will periodically send email notifications regarding new releases, features, and bug fixes to the CASM users notification list. To join the list send an email to [email protected] or visit https://lists.engr.ucsb.edu/mailman/listinfo/casm-users to sign up.

License

GNU Lesser General Public License (LGPL). Please see the file LICENSE for details.

Installation

See INSTALL.md

Getting Started

The casm executable includes extensive help documentation describing the various commands and options. Simply executing casm will display a list of possible commands, and executing casm <cmd> -h will display help documentation particular to the chosen command.

For a beginner, the best place to start is to follow the suggestions printed when calling casm status -n. This provides step-by-step instructions for creating a CASM project, generating symmetry information, setting composition axes, enumerating configurations, calculating energies with VASP, setting reference states, and fitting an effective Hamiltonian. The subcommand casm format provides information on the directory structure of the CASM project and the format of all the CASM files.

All that is needed to start a new project is a prim.json file describing the crystal structure of the material being studied. See casm format --prim for a description and examples. Typically one will create a new project directory containing the prim.json file and then initialize the casm project. For example:

# create a new CASM project directory
mkdir /path/to/my_casm_project

# cd into the CASM project directory
cd /path/to/my_casm_project

# create the prim.json file
# ... create /path/to/my_casm_project/prim.json ...

# initialize the new CASM project
casm init

After initializing a casm project:

  • casm generates code that is compiled and linked at runtime in order to evaluate effective Hamiltonians in a highly optimized manner. If you installed the CASM header files in a location that is not in your default search path you must specify in your CASM project settings where to find the header files. You can inspect the current settings via casm settings -l, and then add the correct include path via casm settings --set-compile-options. For example:

      casm settings --set-compile-options 'g++ -O3 -Wall -fPIC --std=c++11 -I/path/to/include/casm'

  • Shared object compilation options may be set via casm settings --set-so-options. For example (using the default settings):

      casm settings --set-so-options 'g++ -shared -lboost_system'

An html tutorial describing the creation of an example CASM project and typical steps is coming soon.