## Overview

CASM 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.

The public version of CASM supports:

• Constructing, fitting, and evaluating cluster expansion effective Hamiltonians with:
• Occupational degrees of freedom
• Strain degrees of freedom
• Displacement degrees of freedom
• High-throughput calculations using:
• Occupantional cluster expansion Monte Carlo calculations using:
• Semi-grand canonical ensemble
• Canonical ensemble

## Acknowledgements

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, Anna Belak, Liang Tian, Naga Sri Harsha Gunda, Julija Vinckeviciute, Sanjeev Kolli, and Sesha Sai Behara.

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, DMR-1436154, and OAC-1642433.

CASM is released under the GNU Lesser General Public License (LGPL).

## Contributing

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 casm-developers@lists.engr.ucsb.edu.

For a particular major version number, the ccasm program interface, including file input and output formats, will remain stable and backwards compatible. The CASM library libcasm is less stable and may have some breaking changes without changing the major version number.

## Citing CASM

CASM can be cited using the following four references:

• [ref1] CASM, v1.1.1 (2021). Available from https://github.com/prisms-center/CASMcode.
• [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, B. Puchala, A. R. Natarajan, “First-Principles Statistical Mechanics of Multicomponent Crystals”, Annual Review of Materials Research, 48 27-45 (2018).

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].”

If you use CASM in one of your publications, please send the publication information to casm-developers@lists.engr.ucsb.edu so that we can include your citation on our website and demonstrate our impact to our funding agency.

## 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]. Convex hulls are found using Qhull [ref13].

References:

• [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).
• [ref13] C.B. Barber, D.P. Dobkin, and H.T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org.