References and Resources for the Isotropy Software Suite

Isotropy Subgroups

H. T. Stokes, "Introduction to Isotropy Subgroups and Displacive Phase Transitions," unpublished (2006).

H. T. Stokes and D. M. Hatch, Isotropy Subgroups of the 230 Crystallographic Space Groups (World Scientific, Singapore, 1988), 624 pages.

H. T. Stokes and D. M. Hatch, "Equivalence among Isotropy Subgroups of Space Groups," Phys. Rev. B 31, 7462-7464 (1985).

D. M. Hatch and H. T. Stokes, "Phase Transitions in Solids of Diperiodic Symmetry," Phys. Rev. B 31, 4350-4354 (1985).

D. M. Hatch and H. T. Stokes, "Symmetry-Restricted Phase Transitions in Two-Dimensional Solids," Phys. Rev. B 30, 5156-5166 (1984).

H. T. Stokes and D. M. Hatch, "Group-Subgroup Structural Phase Transitions: A Comparison with Existing Tables," Phys. Rev. B 30, 4962-4967 (1984). Erratum published in Phys. Rev. B 31, 4700 (1985).

Isotropy Subgroups Applications

H. Liu, W. Zhang, P. S. Halasyamani, H. T. Stokes, B. J. Campbell, J. S. O. Evans, and I. R. Evans, "Understanding the Behaviour of the Room-Temperature Molecular Ferroelectric 5,6-Dichloro-2-methylbenzimidazole Using Symmetry Adapted Distortion Mode Analysis" J. Am. Chem. Soc. 140, 13441-13448 (2018).

J. W. Lewis, J. L. Payne, I. R. Evans, H. T. Stokes, B. J. Campbell, and J. S. O. Evans, "An Exhaustive Symmetry Approach to Structure Determination: Phase Transitions in Bi2Sn2O7," J. Amer. Chem. Soc. 138, 8031-8042 (2016).

B.J. Campbell, S. Rosenkranz, H.J. Kang, H.T. Stokes, P.J. Chupas, S. Komiya, Y. Ando, Shiliang Li, and Pengcheng Dai, "Long-Range Two-Dimensional Superstructure in the Superconducting Electron-Doped Cuprate Pr0.88LaCe0.12CuO4", Phys. Rev. B 92, 014118-1-7 (2015).

M. Muller, R. E. Dinnebier, A.-C. Dippel, H. T. Stokes, and B. J. Campbell, "A Symmetry-Mode Description of Rigid-Body Rotations in Crystalline Solids: A Case Study of Mg(H2O)6RbBr3." J. Appl. Cryst. 47, 532-538 (2014).

C. Mshumi, C. I. Lang, L. R. Richey, K. C. Erb, C. W. Rosenbrock, L. J. Nelson, R. R. Vanfleet, H. T. Stokes, B. J. Campbell, and G. L. W. Hart, "Revisiting the CuPt3 Prototype and the L13 Structure." Acta Materialia 73, 326-336 (2014).

C. J. Howard, B. J. Campbell, H. T. Stokes, M. A. Carpenter, and R. I. Thomson, "Crystal and Magnetic Structures of Hexagonal YMnO3." Acta Cryst. B 69, 534-540 (2013).

S. Kerman, B. J. Campbell, K. K. Satyavarapu, H. T. Stokes, F. Perselli, and J. S. O. Evans, "The Superstructure Determination of Displacive Distortions via Symmetry-Mode Analysis," Acta Cryst. A 68, 222-234 (2012).

M. Muller, R. E. Dinnebier, N. Z. Ali, B. J. Campbell, and M. Jansen, "Direct Access to the Order Parameter: Parameterized Symmetry Modes and Rigid Body Movements as a Function of Temperature", Materials Science Forum 651, 79-95 (2010).

C. J. Howard and H. T. Stokes, "Structures and Phase Transitions in Perovskites - a Group-Theoretical Approach," Acta Cryst. A 61, 93-111 (2005).

C. J. Howard and H. T. Stokes, "Octahedral Tilting in Cation-Ordered Perovskites - a Group-Theoretical Analysis," Acta Cryst. B 60, 674-684 (2004).

H. T. Stokes, E. H. Kisi, D. M. Hatch, and C. J. Howard, "Group Theoretical Analysis of Octahedral Tilting in Ferroelectric Perovskites," Acta Cryst. B 58, 934-936 (2002).

C. J. Howard and H. T. Stokes, "Group Theoretical Analysis of Octahedral Tilting in Perovskites," Acta Cryst. B 54, 782-789 (1998). Erratum in Acta Cryst. B 58, 565 (2002).

D. M. Hatch, H. T. Stokes, K. S. Aleksandrov, and S. V. Misyul, "Phase Transitions in the Perovskitelike A2BX4 Structure," Phys. Rev. B 39, 9282-9288 (1989).

D. M. Hatch and H. T. Stokes, "Classification of Octahedral Tilting Phases in the Perovskitelike A2BX4 Structure," Phys. Rev. B 35, 8509-8516 (1987). "Erratum published in Phys. Rev. B 36, 7185 (1987).

ISODISTORT

J. W. Lewis, J. L. Payne, I. R. Evans, H. T. Stokes, B. J. Campbell, and J. S. O. Evans, "An Exhaustive Symmetry Approach to Structure Determination: Phase Transitions in Bi2Sn2O7," J. Amer. Chem. Soc. 138, 8031-8042 (2016).

M. Muller, R. E. Dinnebier, A.-C. Dippel, H. T. Stokes, and B. J. Campbell, "A Symmetry-Mode Description of Rigid-Body Rotations in Crystalline Solids: A Case Study of Mg(H2O)6RbBr3," J. Appl. Cryst. 47, 532-538 (2014).

S. Kerman, B. J. Campbell, K. K. Satyavarapu, H. T. Stokes, F. Perselli, and J. S. O. Evans, "The Superstructure Determination of Displacive Distortions via Symmetry-Mode Analysis," Acta Cryst. A 68, 222-234 (2012).

B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, "ISODISPLACE: An Internet Tool for Exploring Structural Distortions," J. Appl. Cryst. 39, 607-614 (2006).

ISOTILT

B. J. Campbell, H. T. Stokes, T. B. Averett, S. Machlus, and C. J. Yost, "The ISOTILT Software for Discovering Cooperative Rigid-Unit Rotations in Networks of Interconnected Rigid Units" J. Appl. Cryst. 54, 1847-1856 (2021). Supporting information.

B. J. Campbell, H. T. Stokes, T. B. Averett, S. Machlus, and C. J. Yost, "Theoretical and Computational Improvements to the Algebraic Method for Discovering Cooperative Rigid-Unit Modes" J. Appl. Cryst. 54, 1664-1675 (2021).

B. Campbell, C. J. Howard, T. B. Averett, T. A. Whittle, S. Schmid, S. Machlus, C. Yost, and H. T. Stokes, "An Algebraic Approach to Cooperative Rotations in Networks of Interconnected Rigid Units" Acta Cryst. A74, 408-424 (2018).

Superspace Groups

H. T. Stokes and B. J. Campbell, "A General Algorithm for Generating Isotropy Subgroups in Superspace," Acta Cryst. A 73, 4-13 (2017).

H. T. Stokes, B. J. Campbell, and R. Cordes, "Tabulation of Irreducible Representations of the Crystallographic Space Groups and Their Superspace Extensions," Acta Cryst. A. 69, 388-395 (2013).

S. van Smaalen, B. J. Campbell, and H. T. Stokes, "Equivalence of Superspace Groups," Acta Cryst. A 69, 75-90 (2013).

H. T. Stokes, B. J. Campbell, and S. van Smaalen, "Generation of (3+d)-Dimensional Superspace Groups for Describing the Symmetry of Modulated Crystalline Structures," Acta Cryst. A 67, 45-55 (2011).

H. T. Stokes, B. J. Campbell, and D. M. Hatch, "Order Parameters for Phase Transitions to Structures with One-Dimensional Incommensurate Modulations," Acta Cryst. A 63, 365-373 (2007).

Irreducible Representations

H. T. Stokes, B. J. Campbell, and R. Cordes, "Tabulation of Irreducible Representations of the Crystallographic Space Groups and Their Superspace Extensions," Acta Cryst. A. 69, 388-395 (2013).

O. V. Kovalev, Representations of the Crystallographic Space Groups: Irreducible Representations, Induced Representations and Corepresentations, edited by H. T. Stokes and D. M. Hatch (Gordon and Breach, Amsterdam, 1993), 390 pages.

H. T. Stokes, D. M. Hatch, and J. S. Kim, "Images of Physically Irreducible Representations of the 230 Space Groups," Acta Cryst. A 43, 81-84 (1987).

A. P. Cracknell, B. L. Davies, S. C. Miller, and W. F. Love, Kronecker Product Tables, Vol. 1 (Plenum, New York, 1979). Based on S. C. Miller and W. F. Love, Tables of Irreducible Representations of Space Groups and Co-Representations of Magnetic Space Groups (Pruett, Boulder, 1967).

Reconstructive Phase Transitions

H. T. Stokes, J. Gunter, D. M. Hatch, J. Dong, H. Wang, and J. P. Lewis, "Bilayer Sliding Mechanism for the Wurtzite-to-Rocksalt Transition," Phys. Rev. B 76, 012102-1-4 (2007).

D. M. Hatch, H. T. Stokes, J. Dong, J. Gunter, H. Wang, and J. P. Lewis, "Bilayer Sliding Mechanism for the Zinc-blende to Rocksalt Transition in SiC," Phys. Rev. B 71, 184109-1-9 (2005).

H. T. Stokes and D. M. Hatch, "Procedure for Obtaining Microscopic Mechanisms of Reconstructive Phase Transitions in Crystalline Solids," Phys. Rev. B 65, 144114-1-12 (2002).

ISOSUBGROUP

H. T. Stokes, S. van Orden, and B. J. Campbell, "ISOSUBGROUP: an Internet Tool for Generating Isotropy Subgroups of Crystallographic Space Groups," J. Appl Cryst. 49, 1849-1853 (2016).

FINDSYM

H. T. Stokes and D. M. Hatch, "FINDSYM: Program for Identifying the Space Group Symmetry of a Crystal," J. Appl. Cryst. 38, 237-238 (2005).

INVARIANTS

D. M. Hatch and H. T. Stokes, "INVARIANTS: Program for Obtaining a List of Invariant Polynomials of the Order Parameter Components Associated with Irreducible Representations of a Space Group," J. Appl. Cryst. 36, 951-952 (2003).

Order Parameters

D. M. Hatch and H. T. Stokes, "COPL: Program for Obtaining a Complete List of Order Parameters for a Group-Subgroup Crystalline Phase Transition," J. Appl. Cryst. 35, 379 (2002).

D. M. Hatch and H. T. Stokes, "The Complete Listing of Order Parameters for a Crystalline Phase Transition: A Solution to the Generalized Landau Problem," Phys. Rev. B 65, 014113-1-4 (2002).

H. T. Stokes and D. M. Hatch, "Coupled Order Parameters in the Landau Theory of Phase Transitions in Solids," Phase Transitions 34, 53-67 (1991).

Frozen Phonons

H. T. Stokes, "Using Symmetry in Frozen Phonon Calculations," Ferroelectrics164, 183-188 (1995).

Computer Algorithms

H. T. Stokes, D. M. Hatch, and J. D. Wells, "Group-Theoretical Methods for Obtaining Distortions in Crystals: Applications to Vibrational Modes and Phase Transitions," Phys. Rev. B 43, 11010-11018 (1991).

D. M. Hatch, H. T. Stokes, and R. M. Putnam, "Symmetry Analysis of the Microstructure and Phase Transitions of a Crystallographic Space Group: Applications," Phys. Rev. B 35, 4935-4942 (1987).

D. M. Hatch and H. T. Stokes, "Practical Algorithm for Identifying Subgroups of Space Groups,"Phys. Rev. B 31, 2908-2912 (1985).