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H. T. Stokes, "Introduction to Isotropy Subgroups and Displacive Phase Transitions," unpublished (2006).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

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

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).

Superspace Groups

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).

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).

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).