A systematic procedure ensuring the determination of all isotropy groups of a given representation of a space group is presented for the first time. Isotropy groups play an important role in various areas of theoretical solid state physics. For example, only isotropy groups may occur in a structural phase transition driven by an order parameter belonging to a given representation. The method uses the chain criterion directly on the image of the representation, employing a labeling of the matrices by space group elements. A notion of a substar of a wave vector associated with the representation is central to the method. Finally, as a detailed illustration the method is applied to a structural phase transition in A15 systems driven by an X‐point order parameter. The result agrees with previously reported ones.

Comment on symmetry changes in A 15 structure

Structural phase transitions in crystals: Broken‐symmetry (isotropy) groups

Symmetry change in continuous phase transitions in two-dimensional systems

The main purpose of this work is to describe the changes of material properties, expressed by tensors of up to the fourth rank, induced by ferroic phase transitions. The results also prepare a firm ground for further analysis of the two main problems of “Continuous Bicrystallography”: 1. The tensor distinction of pairs of domain states. 2. The change of tensor properties across a bicrystallographic interface (domain wall or twin boundary). Since it is our aim to present the information in a standardized manner, we begin with the nomenclature of specifically oriented crystallographic point groups and of their irreducible representations (ireps). The usual Schonflies and Hermann-Mauguin symbols are embellished by subscripts which define the orientation of groups. Matrix form of irreducible representations is associated with so-called typical variables which transform in a well defined way. The transformation properties of material property tensors up to fourth rank are presented in tables of tensor...

Tensor parameters of ferroic phase transitions. I. Theory and tables

The possible non-crystallographic point group of the decagonal quasicrystal phase of AI-Mn alloys has been shown by Bendersky to be either D,,, or C,,,,. For the physically irreducible representations of these groups, we derive the Clebsch-Gordan products, extended integrity bases, stability spaces and tensorial covariants. The point groups which can arise in phase transitions are determined along with corresponding tensorial parameters which could drive the transition. It is shown that equilibrium tensorial properties whose components transform as the components of the electrogyration or elasto-optic tensors can distinguish between the D,,, and C,,,,, point group symmetry of the decagonal phase.

Symmetry and phase transitions in decagonal quasicrystals

This article discusses the application of NMR spectroscopy to the study of structural phase transitions in solids. The various classifications of solid-solid phase transitions are presented. The changes in NMR lineshapes that accompany site symmetry changes during a phase transition are explained. The order-disorder and displacive phase transitions are described as well as how these two types of phase transitions can be distinguished by NMR spectroscopy. Changes in molecular and atomic dynamics frequently occur during structural phase changes. A description of how these changes affect NMR lineshapes and relaxation times is presented. A brief explanation of how Landau theory can be used to relate NMR spectroscopy and structural phase transitions is also presented.


Keywords:

phase transitions;
NMR spectroscopy;
Landau theory;
displacive phase transition;
order-disorder phase transition;
soft modes;
spin-lattice relaxation;
quadrupolar coupling constant;
chemical shift

Comment on symmetry changes in A 15 structure

Citations

Structural phase transitions in crystals: Broken‐symmetry (isotropy) groups

Symmetry change in continuous phase transitions in two-dimensional systems

Tensor parameters of ferroic phase transitions. I. Theory and tables

Symmetry and phase transitions in decagonal quasicrystals

Structural Phase Transitions

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