D. B. Litvin

Possible piezoelectric composites based on the flexoelectric effect

Current piezoelectric composite materials contain two or more phases out of which at least one reveals piezoelectric properties in itself. We show that this is in fact not a necessary condition. The mechanism of the linear stress-polarization response averaged over a composite sample can be also based on flexoelectric properties of one or more constituents. Proper shaping of the composite constituents is required, such that the system as a whole acquires a symmetry allowing for nonzero piezoelectric coefficients even if none of the components is piezoelectric. Externally applied stress is transformed, due to proper geometry of the constituents with different elastic properties, into a strongly nonhomogeneous distribution of induced strain. Flexoelectric properties which are, by symmetry, allowed in all materials, transform the strain gradient into polarization. The proposed piezoelectric composite falls into the category of composites with product properties since it involves different assets of the phases (elastic, flexoelectric and dielectric) and the interaction between the phases, determining the inhomogeneous distribution of stress, is essential.

Non-ferroelastic twin laws and distinction of domains in non-ferroelastic phases

Abstract We show that within continuum description there exist 48 possible relations (twin laws) between structures of two non-ferroelastic domains. All these twin laws can be expressed by dichromatic point groups. For each twin law we give the number of components of important material property tensors that have opposite sign in the two domains under consideration.

Tables of crystallographic properties of magnetic space groups

Tables of crystallographic properties of the reduced magnetic superfamilies of space groups, i.e. the 7 one-dimensional, 80 two-dimensional and 1651 three-dimensional group types, commonly referred to as magnetic space groups, are presented. The content and format are similar to that of non-magnetic space groups and subperiodic groups given in International Tables for Crystallography. Additional content for each representative group of each magnetic space-group type includes a diagram of general positions with corresponding general magnetic moments, Seitz notation used as a second notation for symmetry operations, and general and special positions listed with the components of the corresponding magnetic moments allowed by symmetry.

THE DIPOLE MOMENT EXPANSION FOR A TETRAHEDRAL MOLECULE IN THE GROUND VIBRONIC STATE

Abstract The expansion of the electric dipole moment operator in terms of angular momentum operators is examined in detail for a tetrahedral molecule in the ground vibronic state. The components of this centrifugal distortion moment in the molecule fixed frame are formally expanded to arbitrary order, with the expansion coefficients being given in terms of rotation matrices. For terms of rank j less than 15, general expressions are given for the matrix elements in the symmetric top basis of the space-fixed components of the dipole moment. The dependence of these matrix elements on the K-quantum number is shown to factor in such a way that previous first order calculations can be extended to second order by replacing the first order dipole coupling constant μ 2 (2) with a function of J which involves μ 2 (2) and two second order constants, μ 2 (4) and μ 4 (4) . Different functions are required for Q- and R-branch matrix elements and explicit expressions are given for both. The third order terms are examined in detail in the Appendix. A recurrence relation is derived for j

Ferroic classifications extended to ferrotoroidic crystals

Aizus characterization of the 773 species of phase transitions by magnetization, polarization and strain is extended to include characterization by the recently observed toroidal moment. The resulting distinction quadruplet characterization is then used to classify the species into sub-ensembles, extending Schmids concept of ensembles of species to include classification by toroidal moments. Tables are given of the distinction quadruplet characterization of each species and the species in each ensemble and sub-ensemble. The form of primary and secondary ferroic property tensors invariant under the 122 magnetic point groups have also been tabulated for use in determining the characterization of species and possible domain switching. In both cases, physical property tensors related to the toroidal moment are included.

Transposable domain pairs and domain distinction

Abstract We divide pairs of domain states into three classes: completely, partially and non-transposable domain pairs. We show that two groups can be associated with a domain pair: the twinning group and the symmetry group of the pair. The twinning group determines which secondary order parameters are the same and which are different in two domain states of a domain pair. The symmetry group of a transposable domain pair allows one to express the order parameters and irreducible constituents of material property tensors in such a way that their components in two domain states are either the same or differ only in the sign. The analysis of domain distinction is illustrated on a simple example.

One‐piece Faraday generator: A paradoxical experiment from 1851

In the conventional Faraday generator a conducting disk rotates in an axial magnetic field. If the disk is replaced by a cylindrical permanent magnet that supplies its own magnetic field, the effect is identical. It follows that any moving magnet generates an induced electromotive force due to the presence of its own field: this generalization leads to an apparent paradox in the case of translational motion for it implies the possibility that an observer in an inertial frame could measure his absolute velocity.

Clebsch‐Gordan Coefficients for Space Groups

It is shown that to find Clebsch‐Gordan coefficients of space groups (both single and double), the representations of the groups of k alone are required. This is another example demonstrating the well‐accepted fact that in applications of space groups it is sufficient to know the representations of the groups of k. Final formulas are derived that enable the calculation of the Clebsch‐Gordan coefficients from the representations of the groups of k. As an example the spin‐orbit coupling in solids is considered.

Magnetic space-group types

The interpretation of Opechowski-Guccione symbols for magnetic space-group types is based on coordinate triplets given in the now superceded International Tables for X-ray Crystallography [(1952), Vol. 1, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press]. Changes to coordinate triplets in International Tables for Crystallography [(1983), Vol. A, edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers] lead to misinterpretations of these symbols. A list is provided here of Opechowski-Guccione symbols for the 1651 magnetic space-group types with their original definitions given independent of International Tables.

Non‐magnetic twin laws

Twin laws are groups that express the symmetry relationships between two simultaneously observed domain states (domain pair) and are used to determine physical properties that can distinguish between the observed domains. A tabulation is presented of all possible non-magnetic twin laws, that is, all possible symmetry groups and twinning groups of the domain pair. Additional information is provided related to determining twin laws. This includes the coset and double-coset decomposition of point groups, the indexing and point-group symmetry of domain states, permutations of domain states, and a classification of domain states.