Terms Of Local Symmetry Research Articles

Symmetry crossover in layered MPS3 complexes (M=Mn, Fe, Ni) via near-field infrared spectroscopy

Author(s): Neal, SN; Kim, HS; O'Neal, KR; Haglund, AV; Smith, KA; Mandrus, DG; Bechtel, HA; Carr, GL; Haule, K; Vanderbilt, D; Musfeldt, JL | Abstract: We employ synchrotron-based near-field infrared spectroscopy to reveal the vibrational properties of bulk, few-sheet, and single-sheet members of the MPS3 (M=Mn, Fe, Ni) family of materials and compare our findings with complementary lattice dynamics calculations. MnPS3 and the Fe analog are similar in terms of their symmetry crossovers, from C2/m to P3¯1m, as the monolayer is approached. These states differ as to the presence of a C3 rotation around the metal center. On the other hand, NiPS3 does not show a symmetry crossover, and the lack of a Bu symmetry mode near 450 cm-1 suggests that C3 rotational symmetry is already present, even in the bulk material. We discuss these findings in terms of local symmetry and temperature effects as well as the curious relationship between these symmetry transformations and those that take place under pressure.

Pairings and related symmetry notions

In this paper, we give a purely mathematical generalization of an information table. We call pairing on a given set $$\Omega $$ a triple $$\mathfrak {P}=(U, F, \Lambda )$$ , where U and $$\Lambda $$ are non-empty sets and $$F:U\times \Omega \rightarrow \Lambda $$ is a map. We provide several examples of pairings: graphs, digraphs, metric spaces, group actions and vector spaces endowed with a bilinear form. Moreover, we reinterpret the usual notion of indiscernibility (with respect to a fixed attribute subset of an information table) in terms of local symmetry on U and, then, we study a global version of symmetry, that we called indistinguishability. In particular, we interpret the latter relation as the symmetrization of a pre-order $$\le _{\mathfrak {P}}$$ , that describes the symmetry transmission between subsets of $$\Omega $$ . Hence, we introduce a global average of symmetry transmission and studied it for some basic digraph families. Finally, we prove that the partial order of any finite lattice can be described in terms of the above pre-order.

Structural effects on light wave behavior in quasiperiodic regular and decagonal Penrose-tiling dielectric media: A comparative study

Light wave behaviors in two-dimensional quasiperiodic regular and generalized decagonal Penrose-tiling dielectric media, which display similar long range structure order and different local configurations, are studied comparatively in relation with both global and local orders through the approximant structures. We show that these structures generate analogous photonic band gaps, which are determined by the lattice global average order. Light localization, with frequency levels lying inside the main photonic band gaps, occurs in local regions of high symmetry patterns in the generalized decagonal structure, while it is absent in the regular Penrose tiling. This is analyzed in terms of local symmetry that favors resonances between neighbor scatterers, as well as relations between local and global structure configurations that determine the localized mode frequency levels relative to the photonic band gaps.

31P MAS-NMR study of R′ xR″ yP 6O 18.nH 2O cyclohexaphosphates

Several alkali/alkaline-earth R x +R y 2+P 6O 18.nH 2O cyclohexaphosphates, with R +=Li, Na, K, Cs, NH 4, Tl, DBA; R 2+=Ca, Zn, Cd, have been analyzed by 31P MAS-NMR spectroscopy. From their NMR spectra, the number and the multiplicity of crystallographic sites have been analyzed and compared with those deduced by symmetry considerations from X-ray diffraction data. A linear dependence of the isotropic chemical shift values of NMR components on the POP angles of cycles has been obtained. However, some influence of the charge and polarizing strength of alkali and alkaline-earth cations has also been detected. Finally, principal values of the chemical shift tensor of P atoms have been analysed in terms of local symmetry and tetrahedral ring distortions.

The Infrared Spectra of Rhenium Pentamethyl Cyclopentadienyl Complexes: (n5-C5Me5)Re(CO3) and [(n5-C5Me5)Re(CO)3X]+(X=Cl, Br, I)

Abstract The IR spectra of the title compounds are recorded and an assignment of the normal modes in terms of local symmetry is suggested by comparison with those observed in analogous molecules. A set of force constants calculated for simplified models confirms most of the experimental assignments and reflects the symmetry of the complexes under study. The f CO of the two different CO groups in the cationic complexes indicated that CO groups cis to the halide ligand should be more selective towards nucleophiles.

An improved synthetic method and vibrational study of (pentamethylcyclopentadienyl) dicarbonylrhenium dihalides (η 5-C 5Me 5)Re(CO) 2X 2 (X = C1, Br and I)

An improved synthetic method has been found for the preparation of the pentamethylcyclopentadienyl rhenium dicarbonyldihalide complexes. From the reaction of (η 5-C 5Me 5)Re(CO) 3 with Br 2 or I 2 in THF-H 2O a mixture of cis and trans isomers of (η 5-C 5Me 5)Re(CO) 2X 2 X = Br and I is formed. On the other hand, the reaction of [(η 5-C 5Me 5)Re(CO) 3C1][SbC1 6] in water gives the cis-(η 5-C 5Me 5)Re(CO) 2C1 2 complex. The solid IR spectra of the dicarbonyldihalide complexes are recorded and an assignment of the normal modes in terms of local symmetry is suggested by comparison with those observed in analogous molecules. A normal coordinate analysis performed using a modified general valence force field and considering simplified models, confirms most of the experimental assignments. The set of valence force constants reflects the structure of the isomers under study.

Local elasticity properties of an amorphous structure : evidences for typical sites and shell structure ; dynamic stability

Linear and quadratic Local Elasticity coefficients (LEC) of non periodic structures are defined here. Assuming a macroscopic isotropy, the directions of local symmetry axes need not be considered, thus only 9 relevant LEC remain. This analysis applied to the ML amorphous structure shows that the local hydrostatic constraint p is uniform on each shell of atoms surrounding the centre of the structure, and takes only 5 different values for the 525 central atoms. Thus p defines 5 categories of sites and shells. The analysis of their other LEC confirms the existence of these 5 categories of shells which define bands of values for each of the LEC. Some internal structuration of the shells, i.e. subbands of LEC, is found. Site categories are analysed in terms of local symmetry and topology. Atom dynamics are considered for possible localized modes with evidence for a softening of the frequencies of the modes more or less localized on a shell which encloses some 270 central atoms. These static and dynamics point of view enable us to make simple remarks on the magic numbers which are usual for shell structures. Global elastic properties such as bulk modulus and sound celerity for the ML structures, bare of filled with small, light atoms are derived, result in a radio C 11 /C 44 =2.22, which is independent of the details of a short ranged pair interaction. This ratio is in good agreement with experimental data. Finally the size of frozen fluctuations is shown to be two or three interatomic distances. Applications to different kinds of interactions such as molecule-molecule or nucleon-nucleon interactions are suggested Definition des coefficients elastiques locaux lineaires et quadratiques de structure non periodiques. Mise en evidence de l'uniformite de la contrainte hydrostatique sur chaque couche d'atomes. Definition de cinq categories de sites et de couches, d'une structuration de couches en sous couches et d'un seuil de stabilite de la taille des germes