Aspects of the Solid State

2017 ◽  
Author(s):  
Olle Eriksson ◽  
Anders Bergman ◽  
Lars Bergqvist ◽  
Johan Hellsvik
Keyword(s):  
Solid State ◽  
Band Structure ◽  
Point Group ◽  
Exchange Interactions ◽  
Energy Spectra ◽  
Atomic Magnetic Moment ◽  
Crystalline Materials ◽  
Irreducible Part ◽  
Atomic Exchange ◽  
Group Symmetries

Symmetries play an important role in the theory of the solid state. As will be developed in this Chapter, DFT calculations for crystalline materials are commonly performed for the irreducible part of the first Brillouin zone, an approach which relies on the use of translational and point group symmetries. Two central properties that result from a calculation in reciprocal space are the wave vector resolved energy spectra, the so called band structure, and the energy resolved density of states. For magnetic materials, atomic magnetic moment moments can be defined and calculated, as well as effective inter-atomic exchange interactions.

scholarly journals Sc0.43(2)Rb2Mo15S19, a partially Sc-filled variant of Rb2Mo15S19

2012 ◽  
Vol 68 (5) ◽  
pp. i25-i28 ◽  
Author(s):  
Patrick Gougeon ◽  
Rabih Al Rahal Al Orabi ◽  
Régis Gautier ◽  
Michel Potel
Keyword(s):  
Charge Transfer ◽  
Solid State ◽  
Unique Feature ◽  
Point Group ◽  
Tight Binding ◽  
Median Plane ◽  
Structural Motif ◽  
Space Group ◽  
Group Symmetries ◽  
Cluster Unit

The structure of scandium dirubidium pentadecamolybdenum nonadecasulfide, Sc0.43 (2)Rb2Mo15S19, constitutes a partially Sc-filled variant of Rb2Mo15S19[Picard, Saillard, Gougeon, Noel & Potel (2000),J. Solid State Chem.155, 417–426]. In the two compounds, which both crystallize in theR\overline{3}cspace group, the structural motif is characterized by a mixture of Mo6Si8Sa6and Mo9Si11Sa6cluster units (`i' is inner and `a' is apical) in a 1:1 ratio. The two components are interconnected through interunit Mo—S bonds. The cluster units are centred at Wyckoff positions 6band 6a(point-group symmetries \overline{3}. and 32, respectively). The Rb+cations occupy large voids between the different cluster units. The Rb and the two inner S atoms lie on sites with 3. symmetry (Wyckoff site 12c), and the Mo and S atoms of the median plane of the Mo9S11S6cluster unit lie on sites with .2 symmetry (Wyckoff site 18e). A unique feature of the structure is a partially filled octahedral Sc site with \overline{1} symmetry. Extended Hückel tight-binding calculations provide an understanding of the variation in the Mo—Mo distances within the Mo clusters induced by the increase in the cationic charge transfer due to the insertion of Sc.

scholarly journals β-K3Fe(MoO4)2Mo2O7

2014 ◽  
Vol 70 (7) ◽  
pp. i38-i38 ◽  
Author(s):  
Amira Souilem ◽  
Mohamed Faouzi Zid ◽  
Ahmed Driss
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Title Compound ◽  
Point Group ◽  
Coordination Numbers ◽  
Group Symmetries

The title compound, tripotassium iron(III) bis(orthomolybdate) dimolybdate, was obtained by a solid-state reaction. The main structural building units are one FeO6octahedron, two MoO4tetrahedra and one Mo2O7dimolybdate group, all with point group symmetriesm. These units are linkedviacorner-sharing to form ribbons parallel to [010]. The three K+cations are located between the ribbons on mirror planes and have coordination numbers of 10 and 12. Two O atoms of one of the MoO4tetrahedra of the dimolybdate group are disordered over two positions in a 0.524 (11):0.476 (11) ratio. The structure of the title compound is compared briefly with that of Rb3FeMo4O15.

Friedel'S law breakdown and interpretation of stacking fault images in tetrahedral semiconductors

1987 ◽  
Vol 45 ◽  
pp. 318-319
Author(s):  
Rob. W. Glaisher ◽  
A.E.C. Spargo
Keyword(s):  
Relative Phase ◽  
Point Group ◽  
Binary Compound ◽  
Stacking Fault ◽  
Fold Axis ◽  
Atom Pair ◽  
Tetrahedral Semiconductors ◽  
Group Symmetries ◽  
Thin Crystal ◽  
Phase Differences

Images of <11> oriented crystals with diamond structure (i.e. C,Si,Ge) are dominated by white spot contrast which, depending on thickness and defocus, can correspond to either atom-pair columns or tunnel sites. Olsen and Spence have demonstrated a method for identifying the correspondence which involves the assumed structure of a stacking fault and the preservation of point-group symmetries by correctly aligned and stigmated images. For an intrinsic stacking fault, a two-fold axis lies on a row of atoms (not tunnels) and the contrast (black/white) of the atoms is that of the {111} fringe containing the two-fold axis. The breakdown of Friedel's law renders this technique unsuitable for the related, but non-centrosymmetric binary compound sphalerite materials (e.g. GaAs, InP, CdTe). Under dynamical scattering conditions, Bijvoet related reflections (e.g. (111)/(111)) rapidly acquire relative phase differences deviating markedly from thin-crystal (kinematic) values, which alter the apparent location of the symmetry elements needed to identify the defect.

Hydrothermal Synthesis and Solid-State Laser Refrigeration of Ytterbium-Doped Potassium Lutetium Fluoride (KLF) Microcrystals

2020 ◽  
Author(s):  
Xiaojing Xia ◽  
Anupum Pant ◽  
Xuezhe Zhou ◽  
Elena Dobretsova ◽  
Alex Bard ◽  
...  
Keyword(s):  
Hydrothermal Synthesis ◽  
Solid State ◽  
Information Science ◽  
Point Group ◽  
Solid State Laser ◽  
Lanthanide Ions ◽  
Group Symmetry ◽  
Luminescence Spectra ◽  
Crystalline Phases ◽  
State Laser

Fluoride crystals, due to their low phonon energies, are attractive hosts of trivalent lanthanide ions for applications in upconverting phosphors, quantum information science, and solid-state laser refrigeration. In this article, we report the rapid, low-cost hydrothermal synthesis of potassium lutetium fluoride (KLF) microcrystals for applications in solid-state laser refrigeration. Four crystalline phases were synthesized, namely orthorhombic K<sub>2</sub>LuF<sub>5</sub> (Pnma), trigonal KLuF<sub>4</sub> (P3<sub>1</sub>21), orthorhombic KLu<sub>2</sub>F<sub>7</sub> (Pna2<sub>1</sub>), and cubic KLu<sub>3</sub>F<sub>10</sub> (Fm3m), with each phase exhibiting unique microcrystalline morphologies. Luminescence spectra and emission lifetimes of the four crystalline phases were characterized based on the point-group symmetry of trivalent cations. Laser refrigeration was measured by observing both the optomechanical eigenfrequencies of microcrystals on cantilevers in vacuum, and also the Brownian dynamics of optically trapped microcrystals in water. Among all four crystalline phases, the most significant cooling was observed for 10%Yb:KLuF<sub>4</sub> with cooling of 8.6 $\pm$ 2.1 K below room temperature. Reduced heating was observed with 10%Yb:K<sub>2</sub>LuF<sub>5</sub>

The Energy Band Structure of Polyacene with Soliton Excitation

1997 ◽  
Vol 11 (11) ◽  
pp. 477-483 ◽  
Author(s):  
Z. J. Li ◽  
H. B. Xu ◽  
K. L. Yao
Keyword(s):  
Band Structure ◽  
Charge Density ◽  
Energy Band ◽  
Energy Gap ◽  
Electronic States ◽  
Energy Band Structure ◽  
Energy Spectra ◽  
Energy Band Gap ◽  
The One ◽  
Soliton Excitation

Starting from the extensional Su–Schrieffer–Heeger model taking into account the effects of interchain coupling, we have studied the energy spectra and electronic states of soliton excitation in polyacene. The dimerized displacement u0 is found to be similar to the case of trans-polyacetylene, and equals to 0.04 Å. The energy-band gap is 0.38 eV, in agreement with the results derived by other authors. Two new bound electronic states have been found in the conduction band and in the valence band, which is different from the one of trans-polyacetylene. There exists two degenerate soliton states in the center of energy gap. Furthermore, the distribution of charge density and spin density have been discussed in detail.

Band Structure of Quasi-1-Dimensional Polycondensed π-Systems, 4A)Energy Spectra of a Class of 1-D Ladder Type Polymers

1996 ◽  
Vol 8 (2-3) ◽  
pp. 183-188
Author(s):  
Klaus Müllen ◽  
Markus Müller ◽  
Nikolai Tyutyulkov ◽  
Fritz Dietz
Keyword(s):  
Band Structure ◽  
Energy Spectra

scholarly journals Spin-reversal energy barriers of 305 K for Fe2+ d6 ions with linear ligand coordination

Nanoscale ◽  
2017 ◽  
Vol 9 (30) ◽  
pp. 10596-10600 ◽  
Author(s):  
Lei Xu ◽  
Ziba Zangeneh ◽  
Ravi Yadav ◽  
Stanislav Avdoshenko ◽  
Jeroen van den Brink ◽  
...  
Keyword(s):  
Solid State ◽  
Magnetic Anisotropy ◽  
Point Group ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
State Matrix ◽  
Magnetic Anisotropy Energy ◽  
Spin Reversal ◽  
Ligand Coordination ◽  
Li Ion

A remarkably large magnetic anisotropy energy of 305 K is computed by quantum chemistry methods for divalent Fe2+ d6 substitutes at Li-ion sites with D6h point-group symmetry within the solid-state matrix of Li3N.

Phase Transitions, Superconductivity, and Ferromagnetism in Fullerene Systems

MRS Bulletin ◽  
1994 ◽  
Vol 19 (11) ◽  
pp. 28-30 ◽  
Author(s):  
C.N.R. Rao ◽  
Ram Seshadri
Keyword(s):  
Solid State ◽  
Alkaline Earth ◽  
Point Group ◽  
Group Symmetry ◽  
High Electron ◽  
Chemical Transformations ◽  
Disordered Solids ◽  
High Electron Affinity ◽  
Centers Of Mass ◽  
Image Position

By virtue of their unique structures, fullerenes exhibit novel chemical transformations. Particularly pertinent to this article are the interesting properties exhibited by fullerenes in the solid state. These molecules are spherical or near-spherical in shape. Molecules with high point-group symmetry, which are not bound strongly in the solid state, tend to crystallize into structures with long-range periodicity of the molecular centers of mass, but the molecular orientations are random or even dynamically disordered. When dynamically disordered, themolecules rotate about some preferred axis. C60 and C70 satisfy the criteria for such orientationally disordered solids and exhibit rich phase behavior in the solid state. Since C60 has high electron affinity, it forms anion salts with alkali and alkaline-earth metals as well as with strong organic donor molecules. With tetrakis dimethylaminoethylene (TDAE), which is a very powerful electron donor, C60 forms a 1:1 solid that is ferromagnetic. C60-TDAE is the molecular organic ferromagnet with the highest Tc (of 16 K) known to date. Some of the alkali and alkaline-earth fullerides, on the other hand, show superconductivity, with transition temperatures going up to 33K. We shall briefly examine some of these solid-state properties.

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