scholarly journals Tungsten–niobium oxide bronzes: a bulk and surface structural study

2020 ◽  
Vol 49 (38) ◽  
pp. 13282-13293
Author(s):  
Daniel Delgado ◽  
Patricia Concepción ◽  
Annette Trunschke ◽  
Jose M. López Nieto
Keyword(s):  
Long Range ◽  
Structural Study ◽  
Niobium Oxide ◽  
Tungsten Bronze ◽  
Acid Sites ◽  
Range Order ◽  
Long Range Order ◽  
Oxide Bronzes

The incorporation of Nb in the hexagonal tungsten bronze leads to a loss of long range order in the ab plane of the structure, the stabilization of W5+ species, and an increase in the Lewis nature of surface acid sites.

Electron Energy Loss Spectroscopy Study of ZSM-5 Zeolite and MCM-41 Mesoporous Materials

2001 ◽  
Vol 7 (S2) ◽  
pp. 1072-1073
Author(s):  
F. Paraguay D ◽  
M. Miki-Yoshida ◽  
F. Espinosa-Magaña ◽  
E. Terrés ◽  
J.M. Dominguez
Keyword(s):  
Long Range ◽  
Mesoporous Materials ◽  
Acid Sites ◽  
Range Order ◽  
Atomic Scale ◽  
Long Range Order ◽  
Channel Network ◽  
New Class ◽  
Small Pore ◽  
Electron Energy Loss

Zeolites are crystalline aluminosilicates possessing a regular microporous channel network. Unique properties of zeolites such as the presence of framework cations, acid sites, and their well-defined porous structure-with pore sizes similar to those of small molecules-account for their traditional utilization in ion exchange, catalysis, and separation. in addition, zeolites are being investigated for novel emerging applications in a diversity of areas including optoelectronic devices and reactive membranes because they provide for discrimination, recognition, and organization of molecules with a precision of less 1 Å. However, their applications are limited by the relatively small pore openings; therefore, pore enlargement was one of the main aspects in zeolite chemistry. A new class of porous materials, which contain large uniform spaces in the mesopore size regimen (15-100 Å), was reported. These so-called mesoporous materials have two different characters, disorder at the atomic scale but long range order at the atomic scale but long range order at the mesoscopic scale.

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

Time-Resolved, Laser-Induced Phase Transformation in Aluminum

1984 ◽  
Vol 35 ◽  
Author(s):  
S. Williamson ◽  
G. Mourou ◽  
J.C.M. Li
Keyword(s):  
Point Defect ◽  
Long Range ◽  
Rapid Heating ◽  
Range Order ◽  
Nucleation Theory ◽  
Long Range Order ◽  
Time Resolved ◽  
Aluminum Films ◽  
Thin Aluminum ◽  
Initial Nucleus

ABSTRACTThe technique of picosecond electron diffraction is used to time resolve the laser-induced melting of thin aluminum films. It is observed that under rapid heating conditions, the long range order of the lattice subsists for lattice temperatures well above the equilibrium point, indicative of superheating. This superheating can be verified by directly measuring the lattice temperature. The collapse time of the long range order is measured and found to vary from 20 ps to several nanoseconds according to the degree of superheating. Two interpretations of the delayed melting are offered, based on the conventional nucleation and point defect theories. While the nucleation theory provides an initial nucleus size and concentration for melting to occur, the point defect theory offers a possible explanation for how the nuclei are originally formed.

scholarly journals Finite temperature off-diagonal long-range order for interacting bosons

2020 ◽  
Vol 102 (18) ◽  
Author(s):  
A. Colcelli ◽  
N. Defenu ◽  
G. Mussardo ◽  
A. Trombettoni
Keyword(s):  
Long Range ◽  
Finite Temperature ◽  
Range Order ◽  
Long Range Order

scholarly journals Recovery of long-range order in two-dimensional charge density waves at high temperatures

2021 ◽  
Vol 27 (S1) ◽  
pp. 952-954
Author(s):  
Suk Hyun Sung ◽  
Yin Min Goh ◽  
Noah Schnitzer ◽  
Ismail El Baggari ◽  
Kai Sun ◽  
...  
Keyword(s):  
Charge Density ◽  
Long Range ◽  
High Temperatures ◽  
Charge Density Waves ◽  
Range Order ◽  
Long Range Order ◽  
Two Dimensional ◽  
Density Waves

SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM IN Ti1+xS2

1977 ◽  
Vol 38 (C7) ◽  
pp. C7-202-C7-206 ◽  
Author(s):  
R. MORET ◽  
M. HUBER ◽  
R. COMÈS
Keyword(s):  
Long Range ◽  
Short Range ◽  
Range Order ◽  
Long Range Order
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