Darstellung, Kristallstruktur und Schwingungsspektren von Cs3As7 und Cs3(NH3)As7/Syntheses, Crystal Structure and Vibrational Spectra of Cs3As7 and Cs3(NH3)As7

1989 ◽  
Vol 44 (3) ◽  
pp. 296-306 ◽  
Author(s):  
M. Somer ◽  
W. Hönle ◽  
H. G. von Schnering
Keyword(s):  
Liquid Ammonia ◽  
Three Dimensional ◽  
Correlation Factor ◽  
Membered Ring ◽  
Band Gaps ◽  
First Order ◽  
First Order Phase Transition ◽  
Different Temperatures ◽  
First Order Phase ◽  
Cesium Atoms

Cs3As7, a compound with cage-like As73- anions, has been prepared from the elements in sealed quartz ampoules at 820 K. The ruby-red compound undergoes a first order phase transition at 640 K and is obtained as microcrystalline samples. The structure of the low-temperature α-modification is not known, but β-Cs3As7 belongs to the plastically crystalline β-Rb3P7 type of structure (F m 3̄ m , a (673 K) = 1169,2(1) pm). Cs3As7 melts under its own vapour pressure at 1061 K, and is easily soluble in liquid ammonia. From those solutions ruby red crystals of Cs3(NH3)As7 precipitate. In dynamical vacuum NH3 is evaporated in the region of 300 to 520 K, resulting in Cs3As7. Cs3(NH3)As7 crystallizes in the space group P21/a (a = 2759.0(12) pm, b = 744.1(3) pm, c = 751.5(3) pm, β = 90.16(5)°; Z = 4). The structure is closely related to the plastically crystalline β-Rb3P7 type structure (Li3Bi variant). The heptaarsanortricyclene anion is coordinated by cesium atoms, connecting the anions to a three dimensional arrangement. The anion exhibits a differentiation of As - As bond lengths typical for ionic nortricyclenes (d(basis) = 251.2 pm; d(basis-bridge) = 235.5 pm; d(bridge-bridgehead) = 240.1 pm). The distances Cs to As are in the range 372 to 401 pm. The cesium atoms are surrounded by three resp. four As atoms and the NH3 molecules. The FIR and Raman spectra are given for different temperatures as well as of an en-solution of Cs3(NH3)As7. The valence vibrations of NH3 are found at 3175 (A1) and 3320 cm-1 (E ). The fundamental vibrations of the three-membered ring of different heteronortricyclenes with P and As are compared and yield a correlation factor χ = 0.57(1) for the observed frequencies between P3 and As3. The band gaps EG are determined from the diffuse reflexion at 2.14 eV for Cs3(NH3)As7 and 2.00 eV for Cs3As7.

scholarly journals EFFECTIVE POTENTIALS AND SYMMETRY RESTORATION IN THE CHIRAL ABELIAN HIGGS MODEL

1995 ◽  
Vol 10 (12) ◽  
pp. 997-1009
Author(s):  
JENS O. ANDERSEN
Keyword(s):  
Three Dimensional ◽  
Higgs Model ◽  
Effective Theory ◽  
Gauge Parameter ◽  
Dimensional Theory ◽  
Abelian Higgs Model ◽  
Effective Potentials ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

The chiral Abelian Higgs model is studied at finite temperature. By integrating out the heavy modes, we make a three-dimensional effective theory for the static modes. It is demonstrated that the plasma masses are correctly reproduced to leading order in m2/T2. The effective potential for the composite operator ɸ†ɸ is calculated at one-loop for the resulting three-dimensional theory and it is shown that the result is gauge parameter independent. The numerical investigation of the potential reveals that the symmetry is restored via a first-order phase transition. Comparison with the ordinary ring improved potential is made and it is found that the barrier height at Tc is somewhat higher.

DISORDER DRIVEN MELTING OF MOVING VORTEX MATTER IN LAYERED SUPERCONDUCTORS

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2476-2479 ◽  
Author(s):  
QING-MIAO NIE ◽  
MENG-BO LUO ◽  
QING-HU CHEN ◽  
XIAO HU
Keyword(s):  
Three Dimensional ◽  
Xy Model ◽  
Vortex Matter ◽  
External Current ◽  
Layered Superconductors ◽  
First Order ◽  
First Order Phase Transition ◽  
Bragg Glass ◽  
First Order Phase ◽  
Moving Vortex

The current-driven three-dimensional frustrated anisotropic XY model with strong disorder is simulated to model the moving vortex matter in layered superconductors. The equilibrium disordered state can be driven to a moving Bragg glass (BrG) by applying an external current. As the pinning strength increases, the moving BrG can melt into a moving smectic via a first-order phase transition.

REIDEMEISTER TORSION AND SIMPLICIAL QUANTUM GRAVITY

1993 ◽  
Vol 08 (11) ◽  
pp. 1933-1980 ◽  
Author(s):  
M. CARFORA ◽  
A. MARZUOLI
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Three Dimensional ◽  
Gaussian Model ◽  
Coupling Constants ◽  
First Order ◽  
Homotopy Types ◽  
First Order Phase Transition ◽  
Homology Manifolds ◽  
First Order Phase

We show that three-dimensional simplicial quantum gravity, as described by dynamically triangulated manifolds, is connected with a Gaussian model determined by the simple homotopy types of the underlying manifolds. By exploiting this result it is shown that the partition function of three-dimensional simplicial quantum gravity is well defined in a convex region in the plane of the gravitational and cosmological coupling constants. Such a region is determined by the Reidemeister–Franz torsion invariants associated with orthogonal representations of the fundamental groups of the set of manifolds considered. The system shows a critical behavior and undergoes a first order phase transition at a well-defined value of the couplings, again determined by the torsion invariants. On the critical line the partition function can be explicitly related to a Gaussian measure on the general linear group GL (∞, R), showing evidence of a well-defined thermodynamical limit of the theory, with a stable (vacuum) configuration corresponding to three-dimensional (homology) manifolds. The first order nature of the transition yielding such a configuration seems to support the belief in the absence of a continuum limit of the theory. More generally, the approach presented here provides further analytical support for the picture of three-dimensional simplicial quantum gravity which has been abstracted from numerical simulations.

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