Crystal structure of the synthetic analog of radtkeite Hg<Subscript>3</Subscript>S<Subscript>2</Subscript>Cl<Subscript>1.00</Subscript>I<Subscript>1.00</Subscript>

The results of structural studies of the synthetic analog of the radtkeite mineral Hg₃S₂Cl_1.00I_1.00 are analyzed. The crystal structure of the compound has been refined; the unit cell parameters are a _m = 16.827(4) , b _m = 9.117(1) , c _m = 13.165(5) , = 130.17(2)°, V = 1543.3(8) ³, space group C2/m, Z = 8, R = 0.0527. A possible transition a ₀ = a _m; b ₀ = a _m + 2c _m; c ₀ = –b _m to the pseudo-orthorhombic F cell previously determined for radtkeite, where one of the angles ( ₀ ) is slightly different from 90° (89.55°), has been found. Each sulfur atom in the structure is bonded to three mercury atoms, forming SHg₃ umbrellas with distances 2.240(6) –2.474(8) and angles HgSHg 94.7(2)°–102.9(2)°. The SHg₃ fragments are linked through Hg vertices to form corrugated [Hg₁₂S₈] layers. The halogen atoms lie inside and between the [Hg₁₂S₈] layers; the distances are Hg-Cl and Hg-I 2.783(7) , 2.961(7) , and 3.083(4) –3.311(3) , respectively.Original Russian Text Copyright © 2004 by N. V. Pervukhina, S. V. Borisov, S. A. Magarill, D. Yu. Naumov, V. I. Vasiliev, and B. G. NenashevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 755–758, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Double Short Exact Sequences and K1 of an Exact Category

We introduce a modification of the Bass group K ₁ ^det . Our group is defined by generators and relations, in terms of double short exact Sequences instead of automorphisms. We establish its relation to Quillen's K₁ by dealing with loops in the G-construction.     

Hall effect in hopping conduction in an ensemble of quantum dots

The Hall effect in heterostructures with a two-dimensional array of tunneling-coupled Ge quantum dots grown by molecular-beam epitaxy on Si is investigated. The conductivity of these structures in zero magnetic field at 4.2 K varies in the range of 10^?12?10^?4 Ω^?1, which includes both the diffusive transport under weak localization conditions and hopping conduction. It is shown that the Hall effect can be discerned against the magnetoresistance-related background in both high- and low-conductivity structures. The Hall coefficient in the hopping regime exhibits a nonmonotonic dependence on the occupancy of quantum dots by holes. This behavior correlates with that of the localization length of the hole wavefunctions.     

Contribution of the electron-electron interaction to the optical properties of dense arrays of Ge/Si quantum dots

We present the results of an investigation of the light absorption due to interband and interlevel transitions and the photoconductivity in dense arrays of Ge quantum dots (QDs) in Si formed using the effect of self-organization during molecular-beam heteroepitaxy. It was found that the formation of charged exciton complexes composed of two holes and one electron, as well as of the be-exciton complexes in QDs of type II, leads to an increase in the energy of indirect (in real space) exciton transition, which is explained by the spatial separation of electron and hole. Self-consistent calculations of the wavefunctions for electrons and holes in exciton and in the exciton complexes showed that an electron in a single exciton is localized in the region of maximum stress for Si in the vicinity of the Ge pyramid apex, while a hole is localized near the pyramid base. In a be-exciton complex, electrons exhibit repulsion leading to their spatial separation. As a result, the second electron is bound at the boundary between Si and a continuous Ge layer in which the pyramid bases reside. The experimental data show that an increase in the charge carrier concentration in the ground state of QDs leads to a shortwave shift of the interband resonance and to the narrowing and shape change of the light absorption band, which is explained by depolarization of the external electromagnetic wave due to interaction with the collective charge density oscillations in the lateral direction of the array of Ge nanoclusters. It is established that the hole injection into an excited state of QDs leads to a longwave shift of the photoconductivity peak as a result of decay of the collective excitations and suppression of the depolarization effect.     

Many-electron Coulomb correlations in hopping transport along layers of quantum dots

Experimental data are analyzed on the hopping transport of holes in two-dimensional layers of Ge/Si(001) quantum dots (QDs) under conditions of the long-range Coulomb interaction of charge carriers localized in QDs, when the temperature dependence of the conductivity obeys the Efros-Shklovskii law. It is found that the parameters of hopping conduction significantly deviate from the predictions of the model of one-electron excitations in “Coulomb glasses.” Many-particle Coulomb correlations associated with the motion of holes localized in QDs play a decisive role in the processes of hopping charge transfer between QDs. These correlations lead to a substantial decrease in the Coulomb barriers for the tunneling of charge carriers.     

Modification of the Discrete Singularity Method for Nonuniform Grids As Applied to One-Dimensional Integral Equations with a Strong Singularity in the Kernel

Differential Equations - Formulas are constructed for the approximate calculation of one-dimensional singular and hypersingular integrals over an interval with an arbitrary partition. On the basis...     

Crystallochemistry of mercury chalcogenides. IV. Crystalline structure of two polymorphous modifications of the mercury sulfochalcogenide Hg3S2Br1.5Cl0.5

Two modifications of a new mercury sulfohalide of Hg₃S₂Br_2−x Cl_x (x = 0.5) composition have been grown from the gas phase and explored by X-ray structural analysis. The compounds were obtained at an attempt to synthesize an analogue of the rare mineral arzakite Hg₃S₂(Br, Cl)₂ (Br > Cl). The refinement of the crystalline structures of monoclinic (I) and cubic (II) phases (I: a = 17.824(4) Å, b = 9.238(2) Å, c = 10.269(2) Å, β = 115.69(1)°, V = 1523.8(5) ų, space group C2/m, Z = 8, R = 0.0513; II: a = 18.248(2) Å, V = 6076.4(12) ų, space group Pm3ˉn, Z = 32, R = 0.038) has shown that they are polymorphous modifications of the compound of Hg₃S₂Br_1.5Cl_0.5 formula. The monoclinic modification I is isostractural to the synthetic compound α-Hg₃S₂Br₂. Modification II is isostructural to synthetic β-Hg₃S₂Cl₂. In both structures, each atom S has in its surrounding three atoms of Hg forming umbrella-type groups SHg₃ with spaces Hg—S 2.366–2.430 Å and angles HgSHg 95.66–97.60°. SHg₃-fragments are bound by Hg-apices with the formation of isolated cubic groups [Hg₁₂S₈]. Like that in other structures of mercury chalcohalides, the main role in structure-forming of the investigated compounds is played by atoms of halogens creating a cubic sublattice in which radicals Hg—S are arranged. Original Russian Text Copyright ? 2006 by N. V. Pervukhina, S. A. Magarill, D. Yu. Naumov, S. V. Borisov, V. I. Vasil’yev, and B. G. Nenashev __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 47, No. 2, pp. 318–323, March–April, 2006.