The study of the behavior of Al impurity in ZnO lattice by a fullerene like model

The fullerene like Zn32Al4O36 clusters were investigated and the oxygen interstitial Oi acceptor intrinsic defect formation energy as well as Al ionization energy were calculated. The effect of lattice packing defects on the electroactivity of Al impurity was investigated. Analysis of the defects formation energies shows the smaller formation energy of interstitial Oi in a comparison with a formation of Zn vacancy. This allows us to formulate recommendations of technological conditions for films deposition, with improved electroactivity of Al donor.

The Use of the Lattice Packing Theory for Precise Point Positioning with Ionosphere-Free Measurements in CDMA GNSS

The paper considers the use of the lattice packing theory for Integer Precise Point Positioning (Integer PPP) with the errors usually not exceeding 1–3 cm based on GNSS signals with code division multiple access (CDMA). Positioning is carried out by processing ionosphere-free linear combinations of code and phase measurements with ambiguity resolution employing satellite corrections. The main issue of PPP algorithms is overcoming the rank deficiency problem of the linear equation system obtained by linearization of nonlinear mathematical models of measurements. Nowadays Float PPP is quite well developed, where rank deficiency is tackled by combining systematic biases in measurement models with integer carrier phase ambiguities. As a result, the number of unknowns is reduced to the rank of design matrix, which allows unambiguous estimation of precise user coordinates and values of new variables generated by the performed combinations. However, under such conditions the information about integer nature of carrier phase ambiguities is lost, and this leads to a significant increase in convergence time to obtain user coordinates estimates with the errors of 1–3 cm. It is possible to involve the information on the integer nature of phase ambiguities into processing by applying ambiguity resolution algorithms. Though, as a result of the conducted combinations, the integer nature is destroyed, which makes it impossible to apply these algorithms. In Integer PPP rank deficiency is overcome by projecting the state space of the initial linear equation system onto a so-called S-space, whose dimension is equal to the rank of this system. The orientation of the S-space and the direction of projecting are chosen so that the variables of the initial system corresponding to user coordinates are not changed during the projecting and the projections of integer variables remain integer. This makes it possible to estimate precise user coordinates involving information on the integer nature of phase ambiguities. In the literature on Integer PPP based on CDMA GNSS signals processing the description of the S-space orientation with the desired properties is given, but there is no description of the method to determine this orientation. This paper based on the notions of the lattice packing theory considers an algorithm for determining the S-space with the desired properties. It is shown that there exists an infinite set of such S-spaces connected by unimodular transformations, and a technique is proposed to enable selection from this set the S-space, which requires minimal computational cost. The use of the lattice packing theory to the Integer PPP network solution with CDMA GNSS signals will be considered in the following publication of the authors.

Using of Lattice Packing Theory for Determination of Clock Corrections for Precise Point Positioning Based on CDMA GNSS Signals

Using of lattice packing theory for computation of precise satellite clock corrections based on measurements from a ground network of GNSS CDMA signals (network solution) is considered. Advantage of lattice packing theory for this task solution in comparison with algebraic graph theory is described. Network solution based on of algebraic graph theory was considered in previous paper of the authors [3]. The precise satellite clock corrections are transmitted into the user receiver and applied to get the user coordinates with the errors usually not exceeding 1–3 cm. Ambiguity resolution of carrier phase measurements is used to get such precise satellite clock corrections; it leads to a considerable increase in positioning accuracy and a significant reduction of convergence time for user solution.

New dense superball packings in three dimensions

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the $\begin{array}{} \displaystyle l^p_3 \end{array}$ norm) with p ∈ (1, 1.58]. We conjecture that the family also exists for p ∈ (1.58, log2 3 = 1.5849625…]. Like in the densest lattice packing of regular octahedra, each superball in our family of lattice packings has 14 neighbors.

Cocrystals of Li+ encapsulated fullerenes and Tb(iii) double-decker single molecule magnet in a quasi-kagome lattice

Cocrystallization of a lithium ion encapsulated fullerene with a terbium(iii) phthalocyaninato porphyrinato double-decker single-molecule magnet results in a quasi-kagome lattice packing showing ferromagnetic spin arrangement.

Magnetic Nanocomposites Based on Opal Matrices

Features of obtaining magnetic nanocomposites based on the lattice packing of SiO2 nanoscale (opal matrices) with clusters of multiferroic materials (Li-Zn, Bi, Fe, Dy, Gd and Yb titanates) in their interstitial cavities have been considered. For magnetic nanocomposites creation opal matrices with SiO2 nanoscale of ~ 260 nm in diameter have been used. The composition of nanocomposites has been also studied using X-ray diffractometry and Raman spectroscopy. The results of the frequency dependences measurement for the dielectric constant of the nanostructures obtained have been presented. Hysteresis loops have been examined for the samples obtained in the temperature range from 2 to 400 K.

Hydrogen bond-assisted homochiral lattice packing between inorganic helices built from heterometallic units

Two helical chains have been constructed using heterometallic {TiMn2(μ3-O)} clusters as building blocks, where hydrogen bonding plays a key role for the chirality transmission.