Atoms In Sublattice Research Articles

An interpretation of three intersections of cubic and rhombohedral structures based on the conservative nature of force skeletons

A crystallographic analysis of the structures of inorganic compounds has shown the uniformity of “force skeletons”: pseudotranslational sublattices of atoms determining the structure of different classes of materials. At three specific c hex/a hex ratios, structures with a rhombohedral cell can be considered in the pseudocubic representation with P, I, and F cells (c hex/a hex is, respectively, 1.225, 0.612, and 2.45). The large fraction of structures with c hex/a hex ratios close to these values indicates the stability of these atomic constructions. Force skeletons with a typical hexagonal subcell (different for cations and anions), which reflects the relationship of these structures with the high-symmetry structural types of sphalerite (ZnS) and galena (PbS), have been established for the representative group of sulfides structures with a cell parameter ∼4 A in the direction perpendicular to the mirror plane.

Change in the electronic spectrum of a carbon nanotube during elastic deformation and the relative shear of atomic sublattices

The energy spectrum of the π electrons of a single-layer carbon nanotube is theoretically studied as a function of the elastic strain obtained during uniaxial tension-compression or torsion of the nanotube. The change in the energy spectrum during atomic restructuring of the nanotube is investigated. The energy gap in the spectrum of the carbon nanotube is calculated as a function of the type of deformation.

Features of the crystal structure of disperse carbides in alpha titanium

Investigations of disperse nonmetallic inclusions in unalloyed alpha titanium VT1-0 have been performed by using transmission electron (including scanning and high-resolution) microscopy. Characteristic electron energy losses spectroscopy has shown that these inclusions are titanium carbide particles. It has been revealed that the disperse carbides are formed in the titanium hcp matrix as a phase based on the fcc sublattice of titanium atoms. The inclusion–matrix orientation relationship corresponds to the well-known Kurdyumov–Sachs and Nishiyama–Wassermann relationships $ {\left[ {2\overline {11} 0} \right]_{{\upalpha }}}\parallel {\left[ {011} \right]_{{\updelta }}}{\text{ and }}{\left( {000\overline 1 } \right)_{{\upalpha }}}\parallel {\left( {1\overline 1 1} \right)_{{\updelta }}} $ .

Effect of interlayer bare tunneling on electron-hole coherence in graphene bilayers

The influence of single-particle interlayer coupling on the many-body electron-hole condensation between two graphene monolayers separated by a thin dielectric film is studied. This work extends prior work by treating interlayer coupling, which controls critical interlayer tunneling currents, nonperturbatively. As before, a \ensuremath{\pi}-band tight-binding model of the graphene bilayer is combined with Fock mean-field theory. Our results demonstrate that both the strength and the sublattice distribution of interlayer coupling play essential roles. We consider both Bernal-like and quasi-hexagonal forms, and self-consistently solve for the condensate. We find that stronger bare coupling can considerably affect the nature of the condensate state itself, selecting a preferred pattern of interlayer coherence among the atomic sublattices. When this occurs, the sensitivity of the critical current to the nature of the bare coupling decreases substantially. Because condensate control via gated charge imbalance has been proposed for beyond Complementary Metal-Oxide Semiconductor (CMOS) switching, we also examine the effect of increasing charge imbalance between layers on the condensate strength as well as the critical current.

Synthesis and Crystal Structure of the Trigonal Silver(I) Dithioaurate(I), Ag3AuS2

Crystals of the silver(I) dithioaurate(I), Ag3AuS2, were obtained by fusing the elements in the required stoichiometric amounts. Single-crystal X-ray analysis showed that two phases of a slightly different composition coexist in the products of synthesis: a trigonal phase [a = 13.7104(4) Å, c = 17.1170(6) Å, space group R3̅c] and a cubic one [a = 19.3590(7) Å]. The crystal structure was determined for the first phase. The sublattice of sulfur atoms represents a distorted body-centered cubic packing. The structure contains distinct triatomic linear groups (S−Au−S) and Ag atoms surrounded by four S atoms (from four different linear groups). Comparison was made for the trigonal phase under consideration, cubic petzite (Ag3AuTe2) and fischesserite (Ag3AuSe2) and the tetragonal uytenbogaardtite (Ag3AuS2). The trigonal phase Ag3AuS2 cannot be attributed to the petzite group, because it is a new structure type. Unlike generally accepted opinion, the tetragonal uytenbogaardtite is not a petzite type either.

Electronic Structure and Chemical Modification of Graphene Antidot Lattices

Using the spin-polarized density functional theory, we have demonstrated the electronic structure of graphene antidot lattices (GALs). It is found that due to the symmetry broken of α, β atomic sublattices, GALs behave semiconducting in general. And the triangular GALs present some electronic localized states around the Fermi level, which are half-filled and prone to spin-polarization instability. When the sizes of the antidot increase, the band gaps of the GAL would increase, resulting from the quantum size effect. Moreover, chemical activity of the adatoms could be enhanced by the adsorption of hydroxyl groups, comparing with perfect graphene. At the same time, the adsorption of the hydroxyl group changes the geometrical structures and makes the hybrid type of adatoms transform from sp2 to sp3. Interestingly, we found that the imbalance adsorption on two sublattices induces the magnetism, which is related to the number difference of carbon atoms of the two sublattices in the π conjugation network. This ...

Additive Occupancy in the Cu6Sn5-Based Intermetallic Compound Between Sn-3.5Ag Solder and Cu Studied Using a First-Principles Approach

A Cu6Sn5-based intermetallic compound containing a certain amount of Co or Ni is commonly formed at the interface between a Cu substrate and Sn-based solder. The Co or Ni additive is often found to occupy the Cu atom sublattice in the Cu6Sn5 crystal structure. In this paper, a first-principles approach based on density-functional theory is employed to explore the most favorable occupancy sites of Ni and Co dopants in the Cu6Sn5 crystal structure. It is found that, for up to 27.3 at.% concentration, both Ni and Co atoms tend to substitute for Cu in the Cu6Sn5-based structure and form more thermodynamically stable (Cu,Ni)6Sn5 and (Cu,Co)6Sn5 phases. In comparison, Ni is more effective than Co at stabilizing the Cu6Sn5 phase. At a lower concentration level (9.1 at.%), the Ni or Co atoms prefer to occupy the 4e Cu sublattice. At a higher concentration (27.3 at.%), the Ni atoms will likely be located on the 4e + 8f2 Cu sublattice. Analysis of density of states (DOS) and partial density of states (PDOS) indicates that hybridization between Ni-d (or Co-d) and Sn-p states plays a dominant role in structural stability. Compared with Cu4Ni2Sn5, where Ni occupies the 8f2 Cu sublattice, Cu4Co2Sn5 is less stable due to the lower amplitude of the Co-d PDOS peak and its position mismatch with the Sn-p PDOS peak.

Effect of Stacking Order on the Electric-Field Induced Carrier Modulation in Graphene Bilayers

When planar graphene sheets are stacked on top of each other, the electronic structure of the system varies with the position of the subsequent sublattice atoms. Here, we employ scanning photocurrent microscopy to study the disparity in the behavior of charge carriers for two different stacking configurations. It has been found that deviation from the regular Bernal stacking decouples the sheets from each other, which imparts effective electrostatic screening of the farther layer from the underlying backgate. Electrochemical top-gating is demonstrated as a means to selectively tune the charge carrier density in the decoupled upper layer.

The principle of maximum filling and characteristics of sublattices of hydrogen atoms

The most important characteristics of the Voronoi-Dirichlet polyhedra of 4005928 crystallographically different atoms in sublattices only containing hydrogen atoms were determined in the structures of 151044 inorganic, organoelement, and organic compound crystals. In such sublattices, the Voronoi-Dirichlet polyhedra of H atoms most often had 15 faces, and these faces were most often pentagonal. A comparative analysis of H- and C-sublattices was performed to find that the most important geometric and topological characteristics of H-sublattices were caused by the absence of short-range and local long-range order in the mutual arrangement of hydrogen atoms in the structure of crystals.

Maximum filling principle and sublattices of actinide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A is actinide) in chemically homogeneous sublattices in the crystal structures of 3479 inorganic, coordination, and organometallic compounds are determined. The effect of the actinide nature on the A-A interatomic distances in the crystal structures is considered. In the Th, U, Np, or Pu sublattices, VDP have most often 14 faces and the Fedorov cuboctahedron is the most abundant type of VDP, whereas in Ac, Pa, Am, Cm, Bk, or Cf sublattices, the VDP have mainly 12 faces and are shaped like rhomobododecahedra. In A sublattices that typically form VDP with 14 faces, the actinide atoms occupy, most often, sites with C 1 symmetry (47 to 59% of the sample size). In the case of actinides whose A sublattices tend to form VDP with 12 faces, the C 1 site symmetry is found either very rarely (Pa, Am, Cf) or not at all (Ac, Cm, Bk).

Geometrical Recognition: A General Route to Shape-Controlled Syntheses of Transitional Metal Chalcogenides, Silicides, and Copper(I) Chloride Nanocrystals

In our former publications (J. Phys. Chem. B 2005, 109, 11585; and J. Phys. Chem. B 2006, 110, 14107), we have proposed the geometrically kinetic competition (GKC) mechanism to be responsible for the silica-vapor-pressure-dependent growth of silica-sheathed Fe7S8 and digenite Cu2S nanocrystals. Here, we demonstrate that geometrical recognition (GR), the basis of GKC, can be a general route to shape-controlled syntheses of a host of materials' nanocrystals. According to the types of the metal (or silicon for CoSi and MnSi) atom sublattices, the experimental results are presented, and the mechanisms for the growth of various shapes of products are discussed in detail. SiO4 clusters have been proposed as the competing opponents to SiO3 clusters for shape-controlled syntheses of MnS, CuCl, Cu2S, CdS, ZnSe, and ZnS nanocrystals.

Maximum filling principle and sublattices of lanthanide atoms in crystal structures

Maximum filling principle and sublattices of lanthanide atoms in crystal structures

Six-fold-coordinated phosphorus by oxygen in AlPO4 quartz homeotype under high pressure

AlPO4 belongs to the berlinite quartz homeotype family, which has been the subject of intense high-pressure research triggered by the supposed existence of reversible pressure-induced amorphization. X-ray diffraction experiments, complemented with ab initio calculations, demonstrate the existence of two high-pressure crystalline polymorphs and show that AlPO4 shares the same two-stage densification mechanism as silica. In the first step, a compact hexagonal sublattice of oxygen atoms is formed. In the second step, the cations redistribute in the interstices giving rise to a monoclinic distorted CaCl2 phase. The most outstanding feature of the phase is that phosphorous becomes six-fold coordinated by oxygen, adopting a configuration unknown so far in solid-state science. This finding opens possibilities in the high-pressure chemistry of phosphorus. The close relationship of AlPO4 with silica suggests the existence of completely unexplored families of compounds analogous to those of six-fold-coordinated silicates but based on PO6.

Atomic sublattices: Problems of indexing powder patterns, structural model determination

The second basic theorem of lattice crystallography (by N. V. Belov) underlies the theory of atomic sublattices characteristic of the overwhelming majority of crystal structures we have studied. By the example of structures of particular inorganic compounds (involving mercury chalcohalides) it is illustrated that a priory knowledge of cationic and anionic sublattices typical of a given class of compounds may provide useful information for analyzing powder diffraction patterns of substances with unknown crystal structures. It has been shown that complicated structures can be analyzed “in parts” by identifying their individual components discernable in powder diffraction patterns.

Lattices of Radicals of Ω-Groups

Snider initiated the study of lattices of the class of radicals, in the sense of Kurosh and Amitsur, of associative rings. Various authors continued the investigation in more general universal classes. Recently, Fernández-Alonso et al. studied the lattice of all preradicals in R-Mod. Our definition of a preradical is weaker than theirs. In this paper, we consider the lattices of ideal maps 𝕀, preradical maps ℙ, Hoehnke radical maps ℍ and Plotkin radical maps 𝔹 in any universal class of Ω-groups (of the same type). We show that 𝕀 is a complete and modular lattice which contains atoms. In general, 𝕀 is not atomic. 𝕀 contains ℙ as a complete and atomic sublattice, whereas ℍ and 𝔹 are not sublattices of 𝕀. In its own right, ℍ is a complete and atomic lattice and 𝔹 is a complete lattice. We identify subclasses of 𝕀, ℙ and ℍ that are sublattices or preserve the meet (or join) of these respective lattices.

On quantifying the group-V to group-III interdiffusion rates in InxGa1−xAs/InP quantum wells

The interdiffusion rate of group-V and group-III sublattice atoms in InxGa1−xAs/InP quantum well structures induced by proton implantation has been investigated using differential reflectance (DR), photoluminescence (PL) and theoretical modelling. Based on DR, PL and modelling results, we found the unique value of k (LV/LIII) ratio for three different InGaAs quantum well structures, namely lattice matched (LM), tensile strained (TS) and compressively strained (CS). The k ratio of TS, LM and CS was 1.05, 1.25 and 1.40 respectively. These ratios were slightly higher than unity indicating that the diffusion coefficient of the group-V sublattice was larger than that of the diffusion coefficient of the group-III sublattice. Change in the interdiffusion rate of group V and group III in the lattice-matched and strained (TS, CS) quantum well structures was most likely due to the different strain profile developed in the quantum well region as a result of changing the quantum well composition.

On the crystal structure of Cr2N precipitates in high-nitrogen austenitic stainless steel. II. Order–disorder transition of Cr2N during electron irradiation

The crystal structure and order-disorder transition of Cr2N were investigated utilizing transmission electron microscopy (TEM). Based on the analyses of selected-area diffraction (SAD) patterns, the crystal structure of the ordered Cr2N superstructure was confirmed to be trigonal (P31m), characterized by three sets of superlattice reflections (001), ((11/33)0) and ((11/33)1). During electron irradiation, the superlattice reflections gradually disappeared in the regular sequence (001), ((11/33)0) and ((11/33)1), indicating that the order-disorder phase transition of Cr2N occurred. The convergent-beam electron diffraction (CBED) observation revealed that the space group of disordered Cr2N is P6(3)/mmc, which corresponds to an h.c.p. (hexagonal close packed) sublattice of metal atoms with a random distribution of N atoms in six octahedral interstices. The redistribution model of N atoms through the order-disorder transition is discussed based on the characteristics and disappearing sequence of superlattice reflections.

Geometrical magnetic frustration in rare-earth chalcogenide spinels

We have characterized the magnetic and structural properties of the $\mathrm{Cd}{\mathit{Ln}}_{2}{\mathrm{Se}}_{4}$ $(\mathit{Ln}=\mathrm{Dy},\mathrm{Ho})$, and $\mathrm{Cd}{\mathit{Ln}}_{2}{\mathrm{S}}_{4}$ $(\mathit{Ln}=\mathrm{Ho},\mathrm{Er},\mathrm{Tm},\mathrm{Yb})$, spinels. We observe all compounds to be normal spinels, possessing a geometrically frustrated sublattice of lanthanide atoms with no observable structural disorder. Fits to the high-temperature magnetic susceptibilities indicate these materials to have effective antiferromagnetic interactions, with Curie-Weiss temperatures ${\ensuremath{\Theta}}_{\mathrm{W}}\ensuremath{\sim}\ensuremath{-}10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, except $\mathrm{Cd}{\mathrm{Yb}}_{2}{\mathrm{S}}_{4}$ for which ${\ensuremath{\Theta}}_{\mathrm{W}}\ensuremath{\sim}\ensuremath{-}40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The absence of magnetic long-range order or glassiness above $T=1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ strongly suggests that these materials are a different venue in which to study the effects of strong geometrical frustration, potentially as rich in interesting physical phenomena as that of the pyrochlore oxides.

Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes

We present a theoretical study of degeneracy breaking due to short-ranged impurities in finite, single-wall, metallic carbon nanotubes. The effective mass model is used to describe the slowly varying spatial envelope wave functions of spinless electrons near the Fermi level at two inequivalent valleys ($K$-points) in terms of the four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wave function on the sublattice atoms (``$A$'' and ``$B$''). Using boundary conditions at the ends of the tube that neither break valley degeneracy nor mix pseudospin eigenvectors, we use degenerate perturbation theory to show that the presence of impurities has two effects. First, the position of the impurity with respect to the spatial variation of the envelope standing waves results in a sinusoidal oscillation of energy level shift as a function of energy. Second, the position of the impurity within the hexagonal graphite unit cell produces a particular $4\ifmmode\times\else\texttimes\fi{}4$ matrix structure of the corresponding effective Hamiltonian. The symmetry of this Hamiltonian with respect to pseudospin flip is related to degeneracy breaking and, for an armchair tube, the symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing.

Autosoliton in a Structurally Unstable Crystal

It is shown that a spatially localized collective excitation of the atomic sublattice (autosoliton) appears and propagates in a structurally unstable crystal occurring in a pretransition state. The autosoliton, on the one hand, is a structural defect comprising two interphase boundaries separated by the second phase, and, on the other hand, it can be considered as a pulse of the inelastic strain field.