Computing Some Degree-Based Topological Indices of Honeycomb Networks

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

Crystal structure of chain silicate Cs3LuSi3O9

A caesium lutetium(III) silicate, Cs3LuSi3O9, was synthesized by heating a pelletized mixture of Cs2CO3, Lu2O3 and SiO2 at 1273 K. Single crystals of the title compound were grown in a melted area of the pellet. Cs3LuSi3O9 is a single-chain silicate (orthorhombic space group Pna21) with a chain periodicity of six and is isostructural with Cs3 RE IIIGe3O9 (RE = Pr, Nd and Sm–Yb). The two symmetry-dependent [Si6O18]12− chains in the unit cell lie parallel to the [011] direction. The Lu3+ ions are octahedrally coordinated by O atoms of the silicate chains, generating a three-dimensional framework. Cs+ ions are located in the voids in the framework.

Computation of Nirmala Indices of Some Chemical Networks

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

On Distance-Based Topological Descriptors of Chemical Interconnection Networks

Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, ABC GG index, and NGG index, for chain oxide network COX n , chain silicate network CS n , ortho chain S n , and para chain Q n , for the first time. Moreover, analytically closed formulae for these structures are determined.

Silicate-germanate K2Y[(Si3Ge)O10(OH)] with unusual complex corrugated layer and its correlation to ring silicate gerenite and chain silicate chkalovite

A new silicate-germanate K2Y[(Si3Ge)O10(OH)] was synthesized hydrothermally in a system Y2O3:GeO2:SiO2 = 1:1:2 (T = 280 °C; P = 90–100 atm.); K2CO3 was added to the solution as a mineralizer. Single-crystal X-ray diffraction experiment was carried out at low temperature (150 K). The unit cell parameters are a = 10.4975(4), b = 6.9567(2), c = 15.4001(6) Å, β = 104.894(4)°; V = 1086.86(7) Å3; space group is P 21/c. A novel complex anion is presented by corrugated (Si,Ge) tetrahedral layers connected by couples of YO6 octahedra into the mixed microporous framework with the channels along b and a axes, the maximal size of cross-section is ~5.6 Å. This structure has similarity with the two minerals: ring silicate gerenite (Ca,Na)2(Y,REE)3Si6O18 · 2H2O and chain silicate chkalovite Na2BeSi2O6. Six-member rings with 1̅ symmetry as in gerenite are distinguished in the new layer. They are mutually perpendicular to each other and connected by additional tetrahedra. Straight crossing chains in chkalovite change to zigzag four-link chains in the new silicate-germanate layer.

Topological Indices of mth Chain Silicate Graphs

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

Nolzeite, Na(Mn,□)2[Si3(B,Si)O9(OH)2]·2H2O, a new pyroxenoid mineral from Mont Saint-Hilaire, Québec, Canada

Nolzeite, Na(Mn,□)2[Si3(B,Si)O9(OH)2]·2H2O, is a new mineral found in altered sodalite syenite at the Poudrette quarry, La Vallée-du-Richelieu, Montérégie (formerly Rouville County), Québec, Canada. Crystals are colourless to pale green and are acicular with average dimensions of 5 μm × 8 μm × 55 μm. They occur as radiating to loose, randomly oriented groupings within vugs associated with aegirine, nepheline, sodalite, eudialyte-group minerals, analcime, natron, pyrrhotite, catapleiite, steedeite and the unidentified mineral, UK80. Nolzeite is non-pleochroic, biaxial, with nmin = 1.616(2) and nmax = 1.636(2) and has a positive elongation. The average of six chemical analyses gave the empirical formula: Na1.04(Mn1.69□0.24Fe0.05Ca0.02)∑=2.00(Si2.96S0.04)∑=3.00(B0.70Si0.30)∑=1.00O9(OH)2·2H2O based on 13 anions. The Raman spectrum shows six distinct bands occurring at ∼3600–3300 cm–1 and 1600–1500 cm–1 (O–H and H–O–H bending), 1300–1200 cm–1 (B–OH bending), 1030–800 cm–1 (Si–O–Si stretching) as well as 700–500 cm–1 and 400–50 cm–1 (Mn–O and Na–O bonding, respectively). The FTIR spectrum for nolzeite shows bands at ∼2800 –3600 cm–1(O–H) stretching, a moderately sharp band at 1631 cm –1(H–O–H) bending, strong, sharp bands at ∼650 –700 cm–1, ∼800 –840 cm–1, and ∼900–1100 cm–1(Si–O and B –O) bonds. Nolzeite is triclinic, crystallizing in space group P with a = 6.894(1), b = 7.632(2), c = 11.017(2) Å, α= 108.39(3), β= 99.03, γ = 103.05(3)°, V = 519.27 Å3, and Z = 2. The crystal structure was refined to R = 12.37% and wR2 = 31.07% for 1361 reflections (Fo > 4σFo). It is based on chains of tetrahedra with a periodicity of three (i.e. a dreier chain) consisting of three symmetrically independent SiO4 tetrahedra forming C-shaped clusters closed by BO2(OH)2 tetrahedra, producing single loop-branched dreier borosilicate chains. The chains are linked through shared corners to double chains of edge-sharing MnO5(OH) octahedra. Nolzeite is a chain silicate closely related to steedeite and members of the sérandite–pectolite series. Paragenetically, nolzeite is late-stage, probably forming under alkaline conditions and over a narrow range of low pressures and temperatures.