Water activities, osmotic and activity coefficients of the system (NH4)2SO4–K2SO4–H2O at the temperature 298.15 K

The mixed aqueous electrolyte system consisting of ammonium and potassium sulfates has been studied using the hygrometric method at the temperature 298.15 K. The water activities are measured at total ionic strength values ranging from 0.60 to 8.25 mol kg⁻¹ for different ionic strength fractions (y) of (NH₄)₂SO₄ with y=0.20, 0.50 and 0.80. The obtained data allow the deduction of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii–Stokes–Robinson (ZSR), Kusik and Meissner (KM), Robinson and Stokes (RS), Lietzke and Stoughton (LS II), Reilly–Wood and Robinson (RWR) and Pitzer models. From these measurements, the new Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture.     

Thermodynamic properties of two ternary systems {yCsCl+(1−y)LiCl}(aq) and {yCsCl+(1−y)NaCl}(aq) at temperature 298.15 K

Thermodynamic properties of the mixed aqueous electrolyte systems of the lithium and cesium chlorides and sodium and cesium chlorides have been studied by the hygrometric method at 298.15 K. The water activities of these systems were measured at total molalities from 0.3 mol kg⁻¹ to saturation for different ionic strength fractions y of CsCl for the systems CsCl–LiCl(aq) and CsCl–NaCl(aq) with y=0.33, 0.50 and 0.67. The results allow the deduction of osmotic coefficients. The experimental results are compared with calculations made using the Zdanovskii–Stokes–Robinson (ZSR), Kusik and Meissner (KM), Robinson and Stokes (RS), Lietzke and Stoughton (LSII), Reilly, Wood and Robinson (RWR) rules, and the Pitzer model. From these measurements, the Pitzer mixing ionic parameters are determined and used to obtain the solute activity coefficients of the mixture for different ionic strength fractions y.     

Generalization of rectangular element stiffness matrix and thermal load vector associated with a0 + a1x + a2y + a3xy type interpolation rule

Explicit expressions for the element stiffness matrix K and element load vector p for the rectangular plane-stress and plane-strain finite elements associated with Ψ(x, y) = a₀ + a₁x + a₂y + a₃xy type interpolation rule are given for the general anisotropic material in xy-planc subjected to non-uniform temperature increases. The expressions are optimized with respect to the numerical operations required for the computation of K and p, and they are valid for special cases of material properties and thermal loading.     

Solubility prediction in the ternary systems NaCl–RbCl–H2O, KCl–CsCl–H2O and KBr–CsBr–H2O at 25 C using the ion-interaction model

The component solubilities in NaCl–RbCl–H₂O, KCl–CsCl–H₂O and KBr–CsBr–H₂O systems at 25 C were calculated by using the Pitzer ion interaction model and its extended HW models. Excellent agreement with experimental solubilities indicated that the models can be successfully used to calculate the component solubilities. This study affords the necessary parameters for solubility predictions of complicated systems containing rubidium and caesium and establishes a theoretical basis for the separation of these valuable metals from salt lake brine.     

Thermodynamic properties of aqueous mixed ternaries { y NH4Cl+(1−y) BaCl2 } (aq) and { y NH4Cl+(1−y) CaCl2 } (aq) at 298.15 K

Hygrometric measurements of the water activity are reported for the thermodynamic properties of the mixed aqueous electrolyte systems of ammonium–calcium chloride and ammonium–barium chloride at 298.15 K. The measurements were made at a large number of total molalities, varying from 0.4 mol kg⁻¹ to saturation at three ionic-strength fractions (y$y$) of NH₄Cl for the systems NH₄Cl–CaCl₂ (aq) and NH₄Cl–BaCl₂ (aq) with y=0.20,0.50$y=0.20,0.50$ and 0.80. The experimental data are reported as water activities and osmotic coefficients at various molalities, along with derived values of the activity coefficients of both solutes. The ranges of water activities _aw$a_w$ are 0.800–0.989 for ammonium–barium chlorides and _aw=0.560–0.989$a_w=0.560\text{–}0.989$ for ammonium–calcium chlorides. The activity coefficients were calculated by means of a thermodynamic model based on a variant of the Pitzer ion-interaction equations with extended binary parameters. However, the results were also compared for the precision of the presentation of the osmotic coefficients using an extended model with the calculations of the Zdanovskii–Stokes–Robinson, Kusik and Meissner, Robinson and Stokes, Lietzke and Stoughton, Reilly, Wood and Robinson, and Pitzer models.     

Determination of water activities,osmotic and activity coefficients of the system NH4NO3–LiNO3–H2O at the temperature 298.15 K

The water activities of the mixed aqueous electrolyte {(y) NH₄NO₃+(1−y) LiNO₃)}(aq) are measured at total molalities from 0.2 mol kg⁻¹ to about saturation for different ionic-strength fractions $y$ of NH₄NO₃ with $y=0.20,0.50,0.80$. The results allow the deduction of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii–Stokes–Robinson (ZSR), Robinson and Stokes (RS), Lietzke and Stoughton (LS II), Reilly–Wood–Robinson (RWR) mixing rules and the Pitzer model. From these measurements, the Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture. The excess Gibbs energy is also determined.     

Thermodynamics of the cao-si02 system

In order to maintain consistency, analytical expressions for the free energy of mixing of phases should reproduce not only the phase diagrams but also the experimentally determined activities. Information on the partial molar free energies and the phase boundaries, in turn, can be used to estimate the free energy of formation of compounds.

An examination of thermochemical data in the CaO-SiO₂ system showed that ΔGδf values for -Ca₂Si0₄, which are stable at temperatures above 1710°K, are limited a maximum of 1800°K. The free energy of formation in a temperature range from about 1700 to 2400°K was estimated from the phase boundary and the activity of silica to be as follows:

2Ca0(s) + Si0₂(cristo.) = Ca2Si0₄() ΔG°f = −86303.50 − 34.338 Tjoules

An analytical expression for the free energy of mixing of the liquid phase was obtained for the entire composition range in the CaO-Si0₂ system. Confidence in the estimated G‡f for -Ca₂Si0₄ was demonstrated by good agreement of the calculated phase diagram and the experimentally determined activity of silica.     

Manufacture and characterization of sol–gel V1−x−yWxSiyO2 films for uncooled thermal detectors

V_1−x−yW_xSi_yO₂ films for uncooled thermal detectors were coated on sodium-free glass slides with sol–gel process, followed by the calcination under a reducing atmosphere (Ar/H₂ 5%). The V_1−x−yW_xSi_yO₂ films as prepared inherit various phase transition temperatures ranging from 20 to 70 °C depending on the dopant concentrations and the fabrication conditions. Compared to the hysteresis loop of plain VO₂ films, a rather steep loop was obtained with the addition of tungsten components, while a relaxed hysteresis loop with the tight bandwidth was contributed by Si dopants. Furthermore, the films with switching temperature close to room temperature were fabricated to one-element bolometers to characterize their figures of merit. Results showed that the V_0.905W_0.02Si_0.075O₂ film presented a satisfactory responsivity of 2600 V/W and detectivity of 9 × 10⁶ cm  Hz^1/2/W with chopper frequencies ranging from 30 to 60 Hz at room temperature. It was proposed that with appropriate amount of silicon and tungsten dopants mixed in the VO₂, the film would characterize both a relaxed hysteresis loop and a fair TCR value, which effectively reduced the magnitude of noise equivalent power without compromising its performance in detectivity and responsivity.     

Experimental study and thermodynamic modelling of the ZrO2–LaO1.5 system

Phase relations in the ZrO₂–LaO_1.5 system were studied experimentally in the temperature range from 1673 to 1973 K. X-ray diffraction and scanning electron microscopy were employed to obtain the structural information and the compositions of the tetragonal and pyrochlore (La₂Zr₂O₇) phases. The solubility of LaO_1.5 in the tetragonal phase was determined to be very small. The homogeneity range of the pyrochlore phase is estimated to be less than 2 mol% at 1973 K, and less than 1 mol% at 1673 K according to the present work. Based on the experimental results obtained in this work, as well as the available phase diagram and thermodynamic data in literature, a self-consistent thermodynamic assessment was carried out by using the ionic sublattice solution model.     

Algorithms of discretization of algebraic spatial curves on homogeneous cubical grids

In this paper new methods of discretization (integer approximation) of algebraic spatial curves in the form of intersecting surfaces P(x, y, z) = 0 and Q(x, y, z) = 0 are analyzed.

The use of homogeneous cubical grids G(h³) to discretize a curve is the essence of the method. Two new algorithms of discretization (on 6-connected grid G_6c(h³) and 26-connected grid G₂₆(h³)) are presented based on the method above. Implementation of the algorithms for algebraic spatial curves is suggested. The elaborated algorithms are adjusted for application in computer graphics and numerical control of machine tools.     

The application of explicit Nyström methods to singular second order differential equations

An important class of singular second order initial value problems is y″ + (2/x)y′+f(x,y) = 0, 0 < x < x_f, y(0) = a, y′(0) = 0; this class includes, for example, the well-known singular equations of Emden and Liouville. The purpos of this paper is to show the interesting result that explicit Nyström methods, existing for the direct integration of special second order regular initial value problems, can be used for the integration of this class of singular initial value problems and the methods show their proper respective orders of convergence. This is justified mathematically and demonstrated computationally.     

Micromachined sol–gel carbon nanotube/SnO2 nanocomposite hydrogen sensor

A novel micromachined single wall carbon nanotube (SWCNT) reinforced nanocrystalline tin dioxide gas sensor has been developed. The presence of SWCNT in SnO₂ matrix was realized by a spin-on sol–gel process. The SWCNT/SnO₂ sensor's sensitivity for hydrogen detection has greatly increased by a factor of three, in comparison to that of pure SnO₂ sensor. The novel sensor also lowers the working temperature, response time and recovery time. The greatly improved performances are mainly attributed to the effective gas accessing nano passes through SWCNT plus the smaller distance between adjacent gas accessing boundaries formed by the distribution of tiny SWCNTs. Therefore, both the spatial requirement (D ≤ 2L, D is the distance between adjacent gas accessing boundaries and L is the space charge layer thickness) and surficial requirement (adequate gas activation area) are met and the maximum inherent sensitivity of SnO₂ is achieved.     

An element for static, vibration and buckling analysis of thick laminated plates

A conforming finite element formulation of the equations governing composite multilayered plates using Reddy's higher-order theory is presented. The element has eight degrees of freedom, u₀, v₀, w, ∂w/∂x, ∂w/∂y, ∂²w/∂x∂y, γ_x, γ_y, per node. The transverse displacement of the present element is described by a modified bicubic displacement function while the in-plane displacements and shear-rotations are interpolated quadraticly. The element is evaluated for its accuracy in the analysis of static, vibration, and buckling of anisotropic rectangular plates with different lamination schemes and boundary conditions. The conforming finite element described here for the higher-order theory gives fairly accurate results for displacements, stresses, buckling loads, and natural frequencies.     

Pyroelectric and dielectric properties of sol–gel derived barium–strontium–titanate (Ba0.64Sr0.36TiO3) thin films

The barium–strontium–titanate (BST, Ba_0.64Sr_0.36TiO₃) thin films have been prepared by the sol–gel method on a platinum-coated silicon substrate. The resulting thin films show very good dielectric and pyroelectric properties. The dielectric constant and dissipation factor for Ba_0.64Sr_0.36TiO₃ thin film at a frequency of 200 Hz were 592 and 0.028, respectively. The dependence of the capacitance as a function of the voltage shows a strongly non-linear character, and two peaks characterizing spontaneous polarization switching can be clearly seen in this curve, indicating that the films have a ferroelectric nature. The capacitance changed from 495 to 1108 pF with the applied voltage in the −5 to +5 V range at a frequency of 100 kHz. The peak pyroelectric coefficient at 30 °C is 1080 μC/m² K. The pyroelectric coefficient at room temperature (25 °C) is 1860 μC/m² K, and the figure-of-merit of this film is 37.4 μC/m³ K. The high pyroelectric coefficients and the greater figures-of-merit of Ba_0.64Sr_0.36TiO₃ thin films make it possible to be used for thermal infrared detection and imaging.     

Existence of multiple positive solutions for functional differential equations

In this paper, the existence of at least three positive solutions for the boundary value problem (BVP) of second-order functional differential equation with the form y″(t) + f(t, y^t) = 0, for t ε [0,1], y(t) -βy′(t) =η(t), for t ε [−τ,0], −γy(t) + Δy′(t) = ζ(t), for t ε [1, 1 + a], is studied. Moreover, we investigate the existence of at least three partially symmetric positive solutions for the above BVP with Δ = βγ.     

Resolvability and the upper dimension of graphs

For an ordered set W = {w₁, w₂,…, w_k} of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v | W) = (d(v, w₁), d(v, w₂),…, d(v, w_k)), where d(x, y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have distinct representations. A new sharp lower bound for the dimension of a graph G in terms of its maximum degree is presented.

A resolving set of minimum cardinality is a basis for G and the number of vertices in a basis is its (metric) dimension dim(G). A resolving set S of G is a minimal resolving set if no proper subset of S is a resolving set. The maximum cardinality of a minimal resolving set is the upper dimension dim⁺(G). The resolving number res(G) of a connected graph G is the minimum k such that every k-set W of vertices of G is also a resolving set of G. Then 1 ≤ dim(G) ≤ dim⁺(G) ≤ res(G) ≤ n − 1 for every nontrivial connected graph G of order n. It is shown that dim⁺(G) = res(G) = n − 1 if and only if G = K_n, while dim⁺(G) = res(G) = 2 if and only if G is a path of order at least 4 or an odd cycle.

The resolving numbers and upper dimensions of some well-known graphs are determined. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with dim(G) = dim⁺(G) = a and res(G) = b. Also, for every positive integer N, there exists a connected graph G with res(G) − dim⁺(G) ≥ N and dim⁺(G) − dim(G) ≥ N.     

Solidification structure of CaO–SiO2–MgO–Al2O3 (–CaF2) systems and computational phase equilibria: Crystallization of MgAl2O4 spinel

The solidification behaviour of the CaO–SiO₂–Al₂O₃–CaF₂–10% MgO system, which is similar to the inclusion compositions in the stainless steel and the crystallization of spinel have been investigated using XRD, SEM-EDS, and an image analyser. The solidification mode and the phase equilibria were computed by employing thermochemical software. The liquidus temperature of the oxides containing 5% CaF₂ increases with increasing alumina content from 10% to 30%, while the solidus temperature has little dependence on alumina content. The size of spinel crystals in the final microstructure increases on increasing the content of alumina, resulting from that the oxides spending more time at higher temperatures below the liquidus temperature, where crystal growth is generally faster than nucleation, during slow cooling. The liquidus temperature of the oxides containing 30% Al₂O₃ is scarcely varied, while the solidus temperature decreases by increasing the content of CaF₂ to 10%. The size of spinel crystals decreases as the content of CaF₂ increases, resulting from the fact that the oxides could spend more time at relatively lower temperatures, where nucleation is faster than growth, during the cooling process.     

Solubility prediction for the nonelectrolyte urea–hydrogen peroxide–water system and thermodynamic solubility product calculation for CO(NH2)2 ⋅ H2O2 using the modified Pitzer model

The Pitzer interaction model, which has been applied successfully to the thermodynamic simulation of electrolyte solutions and electrolyte–nonelectrolyte solutions, was extended to nonelectrolyte–nonelectrolyte solution system. In the present work, the modified Pitzer model was used for calculation and correlation of the ternary CO(NH₂)₂–H₂O₂–H₂O system at 283.15 K. The value of the Pitzer interaction parameters for the ternary system and the thermodynamic solubility product of CO(NH₂)₂⋅H₂O₂ were determined using a least-square optimization procedure with coupling activity coefficient and solubility data. The predicted isothermal solubilities agree well with the result obtained from the experiment. The results indicated that the modified Pitzer model could be successfully used to predict the component solubility of the nonelectrolyte–nonelectrolyte system.