Field theoretical calculation of the specific heat exponent for a classical N-vector model in a random external field

We calculate using diagrammatic perturbation theory in the two-loop approximation, the specific heat exponent for the classical N-vector model in a random external field for spatial dimension (D) lying between four and six. The calculation supports the modified hyperscaling , where is the correlation length exponent. Received: 18 March 1998 / Revised: 17 April 1998 / Accepted: 21 April 1998     

Porous Solids Arising from Synergistic and Competing Modes of Assembly: Combining Coordination Chemistry and Covalent Bond Formation

Design and synthesis of porous solids employing both reversible coordination chemistry and reversible covalent bond formation is described. The combination of two different linkage modes in a single material presents a link between two distinct classes of porous materials as exemplified by metal–organic frameworks (MOFs) and covalent organic frameworks (COFs). This strategy, in addition to being a compelling material‐discovery method, also offers a platform for developing a fundamental understanding of the factors influencing the competing modes of assembly. We also demonstrate that even temporary formation of reversible connections between components may be leveraged to make new phases thus offering design routes to polymorphic frameworks. Moreover, this approach has the striking potential of providing a rich landscape of structurally complex materials from commercially available or readily accessible feedstocks.     

Mechanism and kinetics of the isothermal thermodegradation of ethylene-propylene-diene (EPDM) elastomers

The thermal degradation behavior of a range of ethylene-propylene-diene (EPDM) elastomers, covering the whole range of composition, has been examined under isothermal conditions between 410 and 440 °C using thermogravimetric analysis. The kinetic parameters of degradation for the polymers have been evaluated using different mathematical models based on different proposed mechanisms of degradation. The experimental data were fitted to the models using non-linear regression analysis technique based on Marquardt-Levenberg algorithm. It appears that the degradation of EPDMs follows the Avrami-Erofeev two-dimensional nucleation model or a random chain-scission mechanism. No observable trend was found between the ethylene content of EPDM and the activation energy of degradation.     

Microstructure characterization and phase transformation kinetic study of ball-milled m-ZrO2–30 mol% a-TiO2 mixture by Rietveld method

High-energy ball milling of monoclinic ZrO₂–30 mol% anatase TiO₂ mixture at different durations results in the formation of m-ZrO₂–a-TiO₂ solid solution from which the nucleation of nanocrystalline cubic (c) ZrO₂ polymorphic phase sets in. Post-annealing of 12 h ball-milled sample at different elevated temperatures for 1 h results in almost complete formation of c-ZrO₂ phase. Microstructure of the unmilled, all the ball milled and annealed samples has been characterized by Rietveld's X-ray powder structure refinement method. Particle size, rms lattice strain, change in lattice parameters and phase content of individual phases have been estimated from Rietveld analysis, and are utilized to interpret the results. In course of milling, (1 1 1) of cubic lattice became parallel to () plane of monoclinic lattice due to the orientation effect and cubic phase may have been formed on the (0 0 1) of the m-ZrO₂–a-TiO₂ solid solution lattice. A comparative study of microstructure and phase transformation kinetics of ZrO₂–10, 20 and 30 mol% a-TiO₂ ball-milled and post-annealed samples reveals that rate of phase transformation m→c-ZrO₂ increases with increasing a-TiO₂ concentration and 30 mol% of nanocrystalline c-ZrO₂ phase can be obtained within 4 h of milling time in the presence of 30 mol% of a-TiO₂. The post-annealing treatment at 773, 873 and 973 K for 1 h duration each reveals that rate of c-ZrO₂ formation with increasing temperature is retarded with increasing a-TiO₂ concentration but the amount of c-ZrO₂ becomes almost equal (95 mol%) at 973 K. It suggests that almost fully stabilized nanocrystalline c-ZrO₂ can be formed by adding a tetravalent solute to m-ZrO_2.     

Improved color purity in nano-size Eu-doped YBO3 red phosphor

Nano-size YBO₃:Eu³⁺ phosphor has been synthesized by the co-precipitation method. X-ray diffraction (XRD) pattern confirmed the formation of hexagonal vaterite-type structures of YBO₃:Eu³⁺ nanoparticles. The transmission electron microscopy (TEM) study revealed the formation of spherical YBO₃:Eu³⁺ nanoparticles with size 20-40 nm. The photoluminescence spectra revealed that the ratio of the red emission (⁵D₀-⁷F₂) to the orange emission (⁵D₀-⁷F₁) was much higher in the synthesized nano-size YBO₃:Eu³⁺ phosphor. The improved relative intensity, i.e., higher R/O value of emission peaks, is due to a lower symmetry of crystal field around Eu³⁺ ions.     

Control of amplification without inversion in H2 and LiH molecules: Dependence on relative magnitude of probe and coherent field Rabi frequencies in three-level Λ system

Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H₂ and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.     

Convexifactors, Generalized Convexity, and Optimality Conditions

The recently introduced notion of a convexifactor is further studied, and quasiconvex and pseudoconvex functions are characterized in terms of convexifactors. As an application to a chain rule, a necessary optimality condition is deduced for an inequality constrained mathematical programming problem.