A mathematical model has been developed for computing the geometrical dimensions of square-diamond square pass sequence for a continuous billet mill. The model is based on derivation of shape and size factor from the geometry of the pass taking into account pass filling, pass rounding etc. Using these factors and a basic equation of spread for flat rolling, a governing equation incorporating angle of diamond and reduction in consecutive passes has been formulated. Newton’s substitution method has been used to solve the equation. With known reduction between consecutive passes, geometrical dimension of square and diamond passes are computed. A model has been used to calculate pass design of a finishing train of a continuous billet mill producing 60 mm square billet from 120 mm square bloom. The elongation values have been optimized by varying the apex angle of diamond. A close agreement between computed and actual values shows the validity of the model.

A study of ordered structures in ternary hcp alloys has been undertaken. For this, the hcp structure has been divided into several sublattices and used to generate ordered structures with three types of atoms. Nine ground-state ordered structures have been identified on the basis of maximum or minimum number ofAB, BC andCA bonds. Complete crystallographic details about these structures have been worked out. In an alternate approach, ordered ternary structures were obtained by populating 8 types of sublattices (which generate Ti₃Al structure) with three types of atoms. Thus, fortyeight ordered structures were found. For each structure, complete structural details have also been worked out, some of which are reported. Configurational energy of each structure has been calculated using pairwise interactions up to third neighbour distances. To gain insight regarding low-energy structures, some assumptions were utilized to reduce the number of independent parameters in the energy expressions and their consequences explored. Two types of degenerate situations have been observed. One type of degeneracy occurs for ideal hcp alloys where only first neighbour interactions are considered. Another degenerate situation occurs for non-ideal hcp alloys where interactions are considered up to third neighbour distances.

The composite solid electrolyte systems KCl-Al₂O₃ have been synthesized by conventional as well as by solution casting methods and have been characterized by means of complex impedance analysis, XRD and DTA techniques. The samples prepared by solution casting method show about an order of magnitude higher conductivity than those prepared by the conventional method. The enhanced conductivity is attributed to the excess cation vacancies generated in the space charge region of the matrix phase surrounding the Al₂O₃ particles as a consequence of stabilization of cations at the dispersoid surface due to internal adsorption. The XRD and DTA analyses show that no new phase is present. Macroscopically, the compositional and particle size dependence of the conductivity are adequately explained on the basis of random resistor network percolation model.

Nickel ferrite nanoparticles of very small size were prepared by sol–gel combustion and co-precipitation techniques. At the same annealing temperature sol–gel derived particles had bigger crystallite size. In both methods, crystallite size of the particles increased with annealing temperature. Sol–gel derived nickel ferrite particles were found to be of almost spherical shape and moderate particle size with a narrow size distribution; while co-precipitation derived particles had irregular shape and very small particle size with a wide size distribution. Nickel ferrite particles produced by sol–gel method exhibited more purity. Sol–gel synthesized nanoparticles were found to be of high saturation magnetization and hysteresis. Co-precipitation derived nickel ferrite particles, annealed at 400°C exhibited superparamagnetic nature with small saturation magnetization. Saturation magnetization increased with annealing temperature in both the methods. At the annealing temperature of 600°C, co-precipitation derived particles also became ferrimagnetic.

Chemical co-precipitation route was successfully employed to synthesize polyethylene glycol-coated pure and doped Zn$_{1−x}$Mn$_x$S (0 ≤ x ≤ 0.1) nanoparticles. The crystallographic and morphological analyses have been done by X-ray diffraction (XRD) and transmission electron microscopy (TEM), respectively. The formation of cubic crystal structure and quasi-spherical morphology has been revealed by XRD and TEM, respectively. The optical analyses have been done by UV–Vis absorption spectroscopy and energy resolved photoluminescence spectroscopy. Energy dispersive X-ray spectroscopy study has been carried to analyse the elemental composition. The doping concentration dependent photo-catalytic activity was checked to analyse the photo-catalytic potential of Zn$_{1−x}$Mn$_x$S nanoparticles under UV irradiation.

Hf$_x$Zr$_{1-x}$O$_2$ (HZO) ceramics with x = 0.25, 0.50 and 0.75 were prepared by conventional solid-state reaction technique. Structural studies of the synthesized stoichiometric compounds were done by X-ray diffraction. The microstructure/morphology and composition of ceramics were obtained with field emission-scanning electron microscopy and energy dispersive X-ray, respectively. Impedance spectroscopic studies were done to study the temperature-dependentand frequency-dependent dielectric properties. The dielectric constants at 10 kHz of Hf$_x$Zr$_{1-x}$O$_2$ ceramics were increased from 17 to 40 with Hf varying from 0.25 to 0.75 at ambient conditions. Ferroelectric studies were also done on these compositions with the help of a polarization-electric field plot and are discussed.