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An analysis of zero-first and first-first order reaction schemes has been carried out in a fluidised bed with a view to optimising the production of intermediate R for a given bubble diameter. For the zero-first order reaction sequence, the gas residence time at which the maximum concentration of R occurs is shown to be fixed and independent of bubble size in the bed. On the other hand, for a first-first order reaction scheme, an optimum gas residence time exists for the concentration maximum to occur at the bed exit. This interaction between bubble diameter, gas residence time and maximum concentration of intermediate is resolved by recourse to a three dimensional diagram which optimises the production of intermediate for any given value of bubble diameter or gas residence time. © 1981.

World University root node

Chemical Engineering Science

Optimal production of intermediate for zero-first and first-first order reaction sequences in fluidised bed reactors1 1 TNCL Communication Number 2464.

A simple theory for the core-level binding energy shifts at the surfaces of binary alloys AxB1-x is presented. Results are given for the surface core-level shifts of Ni in NixCu1-x alloys and Pd in PdxAg1-x alloys. It has been shown that the surface core-level shifts may depend sensitively on surface segregation. {\textcopyright} 1981.

Solid State Communications

Surface core-level binding energy shifts in alloys

The free energy of segregation at semi-infinite solid binary alloy surfaces is calculated using a quasi-chemical approach. The alloy is treated to be a non-regular solution. The concentration is assumed to be different only at the surface layer. The theory is applied to AgAu alloys. The concentration and the short-range-order parameters at the surface are calculated. {\textcopyright} 1979.

Free energy of segregation at alloy surfaces

We present a quasichemical theory to predict surface segregation in nonregular solutions. Surface concentration and surface short-range-order (SRO) parameters have been calculated for Ag-Au and Ag-Pd systems. Our results show segregation of Ag on the surface in both the systems. It is observed that the nonregular-solution model does not give results much different from the regular-solution model. However, the surface SRO parameters are significantly different from their bulk values. Surface concentrations averaged over the first few layers have also been calculated. Our results are in agreement with the results obtained from Auger electron spectroscopy. {\textcopyright} 1979 The American Physical Society.

Physical Review B

Surface segregation in alloys

We present a theory for segregation at alloy surfaces, where both the bond breaking and strain theories have been combined into one. The formulation can be applied to alloys of any concentration. In addition to it we present some ideas which should be considered while dealing with polycrystalline samples. Good agreement is obtained with Auger electron spectroscopy data on a Ni-Au system. {\textcopyright} 1979.

Surface Science

Segregation at alloy surfaces

A simple method is proposed for applying the self-consistent boundary site approximation (SCBSA) in cluster theories of electronic states in disordered alloys. This method is applicable to lattices of any dimensionality. The electronic densities of states are calculated for binary alloys having the simple cubic and the diamond lattice structures. These results are compared with the results obtained from the method of moments, the disordered field formalism, the coherent-potential approximation and a few other methods. In addition to this, the averaged Green's function has been calculated in the complex energy plane to study its analytic structure. It is found that though the SCBSA is computationally simple and yields densities of states which agree quite well with the available exact results, in three dimensions, the SCBSA shows some unphysical features such as the negative partial densities of states and branch points off the real axis for the averaged Green's function in the strong-scattering regime. {\textcopyright} 1978 The American Physical Society.

Self-consistent boundary site approximation in the cluster theories of disordered alloys

A calculation of the spin-wave spectra of a disordered Heisenberg ferromagnet in which two species of spins are randomly distributed is presented. The theory is developed within a cluster coherent potential approximation in which a cluster of spins consisting of a central spin and the shell of its Z nearest neighbours is embedded in an effective medium and its scattering is considered with respect to the medium. For simplicity it is assumed that scattering due to the cluster depends only on the number of the different types of atoms constituting the shell rather than on their detailed configurations on the shell. Correlated site and bond disorder, an important feature of the magnetic problem, is handled in a relatively simple manner.

Journal of Physics C: Solid State Physics

Theory of substitutionally disordered Heisenberg ferromagnets

The coherent potential approximation has been generalized to incorporate the effects of the local environment in the energy spectrum of disordered alloys described by the simple tight-binding approximation. The effective medium has been characterized by an effective local potential Sigma 1 and an effective hopping integral Sigma 2 between the nearest neighbours though the off-diagonal elements of the alloy Hamiltonian are not assumed to be disordered in the present calculation. The density of states has been calculated for a binary alloy AxB1-x having diamond lattice structure.

Electronic structure of disordered alloys-local environment effects

The renormalized propagator formalism of Niizeki is used to calculate local-environment effects on the density of states of disordered alloys. Random transfer integrals of Shiba's type are included in the theory. Numerical results of density of states of a simple cubic binary alloy AxB1-x are presented. {\textcopyright} 1975 The American Physical Society.

Electronic structure of disordered alloys-Generalized coherent-potential approximation and effects of environment

The authors propose a method which enables one to apply the self-consistent boundary site approximation to a system of any dimensionality. The electronic density of states for a diamond lattice is calculated and compared with results from other theories.