Localized Basis for Effective Lattice Hamiltonians: Lattice Wannier Functions

A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corresponding invariant energy expansion, can be obtained for individual materials using first- principles density-functional-theory total energy and linear response techniques, or any technique that can reliably calculate force constants and distortion energies. A practical approach to the determination of these parameters is presented and the application to ferroelectric $PbTiO_3$ discussed.Comment: extensive revisions in presentation, 32 pages, Revtex, 7 Postscript figure

SiC/Si3N4 nanotubes from peanut shells

Nanotubes and nanoparticles of SiC and Si3N4 were produced from the thermal treatment of peanut shells in argon and nitrogen atmospheres respectively, at temperatures in excess of 1350°C. Using x-ray diffraction, Raman spectroscopy and transmission electron microscopy analysis, the processed samples in argon atmosphere were shown to consist of 2H and 3C polytypes of SiC nanoparticles and nanotubes. Whereas the samples prepared in nitrogen atmosphere consisted of α-phase of Si3N4. Nanostructures formed by a single direct reaction provide a sustainable synthesis route for nanostructured SiC and Si3N4, for potential engineering applications due to their exceptional mechanical and electro-optic properties

Structural and magnetic properties of Fe and carbon nanotubes derived from coconut shells

Ferric oxide (Fe2O3) was directly reduced to metallic Fe using the carbon source from the coconut shells at temperatures above 1400 °C in argon gas atmospheres. X-ray diffraction analysis showed the presence of α-, γ- phases of Fe in addition to the presence of carbon nanotubes (CNTs). By selecting the appropriate ratios of coconut shell powder to Fe2O3, it is demonstrated that pure Fe is produced without any residual ferric oxide. The quantitative analysis of each of the Fe phases and carbon nanotubes was dependent on the temperature and the duration of processing at high temperature. Transmission electron microcopy results showed copious amount of carbon nanotubes in the samples. Magnetic property measurements suggested that, the average magnetic moment is consistent with presence of α-phase and the ferromagnetic γ-phase of Fe. This novel method of producing pure α- and γ-Fe in the presence of carbon nanotubes using coconut shells has potential applications as nanocomposites

Nanoparticles of wurtzite aluminum nitride from the nut shells

Nanoparticles of aluminum nitride were produced from a thermal treatment of a mixture of aluminum oxide (Al2O3) and shells of almond, cashew, coconuts, pistachio, and walnuts in a nitrogen atmosphere at temperatures in excess of 1450 °C. By selecting the appropriate ratios of each nut powder to Al2O3, it is shown that stoichiometric aluminum nitride can be produced by carbo-thermal reduction in nitrogen atmosphere. Using x-ray diffraction analysis, Raman scattering and Fourier Transform Infrared spectroscopy, it is demonstrated that aluminum nitride consists of pure wurtzite phase. Transmission electron microscopy showed the formation of nanoparticles and in some cases nanotubes of AlN