do composto CaTiO
3BARROS, K. L. P.1; MASTELARO, V. R.1
1Instituto de F´ısica de S˜ao Carlos - USP
Nos materiais nanocristalinos, o processo de dopagem tem sido considerado de fundamental importˆancia para estabilizar determinadas fases ou faces cristalinas. A busca por novos materiais tamb´em tem sido baseada no uso de novos m´etodos de s´ıntese como, por exemplo, o m´etodo hidrotermal e solvotermal. (1) Desta forma, a introdu¸c˜ao de dopantes simultaneamente com o uso de uma metodologia de s´ıntese vers´atil mostra-se como uma proposta interessante para obter materiais j´a produzidos por t´ecnicas convencionais, mas que apresentam propriedades diferenciadas. O objetivo do projeto ´e verificar o efeito do m´etodo de s´ıntese utilizado e da adi¸c˜ao de ´ıons dopantes como Mg2+, Ni2+ e Fe2+ nas propriedades
morfol´ogicas e estruturais do composto CaTiO3 que ser´a preparado atrav´es dos m´etodos hidrotermal e
solvotermal sem o uso de microondas. Segundo o estudo realizado por Alfredssom (2) estes ´ıons s˜ao os mais ativos em rela¸c˜ao as mudan¸cas de morfologia na fase CaTiO3. At´e o momento, foram realizados
experimentos verificando o efeito dos parˆametros de s´ıntese (tempo e temperatura) e variando-se os precursores utilizados e a metodologia de s´ıntese, caracteriza¸c˜ao por t´ecnicas como difra¸c˜ao de raios X e microscopia eletrˆonica de varredura, assim como o efeito da substitui¸c˜ao dos ´ıons dopantes no s´ıtio A (Ca) e no s´ıtio B (Ti). Futuramente ser˜ao realizados testes sobre a atividade catal´ıtica e da sensibilidade ao g´as ozˆonio das amostras obtidas.
Palavras-chave: CaTiO3. S´ıntese hidrotermal. Dopantes.
Referˆencias:
1 ALFREDSSON, M. et al. Dopant control over the crystal morphology of ceramic materials. Surface Science, v. 601, n. 21, p. 4793-4800, 2007.
2 YANG, X. et al. Formation mechanism of CaTiO3 hollow crystals with different microstructures. Journal of the American Chemical Society, v. 132, n. 40, p. 14279-14287, 2010.
PG18
Comparative study between 8×8 and 6×6 k·p Hamiltonian: the
case of GaAs zinc blende
BASTOS, C. M. O1; SABINO, F.1; FARIA JUNIOR, P. E1; CAMPOS, T1; SILVA, J. L. F. da2; SIPAHI,
G. M.1
1Instituto de F´ısica de S˜ao Carlos - USP 2Instituto de Qu´ımica de S˜ao Carlos - USP
Nowadays, electronic structure calculations based on quantum-mechanics is of fundamental importance for the development of new materials and for the understanding of new phenomena in solid state physics. One of the most successful first-principles or ‘ab-initio’ approaches, the density functional theory (DFT), employs the electron density as the fundamental variable. Although the DFT framework (Kohn-Sham equations) has been widely applied to the study of molecules, clusters, nanoparticles, surfaces, and bulk materials, those calculations are restricted to small systems, and hence, the study of systems such as quantum wells, wires and dots with thousand or million atoms are far from possible due to its computational cost. An alternative approach for confined systems is the k·p method. The k·p formalism is based on building an Hamiltonian by using perturbation theory around a point of the reciprocal space. The perturbation approach may be further enhanced by using the L¨owdin perturbation scheme, which consists in dividing the states in two classes: A and B, where the states of class are chosen as the basis of the Hamiltonian and the class B all other states. The interaction of states of the class A are taken into account exactly as the interactions among states from both classes are described as perturbative terms in class A states. The symmetries of the crystalline phase are then taken into account in the Hamiltonian through group theory analysis and according to the choices of class A states and the order of the perturbation, different Hamiltonians can be built for the same crystalline phase. In the general case, the Hamiltonian matrix elements can be obtained by fitting the parametrized elements to a previously obtained band structure. This can be done by comparing the analytical coefficients of the secular equation to the numerical values obtained from the calculated band structure. (1) Lastly, we did not find in the literature a study of the validity Hamiltonian and its parameters. The accuracy of the parameters is a key point, since the agreement of the two different methods would allow that the results using the much less computer intensive method directly comparable to the previous one and its findings. In this study, we analyse two different k · p Hamiltonians: the 6×6 proposed by Luttinger and Kohn (2) and the 8×8 Hamiltonian proposed by Kane. (3) After obtaining the parameters for both Hamiltonians we analyse the validity of their models around Γ-point for a bulk zinc blende GaAs system obtained by hybrid HSE-DFT calculation. We show that the agreement of the 8×8 Hamiltonian is enforced for a larger region enclosing Γ-point than the 6×6 one. Properties depending on an extended range of band energy values may be more precisely described by the first.
Keywords: k.p method. DFT. Semiconductors.
1 BASTOS, C. M. de O. Determina¸c˜aoo de parˆametros para Hamiltonianos k.p a partir de estruturas de bandas pr´e-existentes. 2015. 97p. Disserta¸c˜ao (Mestrado em Ciˆencias) - Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, S˜ao Carlos, 2015.
2 LUTTINGER, J. M.; KOHN, W. Motion of electrons and holes in perturbed periodic fields. Physical Review, v. 97, n. 4, p. 869-883, 1955. doi: http://doi.org/10.1103/PhysRev.97.869.
3 KANE, E. O. Band structure of indium antimonide. Journal of Physics and Chemistry of Solids, v. 1, n. 4, p. 249-261, 1957. doi: http://doi.org/10.1016/0022-3697(57)90013-6.