Solution to diffusion equation in a finite single phase sample with variable coefficient

A single-phase sample of α′ (O′3)-type layered sodium cobalt oxide Na x CoO2 (x ∼ 0.78) was prepared and its incommensurately modulated crystal structure was analyzed using the (3+1)-dimensional superspace approach to the powder neutron diffraction data. The crystal structure of the cobaltate is accurately described based on the superspace group C2/m(α0γ)00, wherein the positions of Na atoms are most significantly modulated in the monoclinic a direction to form an ordered arrangement. Such a displacive modulation causes a quasi-periodic shift of Na atoms from the centers of the NaO6 polyhedra between undulated CoO2 sheets, changing the form of the NaO6 polyhedron from an octahedral coordination (O) to a trigonal prismatic (P) one, via an intermediate capped trigonal prismatic NaO7 coordination (C). At the positions where the Na atoms are most significantly shifted, the neighboring Na atoms are located at almost touching distances. However, the occupation factor of Na atoms becomes zero at such positions, yielding Na-deficient sites V Na, sandwiched either between C and P, or C and C-type polyhedra.

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Intermediate-valent CeCoAl – a commensurate modulated structure with short Ce–Co distances

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1515/zkri-2015-1856 ◽

2015 ◽

Vol 230 (9-10) ◽

Author(s):

Oliver Niehaus ◽

Rolf-Dieter Hoffmann ◽

Sophie Tencé ◽

Bernard Chevalier ◽

Rainer Pöttgen

Keyword(s):

Single Phase ◽

Induction Furnace ◽

Structure Type ◽

Furnace Annealing ◽

Single Phase Sample ◽

Modulated Structure ◽

X Ray ◽

Different Temperatures ◽

Phase Sample ◽

Intermediate Valent

AbstractCeCoAl was synthesized by melting of the elements in a sealed niobium tube in an induction furnace. Annealing of the sample gave access to a single phase sample. Its structure was refined on the basis of single-crystal X-ray diffractometer data at different temperatures. Above 271 K CeCoAl crystallizes in its own structure type in the space group

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Stability Analysis and Error Estimation of Variable Coefficient Convection-Diffusion Equation: Generalized Numerical Fluxes

Journal of Physics Conference Series ◽

10.1088/1742-6596/1903/1/012016 ◽

2021 ◽

Vol 1903 (1) ◽

pp. 012016

Author(s):

Yuhang Liu ◽

Hui Bi

Keyword(s):

Stability Analysis ◽

Diffusion Equation ◽

Error Estimation ◽

Variable Coefficient ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Numerical Fluxes

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Structural, magnetic and high frequency (1–6 GHz) parameters of Sr-substituted BaFe2O4 monoferrites synthesized by sol–gel method

Modern Physics Letters B ◽

10.1142/s0217984919502191 ◽

2019 ◽

Vol 33 (19) ◽

pp. 1950219 ◽

Cited By ~ 1

Author(s):

Mukhtar Ahmad ◽

Jawaria Shaheen ◽

Waseem Abbas Hashmi ◽

Majid Niaz Akhtar ◽

Muhammad Asif

Keyword(s):

Single Phase ◽

Sol Gel ◽

Combustion Method ◽

Xrd Analysis ◽

Anisotropy Constant ◽

Dielectric Parameters ◽

Single Phase Sample ◽

Heat Treated Sample ◽

Auto Combustion ◽

Phase Spinel

In this work, Sr-substituted samples of single-phase spinel monoferrites with chemical formula [Formula: see text] (x = 0.00, 0.33, 0.67, 1.00) were synthesized using sol–gel auto-combustion method. In order to confirm the single-phase formation of these samples, a sample (x = 0.00) was chosen for heat treatment at different temperatures (100, 300, 400, 600 and [Formula: see text]) for 4 h. The heat treated sample was then investigated by X-ray diffraction (XRD) analysis and results showed that a single-phase sample can be successfully synthesized at a temperature of [Formula: see text], which is much lower than that reported in earlier literature for synthesis of same structured samples. All the synthesized samples were then sintered at [Formula: see text] for 4 h to achieve better crystallinity. From XRD patterns, lattice parameters, cell volume and XRD density as a function of Sr-substitution were calculated. Scanning electron microscopy (SEM) results showed that the grain size increased as the temperature was increased. Fourier transform infrared spectroscopy (FTIR) results confirmed the single-phase spinel monoferrites at [Formula: see text]. From M–H loops (x = 0.0, 0.33, 0.67 and 1.00), different magnetic parameters such as saturation magnetization [Formula: see text], remanance [Formula: see text], coercivity [Formula: see text] and magnetic moment [Formula: see text] were calculated. Magnetocrystalline anisotropy constant and Y–K angles of Sr-doped Ba monoferrites were also calculated. In addition, the variation of different dielectric parameters (real permittivity, imaginary permittivity, real permeability, imaginary permeability, ac conductivity and loss tangent) as a function of frequency (1–6 GHz) has been discussed in this work. The results suggest that the synthesized materials have many advantages over previously reported single-phase spinel monoferrites.

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