Volume fraction

About: Volume fraction is a research topic. Over the lifetime, 16312 publications have been published within this topic receiving 374181 citations.

Ni substitution effect on the structure, magnetization, resistivity and permeability of zinc ferrites

Abstract: Zn1−xNixFe2O4 ferrites up to x = 1.0 with Δx = 0.2 have been synthesized via solid state reactions and the sol–gel autocombustion technique with step-by-step co-firing. Data on the chemical composition and the surface morphology of the samples have been obtained using a scanning electron microscope. An X-ray powder diffractometer has been used to establish the phase purity and to determine the unit cell parameters. It has been found that the obtained samples had a spinel structure with the Fdm (No. 227) space group. The unit cell parameters decrease with increasing nickel concentration. The a unit cell parameter decreases almost linearly from ∼8.443 A for x = 0.0 down to ∼8.337 A for x = 1.0. The V unit cell volume decreases almost linearly from ∼601.72 A3 for x = 0.0 down to ∼579.52 A3 for x = 1.0. The magnetic characteristics of the obtained samples are determined and discussed. The Curie point of obtained samples varies in the range of 803.5–572.7 K. The maximum spontaneous magnetization of ∼74.6 emu g−1 at room temperature was fixed for the solid solution with x = 0.6. Ac-resistivity drops by more than 3 orders of magnitude in the frequency range 1–106 Hz. The composition with x = 0.6 has the minimum ac-resistivity of 5.3 kOm cm at a frequency of 106 Hz. The maximum value of the (μ′) real part of ∼11.2 and (μ′′) imaginary part of ∼5.2 of the permeability in the frequency range of 50 MHz–10 GHz is observed for the composition with x = 0.4. The composite samples for the microwave study were prepared by mixing of the ferrite powders with molten paraffin wax. The volume fraction of the ferrite filler in the composites was 25%. The largest value of the (μ′) real part of ∼3 and (μ′′) imaginary part of ∼0.63 of permeability is found for the x = 0.4 composite. The formation of the composite significantly reduces permeability.

Intermetallic-reinforced light-metal matrix in-situ composites

Abstract: Transition-metal trialuminide intermetallics such as Al3Zr and Al3Ti, having low densities and high elastic moduli, are good candidates for the in-situ reinforcement of light-metal matrices based on Al and Mg alloys. In this work, in-situ composites based on Al and Al-Mg matrices reinforced with an Al3Zr intermetallic were successfully processed by conventional ingot metallurgy. The microstructural studies showed that “needle” or “feathery”-like particles of Al3Zr phase, whose volume fraction increased with increasing concentration of Zr, were formed in the Al matrix in the investigated range of Zr contents from 0.9 to 11.6 at. pct. Properties of Al-Zr alloys were investigated as a function of volume fraction of Al3Zr. It is shown that the density, hardness, and yield strength of the in-situ Al/Al3Zr composites can be quite adequately described by the composite rule-of-mixtures (ROM) behavior. Alloying of a binary Al-2.4 at. pct Zr alloy with Mg up to ∼25 at. pct reduces profoundly its density and, additionally, strengthens the matrix by a Mg solid-solution strengthening mechanism.

Dual phase continuity in polymer blends

Abstract: The literature on formation of immiscible polymer blends with dual phase continuity is shortly reviewed. When the volume fraction of one phase is low, nearly spherical discrete domains may be formed in flow fields. The critical volume fraction for formation of infinite structures: φcr = 0.156, predicted by percolation theory for monodisperse spherical domains, is in reasonable accordance with experimental data for samples with spherical domains. In simple shear flow and low volume fraction the coalescence and break up processes may lead to the coexistence of long nearly cylindrical domains (large) oriented in the flow direction and (small) spherical domains. A hypothesis predicting a decrease of the percolation threshold value when φL* · φS* · P · 4 is large, is shown to be in accordance with experimental observations. φL* and φS* are the relative volume fraction of large and small domains, respectively, and P is the aspect ratio of the elongated (cylindrical) drops. The applicability of general (scaling) relations based on percolation theory are discussed.

Fluid Dynamics of Two Miscible Liquids with Diffusion and Gradient Stresses

Abstract: This chapter is based on papers by Joseph [1990b], Galdi, Joseph, Preziosi and Rionero [1991], Joseph anu [1991] and Hu and Joseph [1992]. The density of incompressible fluids can vary with concentration and temperature, but not with pressure. The velocity field u of such incompressible fluids is not in general solenoidal: div u ≠ 0. We require that the mass per unit total volume of one of the liquids in a material volume is conserved in the absence of diffusion. This yields the diffusion equation for the mass fraction ψ. Alternatively, if we obtain an equation for the volume fraction φ, then the left hand side of the diffusion equation differs from the usual substantial derivative of φ by the addition of φ div u.