Dependence of critical radius of the cubic perovskite ABO3 oxides on the radius of A- and B-site cations
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Abstract Use of the critical radius for radial heat conduction in thermal insulation systems has been widely reported in the literature. When it is desirable to increase heat dissipation, this critical radius can be used in a definitive manner to maximize the heat dissipation. However, if it is desirable to decrease heat gain or heat loss, the critical radius only serves as a necessary condition, but it is not sufficient. To address design of such thermal systems, a new crossover radius is introduced. A crossover radius is a radius greater than the critical radius and is defined such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system. Both cylindrical and spherical systems are considered.
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A major problem associated with the design of fusion reactors is high energy neutron damage to structural materials. The combination of vacancies formed by atomic displacements with gases produced by transmutation reactions can cause the formation of cavities. An important parameter in the theory of cavity growth is the radius above which the cavity exhibits bias-driven growth. If the cavity radius is less than this “critical radius,” cavities lose as many vacancies due to thermal processes as are gained from the bias-induced influx of vacancies. When bias-driven growth occurs, large amounts of cavitational swelling can result, leading to severe dimensional instability. Cavities can attain the critical radius either by an abnormally high random influx of vacancies or by absorption of gas atoms. The addition of gas atoms to a cavity reduces the value for the critical radius. If the number of gas atoms exceeds a critical number of gas atoms, then the critical radius vanishes. There is then no barrier to bias-driven growth.
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An analytical expression for the critical radius associated with Kessler‐type parameterizations of the autoconversion process is derived. The expression can be used to predict the critical radius from the cloud liquid water content and the droplet number concentration, eliminating the need to prescribe the critical radius as an empirical constant in numerical models. Data from stratiform clouds are analyzed, indicating that on average continental clouds have larger critical radii than maritime clouds. This work further suggests that anthropogenic aerosols affect the autoconversion process by increasing the critical radius and decreasing the characteristic radius, which in turn inhibits the initiation of embryonic raindrops, and by decreasing the autoconversion rate after the initiation process. The potential impact of this work on the evaluation of the second indirect aerosol effect is discussed.
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Based on the earlier work performed by other researchers the authors have derived a formula for the accurate calculation of the critical radius of a spherical liquid droplet under a supersaturation state. In addition, on the basis of available experimental data a formula for the exact prediction of liquid droplet surface tension was obtained by using a fitting process. Then, by a comprehensive consideration of the influence of steam state equation, surface tension and water density calculation method on the calculation of liquid droplet critical radius a specific mode for calculatiing liquid droplet critical radius under a supersaturation state was developed. Finally, through an analysis of the above mentioned calculation formula it is considered appropriate to adopt a simplified form of the critical radius calculation formula during the calculation of liquid droplet critical radius under a low supersaturation state.
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The quantitative relation between atomic radius, positive ionic radius of metal and atomic structure was studied, and a method for calculating the atomic radius and positive ionic radius of metal was proposed.The calculated results showed that the calculated atomic radius and positive ionic radius of metal were in good agreement with the experiment data, and the absolute deviation was 0.004nm for 63 kinds of metals and 87 kinds of ions.
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Abstract The existence of a geometrical and an electrokinetical radius of an ion is suggested. An equation is worked out representing the electrokinetical radius as a function of the geometrical radius and the thickness of the ionic atmosphere.
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The stability of the shape of an infinite cylinder undergoing radial growth controlled by diffusion is studied by a method originated by Mullins and Sekerka (MS). It is found that the circular cross section of a cylinder is stable when its radius is less than and unstable when its radius is greater than a certain radius Rc. This result is analogous to the MS result that a sphere is stable below and unstable above a certain radius Rc, which is seven times the critical radius R* of nucleation theory. However, in the present case, the ratio Rc/R* is not equal to seven, but is a function of S=(c∞-cs)/(C-cs), where c∞, cs, and C are the concentrations of the solute at infinity, at the surface of the cylinder, and in the precipitate, respectively. The case of perturbations in the radius along the length of the cylinder is also treated. Potential application of the result to such problems as the growth of branches on dendrites is discussed.
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This article makes a detailed analysis of the definition of atomic radius and ionic radius, so that the two terms can be well understood and used in the course of teaching.
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