Shrinking sphere equation

The study of the thermal dissociation kinetics of the compounds showed in all cases the decomposition process to be described by the shrinking sphere equation (n = 2/3). The kinetic parameters (in flowing helium) were the following ... 

The data on the dissolution of activated magnesium hydroxide are well described by the equation of shrinking sphere ... 

The ratio of apparent density versus fractional bum-off is also plotted in Figure 5 and closely follows the shrinking sphere model. The initial apparent density, was measured experimentally. The initial shape factor, < ), was obtained from the following equations. 

We can eliminate rc from this equation in favor of /B, from a relation based on the shrinking volume of a sphere ... 

As discussed by Andersen [9, 10] for muffin-tin orbitals, the locally regular components y defined in each muffin-tin sphere are cancelled exactly if expansion coefficients satisfy the MST equations (the tail-cancellation condition) [9, 384], The standard MST equations for space-filling cells can be derived by shrinking the interstitial volume to a honeycomb lattice surface that forms a common boundary for all cells. The wave function and its normal gradient evaluated on this honeycomb interface define a global matching function %(cr). 

Figure 10.19 serves to give an explanation for a sphere. At any equator on the sphere, the surface (or interfacial) tension pulls the two halves toward each other with a force that equals y times the circumference. The surface tension thus causes the sphere to shrink (slightly), whereby the substance in the sphere is compressed and the pressure is increased. At equilibrium, the excess inside pressure times the area of the cross section of... 

Consider a large sphere, radius = rj, which has four small spheres, radius = r, arranged symmetrically (at the corners of a square) around its equator. There are also two small spheres in contact with the large sphere at its poles. The large spheres is now allowed to shrink, keeping the small spheres in contact with it. What is the radius ratio, rjri, when the small spheres come in contact with each other Compare your answer with the numbers in Section 27.3.2. 

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