Radius mismatch

Fig. 9. Residual stresses owing to thermal expansion mismatch between a particle with radius a and thermal expansion coefficient and a matrix with thermal expansion coefficient The stresses illustrated here are for and P is the interfacial pressure.

It has been noted that the conductivity and activation energy can be correlated with the ionic radius of the dopant ions, with a minimum in activation energy occurring for those dopants whose radius most closely matches that of Ce4+. Kilner et al. [83] suggested that it would be more appropriate to evaluate the relative ion mismatch of dopant and host by comparing the cubic lattice parameter of the relevant rare-earth oxide. Kim [84] extended this approach by a systematic analysis of the effect of dopant ionic radius upon the relevant host lattice and gave the following empirical relation between the lattice constant of doped-ceria solid solutions and the ionic radius of the dopants. 

A given mesh reflectivity imposes a lower bound for the beam-waist radius, below which appreciable coupling losses can occur. The basic problem is that a Gaussian beam will continue to diverge upon repeated reflection within a planar interferometer as shown in Fig. 12b. If the spherical mirror of the cavity is designed to match the original (input) beam waist, beam divergence will cause a mismatch at the output, which... 

Furthermore, the redox chemistry of doped ceria is dependent on the ionic radius of the doped cation. The energy due to lattice stresses resulting from mismatch of the host and dopant cation sizes will also go into the free energy balance as briefly described below. 

The explanation of the minimum in activation energy with dopant radius was initially made in terms of the elastic component of the association energy of the simple pairs - that is, in terms of the size mismatch between the host and the substitutional ion (see early references in Ref. [12]). Later computer simulations of... 

Geophysical evidence shows that the Earth has a liquid Fe-Ni-S-alloy outer core with a thickness of 2,260 km, and a solid Fe-Ni-alloy inner core, with a radius of 1,215 km. Temperatures at the top of the core are thought to be in the range 3,500-4,500 K and rise to 5,000-6,000 K at the center of the Earth. There is a mismatch of a few percent between the measured density of the Earth s outer core and that predicted for an iron-nickel alloy at high pressure. This "core density deficit," as it is called, is thought to indicate the presence of other elements as impurities in the core in addition to iron and nickel, and this could be the principal reason why the outer core is molten. The impurities act as a form of "antifreeze" in the liquid metal (Stevenson, 1990). 

To investigate the effect of the porous layer on the state of strain in the epitaxial film, the radius of curvature Rc of the GaN/SiC and GaN/PSC samples using XRD was measured [55,56]. The measurements showed that GaN films grown on nonporous SiC experienced biaxial tensile stress, which resulted from film/substrate mismatches. In contrast, the films grown on PSC were compressed. The Rc measurements also revealed that with increase of the thickness of the PSC layer the value of the compressive stress increased. 

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