Mismatch cation size

The (/a) regime of 1.20 0.02 A in Lno.jAo.sMnOs, which exhibits complex phenomena and properties, including reentrant transitions, deserves further study. It is useful to examine such systems with fixed (rA) and variable cation size mismatch. Charge ordering in the layered manganates has to be investigated in detail. We do not yet have a full understanding of the extraordinary effect of electric fields on the CO state. 

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. 

It is interesting to note that when small mismatches in size occur, the solubility of small molecules in a host lattice of larger ones is more probable than the solubility of a large molecule in a lattice of smaller ones (Hildebrand and Scott 1950). A striking example of this behavior is found in a comparison of impurity incorporation in L-glutanic acid crystals where incorporation decreases with increasing molecular volume of impurity (Harano and Yamamoto 1982). A similar result is found for the incorporation of cationic species in ionic crystals where the uptake is found directly related to the charge on the species and its molecular size (van der Sluis et al. 1986). 

Chen WT, Shen HS, Liu RS, Attfield JP (2012) Cation-size-mismatch tuning of photoluminescence in oxynitride phosphors. J Am Chem Soc 134 8022... 

Chen et al. [32] reported a cation-size-mismatch mechanism to mne the luminescence property in Mi.95Euo.osSi5 xAlxNg xOx lattice. The dopants, which are larger than the host cations in the M = Ca series but smaller than the Ba " host cations, attract the increased oxide coordination in the Ca series and more nitride coordination in the Ba series. Size-mismatch between the host and the dopant cations tunes photoluminescence shifts systematically, which will lead to a blue shift when M is smaller than the Eu " ion in the M = Ca host but a red shift when M is larger in the M = Sr and Ba host. 

This is explained by inspecting the X-ray diffraction patterns. They reveal the presence of MgCr204 spinel impurities as soon as x 0.01, indicating the very limited Mg solubility. The too large cation size mismatch between Cr (r = 0.0615 nm) and Mg (r = 0.0720 nm) could explain this limited range of solubility. Best power factors, PF 2 X 10 " W/m/K, are found for x 0.02 in... 

Figure 20.2 Illustration of how finite size artifacts lead to concentration mismatches in the bulk (A) RNA phosphate-counterion radial distribution functions for the Tar—Tar complex in an 80 A box of 800 mm NaCl. The anion concentration is 15% different than the cation concentration at large separations. (B) RNA phosphate-counterion radial distribution functions for the Tar—Tar complex in a 120-A box of 800 mm NaCl. The anion and cation concentrations agree with each other to within 1% at large radii. Taken from Chen et al. (2009).

The general conclusion is that a salt should be very soluble when there is a severe mismatch in cation and anion size. The presence of large ions means that lattice energies are low, especially if anion-anion or cation-cation contact occurs, and the free energy of hydration of the small ion is almost, by itself, sufficient to ensure dissolution. 

L The activator cation and the host cation need to be matched in size so as to obtain maximal efficiency in the produced phosphor. Mismatch creates strain in the lattice, and limits the actual solubility of the activator in the host lattice. 

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