Size-dependent solute segregation and total solubility in ultrafine polycrystals: Ca in TiO2

Aliovalent Substitutions in Olivine Lithium Iron Phosphate and Impact on Structure and Properties

“…Nanoscale TiO 2 is one system in which size-dependent solid solubility due to interfacial segregation of dopants has been studied. [17] Since the powders prepared in this study generally had <100 nm particle size, it was of concern to us to determine whether the observed high dopant solubility is due to, or at least influenced by, the small crystallite size. Although the interfacial segregation of lattice solutes has not been studied (in part since, until now, solid solution behavior has not been accepted), some predictions are possible from basic theory.…”

Correlation between subgrains and coherently scattering domains

“…The columnlength distribution in the specimen depends on the size, the shape, and the size distribution of the crystallites. In order to obtain the ͑area and/or volume weighted͒ mean size of crystallites or their distributions, specific assumptions have to be made about the shape and the size distribution of these objects ͑Langford and Louër, 1996͒. There is ample experimental evidence that the lognormal size distribution function, f͑x͒, given by the median m and the variance , can describe crystallite size distribution in a wide range of bulk or loose powder materials ͑Va-liev et al, 1994;Terwilliger and Chiang, 1995;Krill and Birringer, 1998;Langford et al, 2000;Scardi and Leoni, 2002͒. Hinds ͑1982͒ has shown that with m and the arithmetic-, the area-, and the volume-weighted mean crystallite diameters are…”

Thermodynamic analysis of the change of solid solubility in a binary system processed by mechanical alloying

“…Observing the data from both systems, we can conclude that Cu solubility in Fe and Cr solubility in Cu reported in the literature are larger than predicted by the model. This fact can be explained by the inability of the model to consider more than one grain size, which is inaccurate since the grain size in many nanocrystalline materials presents a log-normal distribution, as has been reported by several authors [28][29][30]. The free energy contribution due to decrease of grain size is higher than dislocation density, as it is possible to see from Figs.…”