Lattice strain effects

The physical cause of this phenomenon (45) can be most easily explained by means of a one-dimensional chain with equal concentrations of the elements, as an analog to the three-dimensional alloy. The theoretical results can be extended to a three-dimensional system. They are only applicable to a true alloy if lattice strain effects are negligible. 

Mechanism of Activity Enhancement Lattice-Strain Effect... 

The enhanced ORR activities of the dealloyed Pt binary catalysts could be related to a similar lattice-strain effect as revealed in the dealloyed PtCus catalysts. However, it is still unclear what the origin of the different activities of different dealloyed PtM3 catalysts is. Regarding their comparable atomic radius, the alloy elements Co, Ni, and Cu are assumed to induce a similar extent of lattice strain. Nevertheless, due to different redox chemistry of the transition metals, different extent of metal dissolution may exist [47], which might result in different core-shell fine structures and hence different activities. 

In principle, a similar compressive lattice-strain effect as revealed in the dealloyed Pt binary catalysts could also account for the higher activity of dealloyed Pt ternary catalysts compared with the pure Pt catalysts. Nevertheless, the origin of the activity enhancement for dealloyed ternary catalyst compared to the dealloyed Pt binary catalysts is still far from well understood. Exactly what kind of roles that the third element plays needs further studies. 

From studies at extended surfaces, it is well known that undercoordination of surface atoms induces a narrowing of the d-band, causing an increase in the adsorption energy. A lattice contraction, on the other hand, induces a broadening of the d-band, which causes a decrease in the adsorption energy. Both of these effects compete on nanoparticle surfaces. As stated previously, in the case of nanoparticles, the effect of surface-atom undercoordination supersedes the lattice strain effect. 

For the same lattice strains, the larger the valency difference between solute and solvent, the greater the hardening. The strengthening influence of alloying elements persists to temperatures at least as high as 815°C. Valency effects may be explained by modulus differences between the various alloys... 

These techniques have very important applications to some of the micro-structural effects discussed previously in this chapter. For example, time-resolved measurements of the actual lattice strain at the impact surface will give direct information on rate of departure from ideal elastic impact conditions. Recall that the stress tensor depends on the elastic (lattice) strains (7.4). Measurements of the type described above give stress relaxation directly, without all of the interpretational assumptions required of elastic-precursor-decay studies. 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

This expression is relatively imprecise because of the scarcity of data. Also, the oxidation state of Pb in these experiments is not known. However, it is interesting that for those experiments in which both Dpb and Dsr have been determined, the Dpb/Dsr ratio is consistently less than would be predicted from the 2+ lattice strain model using parameters presented above. As in the case of clinopyroxene, increasing the effective Vlll-fold ionic radius of Pb in plagioclase, to 1.38 A, does retrieve the observed ratios. Thus one can... 

Figure 24. Lattice strain model applied to zircon-melt partition coefficients from Hinton et al. (written comm.) for a zircon phenocryst in peralkaline rhyolite SMN59 from Kenya. Ionic radii are for Vlll-fold coordination (Shannon 1976). The curves are fits to Equation (1) at an estimated eraption temperature of 700°C (Scaillet and Macdonald 2001). Note the excellent fit of the trivalent lanAanides, with the exception of Ce, whose elevated partition coefficient is due to the presence of both Ce and Ce" in the melt, with the latter having a much higher partition coefficient into zircon. The 4+ parabola cradely fits the data from Dj, and Dy, through Dzi to Dih, but does not reproduce the observed DuIDjh ratio. We speculate that this is due to melt compositional effects on Dzt and (Linnen and Keppler 2002), and possibly other 4+ cations, in very silicic melts. Because of its Vlll-fold ionic radius of 0.91 A (vertical line), Dpa is likely to be at least as high as Dwh, and probably considerably higher.

There are two major problems associated with the x-ray method. The first problem is encountered during sample preparation. At this step, preferred orientation of the particles must be minimized [1], Reduction of particle size is one of the most effective ways of minimizing preferred orientation, and this is usually achieved by grinding the sample. Grinding, however, can also disorder the crystal lattice. Moreover, decreased particle size can cause a broadening of x-ray lines, which in mm affects the values of /c and /a. The relationship between the crystallite size, t, and its x-ray line breadth, /3, (assuming no lattice strain) is given by the Scherrer equation [2] ... 

The effective mass of the electrons changes due to lattice strain, alloy additions, radiation damage, phase transformation, and phase content, directly relates to the ability to use electronic property measurements to assess microstructure phase stability. Electronic properties, such as thermoelectric power coefficients, resistivity and induced resistivity measurements, have a demonstrated correlation to solute and phase content, potential phase transformations, as well as residual strain. 

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