Lattice parameters solutions

Both sohd-solution hardening and precipitation hardening can be accounted for by internal strains generated by inserting either solute atoms or particles in an elastic matrix (11). The degree of elastic misfit, 5, produced by the difference, Ai , between the lattice parameter, of the pure matrix and a, the lattice parameter of the solute atom is given by... 

Whereas a linear relation between flow stress and lattice-parameter change is obeyed for any single solute element in nickel, the change in yield stress for various solutes in nickel is not a single-valued function of the lattice parameter, but depends directly on the position of the solute in the Periodic Table... 

Above the solution treatment temperature (ca 1250°C), the alloy is single phase with a bcc crystal stmcture. During cooling to ca 750—850°C, the sohd solution decomposes spinodally into two other bcc phases a and lattice parameter composition. The matrix a-phase is rich in Ni and Al and weakly magnetic as compared with which is rich in Fe and Co. The a -phase tends to be rod-like in the (100) dkection and ca 10 nm in diameter and ca 100 nm long. As the temperature is decreased, segregation of the elements becomes mote pronounced and the difference between the saturation polarizations of the two phases increases. 

As has been shown by the X-ray diffraction method the parent metals (i.e. Pd or Ni), the a-phase, and /3-phase all have the same type of crystal lattice, namely face centered cubic of the NaCl type. However, the /9-phase exhibits a significant expansion of the lattice in comparison with the metal itself. Extensive X-ray structural studies of the Pd-H system have been carried out by Owen and Williams (14), and on the Ni-H system by Janko (8), Majchrzak (15), and Janko and Pielaszek (16). The relevant details arc to be found in the references cited. It should be emphasized here, however, that at moderate temperatures palladium and nickel hydrides have lattices of the NaCl type with parameters respectively 3.6% and 6% larger than those of the parent metals. Within the limits of the solid solution the metal lattice expands also with increased hydrogen concentration, but the lattice parameter does not depart significantly from that of the pure metal (for palladium at least up to about 100°C). 

A schematic of epitaxial growth is shown in Fig. 2.11. As an example, it is possible to grow gallium arsenide epitaxially on silicon since the lattice parameters of the two materials are similar. On the other hand, deposition of indium phosphide on silicon is not possible since the lattice mismatch is 8%, which is too high. A solution is to use an intermediate buffer layer of gallium arsenide between the silicon and the indium phosphide. The lattice parameters of common semiconductor materials are shown in Fig. 2.12. 

If the potential applied to the substrate is controlled carefully, it is possible to confine the deposition of copper from the solution to the volume inside the hole. This is so because metal deposition on the Cu(l X 1) stmcture outside the hole is disfavored with respect to metal deposition on the hole, where the lattice parameter of Cu should be close to that of the bulk metal. 

Powder XR diffraction spectra confirm that all materials are single phase solid solutions with a cubic fluorite structure. Even when 10 mol% of the cations is substituted with dopant the original structure is retained. We used Kim s formula (28) and the corresponding ion radii (29) to estimate the concentration of dopant in the cerium oxide lattice. The calculated lattice parameters show that less dopant is present in the bulk than expected. As no other phases are present in the spectrum, we expect dopant-enriched crystal surfaces, and possibly some interstitial dopant cations. However, this kind of surface enrichment cannot be determined by XR diffraction owing to the lower ordering at the surface. 

Bulk Ag-Al alloys, containing up to 12 a/o Al, were electrodeposited from melt containing benzene as a co-solvent. Examination by x-ray diffraction (XRD) indicated that the low-Al deposits were single-phase fee Ag solid solutions whereas those approaching 12 a/o were two-phase, fee Ag and hep i>-Ag2Al. The composition at which ti-Ag2Al first nucleates was not determined. The maximum solubility of aluminum in fee silver is about 20.4 a/o at 450 °C [20] and is reduced to about 7 a/o at room temperature. One would expect the lattice parameter of the fee phase to decrease only slightly when aluminum alloys substitutionally with silver because the... 

Like NiO, CoO and FeO are characterized by the same crystal structure as MgO and have comparable lattice parameters, and, hence, can form CoO/MgO and FeO/MgO solid solutions. Therefore, it was expected that CoO/MgO and FeO/MgO would inhibit carbon deposition and metal sintering, just as Ni/MgO does, resulting in high stability (171). 

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. 

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