LATTICE PARAMETERS AND COMPOSITION

Fig. 1. Correlation between lattice parameter and composition for the series, Pb2lRu2-xpb1c+ )06.5.

It should be noted that the exact cation stoichiometry of the product is highly sensitive to the exact metal concentration of the ruthenium source solution and temperature and pH of the reaction medium (inadvertent increases in both of these parameters lead to increased solubility of lead in the alkaline reaction medium and consequently yield solid products of lower lead ruthenium ratios). While synthesis of a pure lead ruthenium oxide pyrochlore is relatively easy, the precise cation stoichiometry of the product is a property that is not always easy to control. A relatively quick check on the cation stoichiometry of the lead ruthenium oxide product can be obtained, however, by using the correlation between lattice parameter and composition that is displayed in Fig. 1. When lattice parameter and cation stoichiometry are independently determined, the relationship shown in Fig. 1 also provides an assessment of product purity since data points that show significant departures from the displayed linear correlation indicate the presence of impurity phases. The thermal stability of the lead ruthenium oxides decreases with increasing occupancy of tetravalent lead on the octahedrally coordinated site, but all of the ruthenium oxide pyro-chlores described are stable to at least 350° in oxygen. 

Table 11.5 Relations between lattice parameters and compositions of MxSii24nH n)Al(nH ii)OnNi6 ...

Fig. 19. Real space variation of the lattice parameter and composition for the Dy/Lu superlattice, using the X-ray data of fig. 15.

TaC shows a linear relationship between lattice parameter and composition, in contrast to the other carbides. A. L. Bowman (1961) fitted his data by a linear equation which has been used by a number of workers to convert from lattice parameter to composition. In view of the additional information, it is advisable to reexamine this property. Hence, the open points in Fig. 34, which are based on well-characterized material, were used to obtain the equation C/Ta( + 0.01) = -25.641 + 5.9757 by the method of least squares. This amounts to a minor change when compared to the equation given by A. L. Bowman (1961). As can be seen from the figure, the excellent agreement between numerous independent measurements gives overwhelming confirmation to this relationship. In fact, if a measurement is found to deviate from this line, the explanation is best sought in the experimental technique. For example, if a sample has... 

Since there is usually a fairly simple relationship (approaching linearity) between lattice parameter and composition of solid or crystalline solutions, precision measurements of the separation and relative intensities of the lines provide an important and widely used method of materials study and characterization. If proper precautions are observed, one can determine chemical compositions from these structural data sensitivities of 0.1 cases. 

The lattice parameters were found to scale linearly with the relative Au/Pt content. In other words, they follow a Vegard s type law that is frequently observed with binary metallic alloys. This is an important finding because it shows that the correlation between the phase property and the bimetallic composition for nanoscale materials is different from their bulk counterparts. Bulk Au-Pt metals show a miscibility gap and the linear correlation between the lattice parameter and the composition breaks in a very wide composition range extending from 10 to 80% Au. Within the miscibility gap, the lattice parameters corresponding to bulk crystalline Au-Pt samples are independent of the composition. 

Nonetheless, we have ealculated the lattice parameters and t e unit ce vo ume of free Mg which is formed from the decomposition of MgH an oun decreases with increasing content of LiAlH in a composite up to 30 wt c an t en more or less saturates as shown in Fig. 3.33. Such lattice shrinkage is most i e y... 

Copper acetate was used in Ref. 38 it was noted that if chloride was used instead of acetate, no deposition occurred, and this was attributed to adsorption of chloride on the substrate (Pt). The berzelianite phase with a small amount of umangite impurity was obtained. The composition and phase of the film could be altered by electrochemical cathodic polarization (in an aqueous K2SO4 solution). Initially, there occurred an increase in lattice parameters and decrease in x (Cu2-A Se). With continued polarization, a phase change occurred until eventually only orthorhombic Cui xSe was present in the film. The umangite phase also disappeared, and it was believed that this impurity phase catalyzed the phase transformation. The change in composition during cathodic polarization was attributed to reduction of zerovalent Se to Se, which was dissolved in the solution. Based on the study of Fohner and JeUinek [41] discussed earlier, this explanation can be interpreted as reduction of Sei ( monovalent Se) to Se (divalent Se). 

The lattice parameter, and hence the average cavity diameter, is a function of temperature, pressure, and guest composition. The dependence of lattice parameter on guest composition and temperature is illustrated in Figures 2.12a (si), b (sll). 

In order to obtain a good correlation of lattice parameter with composition, sodium-exchanged samples of several materials were obtained from the Initial products by calcining them In air at 5208C to remove trapped TMA+ Ion by oxidation to gaseous products and H+ followed by sodium-exchange with excess 2M NaCl (aq) at 60°C. Elemental analysis showed that this treatment was In fact Inadequate for the exchange,... 

The effect of intercalating like metal atoms is of course to change the atomic ratios, and for example it has been reported that niobium diselenide can intercalate additional niobium atoms to a composition of Nb, jSej There will also be corresponding changes in the crystal lattice parameters, and these are discussed in relation to lubrication properties in Chapter 14. 

The preparation of TcH occurs at 300°C and 1.9 GPa Hj with the composition TcHg j. Both TcHp,3 and the hydrogen-free metal have an hep metal lattice, which makes it difficult, without extensive x-ray work showing the dependence of lattice parameters on composition, to determine whether TcHq is a hydride phase or just a solid solution of hydrogen in Tc. However, from the behavior of the electrical resistance of TcH as a function of composition, it can be deducted that a hydride phase is formed below 300°C. 

In the context of this book, structure solution from first principles (also referred to as the ab initio structure determination) means that all crystallographic data, including lattice parameters and symmetry, and the distribution of atoms in the unit cell, are inferred from the analysis of the scattered intensity as a function of Bragg angle, collected during a powder diffraction experiment. Additional information, such as the gravimetric density of a material, its chemical composition, basic physical and chemical properties, may be used as well, when available. 

The inverse calculation is also possible the content of the unit cell may be determined from the known chemical composition, lattice parameters and density of a material. Assume that the total mass of all atoms located in one unit cell is m. Also, assume that the unit cell volume is V. The latter is known from diffraction analysis as soon as lattice parameters have been established (see Eq. 5.41) Thus, provided the gravimetric density (p) of the crystalline material has been measured, the mass of one unit cell can be easily calculated ... 

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