Lanthanide Ionization Energies and the Sub-Shell Break. Part 2. The Third and Fourth Ionization Energies

By interpolating a 4fq6s → 4fq7s transition within the sequence f1 → f14 rather than between f0 and f14, revised third and fourth ionization energies of the lanthanides have been obtained. The revised values, together with the second ionization energies calculated in a previous paper, are used to calculate values of the standard enthalpies of formation of the gaseous tripositive ions, ΔfHƟ(M3+,g), and of the lattice and hydration enthalpies of some lanthanide compounds and ions in the trivalent and tetravalent states. The displacements of f0 values from nearly smooth f1 → f14 variations exceed 30 kJ mol-1 and indicate substantial subshell breaks

Valencies of the lanthanides

The valencies of the lanthanides vary more than was once thought. In addition to valencies associated with a half-full shell, there are valencies associated with a quarter- and three-quarter-full shell. This can be explained on the basis of Slater’s theory of many-electron atoms. The same theory explains the variation in complexing constants in the trivalent state (the “tetrad effect”). Valency in metallic and organometallic compounds is also discussed

Crambe as a Specialty Crop in North Dakota

Production Economics,

Rural Land-Use Trends in the Conterminous United States, 1950-2000.

In order to understand the magnitude, direction, and geographic distribution of land-use changes, we evaluated land-use trends in U.S. counties during the latter half of the 20th century. Our paper synthesizes the dominant spatial and temporal trends in population, agriculture, and urbanized land uses, using a variety of data sources and an ecoregion classification as a frame of reference. A combination of increasing attractiveness of nonmetropolitan areas in the period 1970–2000, decreasing household size, and decreasing density of settlement has resulted in important trends in the patterns of developed land. By 2000, the area of low-density, exurban development beyond the urban fringe occupied nearly 15 times the area of higher density urbanized development. Efficiency gains, mechanization, and agglomeration of agricultural concerns has resulted in data that show cropland area to be stable throughout the Corn Belt and parts of the West between 1950 and 2000, but decreasing by about 22% east of the Mississippi River. We use a regional case study of the Mid-Atlantic and Southeastern regions to focus in more detail on the land-cover changes resulting from these dynamics. Dominating were land-cover changes associated with the timber practices in the forested plains ecoregions and urbanization in the piedmont ecoregions. Appalachian ecoregions show the slowest rates of landcover change. The dominant trends of tremendous exurban growth, throughout the United States, and conversion and abandonment of agricultural lands, especially in the eastern United States, have important implications because they affect large areas of the country, the functioning of ecological systems, and the potential for restoratio

Degenerate four-wave mixing in triply-resonant Kerr cavities

We demonstrate theoretical conditions for highly-efficient degenerate four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency $\omega_0-\Delta \omega$ can, in the presence of pump light at $\omega_0$, be converted with quantum-limited efficiency into an output shifted signal of frequency $\omega_0 + \Delta \omega$, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes $\sim10$ cubic wavelengths and quality factors $\sim1000$. The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting "quantum" arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.Comment: 13 pages, 8 figures. To appear in Physical Review