Rare earth elements equation

Assuming that half a percent liquid is trapped with the residue, equating the concentration in the rock to that in the solid residue will result in a severe bias for incompatible elements with Df<0.01 and in pure nonsense for elements with Dt<0.001. A typical example is represented by rare-earth elements in peridotites. Even separated clinopyroxenes can be suspected to have incorporated most of the REE from whichever trace amounts of liquid happened to be trapped in the cooling rock. If the rest of the minerals do not take any REE, it is left to the reader as an exercise to show that the concentration in clinopyroxene after uptake of incompatible elements is related to that in the clinopyroxene from a liquid-free residual peridotite through... 

White J. C. (2003) Trace element partitioning between alkali feldspar and peraUcalic quartz trachyte to rhyolite magma Part 11. Empirical equations for calculating trace element partition coefficients of large-ion lithophile, high field strength and rare-earth elements. Am. Mineral. 88, 330-337. 

Converting the absorption lines into abundances requires knowledge of line positions of neutral and ionized atoms, as well as their transition probabilities and lifetimes of the excited atomic states. In addition, a model of the solar atmosphere is needed. In the past years, atomic properties have seen many experimental updates, especially for the rare earth elements (see below). Older solar atmospheric models used local thermodynamic equilibrium (LTE) to describe the population of the quantum states of neutral and ionized atoms and molecules according to the Boltzmann and Saha equations. However, the ionization and excitation temperatures describing the state of the gas in a photospheric layer may not be identical as required for LTE. Models that include the deviations from LTE (=non-LTE) are used more frequently, and deviations from LTE are modeled by including treatments for radiative and collision processes (see, e.g., [27,28]). 

Murray, R.W. and Leinen, M., 1993, Chemical transport to the seafloor of the equatorial Pacific across a latitudinal transect at 135°W Tracking sedimentary major, minor, and rare earth element fluxes at the equator and the inner tropical convergence zone. Geochimica Cosmochimica Acta, 57 4141-4163. 

Na2C03 was used as precipitant in obtaining a solid solution based on CeO by carbonates precipitation from the chloride solution of rare earth elements (REE). Precipitator consumption was 80% and 95% based on the amount required for the stoichiometric reaction for the precipitation of average REE carbonate - Ln (C03)j 3. Then, the samples were fluorinated in order to increase Ce02 concentration in the solid solution, which, according to [1], should lead to the increase of polishing ability of the material. The cumulative equation is ... 

Diakonov, I.I., Tagirov, B.R., and Ragnarsdottir, K.V. (1998) Standard thermodynamic properties and heat capacity equations for rare earth element hydroxides. I. La(OH)j(s) and Nd(OH)3(s). Comparison of thermochemical and solubility data. Radiochim. Acta, 81, 107-116. 

The criterion for the minimum solute concentration, Ng, of a binary A B alloy required for the second transition process has been derived based on thermodynamic and kinetic analyses. Using this equation the effects of oxygen partial pressure, addition of rare earth elements, surface micro-crystallization, and the gettering effects on the transition between external and internal oxidations can be explained. 

The spin-Hamiltonian of Equation (31) can also be used to describe EPR data (1 5, HO) of ions of the palladium and platinum transition groups, the rare earths, and the trans-uranic group. Experimental data, however, are not presently as plentiful for these elements as for those of the iron group. 

The adsorptive and catalytic properties of zeolites HY, HZSM-5 and HM (natural and synthetic) subjected to dealumination, ion exchange with rare-earth and transition elements have been studied.The changes in conversion and selectivity for w-xylene and n-pentane are shown to be connected with the changes of the zeolites microporous structure.These changes are in conformity with DR equation parameters. The DR equation could be applied to the simple test method elaboration of the starting and modified zeolites microporous structure through their adsorptive properties. 

As was pointed out in the introduction, the matrix elements for the trivalent rare earth appearing in equation (2) (f ip J Ua P ip J ) do not depend strongly on the host lattices and do not differ significantly from their free ion values. Hence, the three quantities are mainly responsible for the variation of intensity with host matrix. The explicit dependence of the T of the crystal field in Axe s notation is (28). 

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