Phase refinement averaging

X-ray diffraction (XRD) patterns were measured at room temperature with a Siemens D-5000 Diffractometer that had a Cu Ka radiation. Intensity was measured by step scanning in the 20 range between 20 and 110° with a step of 0.02° and a measuring time of 2s per point. The DBWS-9600PC and WYRIET programs were used for crystalline structure refinements with the Rietveld method. From this refinement, the different phases and average crystalline... 

Our preliminary results with this model indicate that distinctly bimodal MWD s are formed for some values of the parameters whereas near equality of the average values for each phase leads to a somewhat broadened unimodal MWD for other parameter choices. These results will be presented in detail, and we will explore some refinements to the above described model in a forthcoming publication (18). 

The terms space time and space velocity are antiques of petroleum refining, but have some utility in this example. The space time is defined as F/2, , which is what t would be if the fluid remained at its inlet density. The space time in a tubular reactor with constant cross section is [L/m, ]. The space velocity is the inverse of the space time. The mean residence time, F, is VpjiQp) where p is the average density and pQ is a constant (because the mass flow is constant) that can be evaluated at any point in the reactor. The mean residence time ranges from the space time to two-thirds the space time in a gas-phase tubular reactor when the gas obeys the ideal gas law. 

V. S. (1997). wARP improvement and extension of crystallographic phases by weighted averaging of multiple refined dummy atomic models. Acta Crystallogr. D 53, 448-455. 

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. 

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