Multiple phase refinement

The presence of a minor second phase impurity can be added either in the form of the actual structural model of Ni or as a Le Bail s phase, where only the unit cell and peak shape parameters are taken into account. The latter option has been chosen since we are not interested in the crystal structure of this minor impurity, and it may be a difficult task given its small contribution to the total scattered intensity. 

The refinement with both crystalline phases contributing to the computation of the scattered intensity (row 9, Table 7.3) converges rapidly and yields the residuals, which are only slightly higher than those, obtained when no model of the crystal structure was present during a full pattern 

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Rietveld refinement (Chapter 7, section 7.3.5 and the example in section 7.3.8) of multiple phase samples may be used for relatively accurate quantitative analysis. It requires knowledge of the atomic structure for each phase present in the mixture. Structural data are needed to calculate corresponding intensities. Scale factors for every phase present in the mixture, which are determined quite accurately during Rietveld refinement, are proportional to the fraction of the unit cells present in the irradiated volume of the sample. The latter directly follows from Eqs. 

Considering Eqs. 7.6 and 7.7, it is clear that each additional crystalline phase adds multiple Bragg peaks plus a new seale factor along with a set of eorresponding peak shape and structural parameters into the non-linear least squares. Even though mathematically they are easily aceounted for, the finite accuracy of measurements as well as the limited resolution of even the most advanced powder diffractometer, usually result in lowering the quality and stability of the Rietveld refinement in the case of multiple phase samples. Thus, when the precision of structural parameters is of concern, it is best to work with single-phase materials, where Eqs. 7.3 and 7.4 are applicable. On the other hand, since individual scale factors may be independently... 

Gibbs principle of multiple phase equihbria is applied to model polymer solutions to explore the possible types of heterophase coexistence and phase transitions. The fundamental properties of dilute polymer solutions and hquid-hquid phase separation driven by van der Waals-type interaction is reviewed within the framework of Flory-Huggins theory. No specific molecular interactions are assumed. Refinement of the polymer-solvent contact energy beyond Flory-Huggins description is attempted to study the glass transition of polymer solutions at low temperatures. The scaling description of semiconcentrated polymer solutions is summarized. 

ISCST3 - Industrial Source Complex - Short Term This model is used in more detailed studies of maximum air quality impacts (Phase 3 - Refined Modeling Analysis). The purpose is to compute short term concentration or deposition values, from multiple sources, on specified locations (i.e., receptors). To download the file, click the filename. This is the latest version of the regulatory model ISCST3 (00101) which was released by U.S. EPA on April 27, 2000. The file ISCST.ZIP is 1.60 MB (Executable, Source, Test Cases). You can also download the ISCST3 model evaluation references. 

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. 

If the human genome is partitioned into haplotype blocks, the definition of LD can be refined. Because a given local haplotype block has multiple variants, the probability that SNPs that are in LD but are not located on the same haplotype block will be in phase (i.e., part of the same local haplotype structure) is a function of increasing distance. For instance, in a hypothetical situation in which two variants or forms are available for every haplotype block, the probability that pairwise SNPs in LD will not be part of the same local haplotype (in phase) is 0.5"+1, where n represents the number of haplotype blocks that separate the two SNPs. For example, if the SNPs are on adjacent blocks (zero block separation), the probability that they will be part of the same local haplotype is 0.5 or 50%. This is the upper limit for SNPs not present on the same haplotype block in this situation. If SNPs are separated by four blocks, the probability that they are part of the same local haplotype falls to 0.03 or 3%, because now there are more blocks and hence more possibilities for variation between the SNPs. 

X-ray and neutron diffraction patterns can be detected when a wave is scattered by a periodic structure of atoms in an ordered array such as a crystal or a fiber. The diffraction patterns can be interpreted directly to give information about the size of the unit cell, information about the symmetry of the molecule, and, in the case of fibers, information about periodicity. The determination of the complete structure of a molecule requires the phase information as well as the intensity and frequency information. The phase can be determined using the method of multiple isomor-phous replacement where heavy metals or groups containing heavy element are incorporated into the diffracting crystals. The final coordinates of biomacromolecules are then deduced using knowledge about the primary structure and are refined by processes that include comparisons of calculated and observed diffraction patterns. Three-dimensional structures of proteins and their complexes (Blundell and Johnson, 1976), nucleic acids, and viruses have been determined by X-ray and neutron diffractions. 

The oil phase, Soltrol 130, a refined kerosene, was doped with iodated oils of similar molecular structure. The dopants are strong photoelectric absorbers and increase the accuracy of saturation determination by increasing the X-ray attenuation. The refined, nearly single-component, oil was also used to insure complete first-contact miscibility. Because this is a single-component oil, multiple contact developed miscibility is not observed below the miscibility pressure. 

Observations of star-forming regions have advanced our understanding of the star-formation process considerably in the last few decades. We now can study examples of nearly aU phases of the evolution of a dense molecular cloud core into a nearly fully formed star (i.e., the roughly solar-mass T Tauri stars). As a result, the theory of star formation is relatively mature, with fumre progress expected to center on defining the role played by binary and multiple stars and on refining observations of known phases of evolution. 

Liquid-liquid extraction (LLE) uses two immiscible liquids as the two phases. The sample is dissolved in one of the liquids (refinate) which comes in contact with the other liquid (extractant) into a separatory funnel, under agitation, to increase the contact area among the phases. Some mixing time is usually necessary for efficient phase exchange. Multiple extractions are also mandatory if quantitative extraction is desired. Sample transfer can become a problem, especially if phase emulsions are produced. 

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