Analysis mixed crystals

Classified removal of course material also can be used, as shown in Figure 16. In a crystallizer equipped with idealized classified-product removal, crystals above some size ate removed at a rate Z times the removal rate expected for a perfecdy mixed crystallizer, and crystals smaller than are not removed at all. Larger crystals can be removed selectively through the use of an elutriation leg, hydrocyclones, or screens. Using the analysis of classified-fines removal systems as a guide, it can be shown that the crystal population density within the crystallizer magma is given by the equations... 

The crystal of 2 OPr recrystallized from EtOH/H20 solution, and the mixed crystal of the same ethyl and propyl cinnamate derivatives (2 OEt and 2 OPr), on photoirradiation for 2h at room temperature with a 500 W super-high-pressure Hg lamp, afforded the highly strained tricyclic [2.2] paracyclophane (2 OEt-2 OPr-cyclo) crystal quantitatively (Maekawa et ai, 1991b). A crystal structure analysis was carried out of a single crystal of the complex of 2 OEt-2 OPr-cyclo with HFIP (recrystallization solvent) in a 1 2 molar ratio. Fig. 13 shows the molecular structure of 2 OEt-2 OPr-cyclo viewed along the phenylene planes. The short non-bonded distances and deformation of the benzene rings, as seen in Fig. 13, are common to those of [2.2] paracyclophanes, as previously reported (Hope et ai, 1972a,b). 

Meyer B, Zhang S, Scholz F (1996) The quantitative analysis of mixed crystals CuSxSel-x with abrasive stripping voltammetry and a redetermination of the solubility product of CuSe and the standard potendal of hte Cu/CuSe electrode. Fresenius J Anal Chem 356 267-270. 

The EPR of a Mn2+ impurity in mixed crystal N ClajIm has been observed38 between X-band and 250 GHz. Spectra from three magnetically inequivalent, but physically equivalent, Mn2+ ions were observed. The temperature dependence of the linewidth revealed phase transitions at 228 K and 242 K. The analysis of all the spectra was consistent with a model of an axially symmetric crystal field... 

G. Tammann found that potassium and sodium chlorides form a continuous series of mixed crystals between 660° and 500°. Since neither salt has a transition point, the phenomena observed when the mixed crystals are cooled must be attributed to separation of the components. With diminishing temperature, therefore, either the attractive forces within the molecules of the respective chloride must increase, or those between the unlike molecules must be greatly weakened. The results obtained by etching the individual crystals at the ordinary temperature indicate that the intra-molecular forces of the potassium chloride crystals differ from those of the sodium chloride crystal, or, more precisely, that certain lattice regions are more closely united in the former, whilst such differences are not observed in the latter. In the light of these observations, it is surprising that the X-ray analysis indicates the same lattice for each crystal. 

Mixed crystals are mentioned here chiefly as an introduction to the idea that sites equivalent according to space-group theory may in some circumstances be occupied by different atoms. As far as structure determination is concerned, we need not be detained by further consideration of mixed crystals nobody is likely to attempt to determine the structure of a mixed crystal without first knowing the structures of the pure constituents. The function of X-ray analysis here is to determine, as in the example of Cu3Au, whether a substance thought to be... 

In the case of NNMe3, the two phase curves were found to intersect at two points around 35% ee (Figure 7).18 The X-ray crystallographic analysis of the nearly racemic crystal indicated that the phase curve in the range of 0 15% ee corresponds to a highly ordered racemic mixed crystal which can hardly be distinguished from a racemic compound (see the section 6.2). On the other hand, the overall flat phase curve in the range of more than 40% ee proved to correspond to a less ordered racemic mixed crystal composed of different amounts of the R and S enantiomers in the crystal lattice. 

The formation of mixed crystals by means of a solid-state reaction occurs under kinetic control and may be subject to different constraints than the formation of mixed crystals grown closer to equilibrium conditions from the melt or from solvents. However, whether or not mixed crystallization is possible, and to what extent, is still determined by the structural similarity of the reactant and the product. Kitaigorodskii suggested guidelines based on a volume analysis which indicate that chemically compatible compounds which have optimized overlapping volumes larger than ca. 75% are likely to form solid solutions [66],... 

In the intermediate domain of values for the parameters, an exact solution requires the specific inspection of each configuration of the system. It is obvious that such an exact theoretical analysis is impossible, and that it is necessary to dispose of credible procedures for numerical simulation as probes to test the validity of the various inevitable approximations. We summarize, in Section IV.B.l below, the mean-field theories currently used for random binary alloys, and we establish the formalism for them in order to discuss better approximations to the experimental observations. In Section IV.B.2, we apply these theories to the physical systems of our interest 2D excitons in layered crystals, with examples of triplet excitons in the well-known binary system of an isotopically mixed crystal of naphthalene, currently denoted as Nds-Nha. After discussing the drawbacks of treating short-range coulombic excitons in the mean-field scheme at all concentrations (in contrast with the retarded interactions discussed in Section IV.A, which are perfectly adapted to the mean-field treatment), we propose a theory for treating all concentrations, in the scheme of the molecular CPA (MCPA) method using a cell... 

See, for instance, M. Lax, in Multiple Scattering and Waves in Random Media, P. L. Chow, W. E. Kohler, and G. C. Papanicolaou, Eds., North Holland, 1981, and references therein J. Klafter and M. S. Schlesinger, Proc. Nat. Acad. Sci. U.S.A. 83, 848 (February 1986), and references therein R. Brown, Thesis, University of Bordeaux 1,1987 R. Brown et al. J. Phys. C20, L649 (1987) 21 (1988) in press. (This last work thoroughly discusses the applicability of fractal theory to isotopically mixed crystals as disordered system. Serious criticism is presented both of the analysis of the experimental data and of the fundementals of their description in the present theory of fractals. For this reason we omit all works treated there. 

NMR is a powerful technique for providing information about the distribution and dynamics of local RFs, characteristic of such systems. While the quadrupole-perturbed NMR line shape analysis gives details about the distribution of local RFs, spin-lattice relaxation (SLR) studies can give information on the dynamics in the frustrated state of these systems. From the literature, it can be seen that most of the NMR experiments have been carried out in RADP mixed systems and its deuterated analogues. ETFI group published a number of results21-23 on various mixed crystals. 

Five kinds of mixed crystals with different R S ratios were grown frodl aqueous methanol solutions in which the complexes with R-1 -cyanoethyl and S 1-cyanoethyl groups were dissolved in the desired portions. Crystals with R ratios 50 50, 57 43, 75 25, 87 13 and 100 0 were prepared these are abbreviated hereafter pip-1, pip-2, pip-3, pip-4, and pip-5, respectively. Of course, the racemid and chiral ones described above are pip-1 and pip-5, respectively. These crystal are isostructural to each other. The real R S ratio in each crystal was determin by x-ray crystal structure analysis. The observed ratios in the crystals of pi 1, pip-2, pip-3, pip-4, and pip-5 were 50 50, 62.38, 74 26, 87 13, and 100 0, respectively, which are very similar to the corresponding ones in solutions. 

The molecular formula of staphisine, isolated from Delphinium staphisa-gria, was corrected to C43H60N2O2 by X-ray diffraction studies (47). The first analysis was puzzling due to the diffuse appearance of a methoxy group in an electron-density map and the unusually low microanalyses for methoxy. Subsequently, it had been discovered that the crystal used for analysis was a mixed crystal of staphisine and the nonmethoxy alkaloid staphidine. A separation of the two alkaloids led to a pure staphisine crystal that was reexamined by X-ray diffraction. 

Briggs2 therefore reinvestigated the matter, and showed that the supposed isomeride or j8 variety consists of mixed crystals of potassium ferrocyamde and aquopcntacyanoferrite, K3[Fe(CN)5H20], the amount of the latter being too small to detect by qualitative analysis. Since the j8 salt is formed when the a variety is repeatedly recrystallised from water, it is concluded that the compounds are, in aqueous solution, in a state of equilibrium, thus —... 

These two equations are plotted in Fig. 25, from which it is seen that in a perfectly mixed crystallizer the dominant-size fraction (mode) appears at l/L = 3. Saeman illustrated his analysis with data from large-scale vacuum crystallization of ammonium nitrate (M9, SI). 

C. Equilibrium between Solid and Liquid Phases only. I. The Components are Completely Miscible in the Liquid State. a) The pure components only occur as solid phases. Polymorphism of components. Determination of the equilibrium curve. Example, b) Compounds are formed with a congruent meltings point. The indifferent point. Determination of the composition of a compound by thermal analysis. Examples, (c) Compounds are formed with an %ncongruent melting-point. Determination of the composition of the coinpound by thermal analysis. Example. (d) Solid solutions or " mixed crystals are formed, i) The two components can form an unbroken series of solid solutions. Examples. Melting-point curve. Example. Fractional crystallisation of solid solutions, h) The two components do not form a continuous series of solid solutions. Examples. Changes in solid solutions with the temperature. II. The Components are not Completely Miscible in the Liquid State. Suspended transformation. 

---