Correlations and Conclusions

Another frequently quoted criterion for CS phases is that the cations must have a strong preference for octahedral co-ordination. Once again this does not provide an adequate guide line for our purposes. This is clearly illustrated by the behaviour of those oxides and fluorides which possess the rutile structure. Out of this considerable number of compounds, only two or possibly three, Ti02, VO2, and perhaps Cr02 show CS behaviour. The others show little range of stoicheiometry and point defects seem to be a reasonable structural description to account for this range. 

To date, therefore, crystal-chemical reasoning is unable to predict whether a particular material will display a complex non-stoicheiometry region whose structural motif is a planar fault and in which a homologous series of compounds forms if the planar faults order. This suggests that it is necessary to turn towards physical criteria in order to gain more insight into this aspect of defect structures. 

Bursill, B. G. Hyde, and M. O Keeffe, Solid State Chemistry , Nati. Bur. Stand[U.S.) Spec. 

We can finally conclude that the number of chemical systems which appear to reject point-defect populations as a mode of accommodating their non-stoicheiometric behaviour is large and varied and here we have touched upon only a few which make use of planar faults or parallel lamellar or foliar intergrowth structures. The results presented show that physical terms, such as elastic strain, are of importance in controlling the microstructures of such phases, but whether they form or whether they coexist with some form of point-defect clusters may well depend in a sensitive way to the anion-cation bonding within the individual co-ordination polyhedra which made up the structure. The continuing research in this area is certain to produce new and unexpected results before complete answers to the problems posed here are found. 

Acknowledgements. I would like to thank the many people who kindly provided photographs, and in some instances preprints of papers, for use in this review. 

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There have been remarkably few reviews of the chemistry of decompositions and interactions of solids. The present account is specifically concerned with the kinetic characteristics described in the literature for the reactions of many and diverse compounds. Coverage necessarily includes references to a variety of relevant and closely related topics, such as the background theory of the subject, proposed mechanistic interpretations of observations, experimental methods with their shortcomings and errors, etc. In a survey of acceptable length, however, it is clearly impossible to explore in depth all features of all reports concerned with the reactivity and reactions of all solids. We believe that there is a need for separate and more detailed reviews of topics referred to here briefly. The value of individual publications in the field, which continue to appear in a not inconsiderable flow, would undoubtedly be enhanced by their discussion in the widest context. Systematic presentation and constructive comparisons of observations and reports, which are at present widely dispersed, would be expected to produce significant correlations and conclusions. Useful advances in the subject are just as likely to emerge in the form of generalizations discerned in the wealth of published material as from further individual studies of specific systems. Perhaps potential reviewers have been deterred by the combination of the formidable volume and the extensive dispersal of the information now available. 

However, the market researcher has to form an opinion based on all the data. Various methods exist for manipulating the opinions, facts, and numerical data iato forecasts and conclusions. Techniques ia use include statistical analysis, correlations with external factors, correlations with other products, and informed opinion. 

The many problems with correlation and good shop tests discussed in this chapter would seem to lead to the conclusion that one should field test. It is still better, however, if at all possible, to test in the shop. The new compressor field tests should be limited to only those units where performance is in doubt and shop test correlation is just too difficult. A four sidestream multi-component hydrocarbon gas would probably qualify as difficult to shop test. 

It should be emphasized that the correct description of the peculiar effect brought about by the presence of two or more sp -nitrogen centers within a molecule can be reproduced reliably only by high level ah initio calculations accounting for electron correlation. This conclusion is well justified by the examples of benzotriazole, 3-amino-l,2,4-triazole, and tetrazole, as described in Sections II,B,3 II,B,4 and II,B,5, respectively. 

For many years, the lectures of Yngve Ohrn on the theory of chemical bonding have been models of clarity and incisiveness to graduate students at the University of Florida and at various topical schools. Their success in introducing the assumptions and conclusions of molecular orbital theory, group theory, electron correlation methods and related subjects has engendered a critical, but liberal attitude toward competing doctrines. 

Gerike P, WK Fischer (1981) A correlation study of biodegradability determinations with various chemicals in various tests. 11. Additional results and conclusions. Ecotoxicol Environ SafS 45-55. 

The rate of bubble collapse Rcl is primarily important in the first transition zone where the bulk liquid is subcooled. A number of studies have been published on subcooled boiling as well as the prediction of the point of net vapor generation, characteristics defining Transition Zone I, and the onset of nucleation. These studies all result in empirical correlations, and have not led to quantitative conclusions which can be generalized. The radial velocity... 

In part II of the present report the nature and molecular characteristics of asphaltene and wax deposits from petroleum crudes are discussed. The field experiences with asphaltene and wax deposition and their related problems are discussed in part III. In order to predict the phenomena of asphaltene deposition one has to consider the use of the molecular thermodynamics of fluid phase equilibria and the theory of colloidal suspensions. In part IV of this report predictive approaches of the behavior of reservoir fluids and asphaltene depositions are reviewed from a fundamental point of view. This includes correlation and prediction of the effects of temperature, pressure, composition and flow characteristics of the miscible gas and crude on (i) Onset of asphaltene deposition (ii) Mechanism of asphaltene flocculation. The in situ precipitation and flocculation of asphaltene is expected to be quite different from the controlled laboratory experiments. This is primarily due to the multiphase flow through the reservoir porous media, streaming potential effects in pipes and conduits, and the interactions of the precipitates and the other in situ material presnet. In part V of the present report the conclusions are stated and the requirements for the development of successful predictive models for the asphaltene deposition and flocculation are discussed. 

For example, the volume of a cube is perfectly correlated to the length of each side as V = s Likewise the volume of a sphere is perfectly correlated to its radius as V = 4/377r However, the mass of such objects will be highly correlated to, v or r only when the density (d) of the materials used to form the shapes are identical, since d = mass/volume. There is no correlation of mass to s or r when vastly different densities of material are used for comparison. Thus a first-order approximation for s and r vs. mass for widely different materials would lead one to believe that there is not a relationship between volume and mass. Conversely, when working with the same material one would find that volume and mass are perfectly correlated and that there is a direct relationship between volume and mass irrespective of shape. This simple example points to the requirements for a deeper understanding of the underlying phenomena in order to draw conclusions regarding cause and effect based on correlation. 

In the following sections, major emphasis has been placed on recent literature, appearing in the years 1955-62. The term literature means those technical journals in which research or experimental conclusions are commonly published much excellent data, and many useful correlations and observations, are available only in theses, or in institutional, industrial, or government reports. Although reports of this type which contain unique results are included in the present discussion, a deliberate attempt has been made to give priority in discussion to those articles which have been most widely circulated and are therefore most readily available. 

In elementary particle physics the need to eliminate virtual processes is emphasized in many excellent texts.5,17 For quite different reasons we come to a conclusion rather near to that derived from the 5-matrix theory. There is a consistent particle picture. But at this point we have lost mechanics in the usual sense. We no longer deal with forces, correlations, and virtual particles, but with scattering cross sections and lifetimes. 

RN Kondrikov, Methods for Determining the Sensitivity of Explosives to Shock , VzryvnoeDelo 1970, No 68/25,168-73 (Russ) CA 73, 79058 (1970) [The author presents a method of correlating previously independently measured expl impact sensitivity values. Thus, the frequency of sample functioning is detd. at initiation and conclusion of a control series using... 

The X-ray-excited O(ls) photoelectron spectra of various compounds of the type RMn(CO)5 have been correlated with infrared carbonyl stretching frequencies, and conclusions have been drawn about the extent of 7r-donation from metal to ligands in particular, it is inferred that the SiCl3 group in Cl3SiMn(CO)5 is a rather poor it-acceptor (265). 

Comment. The Lockett and Banik correlation confirmed the prediction of the Hsieh and McNulty correlation, and as expected, gave a more conservative answer. The weep fraction is small and can be tolerated. This conclusion is further supported by the observation that... 

Fig. 12.2 Bromide as a function of chlorine in unconfined wells of the Murray-Malee region, Australia. The observed positive linear correlation and the fact that the sea value (x) falls on the same line lead to several conclusions that are discussed in the text in the context of groundwater dating by 36C1. (Following Mazor, 1992.)...

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