General Concepts and Definitions

In geology it is customary to consider systems in which the intensive variables pressure (P) and temperature (T) are characteristic of the ambient and, therefore, are prefixed and constant. In these conditions, the Gibbs free energy of the system (G) is at minimum at equilibrium. The treatments presented in this chapter are based on this fundamental principle. Let us first introduce in an elementary fashion some fundamental definitions. 

PHASE - A phase is defined as a fraction (region) of a system that has peculiar and distinguishable chemical and physical properties. For instance, a magmatic system may be composed of mineral solid phases, fluids (H2O, CO2, etc.), and melts. 

COMPONENT - Each phase in a system is in turn composed of chemical components. The choice of the various components is, under certain provisos, arbitrary. For instance, the olivine solid mixture (Mg, Fe)2Si04 may be considered to be composed of fayalite (Fe2Si04) and forsterite (Mg2Si04) end-members, of oxides 

SOLUTION and MIXTURE - There is some confusion between these two terms in geological literature. According to the I.U.P. A.C. (International Union for Pure and Applied Chemistry), the term mixture must be adopted whenever all components are treated in the same manner , whereas solution is reserved for cases in which it is necessary to distinguish a solute from a solvent. This distinction in terminology will be more evident after the introduction of the concept of standard state. It is nevertheless already evident that we cannot treat an aqueous solution of NaCl as a mixture, because the solute (NaCl) in its stable (crystalline) state has a completely different aggregation state from that of the solvent (H2O) and, because NaCl is a strong electrolyte (see section 8.2), we cannot even imagine pure aqueous NaCl. 

To understand fully the chemical reaction processes that take place in rock assemblages, it is necessary to introduce the concept of chemical potential Much the same as in a gravitational potential, in which an object tends to fall from a high to a low altitude, in a chemical potential field the reaction or flow direction of components always tends to proceed from a high to a low chemical potential region. 

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We now introduce the general concepts and definitions behind studies of alignment and orientation in electron—atom collisions. Let us consider the scattering process (8.1) in some detail. We must first understand the concept of coherence. We illustrate it by considering the initial state of the atom... 

This chapter is a brief introduction to the general concepts and definitions of the amorphous state. Techniques for the characterization of amorphous materials and their transformations are reviewed. Also, structural and chemical changes which can lead to inhomogeneities, and the detection of these inhomogeneities, are discussed. Because of the difficulty in completely characterizing amorphous materials, one must be aware of the possible structures, transformations, and inhomogeneities which can occur in order to better interpret measured properties. 

Here, several general statistical concepts are briefly discussed as a complement to the material covered in this book. The books of Davis and Goldsmith (1972) and Mikhail (1976) are excellent sources for such information. Most of the concepts and definitions presented in this Appendix were extracted and summarized from these references, and for more detailed information, the reader is referred to these publications. 

This document presents clear concepts and definitions of general and specific terms relating to reactions of polymers and functional polymers. The document is divided into three seetions. In Seetion 1, terms relating to reaetions of polymers are defined. Names of individual ehemical reaetions (e.g., chloromethylation) are omitted from this doeument, even in eases where the reaetions are important in the field of polymer reaetions, beeause sueh names are usually already in widespread use and are well defined in organie... 

Concepts and definitions. Two concepts are potentially useful in establishing exemption levels for radioactive waste. The first is the concept of a generally applicable negligible (de minimis) dose or risk, and the second is the concept of amounts of radionuclides that are exempt or below regulatory concern (BRC) for particular practices or sources. 

This publication is the second of three contributions on traceability in chemical analysis. The first was published in this Journal [1] and deals with the general principles, whereas the third is planned chiefly to present examples, but also to suggest implementation procedures, to assess comments from chemical groups and to introduce possible modifications of concepts and definitions [2, 3],... 

Abstract In continuing their attempt to bring general issues concerned with trustworthy chemical measurements to review and international discussion, the authors propose basic aims and requirements for protocols of chemical-measurement procedures with traceability to the SI or, where this is not possible, to units of internationally recognized measurement scales. Documents describing such protocols could be useful in science, technology, law, or trade. Concepts and definitions for protocols have been introduced in Part I of this contribution. Part II here deals with the development and application of protocols for intended in-laboratory, commercial, national, or international recognition. Protocols deal with measure-... 

The most recent definitions of reference materials (RM) and certified reference materials (CRM) were given in the International vocabulary of metrology - basic and general concepts and associated terms (VIMS) [1]. 

Membrane-based reactive separation (otherwise also known as membrane reactor) processes, which constitute the subject matter of this book, are a special class of the broader field of membrane-based separation processes. In this introduction we will first provide a general and recent overview on membranes and membrane-based separation processes. The goal is to familiarize those of our readers, who are novice in the membrane field, with some of the basic concepts and definitions. A more complete description on this topic, including various aspects of membrane synthesis can be obtained from a number of comprehensive books and reviews that have already been published in this area [1.1, 1.2, 1.3,... 

Basic Concepts and Definitions. The task of relating thermometer output (i.e., magnitude of the variable dependent on temperature) to its temperature is achieved through calibration. Two general means of calibration are available (1) fixed-point calibration, and (2) compari-... 

After some basic concepts and definitions (Chapter 2), a general toxicity approach for plastics and rubbers is presented in Chapter 3. This discusses the general toxicity issue for plastics and rubbers due to additives (in the same chapter), followed by a consideration of health effects due to the polymers and other main ingredients (except additives), in the following chapter. 

The cybernetic description of systems of different types is characterized by concepts and definitions like feedback, delay time, stochastic processes, and stability. These aspects will, for the time being, be demonstrated on the control loop as an example of a simple cybernetic system, but one that contains all typical properties. Thereby the importance of the probability calculus and communication in cybernetics can be clearly explained. This is then followed by a general representation of cybernetic systems. 

In the first few chapters we shall discuss some simple, but important, particle systems. This will allow us to introduce many basic concepts and definitions in a fairly physical way. Thus, some background will be prepared for the more formal general development of Chapter 6. In this first chapter, we review briefly some of the concepts of classical physics as well as some early indications that classical physics is not sufficient to explain all phenomena. (Those readers who are already familiar with the physics of classical waves and with early atomic physics may prefer to jump ahead to Section 1-7.)... 

Another link exists between the PIF concept and the sociotechnical assessment methods described in Section 2.7 The checklists used in the TRIPOD methodology are essentially binary questions which evaluate whether the sets of PIFs making up each of the general failure types are adequate or not. The hierarchical sets of factors in HRAM are essentially PIFs which are expressed at increasingly finer levels of definition, as required by the analyst. The audit tool which forms MANAGER also comprises items which can be regarded as PIFs which assess both management level and direct PIFs such as procedures. 

A typical behavior of amplitude dependence of the components of dynamic modulus is shown in Fig. 14. Obviously, even for very small amplitudes A it is difficult to speak firmly about a limiting (for A -> 0) value of G, the more so that the behavior of the G (A) dependence and, respectively, extrapolation method to A = 0 are unknown. Moreover, in a nonlinear region (i.e. when a dynamic modulus depends on deformation amplitude) the concept itself on a dynamic modulus becomes in general not very clear and definite. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

Although the concepts of specific acid and specific base catalysis were useful in the analysis of some early kinetic data, it soon became apparent that any species that could effect a proton transfer with the substrate could exert a catalytic influence on the reaction rate. Consequently, it became desirable to employ the more general Br0nsted-Lowry definition of acids and bases and to write the reaction rate constant as... 

Since Huisgen s definition of the general concepts of 1,3-dipolar cycloaddition, this class of reaction has been used extensively in organic synthesis. Nitro compounds can participate in 1,3-dipolar cycloaddition as sources of 1,3-dipoles such as nitronates or nitroxides. Because the reaction of nitrones can be compared with that of nitronates, recent development of nitrones in organic synthesis is briefly summarized. 1,3-Dipolar cycloadditions to a double bond or a triple bond lead to five-membered heterocyclic compounds (Scheme 8.12). There are many excellent reviews on 1,3-dipolar cycloaddition, in particular, the monograph by Torssell covers this topic comprehensively. This chapter describes only recent progress in this field. Many papers have appeared after the comprehensive monograph by Torssell. Here, the natural product synthesis and asymmetric 1,3-dipolar cycloaddition are emphasized.630 Synthesis of pyrrolidine and -izidine alkaloids based on cycloaddition reactions are also discussed in this chapter. 

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