Existence diagrams

Finally, the framework formed by the boron clusters is relatively rigid and therefore, there are constraints on the size of the metal atoms/ions which can occupy the voids. That is why there are different boundaries regarding which rare earth atoms can form each particular higher boride (as will be seen in the following sections). A rare earth existence diagram for all the higher borides will be presented at the end of this review, see Section 13. 

First of all, a rare earth existence diagram is given in Figure 45 for all the higher boride compounds discussed in this review. As noted before, size constraints on the voids which are created among the boron cluster networks result in different ranges of possible rare earth elements for the different compounds. 

Table II. Existence Diagram for Rn02n-2 Phases of Some Lanthanide and Actinide Elements...

Figure 4.16 The iron-rich region of the iron-carbon existence diagram. The phase cementite (FesC not shown) occurs at 6.70 wt% carbon. This phase is a nonequilibrium phase and does not occur on the equilibrium phase diagram, which is between iron and graphite. The diagram is not to scale, and the a-ferrite and 5-ferrite phase fields have been expanded for...

Figure 4.17 The iron-carbon existence diagram showing the approximate composition ranges for various plain carbon steels and cast irons...

Fig. 20. Existence diagram of various wave forms in the excitable region of model (5). N no waves, F flat solitary pulses, S rigidly rotating spirals, M meandering spirals, T turbulence. For even larger e a limit cycle forms in a saddle-loop bifurcation and subsequently vanishes in a Hopf bifurcation. Turbulence also exists between these two lines after [114]. ...

Figure B.l shows a pair of composite curves divided into vertical enthalpy intervals. Also shown in Fig. B.l is a heat exchanger network for one of the enthalpy intervals which will satisfy all the heating and cooling requirements. The network shown in Fig. B.l for the enthalpy interval is in grid diagram form. The network arrangement in Fig. B.l has been placed such that each match experiences the ATlm of the interval. The network also uses the minimum number of matches (S - 1). Such a network can be developed for any interval, providing each match within the interval (1) satisfies completely the enthalpy change of a strearh in the interval and (2) achieves the same ratio of CP values as exists between the composite curves (by stream splitting if necessary).

Using this mixture as an example, consider starting at pressure A and isothermally reducing the pressure to point D on the diagram. At point A the mixture exists entirely in the liquid phase. When the pressure drops to point B, the first bubble of gas is evolved, and this will be a bubble of the lighter component, ethane. As the pressure continues to drop, the gas phase will acquire more of the heavier component and hence the liquid volume decreases. At point C, the last drop of liquid remaining will be composed of the heavier component, which itself will vaporise as the dew point is crossed, so that below... 

Well completions are usually tailored to individual wells, and many variations exist. The following diagrams show a completion with a gravel pack, designed to exclude sand production downhole, and a dual completion, designed to allow controlled production from two separate reservoirs. 

From an overall economic viewpoint, any investment proposal may be considered as an activity which initially absorbs funds and later generates money. The funds may be raised from loan capital or from shareholders capital, and the net (after tax and costs) money generated may be used to repay interest on loans and loan capital, with the balance being due to the shareholders. The shareholders profit can either be paid out as dividends, or reinvested in the company to fund the existing venture or new ventures. The following diagram indicates the overall flow of funds for a proposed project. The detailed cash movements are contained within the box labelled the project . 

The diagram gives regions of existence, i.e. for a particular combination of pH and redox potential it can be predicted whether it is thennodynamically favourable for iron to be inert (stable) (region A), to actively dissolve (region B) or to fonn an oxide layer (region C). 

For database handling it is necessary to compare existing database entries with new ones. Consequently, database registration and retrieval are dependent on isomorphism algorithms which compare two graphs or structure diagrams to determine whether subgraphs are identical or not. 

However, care has to be taken to keep this graphical 3D information in 2D structure diagrams unambiguous. Since the reference plane can be chosen arbitrarily, there exist different possible ways of displaying the stereochemistry (Figure 2-68). 

The Universal Modeling Language is used to describe a software system [4, 5], Several kinds of diagrams exist to model the diverse properties of the system. Thus a description of the system can be developed that enables the systematic and uniform documentation of the system. The class diagram, for example, represents the classes and their relationships. But also interacting diagrams exist, to describe the dynamic behavior of the system and its objects. 

Derivation of an energy level diagram shows that it consists of two sets of energy levels, one corresponding to the single lines and the other to the double lines, and that no transitions between the two sets of levels are observed. For this reason it was suggested that helium exists in two separate forms. In 1925 it became clear that, when account is taken of electron spin, the two forms are really singlet helium and triplet helium. 

---