Phase relationships

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

Although 0-switching produces shortened pulses, typically 10-200 ns long, if we require pulses in the picosecond (10 s) or femtosecond (10 s) range the technique of mode locking may be used. This technique is applicable only to multimode operation of a laser and involves exciting many axial cavity modes but with the correct amplitude and phase relationship. The amplitudes and phases of the various modes are normally quite random. 

Table 6. Phase Relationships and Crystallographic Properties of Plutonium Metal ...

Al—Li [12042-37-4] 5. The nature of the phase relationships involving 5 has been the subject of much discussion. Portions of the metastable phase boundaries have not yet been agreed upon. 

Phase relationships ia the system K O—B2O2—H2O have been described and a portion of the phase diagram is given ia Figure 8. The tetrahydrate, which can be dried at 65°C without loss of water of crystallisation, begias to dehydrate between 85 and 111°C, depending on the partial pressure of water vapor ia the atmosphere. This conversion is reversible and has a heat of dehydration of 86.6 kj/mol (20.7 kcal/mol) of H2O. Thermogravimetric curves iadicate that two moles of water are lost between 112 and 140°C, one more between 200 and 230°C and the last between 250 and 290°C (121). 

Diammonium Tetraborate Tetrahydrate. Diammonium tetraborate tetrahydrate, (NH 2 4Dy 4H2O or (NH 2D 2B202 H2O formula wt, 263.37 monoclinic sp gr, 1.58 is readily soluble ia water (Table 9). The pH of solutions of diammonium tetraborate tetrahydrate is 8.8 and iadependent of concentration. The compound is quite unstable and exhibits an appreciable vapor pressure of ammonia. Phase relationships have been outlined and the x-ray crystal stmcture formula is (NH 2P4D5(OH)J 2H20 (124). 

The properties of calcium chloride and its hydrates are summarized in Table 1. Accurate data are now available for the heats of fusion of the hexahydrate, the incongment fusion of the tetrahydrate, and the molar heat capacities of the hexahydrate, tetrahydrate, and dihydrate (1). These data are important when considering the calcium chloride hydrates as thermal storage media. A reevaluation and extension of the phase relationships of the calcium chloride hydrates, has led to new values for the heats of infinite dilution for the dihydrate, monohydrate, 0.33-hydrate, and pure calcium chloride (1). 

These three equations represent saturation with respect to the hexahydrate, tetrahydrate, and dihydrate in the temperature ranges indicated. The phase relationships among calcium chloride, its hydrates, and a saturated solution are illustrated in the diagram in Figure 1. 

Fig. 1. The phase relationships among calcium chloride, its hydrates, and a saturated solution.

This class may be selected for protective devices that operate on the basis of phase relationship between the voltage and the current phasors, such as in a directional overcurreni protection, reverse power or directional distance protection. 

The generally applicable relations for a two-conductor model are derived in the following section. For simplicity, local potential uniformity is assumed for one of the two conductor phases. Relationships for the potential and current distributions, depending on assumed current density-potential functions, are derived for various applications. 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

Elucidation of the phase relationships between the different forms of carbon is a difficult field of study because of the very high temperatures and pressures that must be applied. However, the subject is one of great technical importance because of the need to understand methods for transforming graphite and disordered forms of carbon into diamond. The diagram has been revised and reviewed at regular intervals [59-61] and a simplified form of the most recent diagram for carbon [62] is in Fig. 5. 

Phase Relationship between the Solid and Liquid. A phase relationship may involve a number of crystalline forms from which materials can be separated. When a solid material is precipitated as a result of the solution becoming supersaturated, crystallization occurs. Crystallization may be achieved by... 

Figure 14-9. Phase Relationship in alternating circuits. (Used by permission Peach, N. Power, p. 138. July, 1957. McGraw-Hill, Inc. All rights reserved.)...

The details of alternating current phase relationship are presented by Peach, N. and used by permission ... 

Ratio measurement, polarity check and phase relationship ... 

In addition, it should be noted that frequency-domain analysis can be used to determine the phase relationships for harmonic vibration components in a typical machine-train spectrum. Frequency-domain normalizes any or all running speeds, where time-domain analysis is limited to true running speed. 

Angular misalignment can take several signature forms and excites the fundamental (lx) and secondary (2x) components. It can excite the third (3x) harmonic frequency depending on the actual phase relationship of the angular misalignment. It also creates a strong axial vibration. 

Although the definition of dynamic imbalance covers all two-plane situations, an understanding of the components of dynamic imbalance is needed so that its causes can be understood. Also, an understanding of the components makes it easier to understand why certain types of balancing do not always work with many older balancing machines for overhung rotors and very narrow rotors. The primary components of dynamic imbalance include number of points of imbalance, amount of imbalance, phase relationships, and rotor speed. 

The phase relationship of each point of imbalance is the third factor that must be known. Balancing instruments isolate each point of imbalance and determine their phase relationship. Plotting each point of imbalance on a polar plot does this. In simple terms, a polar plot is a circular display of the shaft end. Each point of imbalance is located on the polar plot as a specific radial, ranging from 0 to 360°. 

However, the horizontal reading on one bearing will not show the same phase relationship as the vertical reading on the same bearing. This is due to the pickup axis being oriented in a different angular position, as well as the phase adjustment due to possible resonance. For example, the horizontal vibration frequency may be below the horizontal resonance of various major portions of machinery, whereas the vertical vibration frequency may be... 

This paper reviews data on certain thermodynamic aspects of the nonstoichiometric Pu-0 system, which may serve as a basis for use In reactor safety analysis. Emphasis Is placed on phase relationships, vaporization behavior, oxygen-potential measurements, and evaluation of pertinent thermodynamic quantities. Limited high temperature oxygen potential data obtained above the fluorite, diphasic, and sesquioxide phases In the Pu-0 system are presented. 

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