System phase relations

As shown in the above Bi-W-S system, phase relations and reactions can be deduced easily using sulfur activity data from the literature. Other systems are either incomplete or require corrections, for instance when ternary phases occur, which is discussed in the following. 

Table 1. Investigations of flie C-Fe-Nb System Phase Relations, Straetures and Thermodynamies ...

No complete phase diagram is available for the Sc-Gd-Ge system phase relations along ScGe2-GdGe2 were studied by Shpyrka (1990). From X-ray powder dif action data for arc melted alloys annealed at 870 K, the solubility of ScGc2 in GdGe2 was found to extend up to 8 at.% Sc. 

Obemdorff, P. Lead-Free Solder Systems Phase Relations and Microstructures. PhD Thesis. Technical University of Eindhoven The Netherlands, 2001. 

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... 

It is beyond the scope of these introductory notes to treat individual problems in fine detail, but it is interesting to close the discussion by considering certain, geometric phase related, symmetry effects associated with systems of identical particles. The following account summarizes results from Mead and Truhlar [10] for three such particles. We know, for example, that the fermion statistics for H atoms require that the vibrational-rotational states on the ground electronic energy surface of NH3 must be antisymmetric with respect to binary exchange... 

The choice of separation method to be appHed to a particular system depends largely on the phase relations that can be developed by using various separative agents. Adsorption is usually considered to be a more complex operation than is the use of selective solvents in Hquid—Hquid extraction (see Extraction, liquid-liquid), extractive distillation, or azeotropic distillation (see Distillation, azeotropic and extractive). Consequentiy, adsorption is employed when it achieves higher selectivities than those obtained with solvents. 

The acidic character of siUca is shown by its reaction with a large number of basic oxides to form siUcates. The phase relations of numerous oxide systems involving siUca have been summarized (23). Reactions of siUca at elevated temperatures with alkaU and alkaline-earth carbonates result in the displacement of the more volatile acid, CO2, and the formation of the corresponding siUcates. Similar reactions occur with a number of nitrates and sulfates. Sihca at high temperature in the presence of sulfides gives thiosiUcates or siUcon disulfide, SiS2. 

The existence of tridymite as a distinct phase of pure crystalline siUca has been questioned (42,58—63). According to this view, the only tme crystalline phases of pure siUca at atmospheric pressure are quart2 and a highly ordered three-layer cristobaUte having a transition temperature variously estimated from 806 250°C to about 1050°C (50,60). Tridymites are considered to be defect stmctures in which two-layer sequences predominate. The stabihty of tridymite as found in natural samples and in fired siUca bricks has been attributed to the presence of foreign ions. This view is, however, disputed by those who cite evidence of the formation of tridymite from very pure siUcon and water and of the conversion of tridymite M, but not tridymite S, to cristobahte below 1470°C (47). It has been suggested that the phase relations of siUca are deterrnined by the purity of the system (42), and that tridymite is not a tme form of pure siUca but rather a soHd solution of minerali2er and siUca (63). However, the assumption of the existence of tridymite phases is well estabUshed in the technical Hterature pertinent to practical work. 

Flexible rotors are designed to operate at speeds above those corresponding to their first natural frequencies of transverse vibrations. The phase relation of the maximum amplitude of vibration experiences a significant shift as the rotor operates above a different critical speed. Hence, the unbalance in a flexible rotor cannot simply be considered in terms of a force and moment when the response of the vibration system is in-line (or in-phase) with the generating force (the unbalance). Consequently, the two-plane dynamic balancing usually applied to a rigid rotor is inadequate to assure the rotor is balanced in its flexible mode. 

This measurement ean be aeeomplished by using a meehanieal system or various types of eleetronie systems. All of these systems are expensive and in many eases require repeated ealibration. The meehanieal system (Figure 19-14) is a three-gear, phase-related system whieh measures the displaeement between two gears and the proportionate shaft twist. A third gear is situated so that any variations other than shaft twist will oeeur in the first two gears. This signal is used to eliminate errors eaused by these variations. 

Frequeney domain analysis is eoneerned with the ealeulation or measurement of the steady-state system output when responding to a eonstant amplitude, variable frequeney sinusoidal input. Steady-state errors, in terms of amplitude and phase relate direetly to the dynamie eharaeteristies, i.e. the transfer funetion, of the system. 

The phase relations in the tellurium-halogen systems have only recently been elucidated... 

The Fourier transform H(f) of the impulse response h(t) is called the system function. The system function relates the Fourier transforms of the input and output time functions by means of the extremely simple Eq. (3-298), which states that the action of the filter is to modify that part of the input consisting of a complex exponential at frequency / by multiplying its amplitude (magnitude) by i7(/)j and adding arg [ (/)] to its phase angle (argument). 

Second, Schneider s article reviews recent work (notably by Rowlinson, Kohn and co-workers) on phase relations in binary liquid systems where one of the components is much more volatile than the other (D1, D2, E3, M8, R9). Such systems may have lower critical solution temperatures for these systems, an increase in temperature (and, indirectly, pressure) causes precipitation of the heavy component, thereby providing a possible separation technique, e.g., for the fractionation of polymers. 

This relationship applies quite closely for the conditions normally encountered in practice. For other systems, the relation between the heat and mass transfer coefficients in the gas phase is given by ... 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

Kaolin minerals (kaolinite, dickite, nacrite), pyrophyllite and mica-rich mica/smec-tite mixed layer mineral occur as envelopes around barite-sulfide ore bodies in the footwall alteration zones of the Minamishiraoi and Inarizawa deposits, northern part of Japan (south Hokkaido) (Marumo, 1989). Marumo (1989) considered from the phase relation in Al203-Si02-H20 system that the hydrothermal alteration minerals in these deposits formed at relatively lower temperature and farther from the heat source than larger sulfide-sulfate deposits in the Hokuroku district. 

Barton, P.B. Jr. and Toulmin, P. Ill (1966) Phase relations involving sphalerite in the Fe-Zn-S system. Econ. Geol, 61, 815-849. 

Bird, D.K. and Norton, D.L. (1981) Theoretical prediction of phase relations among aqueous solutions and minerals Salton Sea geothermal system. Geochim. Cosmochim. Acta, 45, 1479-1494. 

Moh, G.H. (1975) Tin-containing mineral systems. Part II. Phase relations and mineral assemblages in the Cu-Fe-Zn-Sn-S system. Chem. Erde, 34, 1-61. 

A. Muan, The Effect of Oxygen Pressure on Phase Relations in Oxide Systems, Am. J. Sci, 256, 171-207 (1958). 

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