Line phases

If the miscibility gap of Pri+xl2 is temperature dependent (which they usually are), then Prl2 could be a line phase at, say, ambient temperature, i.e., x = 0. Hence, on quenching or when the annealing process progresses, the metastable i+xh phase must release praseodymium metal. This surplus praseodymium metal can be released from both the 3 a (heavily under-occupied) and 3 b (fully occupied) positions combined with site changes from 3 b to 3 a, or not. These... 

The results of such experiments, carried out over a range of temperatures, are summarized on a phase diagram (Fig. 4.1 b), which can be used to predict the outcome of any preparation in the NaF-ZnF2 system. In such diagrams, each phase is drawn as a line, as in the example of NaZnF3 above, because they show no composition range. Such compounds are referred to as stoichiometric compounds and, sometimes, with the appearance of the phase diagram in mind, line phases. 

In the case of a ternary system, the formation of several, binary and ternary, stoichiometric phases, and different types of variable composition phases can be observed. One may differentiate between these phases by using terms such as point compounds (or point phases), that is, phases represented in the composition field by points, line phases , field phases , etc. 

Considering for instance the formation of compounds, several variants may be observed due to the possible existence of binary (point or line) phases and/or of ternary, stoichiometric or solid solutions phases. Notice that true ternary phases may be formed (that is phases corresponding to homogeneity regions placed inside the diagram and not connected with the components or any binary phases). However within the ternary composition fields, phases are observed which contain all the... 

The high resolution for controlling the stoichiometry allows us to determine even very narrow ranges of stoichiometry including that of so-called line phases. Non-stoichiometries of the order of 10 or lower may be readily resolved. Knowledge of the variation of the cell voltage... 

Since F = 2 results in an area (phase field), and F = 1 results in a line (phase boundary), we can predict that F = 0 should occur at a point, and indeed it does. Point B is such a point = 3 graphite, diamond, and liquid C = 1, carbon), as is... 

An isolated cs plane or a random array of cs planes, known as the Wadsley defect, still gives rise to nonstoichiometry. Regularly recurring cs planes result in a homologous series of stoichiometric intermediate phases. Occurrence of such equidistant cs planes in a crystal indicates a cooperative mechanism. The formula of a cs phase depends on the cs plane index as well as the width of the parent slab between cs planes. If MO is the formula of the parent line phase, the formula of the homologous series of oxides resulting from cs may be represented as where n is the width (number of... 

The phase diagram of the Ga-As system is shown in Fig. 3.31, which indicates the existence of the compound GaAs. In this figure, the GaAs phase is represented by a line, suggesting a line phase or stoichiometric compound. Straumanis and Kim demonstrated that GaAs is a non-stoichiometric... 

It can also be observed from the schematic of the interactions shown in Fig. 10 that interaction zones that provide the possibility for sharing sulfur atoms by the two different phases exist. The structure of these interaction zones are crucial to understanding the interaction of sulfides with supports and promoter phases. The basal plane interaction with a second phase can be expected to be weak, but charge transfer might be expected if metal atoms are exposed on the second phase. Such an interaction would be similar to an intercalation interaction. The edge interaction will be much stronger, and here a transition zone with a possible epitaxial relationship between MoS2 and the second phase is expected. It is in this zone that we can expect to find the surface phases as described above (for example, the CoMoS phase). But in the cases described here, the surface phase becomes a line phase at the boundary between the two bulk phases. It is our belief that the detailed study of these phases represents a key area for future research in TMS catalysis. 

Figure 11.10 Schematic representation of co-Clapeyron vector orientations of (a) base T), P) vectors and (b) resultant Clapeyron vectors X) (dotted), illustrating the geometrical condition (11.165a) for coexistence of a (solid line) and /3 (dashed line) phases. The coordinate origin is marked with a small square in each panel. [Vector lengths, angles, ya, and ASap, AVap, values are chosen purely for illustrative purposes the Clapeyron-matching condition cannot be sensibly illustrated in Si-based units for any real system (Sidebar 11.6).]...

In this system, C = 2. If we choose a point which does not fall on the vapor-liquid equilibrium line, then all three variables must be known to describe the system. However, by choosing a point on the vapor-liquid line phases, P=2 and thus, degrees of freedom F = 2-2+2 =2. In other words, only two of the three degrees of freedom (variables) must be known. Referring to Figure 2.3b, if we have a 50/50 mole fraction solution of A and B, the mixture boils at 92°C and the vapor contains 78 mole % of B. In Figure 2.3a the dotted lines indicate the partial pressure of each of the components, that is, the equation of each line defines Raoult s law ... 

Fig. 5.17. Changes in the SH intensity (solid line), phase (broken line), and cathodic charge passed (open circles) as a function of applied bias potential. Ag(110) in 0.25 M Na2S04, 5 mM T12S04, pH = 3.0. Incident wavelength = 1064 nm. From Ref. 146.

Figure 16 IR reflectivity of the low-temperature (solid line) and high-temperature (dashed line) phases of MEM(TCNQ)2 single crystals. (From Ref. 97.)...

The frequency response measured between a pair of transducers having A<, = 32 ftm and Np = 50 finger pairs is shown in Figure 3.21 (page 79). The amplitude, shown on a log (decibel) scale, shows the characteristic sin(X)/X behavior. The delay line phase shift

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The chemistry of phases with intermediate compositions REX (2.0 < n < 3.0), which are complex mixed valent RE(II)/RE(III) halides, reminds on the AX2/REX3 systems (A = Ca, Sr, Ba). In fluorides REF (n 2.0-2.2) divalent ions and trivalent ions occnpy the sites within a flnorite-type variant, in which, for charge compensation, interstitieUhahdes are incorporated into the primitive anion snblattice and solid solutions REX2/REX3 are observed. For higher n, the anions form clusters and line phases are formed which crystallize as so-called anion ordered excess flnorite-type variants or in other complicated structure types. 

Numerical solutions of (6.1.48) show that already for moderate microwave field strengths the smooth straight line phase-space orbits shown in Fig. 6.3 start to deform. At higher field strengths they break up entirely. This scenario strongly resembles the analogous scenario already encountered in Chapter 5 in connection with the kicked rotor. Once the... 

Figure 32 Dissociation rates of rotationally cold NO2 as function of the mean excitation energy. Thick solid line phase space theory (PST). The two vertical dashed lines are reaction thresholds for NO2 starting in its lowest rotational level (i.e., Do) and its first excited rotational level. Reprinted, with permission of the American Institute of Physics, from Ref. 275.

Figure 9-1 Schematic phase diagram of a binary fluid mixture of small molecules. The two-phase region lies under the binodal line, the apex of which defines the critical temperature Tc and critical composition Between the binodal and the spinodal lines, phase separation is by nucleation and growth (NG), while under the spinodal line it is by spinodal decomposition (SD). Within the region of spinodal decomposition, near the compositional symmetry line, there is a region where the morphology is initially bicontinu-ous. Outside of this region, one of the phases is a discontinuous droplet phase. Eventually,...

The entire region enclosed by the outer dome represents immiscibility. The inner dome is known as the spinodal. The outer dome is known as the binodal. In the region of composition between the binodal and spinodal lines, phase separation occurs by the nucleation and growth mechanism and leads to the formation of dispersed micro-spherical glass particles in the matrix (see also Shelby, 1997). Spinodal decomposition which takes place inside the dotted region is a special type of phase separation. In order to understand this, consider two materials A and B, melts of which... 

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