Stability diagram boundaries

Fig. 7.67 Phase stability diagram for a metal-sulphur-oxygen (M-S-O) system at I 000 K. (For the thermodynamic data AC 000 for the various across-boundary reactions, see Table 7.37)...

Therefore, the calculated coordinates of the triple point for the coexistence of MO, MS and A/SO4 are logPso2 = +2 and logpo = - 12 and the slope of the MO/MSO4 boundary is - y. The straight line from point B having slope — y gives the boundary line (i) between the stability areas of MO and A/SO4. This completes the construction of the phase stability diagram forM-S-O at 1000 K. 

Fig. 7.70 Phase stability diagram for the Cr-O-S system on Incoloy 800H at 1 023 K showing thermodynamic and kinetic boundaries (after Natason )...

Fig. 7.77 Thermodynamic stability diagram for the Fe-Ni-Cr system at 1 143 K, assuming metal activities to be unity.-, phase boundaries involving Fe —phase boundaries involving Ni ----, phase boundaries involving Cr. The location of environments 1, 2, 3, and 4 are...

Because of the financial importance of this process to steel producers (about one-third of all the steel produced in the world is subsequently galvanised) a great deal of research has been carried out throughout the world to establish the true equilibrium phase boundaries in the Fe,, -Zn( system and the critical temperature of stability of the f phase. Since the AG -7 diagrams or the phase stability diagrams could not account for these discrepancies in this system, AG ,-concentration curves were used for... 

Fig. 11.9. The stability diagram for a quadrupole mass filter. The shaded area represents solutions for the Mathieu equations that result in stable ion trajectories through the device. The area outside the boundaries represents solutions for the equations that produce unstable trajectories.

By expanding the circled region in Fig. 13, the ion-trap stability diagram (Fig. 14) plotted in terms of the parameters az and qz is obtained. These parameters are directly related to the RF (qz) and DC (az) voltages applied to the ion-trap electrodes. The areas of stability have boundaries where the (lu parameters (u — z or r) have values 0 and 1. fju is a complex function of au and qu and is directly related to the fundamental secular frequency of the ion (mu) and the main RF frequency (Q) by the equation... 

In a similar manner, one may also derive equations describing complex pe-pH stability diagrams for Fe-0-H20 at 25°C and 1 atm pressure involving gas, solution, and solid phases H2(g), 02(g), H20, Fe2+, Fe3+, Fe203, and Fe304 (Drever, 1982). In this case, stability lines can be drawn using the equations describing upper and lower boundary limits of H20 (referred to as step 1) as demonstrated above (Fig. 5.8). 

Figure 2.33 Stability diagram for a flat plate boundary layer showing the nentral curve superposed over c = const, disturbance propagation contours shown by thin lines. Note that the line c = 1 corresponds to the case of pure convection of...

Our results are summarized in the stability diagram in Figure 8.3.4. The boundary between the two regions is given by the Hopf bifurcation locus b = 3a/5 - 25/a. ... 

From this stability diagram, let us now consider the various regions. The system is stable below the boundary ZXW and unstable above it. In the lower-right-hand quadrant, both contributions to the density gradient are stable and so the system is obviously stable. 

Figure 12-6. A sketch of the stability diagram for double-diffusive convection. The stability boundary is the solid line ZXW. The dashed line PQ denotes the boundary for static stability where the net density gradient is equal to zero. It is assumed in this sketch that Pr/Sc < 1.

Fig. 10.13. Stability diagram established as a function of the rates of cyclin synthesis, Vj, and degradation, v, in the minimal cascade model of fig. 10.4. The domain of oscillations is determined as in fig. 10.8 parameter values are as in fig. 10.6. A narrow region of hard excitation (not shown) in which a stable limit cycle coexists with a stable steady state is observed just above part of the upper boundary of the instability domain (J.M. Guilmot A. Goldbeter, unpublished results).

The trapping parameters, expressed generally as and q, are the axes of the well-known stability diagram. The boundaries of the stability regions in the axial and radial directions are defined by an additional trapping parameter calculated from a continued fraction of the form... 

The second method involved the application of a DC potential to the connected end-cap electrodes and varied adiabatically, that is, the DC potential was varied slowly such that the ion cloud was not disturbed by this variation. The variation of the fluorescence as a function of the adiabatically-varied DC voltage, in the absence of any other external excitation, reveals two important properties of trapped ion dynamics first, the boundaries of the stability diagram and, second, the intensity of possible black canyons (see Chapter 3 in Vol. 1 of this series). 

FIG U RE 11.15 Limits of the stability diagram as observed from the fluorescence of a small Ca -ion cloud as compared to the stability diagram of an ideal Paul trap (solid lines). The observed right-hand-side limit corresponds to a (3 = 1/2 canyon no ion could be confined beyond this boundary. 

As an alternative to the methods above described, a further ion activation method was proposed in 1991 [11-14]. In this method, the working point (that is, the point (a, on a QIT stability diagram defined by the magnitudes of the trapping parameters and is moved close to one of the boundaries of the stability diagram this method can be realized with the combined effect of suitable DC and RF potentials applied to the ion trap... 

FIGURE 12.9 Leucine encephalin [M+H]+ mass spectra (a), inside the stability diagram (b), the monoisotopomer of the molecular ion cluster is located on the 3 =1 boundary of the stability diagram. 

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