Stability areas

Since does not take part in the reaction, the boundary line between M and MO is independent of logPsoj d so given by a straight vertical line at logPo2 = 16, parallel to the -axis (line 1 in Fig. 7.67). It should be noticed that stability areas across the boundary follow the sequence of condensed phases shown in the equation, i.e. on the left-hand side of the boundary pure metal is the stable phase and on the right-hand side the pure metal oxide. 

These calculated data are now sufficient to draw the boundary line between the stability areas of M and A/S. This is constructed by drawing a straight line having a slope of + 1 from the point of intersection A. Next, the position of the boundary between MS and MO can be calculated from the reaction ... 

The boundary between the MS and AfS04 stability areas is calculated from the reaction ... 

Since SOj does not take part in the above reaction, the boundary between MS and MSO4 stability areas is independent of logpsoj and is given by a vertical line (4) at logpo, = —12 parallel to the logpsoj axis. The intersection point of the MS/MSO4 line (4) with that of MO/MS boundary line (5) at point B of Fig. 7.67 completes the stability area of the MS phase (lines 2, 3 and 4). 

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. 

These isothermal diagrams can be used to consider the phase stability areas for more than one metal in contact with a common atmosphere and thus to assess the condensed phases which can be stable under the prevailing conditions. Figure 7.75 shows a stability diagram having phase areas for Co-S-O solid lines) and for Cu-S-O system broken lines). From this diagram it can be seen clearly that at 950 K at certain gas mixtures, pure metals Co and... 

It is also clear that small changes in the position of points P and Q can have a significant effect on the phase distribution in the surface layers. From the diagrams it is also seen that, when the metal A is saturated with oxygen and sulphur, and therefore the point Q is located at the corner of the rectangle giving the stability area of the metal A, then the innermost phase layer will consist of a mixed sulphide and oxide layer. 

The relationship between Tg and microbial stability is the least studied of all the stability areas. Based mainly on mold germination data, Slade and Levine (1991) postulated that glass transition parameters, specifically Tm/Ts ratio, T g and W g (related to C defined previously in Figure 32), could be useful for predicting the microbial stability of concentrated and... 

In addition to Fig. 10 in Fig. 12 some data are given regarding phase relations and stability areas with different rare earth cations. The lowest x-value for trivalent cations is 0.33 for Ca2+ the lowest value is 0.3 [123-127, 169, 187], It should be emphasised that all ass do not include the pure a-Si3N4. The atomic positions for different cations M are listed in Table 5, showing that the Si- and N-positions do not differ significantly from that in pure a. This is... 

The stability areas of the a-solid solutions depend both on the size of the rare earth ion and the temperature [147]. Increasing the size of the rare earth and decreasing temperature leads to a reduced solubility of A1 and O in the ass, e.g., to lower maximum n values [188], On the other hand, recent results show a more extended ass with more than one stabilising cation, as can expected with only one stabilising cation (different rare earths and Sr or Ca [128]). Even elements like La or Ce, which alone do not form an ass, can be effective as stabiliser together with Ca or Yb [131, 189]. Those multi-cation a-solid solutions offer additional possibilities of variations in processing and properties [154],... 

The stability areas for the x- and y-dimensions are both shown in Fig. 7, the x-stable areas pointing down and the y-stable pointing up. There are regions in this a-q space where ions can be x-stable but not y-stable and vice versa. 

Fig. 13. Stability areas in the r and z-directions in an ion trap. The highlighted area of common stability is displayed enlarged in Fig. 14.

All registrations stability studies, both accelerated and long-term, must of course be carried out in full compliance with cGMPs. Example 5 presents stability areas often cited as deficient during regulatory inspections. 

Theory Area of best physico-chemical stability Area of onset of reversible aggregation Area of marked aggregation... 

Stability areas for an ion along x or y (above) and along x and y (below) u represents either x or y. The four stability areas are labelled A to D and are circled. The area A is that used commonly in mass spectrometers and is enlarged. The direct potential part is shown for positive U (shaded) or negative U. From now on we will consider the positive area. Reproduced (modified) from March R.E. and Hughes R.J., Quadrupole Storage Mass Spectrometry, Wiley, New York, 1989, with permission. 

If II = 0, there is no direct current and the resolution becomes zero. However, the value of V imposes a minimum on stable masses. Thus, if V is increased from 0 to V so as to reach slightly beyond the stability area mi, all of the ions with masses equal to or lower than mi will have an unstable trajectory, and all of those with masses above mi will have a stable trajectory. 

Figure 2.15 displays the iso-p lines for pu = 0 and pu = 1 respectively. One of the two diagrams refers to the z coordinate and the other to the r coordinate. Remember that au = az = -2ar and qu = qz = -2qr. The area inside these limit values for pu corresponds to a, q values for a stable trajectory. However, for an ion to be stable in the ion trap, it must have a stable trajectory along both z and r, which correspond to the overlap of the stability areas of the two diagrams. 

Stability area for ions simultaneously stable along r and z. 

A reduction of the stability of the liquid crystalline phase means a reduced region where it is stable and a corresponding increase of the region for the inverse micellar solution. The present results agree with these predictions, and it is justifiable to relate the changes in stability areas mainly to modifications of the potential distribution within the electric double layers. 

SECTION THROUGH STABILIZED AREA Figure 19.11 Grouting plan. (From Ref. 8.)... 

It can be concluded from the position of the equilibrium line for 8O2 that ZnO is produced when ZnS is roasted in O2 at 1600 K. The 8O2 content of the exhaust gases in technical processes is from 5 to 80% by volume. ZnO is the stable zinc compound under these circumstances. In contrast the 8O2 line at 1900 K lies in the stability area of gaseous zinc. 80 roasting at 1900 K can yield zinc vapor as well as 8O2. 

Fig. 7.4 Stability areas of the components in the system Zn-O-S at 1600K and I900K with = 1 bar. The equilibrium line for the reaction yS2 +O2 = SO2 is plotted for = 1 bar.

Sc + and In3+, which are even smaller than Lu +. The reason for the extensive stability area of this thortveitite structure (see also Fig. 42) might be seen in the almost closest packing of the oxygens with the silicons emd rare earths on the tetrahedral and octahedral sites respectively. On the other hand, the smaller stability range of the larger rare-earth disilicate structures is best demonstrated by the large variance in coordination numbers and in RE—O distances found in the individual coordination shells. This is also shown by the data of. e.g. PrDi A. as compared to Yb Di C in Table 22. Tables 22 and 23 present the coordination data on (RE—0 )polyhedra and (Si04)tetrahedra of the individual structures. Structural data of compounds other than the binary compounds have not been taken into consideration because of their relatively poor accuracy. 

Figure 2.55 Gypsum and anhydrite stability areas vs. moisture activity and temperature (Hardie, 1967)...

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