Isopleth section

Fig. 1.19.2. Isoplethal section of the solid-liquid state diagram for R = 0.1. Section fields ...

Isoplethal sections for 10, 20, 30 and 45 mass% Mo were constructed by [1932Koel] using frieiinal analysis. However, as no indication of the experimental conditions used was given, and also because of flie problems associated with the binary phase diagrams used in their analyses, these seetions are deemed to be unreliable and are not reproduced here. 

Figure la. The isopleth section Pb.80Sn.20Te of the Pb Sn-Te phase diagram. ... 

FIGURE 4-18 Ozone isopleths (vertical cross section) from southern Caltfomta coast air basin survey, August 11, 1971. Reprinted with permission from Gloria et al. ... 

Because of this increase in the VOC/NOa ratio as the air mass moves downwind, isopleths appropriate for one portion of an air basin, e.g., the upwind portion, will not necessarily be applicable to other regions, such as the downwind areas. The development of sophisticated grid-based models and their application to entire air basins have allowed modelers to include continuing emissions, transport, and transformation processes (see Section A.3). 

Fig. 5. Temperature-concentration section (isopleth) through the Si-N-0 phase diagram from Si02 to Si3N4 [69]. Below 2114 K it is a quasi-binary system. G = gas phase LS = oxide nitride liquid LM = metallic liquid...

Figure 11.11. An isothermal horizontal section (a), a vertical section, or isopleth (h), and the liquidus surface from the isometric projection of Figure 11.10.

Figure 7. The rising isopleths of seawater ammonium along an offshore-onshore section at Long Point, Los Angeles.

The existence of pseudobinary sections was tracked by most of the groups dealing with Si-B-C. Most of the authors assumed a composition B4+aC with 5 = 0. The phase equilibria of four different isopleths have been m2iinly investigated experimentally in this system B4C-SiC, B-SiC, B = const. = 80 at.% and B4C-Si. An overview of experimental investigations of the Si-B-C phase diagram is shown in Table 16 [4, 217-224],... 

Numerous thermodynamic calculations of phase equilibria in the Si-C-N system have been published but only few experimental investigations are documented. Calculated isothermal sections [117, 234-237], isopleths [117, 234], different types of potential phase diagrams [234,235,238-244] and phase fraction diagrams [234, 239] were presented. Additional information is provided by [245]. No or very low solid solubilities between SiC and Si3N4 could be detected by X-ray diffraction up to 2500 K [246, 247]. Also the nitrogen solubility in SiC is low. For more experimental information see [248, 249]. 

Fig. 2.3.2-1 P-T-x-y phase diagram of a simple binary mixture (schematic) with three sections isotherms (P-x diagram, light), isoplethes (P-Tdiagram, hatched), and isobars (T-x diagram, dark).

Figures 16 and 17 show isothermal sections of the Ti-B-C system at 1400°C and 2100°C, respectively [104, 105]. The diagrams based upon the work of Rudy et al. [99] are wrong below 2100°C as they neglect the Ti3B4 phase. Technically interesting isopleths are shown in Fig. 18 (TiC-B), Fig. 19 (TiB2-B4Q, Fig. 20 (B4C-Ti), and Fig. 21 (B4C-TiC). The equilibria of the various titanium borides with TiC] ( have been studied in more detail by Brodkin and Barsoum [106].

Figure 24. Isopleth of the Fe-TiB2 section [124], both 1992 refs ...

Figure 90. Isopleth of TiB2-(Fe + 2 at.-% Ti) section (after [320]). Note the difference to Figure 89 concerning the stability of a —> y Fe and the appearance of the liquid phase.

Non-quasibinary T-x sections (or vertical sections, isopleths, polythermal sections) show the phase fields where generally the tie lines are not in the same plane as the section. The notation employed for the latter (see Fig. 5) is the same as that used for binary and quasibinary phase diagrams. 

Two invariant reactions were also found in the solid phase region by [1957Bec], who published isopleths for 70 and 80 mass% Fe, and [1986Liu], who presented the section for 16 mass% Mo. The exact reaction temperatures were not established in these studies, and there are discrepancies in the positioning of the reactions and in the reaction sequence in comparison with the work of [1988And]. Therefore, the theoretical assessment based on [1988And] was used in combination with their experimental results to establish the probable type of invariant reactions. The invariant reactions are given in Table 3. The probable reaction sequence is shown in Fig. 2. 

Only the isopleth for 16 mass% Mo published by [1986Liu] in the range 700-1000°C is available in the recent literature. This isopleth corresponds reasonably well with the accepted isothermal sections. The exception is the lower temperature limit of the R phase (about 930°C) compared with [1988And]. For that reason, this isopleth indicates a different invariant reaction than that accepted in this evaluation. Therefore, no temperature-composition section is published here. 

The isopleflis at 1 mass% Ni and 0.3 mass% C have been experimentally determined in flic iron rich comer of the C-Fe-Ni system [1970Zem], The polyfliermal section proposed at 0.3 mass% by [1970Zem] does not fit well wifli the binary C-Fe and has been rejected. The accepted isopleth at 1 mass% Ni from [1970Zem] shown in Fig. 15 matches well wifli flic Fe-Ni binary system. The solubility of C in (aFe,Ni) (1 mass% Ni) presents a maximum of 0.022 mass% at 800°C... 

Consequently, only the vertical section constructed by [1968Pat] is depicted in Fig. 26 showing the two maxima at 1170°C (maximum 07) and 1198°C (maximum ee). The hquidus curve has been taken fiom [1984Sch] who presented more careful and more precise data compared to [1968Pat]. The Fe rich part of the isopleth has been modified to be in agreement with the accepted hquidus surface. 

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