Binary joins

If we consider the seven components in tables 5.12 and 5.13 as representative of the chemistry of natural olivines, it is clear that 21 regular binary interaction parameters (disregarding ternary and higher-order terms) are necessary to describe their mixing properties, through a combinatory approach of the Wohl or Kohler type (cf section 3.10). In reality, the binary joins for which interactions have been sufficiently well characterized are much fewer. They are briefly described below. 

Figure 5.11 Gibbs free energy of mixing in binary join Mg2Si04-Ca2Si04 dXT = 600 °C and P = bar, calculated with a static interionic potential approach. Reprinted from G. Ottonello, Geochimica et Cosmochimica Acta, 3119-3135, copyright 1987, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Figure 5,17 Enthalpic interactions in the various binary joins of aluminiferous garnets. calorimetric data results of interionic potential calculations. The corresponding subregular Margules interaction parameters are listed in table 5.26 (from Ottonello et al., in prep.).

Figure 5,27 Phase stability relations along binary join CaFeSi206-Fe2Si206 under various P conditions. From Lindsley (1982). Reprinted with permission of The Mineralogical Society of America.

For the binary join CaFeSi206-Fe2Si206, Lindsley (1981) proposed a thermo-... 

Figure 5.41 G-X diagram illustrating application of Darken s Quadratic Formalism to a binary join. Although mixing behavior of components 1 and 2 in phases a and ]8 is nonideal (heavy lines), in each of the simple regions it is modeled by an ideal mixing model (light lines) by means of an appropriate choice of the Active standard state potential /x. From Will and Powell (1992). Reprinted with permission of The Mineralogical Society of America.

Figure 5,59 Effects of structural and coherence state on extent of unmixing in the NaAl-Si308-KAlSi30g binary join. (A) Maximum microcline-low albite, based on data from Bachinski and Muller (1971) and Yund (1974). (B) Sanidine-high albite, based on data from Thompson and Waldbaum (1969) and Sipling and Yund (1976).

Table 5.66 Margules subregular parameters for the NaAlSi30g-KAlSi308 (Ab-Or) binary join (Ganguly and Saxena, 1987). (1) Brown and Parson (1981) (2) Thompson and Waldbaum (1969) (3) Hovis and Waldbaum (1977), Thompson and Hovis (1979) (4) Haselton et al. (1983). Note that Wn = TWs,u + Pf Ki2andG,essm mg = XiZ2(fPi2X2 +...

On the basis of the experimental data of Lindsley and Dixon (1976) on the CaMgSi20g-Mg2Si205 binary join and accounting for the observed compositions of natural pyroxenes coexisting at equilibrium, Kretz (1982) proposed two empirical thermometric equations applicable to clinopyroxene and valid, respectively, for T > 1080 °C and T < 1080 °C ... 

Figure 6.9 shows how the calculated phase boundaries compare with the experimental observations of Bowen and Schairer (1935) on the same binary join. The satisfactory reproduction of phase assemblages clearly indicates that the... 

Figure 7.5 Phase stability relations in binary join CaAl2Si208-NaAlSi308 (anorthite-albite).

Figure 7.10 Phase stability relations in a ternary system in which components are totally immiscible at solid state, and relationships with three binary joins.

S. Sen, H. Maekawa and G. N. Papatheodorou, Short-range structure of invert glasses along the pseudo-binary join MgSi03-Mg2Si04 results from Si and Mg MAS NMR spectroscopy. /. Phys. Chem. B, 2009,113,15243-15248. 

Fig. 5.10. Calculations of the properties of olivine solid solutions (see Ottonello, 1987, for full details and data sources) (a) Calculated phase field boundaries in the system (Mn,Mg),Si04 full circles are calculated boundaries, dashed curves are extrapolated, dotted lines are experimental solubility gap. (b) Plot of site occupancy versus molar composition along the binary join (Ni,Mg)2Si04-...

Kihlborg and Gebert 1970). As with wolframite, the sanmartinite structure belongs to space group P2/c, but that for cuproscheelite is 1. Nevertheless, these minerals exhibit complete solid solution across the binary join (Schofield and Redfem 1992). Explorations of the transition behavior in this system are motivated by their technological potential. Cuproscheelite is an -type semiconductor with possible uses as a photoanode, and sanmartinite may serve as a high Z-number scintillator (Doumerc et al. 

To determine whether titanium substitution would occur in the presence of excess antimony, catalyst 9 (Table I) was prepared as described in a Distillers patent (JL ), while catalyst 10 was prepared by our standard coprecipitation method. Small, amounts of Ti02 could be detected in both catalysts. Catalyst 9, which was calcined at a lower temperature than catalyst 10, contained USbO in addition to Ti02 The shift in d-spacing for the 004 reflection noted with the titanium-substituted phases was not seen for catalysts 9 and 10. Thus, the presence of excess antimony appeared to inhibit titanium substitution. These compositions were well above (on the excess antimony side) the binary join expected to facilitate titanium substitution for antimony. 

The number of components C is the minimum number of constituents needed to fully describe the compositions of all the phases present. When one is dealing with binary systems, then perforce the number of components is identical to the number of elements present. Similarly, in ternary systems, one would expect C to be 3. There are situations, however, when C is only 2. For example, for any binary join in a ternary phase diagram the number of components is 2, since one element is common. 

Two coexisting, non-colinear binary solutions, a(l-2) and b(l-2), form a ternary reciprocal system at 650°C and 2000 bars. At this temperature and pressure there is not ternary solution away from the binary joins. The following values have been determined for the Margules parameters of solutions a and b ... 

To extract the fugacity or activity of a species in a two component system (such as C02 H20) using P-V-T methods requires measurement of several different compositions alorig the binary join. That is because the partial molar voliame (V.) in equation (2) can only be obtained by taking the slope of the mean molar voliame vs composition curve. Because the P-V-T measurements must... 

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