Activity-composition relationships

In order to derive activity-composition relationships for ThMgAl206 in clinopyroxene, Landwehr et al. (2001) used a mixing-on-sites model assuming complete short-range order between M and T sites. The activity of ThMgAl206 in clinopyroxene is thus given by ... 

Horita J, Wesolowski DJ, Cole DR (1993a) The activity-composition relationship of oxygen and hydrogen isotopes in aqueous salt solution 1. Vapor-liquid water equilibration of single salt solutions for 50 to 100°C. Geochim Cosmochim Acta 57 2797-2817... 

It can easily be deduced from equations 3.147 and 3.148 that the activity-composition relationships for the two components are symmetric in the compositional field (see also figure 3.9C). 

Hensen B. I, Schmid R., and Wood B. J. (1975). Activity-composition relationship for pyrope-grossular garnet. Contrib. Mineral Petrol, 54 161-166. 

Horita X, Wesolowski D. X, and Cole D. R. (1993a). The activity-composition relationship of... 

Koziol A. M. (1990). Activity-composition relationship of binary Ca-Fe and Ca-Mn garnets determined by reversed, displaced equilibrium experiments. Amer. Mineral, 75 319-327. 

Will T. M. and Powell R. (1992). Activity-composition relationships in multicomponent amphi-boles An application of Darken s quadratic formalism. Amer. Mineral, 77 954-966. 

In the rough experimental space the distance between discrete levels of the experimental variables is relatively large. After testing three - four catalyst generations different Data Processing methods, such as general statistical approaches or Artificial Neural Networks (ANNs), can be applied to determine the contribution of each variable into the overall performance or establish the Activity - Composition Relationship (ACR). 

As emerges from Figures 1 all variables have six concentration levels, i.e. the total number of combinations in this experimental space is 1296. The activity of samples above 89 % conversion is shown by a white color, while that of below 50 % is shown by black. The maximum value of conversion is shown by a cross. The analysis of these holograms shows the following activity composition relationship ... 

Refinement, i.e., establishment of the activity - composition relationship by using ANNs as an information mining tool ... 

Reversibility has been demonstrated by the repeated appearance on a single curve of points obtained nonconsecutively, the appearance of consecutive points attributable to a single curve in which there is reversal of direction with respect to composition during the series, the fact that the system can be maintained within a given activity-composition relationship for days and then moved rapidly to a new relationship in which it is equally stable, the fact that the same family of activity-composition relationships can be rediscovered repeatedly as shown in Figure 2, and the fact that the system has returned repeatedly to the upper structure of Figure 1 with its broad solid solubility range. 

The above case was OK for approximate calculations, but not for precise calculations. It was found that activity-composition relationship was rarely linear up to 1 weight % of the constituent. 

Although there is no general model for activity-composition relationships in silicate melts, several studies have shown that, under certain circumstances, a semi-empirical approach works reasonably well. Blundy et al. (1995) investigated the partitioning behavior of sodium between clinopyroxene and silicate melts over wide ranges of pressure and temperature. They showed that the crystal-liquid partition coefficient Dfja bears a very simple relationship to the equilibrium constant Xj,ja for the melting reaction ... 

R (D), and aqueous phase pH (E) on the KGF activity upon liberation from a series of BP-based films. These results provide a roadmap that delineates activity-composition relationships over a wide range of formulation chemistry. In addition, these results revealed that the use of a binary polymer mixture in concert with AOT surfactants yielded materials that were capable of delivering up to 60% active KGF. As a benchmark, the standard approach of sequestering KGF directly within a PLA-based BP yielded <4% active KGF.70... 

Koziol AM (1996) Quaternary (Ca-Fe-Mg-Mn) garnet Displaced equilibrium experiments and implications for current garnet mixing models. Eur J Mineral 8 453-460 Koziol AM, Newton RC (1989) Grossular activity-composition relationships in ternary garnets determined by reversed displaced-equilibrium experiments. Contrib Mineral Petrol 103 423-433 Kretz R (1983) Symbols for rock-forming minerals. Am Mineral 68 277-279... 

Powell, R., 1977, Activity-composition relationships for crystalline solutions, in D.G. Fraser, ed.. Thermodynamics in Geology Boston, Reidel, pp. 57-65. 

The first object of this paper is to review the general approach to determining activity-composition relationships for binary and ternary solid solutions. The latter part of the paper will be devoted to some new and recently published results on garnet and alimiinous clinopyroxene solutions. 

Experimental determinations of activity-composition relationships may be broadly grouped into those in which the activity of i, ai is varied by varying the bulk composition of the system at constant P and T and those in which this variation is produced by varying one of the intensive parameters at constant bulk composition. 

Fig. 2. Activity-composition relationships for sanidine-high albite solid solutions at TOQOC.

These authors determined the empirical partition coefficient K], and, since activity-composition relationships were available for MgO-FeO oxide solutions were able to obtain t-Qn... 

The principal problem associated with the determination of the mixing properties of aluminosilicate garnets is that most of the solutions involved are stable only at high pressures. The apparatus used in experimental studies at these pressures does not, of course, enable as accurate a control of the intensive variables as is possible at 1 atmosphere. Nevertheless, activity-composition relationships determined at high pressures need not necessarily have extremely large uncertainties provided that the equilibria used to fix activities are carefully chosen. 

Newton (accompanying paper) has found positive values of for this solid solution series, confirming the general form of the activity-composition relationships discussed here. It is doubtful, however, whether calorimetric results on the solid solutions provide a good constraint on the standard state data because of lack of knowledge of excess entropy contributions to G . The author s results on Ca0-Al203-Si02 lead him to prefer the upper curve for G s in Fig. 7 and lower activity curves in Fig. 6. 

Values of can, in principle, be determined calormetrically and the expression of activity-composition relationships for components in mineral solid solutions has been discussed in previous chapters. Moreover many of the components which have been shown to influence the crystallization behaviour of rockforming minerals (e.g. H2O, CO2, K2O, P2O5) have such small solubilities in the solid phases that the activities of the mineral components in the solid state will be almost unaffected by varying amounts of H2O, CO2, K2O etc. in a system. 

The book begins with a chapter on calorimetry (Navrotsky) followed by two chapters on the experimental determination of activity-composition relationships of mineral solid solutions by phase equilibrium experiments (Wood) and by high temperature solution calorimetry (Newton). After chapters on the nature of activity-composition relationships (Powell) and the expression of non-ideal behaviour using Margules equations (Grover), a review of experimental techniques available for determining site occupancy is given (Whittaker). 

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