Exsolution by spinodal decomposition in multicomponent mineral solutions

Abstract

Phase separation in a three-component system that results from the uphill diffusion of chemical components is considered. The binary decomposition model of Cahn and Hilliard is generalized to account for the interdiffusion of several chemical components with considerably different diffusion constants. Thereafter the decomposition dynamics and the phase relations of the final system state are investigated by means of finite-element modeling. Examples from a hypothetical regular solution and from ternary feldspar are addressed. Special attention is given to situations in which different diffusivities affect decomposition dynamics and the final system states. Good qualitative agreement between our modeling and petrographic observations on exsolved feldspar is achieved. Our model explains systematic deviations from equilibrium element partitioning between the two phases exsolving from an initially homogeneous ternary feldspar during slow cooling.

Sodium-potassium interdiffusion in potassium-rich alkali feldspar I: Full diffusivity tensor at 850 C

“…In the context of homogenization experiments on synthetic and natural cryptoperthite Brady and Yund (1983) remarked that considerable composition dependence of the interdiffusion coefficient may be expected at physical conditions where a solid-solution deviates significantly from a thermodynamic ideal solution. This notion is also inherent in exsolution by spinodal decomposition and can be predicted from theoretical considerations Abart, 2009, 2012). It is also manifest in equation (1), in which the expression in parentheses corresponds to the "thermodynamic term" accounting for the non-ideality of the solution phase.…”

“…The interdiffusion of Na ϩ and K ϩ on the alkali sublattice plays a pivotal role in the re-equilibration of Na-K partitioning between alkali feldspar and other Na-and K-bearing minerals in rocks undergoing pressure-temperature change (Voll and others, 1994). Knowledge of Na-K interdiffusion in alkali feldspar is crucial for the application of geo-thermobarometers such as the two feldspar thermometer (Fuhrman and Lindsley, 1988;Benisek and others, 2010) and for quantifying the kinetics of exsolution during cooling (Yund, 1984;Petrishcheva and Abart, 2009;Abart and others, 2009b;Abart and others, 2009a;Petrishcheva and Abart, 2012).…”

Thermodynamic stability, phase separation and Ag grading in (Ag,Cu)(In,Ga)Se2 solar absorbers

“…We consider ACIGS as a substitutional alloy within the regular solution model, [34][35][36] which denes the free energy of mixing as G mix ¼ H mix À TS mix , where H mix is the mixing enthalpy for the studied system, S mix is the congurational entropy of mixing for ideal solution, and T is the temperature. For a binary alloy, the mixing enthalpy is equivalent to the bowing parameter (parabolic t) of the formation energy versus composition that can be computed using rst-principles methods.…”

“…To assess thermodynamic stability, binodal lines were calculated from the common tangent construction; 35,36 in this conception, an alloy with a given composition (x, y) is stable if a tangent plane to the free energy surface DG(x,y) at the given composition point does not cross the surface at any other composition. The spinodal curve for the alloy was constructed by solving the following equation:…”

Lattice strain across Na–K interdiffusion fronts in alkali feldspar: an electron back-scatter diffraction study

“…Chemical alteration of alkali feldspar in the solid state requires the interdiffusion of and and potentially substituting minor components on the respective sublattice. Na–K interdiffusion is relatively rapid (Cherniak 2010 ), and Na–K cation exchange reactions involving alkali feldspar, such as the two feldspar thermometer (Benisek et al 2004 ), and the compositions of the albite- and orthoclase-rich phases in a perthite (Yund 1984 ; Abart et al 2009 ; Petrishcheva and Abart 2012 ) are prone to re-equilibration during slow cooling. Quantification of these potential effects requires knowledge of the Na–K interdiffusion coefficient in alkali feldspar.…”