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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.

Fracturing in alkali feldspar during Na + -K + cation exchange with a NaCl-KCl salt melt was studied experimentally. Due to a marked composition dependence of the lattice parameters of alkali feldspar, any composition gradient arising from cation exchange causes coherency stress. If this stress exceeds a critical level fracturing occurs. Experiments were performed on potassium-rich gem quality alkali feldspars with polished ( 010) and ( 001) surfaces. When the feldspar was shifted towards more sodium-rich compositions over more than about 10 mole %, a system of parallel cracks with regular crack spacing formed. The cracks have a general (h0l) orientation and do not correspond to any of the feldspar cleavages. The cracks are rather oriented (sub)-perpendicular to the direction of maximum tensile stress. The critical stress needed to initiate fracturing is about 325 MPa. The critical stress intensity factor for the propagation of mode I cracks, K Ic , is estimated at 2.30 to 2.72 MPa m 1/2 (73 to 86 MPa mm 1/2 ) from a systematic relation between characteristic crack spacing and coherency stress. An orientation mismatch of 18 o between the crack normal and the direction of maximum tensile stress is ascribed to the anisotropy of the longitudinal elastic stiffness which has pronounced maxima in the crack plane and a minimum in the direction of the crack normal.

Na-K interdiffusion in disordered potassium-rich alkali feldspar was studied experimentally using cation exchange between gem quality sanidine from the Eifel and alkali-halide melt at temperatures of 800°C to 1000°C and at close to ambient pressure. Sodium-potassium interdiffusion coefficient D NaK was determined for potassium mole fractions in the range 0.65 < X Or < 0.99. At 0.65 < X Or < 0.95 the sodium-potassium interdiffusion coefficient is largely independent of composition. At X Or > 0.95, it rises sharply with increasing potassium mole fraction. Diffusion perpendicular to (001) is about one order of magnitude faster and less strongly temperature dependent than perpendicular to (010). The parameters of the Arrhenius equation describing the temperature dependence of the sodium-potassium interdiffusion coefficient D NaK ‫؍‬ D 0 Exp (؊E A /RT) were estimated as D 0 Ќ(001) (0.92) ‫؍‬ 5.18 ⅐ 10 ؊8 m 2 /s, E A Ќ(001) (0.92) ‫؍‬ 179kJ/mole D 0 Ќ(001) (0.98) ‫؍‬ 1.82 ⅐ 10 ؊7 m 2 /s, E A Ќ(001) (0.98) ‫؍‬ 182kJ/mole D 0 Ќ(010) (0.92) ‫؍‬ 5.81 ⅐ 10 ؊5 m 2 /s, E A Ќ(010) (0.92) ‫؍‬ 272kJ/mole D 0 Ќ(010) (0.98) ‫؍‬ 1.34 ⅐ 10 ؊4 m 2 /s, E A Ќ(010) (0.98) ‫؍‬ 269kJ/moleThe results of our direct determinations are compared with theoretical calculations using the corresponding sodium-and potassium tracer-diffusion coefficients, and the processes underlying the observed composition-and temperature dependence of sodium-potassium interdiffusion are discussed.