Stress and strain in cryptoperthite lamellae and the coherent solvus of alkali feldspars

Transmission electron microscope observations of a cryptoperthitic alkali feldspar from Larvik (Norway) show that the exsolution lamellae are fully coherent, that is, they maintain full continuity of their lattices across the lamellar interfaces; this confirms X-ray work by previous authors on other crytoperthites.

Coherency imposes elastic strains in individual lamellae, causing the lattice parameters to differ from those of unstrained crystals of the compositions. From known elastic constants and known compositional variation of stress-free lattice parameters, elastic strain and stress components in a lamella are calculated as linear functions of (X-X°) (where X = mole fraction KAlSi₃O₈; X° = average value for bulk crystal). The assumption that elastic strain entails no volume change and the resulting method of determining compositions of individual lamellae (Smith, 1961) can therefore be evaluated; an alternate simple method is proposed, which makes use of the fact that there are linear combinations of two ((h0l)) spacings which are not affected by the elastic strain.

The elastic strain energy varies as (X-X°)². When strain energy is takeninto account in the thermodynamic treatment of exsolution, a 'coherent solvus' can be calculated, with a crifical temperature 70° to 85°C below the critical temperature of the solvus for unconstrained phases (e.g., Luth and Tuttle, 1966). This agrees well with the hitherto unexplained results of annealing experiments on single crystals by Tuttle and Bowen (1958) and Smith and MacKenzie (1958).

Lamellar exsolution occurs in many other mineral systems. If the lamellae have retained coherency, the relevant phase diagram is the coherent solvus, not the unconstrained one determined in hydrothermal experiments. Other transformations within crystals may also give rise to elastically strained phases coexisting along coherent interfaces. The corresponding strain energy must be taken into account in the thermodynamic analysis and the geologic interpretation of such transformations.