Anisotropic diffusion is described by a tensor of diffusivities, D_αβ, which may be composition dependent leading to nonlinear anisotropic diffusion. In this work the practical problem of reconstructing such a tensor for Na-K interdiffusion in potassium-rich alkali feldspar in the composition range 0.85 ≤ X_Or ≤ 1.00 is addressed. Gem quality sanidine with an initial composition of X_Or = 0.85 was exchanged with KCl salt melt at 850 °C and ≈1 bar. The diffusivity tensor D_αβ(X_Or) and its composition dependence was reconstructed from composition profiles produced by cation exchange in six different crystallographic directions using a generalization of the Boltzmann approach. Na-K interdiffusion in potassium-rich alkali feldspar is considerably anisotropic and composition dependent. The principal axes of the diffusivity tensor representing the directions of highest and lowest diffusivity lie in the a-c plane with highest diffusivity parallel to the [101] direction, lowest diffusivity perpendicular to the (101̄) plane, and the direction with intermediate diffusivity parallel to the crystallographic b-axis. All diffusivities D_αβ(X_Or) increase as X_Or tends to unity. Our main result is given in the form of numerical values for all components of the D_αβ(X_Or) tensor for 0.85 ≤ X_Or ≤ 1.