Abstract: The microstructure of various compounds of the Ti-Ni-Au alloy system is investigated by transmission electron microscopy in relation with changing lattice parameters improving the compatibility conditions between austenite and martensite expressed by the lambda(2) = 1 equation based on the Geometrically NonLinear Theory of Martensite (GNLTM). Although local differences in microstructure are observed, when increasing the gold content compound twins are replaced by Type I twins, while twinned lamellar structures are replaced by untwinned plates and self-accommodating structures when lambda(2) = 1 is approached, all confirming the predictions of the GNLTM. (c) 2013 Elsevier B.V. All rights reserved.