The size of the hysteresis measured during temperature-induced or stress-induced transformation is a critical

parameter governing many applications, such as actuators and medical devices.  A set of criteria governing the

hysteresis of shape memory materials is derived from the Geometrically Nonlinear Theory of Martensitic

Transformations. The theory indicates that alloys with lattice parameters satisfying these criteria will have the

smallest hysteresis. A systematic experimental program on the TiNiX (X = Cu, Pd, Pt, Au, Hf, Zr) system is conducted

to search for the alloys satisfying the proposed criteria.  The ranges of composition in the TiNiX alloys with

special lattice parameters are located, and the relation between the lattice parameters and hysteresis predicted by

the theory is verified. The results of this experimental study show that the criteria are excellent guides for the

development of shape memory alloys with low hysteresis and also long fatigue life.