Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain.

Ni-Ti is one of the most popular shape-memory alloys, a phenomenon resulting from a martensitic transformation. Commercial Ni-Ti-based alloys are often thermally treated to contain Ni(4)Ti(3) precipitates. The presence of these precipitates can introduce an extra transformation step related to the so-called R-phase. It is believed that the strain field surrounding the precipitates, caused by the matrix-precipitate lattice mismatch, lies at the origin of this intermediate transformation step. Atomic-resolution transmission electron microscopy in combination with geometrical phase analysis is used to measure the elastic strain field surrounding these precipitates. By combining measurements from two different crystallographic directions, the three-dimensional strain matrix is determined from two-dimensional measurements. Comparison of the measured strain matrix to the eigenstrain of the R-phase shows that both are very similar and that the introduction of the R-phase might indeed compensate the elastic strain introduced by the precipitate.