3D strain fields surrounding Ni₄Ti₃: direct measurement and correlation with the R-phase.

Abstract
Strain fields introduced by coherent Ni₄Ti₃ precipitates in austenitic Ni-Ti are believed to be a possible origin of why the R-phase transformation is introduced as an extra step before transforming to the B19'. The presence of this strain field was already confirmed in the past by conventional transmission electron microscopy (TEM) techniques and measured quantitatively by high resolution TEM (HRTEM). This time the geometrical phase method is applied on HRTEM micrographs to measure the full 3D strain tensor of the strain fields. Since each atomic resolution micrograph only results in a 2D measurement of the strain, observations in two different zone orientations are combined to retrieve the 3 × 3 strain tensor. In this work observations in a [1-1 1]_B2 and [1 0-1]_B2 zone orientation are used and this in case of precipitates with a diameter of around 50nm. In a next step the measured strain tensor is compared to the calculated eigenstrain of the R-phase in reference to the B2 matrix. This comparison shows that the introduced strain is very similar to the eigenstrain of one R-phase variant. Since for both structures, Ni₄Ti₃ and Rphase, four orientation variants are possible, each variant of the R-phase is thus able to accommodate the strain field of one of the Ni₄Ti₃ variants.