To better quantify the longitudinal

To better quantify the longitudinal compressive strains developed during the cold sintering process with water, we evaluate in more details the displacement gradients formed within the wet specimen pressed at 500 MPa. Longitudinal strains are directly obtained from the slope of the line fitted to the z displacement value, , when plotted against the height (z) of the sample: . Using this fitting approach, strain data at selected radial positions at the center and edges of the compact were derived from the reconstructed tomographs (Fig. 4c). The slopes of the fitted data show that the wet samples subjected to 500 MPa reach longitudinal strain values as high as 2% and 3% at the edge and close to the center of the compact, respectively. The lower strain at the edge of the compact may result from the friction of the powder that is located closer to the walls of the alumina die. The observed difference in compressive strain leads inevitably to a densification gradient between the center and the edge of the compact. Taking the experimentally-measured relative density of 79% at the beginning of the stress relaxation test, we estimate the relative densities at the center and at the edge of the compact to reach, respectively, 81% and 82% at the end of the experiment.