(Color online) Schematic of (a) dislocation loops comprising an IKB; (b) schematic of what could be occurring below the indented surface. The emission of mobile dislocation walls that, in turn, form kink boundaries, are shown. Upon re-loading, the IKBs form within the kink boundaries or twins formed during the pop-in events. (c) Typical stress-strain curve for a KNE solid obtained under spherical nanoindentations, showing the definition of non-linear strain, ɛ NL, and the energy dissipated per unit volume per cycle, Wd.
(Color online) Typical NI load-displacement curves when an unirradiated C-plane LiTaO3 single crystal is loaded 20 times to 550 mN with the 21 μm radius indenter. Note presence of small pop-ins. Bottom right inset shows the same plot for the 5 μm radius tip loaded twenty times to 100 mN. In both cases, for clarity’s sake, only a few cycles are plotted.
(Color online) Load-displacement cycles 2, 3, 6, 10, 15, and 20 obtained when the 21 μm tip was indented along the  into an irradiated surface. The curves were shifted to the right from their original position for clarity. Cycles 2 and 3 are open; cycles 6 to 20 are closed and equal in area. Re-loading to a lower load after loading to the maximal load always results in closed, reversible nested loops, shown for cycle 2 only. Inset plots the corresponding load-displacement loops’ areas vs cycle number obtained with the 21 μm tip on an unirradiated surface. After about 6 cycles, the areas are constant.
(Color online) (a) The S vs a curves for the 1.4 μm and 5 μm tips. (b) Typical NI stress–strain curves obtained after a given location was indented to the highest loads (550 mN for 21 μm, 100 mN for 5 μm, and 20 mN for 1.4 μm tips) for two cycles, unloaded and progressively loaded to higher stresses to obtain the nested loops (three left curves). Plot shown on extreme right shows the reproducible NI stress-strain loops for 1.4 μm indenter; it was shifted to the right from its original position for clarity. Dashed horizontal and inclined lines represent the Vickers microhardness, Berkovich hardness, and elastic moduli obtained from the S vs a curves, respectively. Pop-ins were only observed when the 21 μm tip indenter was used.
(Color online) Plot of Weibull probabilities (SP) vs pop-in stresses (σ) for 21 μm indenter for both unirradiated and irradiated samples. The Weibull moduli, m, are shown on the figure.
(Color online) Plots of (a) Wd vs σ 2 and (b) Wd vs ɛNL as a function of indenter radius. The slope dependence on the tip size is clear in (b). Each line represents a different location.
(Color online) SEM images of NI mark on unirradiated sample made with the (a) 1.4 μm tip loaded to 20 mN after first cycle, (b) 5 μm tip loaded to 100 mN after first cycle, and 21 μm tip loaded to 550 mN after (c) 5 cycles and (d) 20 cycles; (e) same as (d) but tilted 75°. Note three-fold symmetry of the linear surface features best seen in (b) and (c). The top inset in (a) is a schematic of domains forming in the twins. Top inset in (b) shows three-fold symmetry of twins, which form in LiNbO3, adapted from Ref. 48. The features with very sharp radii of curvature in (d) and (e) are kink boundaries.
(Color online) RBS spectra from unirradiated random, unirradiated aligned, and irradiated aligned. The χ min = l.5% (ratio of aligned to random yield just below the surface peak) indicated very good quality of the unirradiated sample. The aligned spectrum did not change after irradiation because the concentration of defects in the near surface region is quite small.
(Color online) Hall-Petch-like correlation between the CRSS of the IKB dislocations (Ω/b) and 1/√domain size, where the domain size is assumed to be 2α, 2β, or R. The black dashed inclined line represents Ω/b vs 1/√R for LiNbO3 (see Ref. 25).
Summary of various measured and calculated parameters as a function of R. The following was assumed: γ = 0.05, w = b = 0.515 nm, G = 96.8 GPa, ν = 0.25, M = 2, and k1 = 2.
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