Nonhysteretic Superelasticity of Shape Memory Alloys at the Nanoscale

We perform molecular dynamics simulations to show that shape memory alloy nanoparticles below the critical size not only demonstrate superelasticity but also exhibit features such as absence of hysteresis, continuous nonlinear elastic distortion, and high blocking force. Atomic level investigations show that this nonhysteretic superelasticity results from a continuous transformation from the parent phase to martensite under external stress. This aspect of shape memory alloys is attributed to a surface effect; i.e., the surface locally retards the formation of martensite and then induces a critical-end-point-like behavior when the system is below the critical size. Our work potentially broadens the application of shape memory alloys to the nanoscale. It also suggests a method to achieve nonhysteretic superelasticity in conventional bulk shape memory alloys.

Figure 1

(a) The relation between martensitic transformation and particle diameter ($D$). The dashed line indicates the border for nonhysteretic superelasticity obtained from Eq. (3). (b) and (c) The lattice correspondence between the parent phase and martensite. (d) Stress-strain curves of particles at 300 K with (d1) $D=2.0\mathrm{nm}$, (d2) $D=3.4\mathrm{nm}$, and (d3) $D=8.6\mathrm{nm}$. Inset shows the stress-strain curves of particles at 900 K with (d4) $D=3.0\mathrm{nm}$ and (d5) $D=8.6\mathrm{nm}$.

Figure 2

(a) The relation between principal distortions (${\eta }_1$, ${\eta }_2$, and ${\eta }_3$) and loading direction. (b) Principal distortions as a function of compressive strain for the particle with $D=3.4\mathrm{nm}$. (b1)-(b4) Corresponding microstructures at strain of 2.82%, 5.67%, 7.78%, and 9.89% upon loading. (c) Principal distortions as a function of compressive strain for the particle with $D=2.0\mathrm{nm}$. (c1)-(c4) Corresponding microstructures at strain of 3.1%, 6.0%, 7.42%, and 8.05% upon loading. Atoms are colored by ${\eta }_1-{\eta }_3$, where ${\eta }_1-{\eta }_3=0$ represents elastic distortion; ${\eta }_1-{\eta }_3>0$ represents inelastic distortion to the orthorhombic phase.

Figure 3

Spatial distribution of orthorhombic lattice distortion ${\eta }_1-{\eta }_3$ upon loading in particles with (a) $D=2.0\mathrm{nm}$ and (b) $D=3.4\mathrm{nm}$.

Figure 4

(a) Free energy landscape of nanosized SMAs with interior and surface regions. $P$ represents the parent phase; $M$ and $M^{\prime }$ represent martensite. (b1), (b2), and (b3) Free energy curves of particles at 300 K with $D<D_c$, $D\sim D_c$, and $D>D_c$. (c1), (c2), and (c3) Corresponding tilted free energy curves upon loading. (d1), (d2), and (d3) Corresponding stress-strain curves obtained by taking variation of their free energy curves with respect to the order parameter $e$ [30].