Blocking of the martensitic transition at the nanoscale in a ${\mathrm{Ti}}_2\mathrm{NiCu}$ wedge

Shape memory effect associated with martensitic transformations is a rapidly developing field in nanotechnologies, where industrial use of systems established on that effect provide greater flexibility on the nanodevice fabrications of various kinds. And therefore it addresses questions to the phase transition phenomena at low scale and its limitations and control. In this report we studied the crystal structure of tapered plates of ${\mathrm{Ti}}_2\mathrm{NiCu}$ alloy and the temperature $T_c$ at which the martensitic transition occurs. We demonstrated that $T_c$ has a strongly descending character as a function of the plate thickness $h$. The critical thickness value at which the transition is completely suppressed is 20 nm. Moreover, the obtained results for $T_c\left(h\right)$ curves indicate the hysteretic nature of the transition. These findings open the pathway for size limit indications and regime modulations where the alloy-based nanomechanical devices can be tuned to operate more efficiently.

Figure 1

(a) Microphotographs and microdiffraction of ${\mathrm{Ti}}_2\mathrm{NiCu}$ ribbons in the amorphous state and annealed ribbon in the crystalline state (martensite phase at room temperature). Yellow and green colors indicate amorphous and crystalline bulk phases correspondingly. This ribbon was thinned later using the argon ion polishing of focused ion beam specimens in the precision ion polishing system (PIPS) method. (b) High-resolution microphotographs of the wedge local areas in the imaging and in the diffraction mode at room temperature immediately after applying PIPS.

Figure 2

Microphotographs obtained using TEM in the fixed area of the ${\mathrm{Ti}}_2\mathrm{NiCu}$ wedge sample, near the edge of the sample at different temperatures. The transition boundary between phases is clearly visible and indicated by the red-orange line. The blue arrow corresponds to the cooling process (snowflake symbol), while the red arrow indicates temperature change during the heating process (flame symbol).

Figure 3

(a) TEM microphotograph of the studied ${\mathrm{Ti}}_2\mathrm{NiCu}$ ribbon where a wedge-shaped plate is indicated by the light-green color. The wedge boundaries are indicated by the red-dashed line next to the platinum substrate (bluish color) and amorphous phase. (b) The local area of the wedge-shaped part of a sample made using the focused ion beam (FIB) method and loaded into the TEM to examine its cross section. To prevent the destruction of the surface by an ion beam, the sample was initially coated with a protective film of platinum of 400 nm thickness. The dark area in the upper part of the photo above the wedge-shaped sample is a protective film of platinum.

Figure 4

Dependence of the martensitic transformation temperature on the plate thickness both for cooling and heating processes. Schematic representation of embedded nanocrystal of martensitic phase into a parent austenitic phase. Unit cell of $B2$ and $B19$ phases where red arrows indicate correspondence in the lattice parameters between two phases. The dashed green line represents the result of the dislocation-kinetic approach. The red-orange arrows indicate the relation between lattice parameters for the parent and daughter phases according to the Bain transformation. The inset indicates a zoomed region of the graph between 280 and 340 K where the main part of hysteresis is situated.

Figure 5

Calculated phonon spectra of the $B2$ ${\mathrm{Ti}}_2\mathrm{NiCu}$ phase using DFPT method. Imaginary frequencies of unstable modes are plotted as negative values, and the mode responsible for the $B2$ to the $B19$ transition is marked by the red arrow at the bottom. The corresponding acoustic phonons mode is shown on the right side where light-gray arrows indicate normalized atoms displacements in the $B2$ unit cell. Ti atoms in the cubic cell are marked with light-blue balls, while the virtual Ni/Cu atom is indicated by the small black ball.