(Color online) Schematics of a tetragonal unit cell (green lines) and four cubic unit cells (black lines) in the lattice of untransformed B2 parent phase. Only Ni atoms are shown for clarity. The orthonormal vectors are along the cube axes, and the orthonormal vectors are along the cube directions of , , and , respectively.
(Color online) Relaxed atomic structures of single phase, equiatomic NiTi, viewed from the  direction in the basis of Fig. 1. (a) B2 phase, the rectangle indicates a tetragonal unit cell. (b) B19′ phase, the parallelogram indicates a monoclinic unit cell with the monoclinic angle . (c) Base-centered orthorhombic (BCO) phases, the rectangle (white lines) indicates a BCO unit cell; the BCO structure can also be considered as a twinned B19′ and each variant consists of one layer of monoclinic unit cell (green lines) with .
(Color online) Relaxed structures of compound twins. The mirror twin plane (dashed line) is located on (a) the pure Ni laden layer and (b) the pure Ti layer, respectively.
(Color online) Relaxed structures of (010) compound twins. The mirror twin plane (dashed line) is located (a) off the (010) atomic planes, and (b) on the (010) atomic plane. The front atomic layer in (b1) and (b2) exposes one of the two different (100) atomic planes of the same relaxed structure. The white unit cell of Ti atoms in (b1) and that of Ni in (b2) straddle the twin plane (dashed line), respectively, and remain the rectangular shape.
(Color online) Atomistically simulated twin structures with different twin widths, i.e., each green-colored twin variants comprises (a) two, (b) three, or (c) six layers of monoclinic unit cells. Black lines are drawn for guiding eyes, equivalent to the white lines in the TEM image by Waitz et al. (Fig. 2 in Ref. 26).
(Color online) Relaxed atomic structures of twins with the smallest thickness (about 0.5 nm), and each variant consists of one layer of monoclinic unit cells, i.e., two atomic planes. (a) Schematics of four sets of interpenetrating simple orthorhombic sublattices. One Ni sublattice is represented by a 3D green box, and the other Ni sublattice is indicated by a 2D pink rectangle instead of a 3D box for clarity. The two Ti sublattices are indicated by the orange and blue rectangles, respectively. (b) All sublattices are twinned, as indicated by the sheared unit cells. (c) A subset of interpenetrating sublattices is twinned. The front atomic layer of (c1) and (c2) exposes one of the two different (100) atomic planes, respectively. The Ni sublattice in (c1) and Ti sublattice in (c2) are twinned.
(Color online) MD simulation of phase transformation for different sizes of the simulation box. (a) The order parameter W as a function of temperature T for three stages of temperature loading: (I) heating (blue), (II) cooling (black), and (III) reheating (red). Symbols represent time-averaged values and lines are drawn to guide eyes. (b) The monoclinic B19′ phase at the beginning of stage I of heating. (c) The cubic B2 phase at the end of stage I of heating. (d) The B19′ phase at the end of stage II of cooling, forming nanotwins indicated by dashed lines. (e) Same as (a) except that the volume is 1/8 of that in (a). (f) Same as (a) except that the volume is 8 times of that in (a).
(Color online) Illustration of shear transformation and the rotation of the mirror twin plane during the formation of and compound twins. (a) The (010) mirror twin plane (in blue) is unrotated after the shear transformation of the red rectangle to green parallelogram in the plane along the direction. (b) The (001) mirror twin plane (in blue) is rotated after the same shear transformation as (a). (c) The (001) mirror twin plane (in blue) is unrotated after the shear transformation of the red rectangle to green parallelogram in the plane along the direction.
Potential parameters for NiTi.
Comparison of lattice constant, a, b, c, monocline angle , and the energy per atom E for single phases and compound twins, as well as their differences with the energy of the B2 phase . Results from this work are indicated by the Finnis–Sinclair (FS) potential. The experimental and ab initio values are taken from Knowles and Smith (Ref. 50) and Wagner and Windl (Ref. 32), respectively. The last two rows list the properties of nanotwins with monolayers of monoclinic unit cells, shown in Figs. 6(b) and 6(c), respectively.
Elastic constants (GPa) of the B2 phase calculated from the Finnis-Sinclair (FS) potential of this work, in comparison with ab initio calculations and experimental measurements at different temperatures.
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