Introduction

Ti–Nb–Zr shape memory alloys (SMA) are promising materials for biomedical applications due to their excellent manufacturability and biocompatibility [1,2,3,4,5,6,7,8,9]. Their most important mechanical characteristic is the low Young's modulus (< 50 GPa), which ensures their biomechanical compatibility with bone tissue [3, 10,11,12] and non-linear superelastic behavior [8, 9]. The superelasticity of titanium SMA is based on the reversible thermoelastic martensitic transformation of the parent BCC β-phase into the martensitic orthorhombic α″-phase [13]. To improve the superelastic behavior, it is very important to obtain in these alloys the largest difference between the dislocation and transformation yield stresses for a more complete implementation of the stress-induced β ↔ α″ martensitic transformation without involving irrecoverable true plastic deformation [14,15,16,17,18,19,20]. One of the ways to improve superelastic behavior is dispersion hardening of the alloys by aging due to the precipitation of ω-phase particles [13, 21, 22]. Dispersion hardening is of particular interest, since it does not require the use of plastic deformation and can be used for foam materials or complex structures or even devices obtained by additive manufacturing [23, 24]. Today, the ω-phase is classified into isothermal phase (ωiso) [25, 26] formed during isothermal holding (aging), athermal phase (ωath) [27, 28] formed during cooling (quenching), and deformation phase (ωdef) formed under the influence of external stress [29, 30].

It was shown earlier that the precipitation of isothermal ωiso-phase has C-shaped kinetics and is very sensitive to the “initial” internal stress level providing preferable sites for the ωiso-phase formation and to the cooling-heating rate and direction of approach to the precipitation temperature range [31]. It was reported in [32, 33] that the ωiso-phase formation in some β-type alloys is accompanied by the redistribution of elements through the ωiso-phase particle boundaries, however, the initial (embryonic) stage of the ωiso-phase formation is a diffusionless process [33]. However, recent results in [31] exhibit a predominant role of shear mechanism of β → ωiso transformation in the Ti–22Nb–6Zr (at.%) alloy and a marginal role of the diffusion-related mechanisms. However, there is no direct evidence of how the diffusion phenomenon affects chemical composition of the β-phase matrix in the Ti–22Nb–6Zr alloy. Thus, a contribution of the diffusional mechanisms to the ωiso-phase formation under different aging conditions remains unclear. It is important to bear in mind that the proven absence of diffusional redistribution of elements across the β/ω interface during the formation of the ωiso-phase would indicate the shear nature of this process, as in the case of the formation of the athermal ωath-phase. We also note that during heating of the same alloy, β → ωiso → β transformation occurred, while this transformation was not detected during subsequent cooling [34, 35], that brings attention to the ωiso-phase formation thermocycling stability: repeatability upon repeatable heating–cooling cycles. The repeatability of the β → ωiso transformation is very important for the practical application of the recently discovered atypical Elinvar effect in Ti–22Nb–6Zr SMA [34]. An in-depth understanding of the β → ωiso transformation mechanism is an important factor in controlling the functional properties of Ti–22Nb–6Zr alloys used as shape memory alloys and Elinvar materials.

Thus, the aim of this work was to study the role of the element diffusion in the process of ωiso-phase formation and impact of this phenomenon on the β → ωiso transformation thermocycling stability in Ti–22Nb–6Zr SMA.

Experimental

An 8 kg Ti–22Nb–6Zr (at.%) ingot was produced by vacuum-arc melting in DVV-125 furnace, hot forged (I.P. Bardin Central Research Institute of Ferrous Metallurgy, Russia) and homogenized at 1100 °C for 30 min. The ingot had a low impurity content of O < 0.05, C < 0.01, N < 0.01, H < 0.01 (wt. %). After homogenization annealing, the ingot was EDM-cut into 20 × 10 × 50 (mm) billets, cold-rolled with a true strain of e = 0.3 and annealed at 600 or 750 °C for 30 min to form in this alloy a polygonized dislocation substructure (P state) or recrystallized structure (R state) states of β-phase, respectively [36]. For the Ti–22Nb–6Zr alloy, the polygonized dislocation substructure provided an optimal combination of functional properties [18, 37,38,39], such as recovery strain and lifetime under severe conditions of cyclic tensile tests. The recrystallized structure of the β-phase provided a state with a small number of crystal lattice defects commonly used as a reference treatment [38]. Then thermomechanically treated billets were aged at 300 or 375 °C for 3 h and water-cooled. The choice of aging temperatures was based on the following considerations about the ωiso-phase formation: (1) 300 °C corresponds to the most intense ωiso-phase formation during isothermal holding obtained in the study of C-shape kinetics [31]; and (2) 375 °C corresponds to the conditions under which the diffusion mobility of elements is increased while the ω-phase dissolution has not yet begun [34].

The structure and the phase composition after aging at 300 and 375 °C (3 h) with subsequent water-cooling were studied using a transmission electron microscope JEOL JEM-2100 at 200 kV. Then an FEI Technai Osiris high-resolution scanning transmission electron microscope (STEM) equipped with the SuperX EDX system at 200 keV was used to study the distribution of chemical elements in areas surrounding the ωiso-phase particles in the polygonized Ti–22Nb–6Zr alloy. The energy dispersive X-ray spectroscopy linear scanning analysis was performed with 0.4 nm step and 0.3 nm beam width. Both studies were carried out using 80–100 nm thick lamellas cut by the focused ion beam method on a Strata FIB 205.

To determine the statistical significance of the obtained differences in the Ti and Nb concentrations in the β-phase matrix, inside and around ω-phase particle, the statistical Student's test was used with an average significance level of 0.05 for the entire scanned range and separate ranges corresponding to the matrix and the particle. The mean values of Ti and Nb concentrations in each studied range were calculated using the Eq. (1):

$$\overline{x} = \frac{{\mathop \sum \nolimits_{i} x_{i} }}{n},$$
(1)

where \({x}_{i}\) is the Ti or Nb concentrations in ith point of a given range and \(n\) is the number of measurements in this range. The standard deviation was calculated using the Eq. (2):

$${\upsigma } = \sqrt {\frac{{\mathop \sum \nolimits_{i} \left( {\overline{x} - x_{i} } \right)^{2} }}{n}} .$$
(2)

The absolute confidence error was calculated using the Eq. (3):

$${\Delta } = t_{P, k} \times \frac{{\upsigma }}{\sqrt n },$$
(3)

where \({t}_{P, k}\) is the critical values of the Student's coefficient for the confidence probability P = 0.95 and the number of freedom degrees k = n − 1.

To assess stability of the phase state after heating–cooling cycles and after water quenching from the characteristic temperatures reached on heating to 250, 375, and 550 °C in accordance with [34], a room-temperature X-ray diffraction analysis was carried out for the 1st, 4th, and 10th heating–cooling cycles (Fig. 1) using a DRON-4 diffractometer with CuKα radiation on 8 × 10 × 1…2 mm specimens. The average heating–cooling rate before quenching from the characteristic temperatures was ~ 2.5 °C/min. Before studies, the specimen surfaces were grinded with P320–P1200 abrasive paper and chemically etched in 1HF: 3HNO3: 6H2O solution to remove the oxidized and mechanically damaged surface. The β-phase lattice parameter was calculated using the Nelson–Riley extrapolation. The lattice parameters of ωiso-phase were calculated by the least-squares method previously used in [39]. The width of {110}β and {211}β X-ray line profiles was measured at half the height of the profile peak (half-height line width).

Fig. 1
figure 1

Sequence of the X-ray diffraction experiment during thermal cycling

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Results and Discussion

Study of β→ωiso Transformation Mechanism

To answer the question whether the diffusional redistribution of elements contributes to the β → ωiso transformation, the distribution of Ti, Nb, and Zr compositions across the ω-phase particles and in the β-phase areas surrounding the ω-phase particles were studied after aging at 300 and 375 °C (3 h) of an annealed at 600 °C, 30 min Ti–22Nb–6Zr alloy were studied. Figure 2 shows the TEM bright and dark field images of the alloy microstructure after aging, along with the corresponding SAED patterns.

Fig. 2
figure 2

TEM after aging for 3 h at 300 (a) and 375 °C (b) of the annealed at 600 °C Ti–22Nb–6Zr SMA: BF—bright field images, DF—dark field images, SAEDP—selected area electron diffraction patterns. DF images are taken from ω-phase reflexes indicated by rings

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After aging at both temperatures, elongated ωiso-phase particles are formed, which is consistent with data of [26, 31]. This could indirectly indicate that the β → ω transformation is predominantly initiated by the shear mechanism. Otherwise in case of diffusion controlled precipitation, particles are tend to be more equiaxed [40, 41]. The size of the ωiso-phase particles after aging at 300 °C, 3 h is 5…7 × 15…30 nm. Increase of the aging temperature to 375 °C leads to an increase in the ωiso-phase average particle size by about three times.

STEM images of the microstructure at lower and higher magnifications after aging at 300 and 375 °C and the corresponding distribution of local concentrations of Ti, Nb, and Zr elements in the β-phase areas surrounding the ω-phase particle and across this ω-particle is shown in Fig. 3. After aging at 300 °C, the Ti and Nb concentration curves exhibit disordered opposite oscillations along a scanning line (Fig. 3a). These oscillations are observed in the β-phase matrix as well as inside the ω-phase particles. The magnitudes and widths of such oscillations inside the particles do not differ from those observed in the matrix. It means that the ω-phase particles “inherited” the distribution of elements that existed in the β-matrix before the β → ωiso transformation without any distinct sign of the element diffusion. On the contrary, distributions of Ti and Nb concentrations scanned after annealing at 375 °C demonstrate clear opposite changes within the ω-phase particle: a peak in Zr concentration and a dip in Nb concentration (Fig. 3b). This corresponds to the expected opposite changes in the concentrations of these elements in the ω-phase particles in the case of their diffusional redistribution in accordance with [32].

Fig. 3
figure 3

STEM at lower and higher magnifications after aging for 3 h at 300 (a) and 375 °C (b) (BF) of the annealed at 600 °C Ti–22Nb–6Zr SMA. The energy dispersive X-ray spectroscopy linear scanning analysis in the area near the ωiso-phase particle after aging for 3 h at 300 (c) and 375 °C (d)

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Next, the statistical significances of the differences in the distribution of Ti and Nb concentrations (at.%) in the β-phase areas surrounding the ωiso-phase particle and across these ωiso-particles after aging at 300 and 375 °C for 3 h were determined using the Student's test. For this purpose, the whole scanned range was separated into three ranges: I—β-phase matrix “on the left” from the ω-phase particle, II—area across ω-phase particle, III—β-phase matrix “on the right” from the ω-phase particle (Fig. 3). Concentrations of Ti and Nb were averaged over each range separately and over the entire scanned range (I + II + III) after aging at 300 and 375 °C for 3 h (see Table 1).

Table 1 Concentrations of Ti and Nb (at.%) averaged over concentration ranges I, II, III (Fig. 3) separately and over the entire scanned range (I + II + III) after aging at 300 and 375 °C
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As can be seen from Table 1, average concentrations of Ti and Nb in the entire (I + II + III) ranges are the same within the error limits after both agings at 300 and 375 °C for 3 h. This means that the whole alloy composition remains stable during aging. For aging at 300 °C, all three ranges (I, II, and III) as well as the entire (I + II + III) range exhibit the same average concentrations of Ti and Nb within the error limits. Therefore, it should be concluded that the there is no statistically significant diffusional element redistribution. After aging at 375 °C, the concentration values in the range I and the entire range (I + II + III) are the same within the error limits. In the range II embracing the ω-phase particle formed, there are large (about 6–7%) increase in Ti and decrease in Nb concentrations, while in the range III, small but statistically significant decrease in Ti and increase in Nb concentrations are observed. It is explained by local diffusional element redistribution which occurs in a local zone of β-phase matrix adjacent to the ω-phase particle on the right (Fig. 3b).

The precision of the applied X-ray spectroscopy technique might seem insufficient to resolve the difference in chemical composition in small ω-phase particles after aging at 300 °C in cases if it is of the same order as or lower than those observed in large ω-phase particles after aging at 375 °C. However, it should be taken into account, that the ω-phase formation manifests C-shape kinetics with maximum rate at 300 °C in the studied alloy, while the ω -phase formation is much slower and weaker at 375 °C [31]. In accordance with [31], the volume fraction of ω-phase after aging at 300 °C is almost three times greater than that after 375 °C. Therefore, if the element diffusion plays the primary role in ω-phase formation, the average changes in the composition after aging at 300 °C should be about three times greater than those observed for 375 °C. Moreover, it should be borne in mind that for the experimental study of the distribution of element concentrations after annealing at different temperatures, ω-phase particles of approximately the same size were selected, and the lengths of the scanning lines from one particle boundary to the other were the same and amounted to 6–7 nm (see Fig. 3a, b). Taking into account the shape of a real C-curve, it seems that the scanning line in Fig. 3b passes through the particle just formed at 375 °C, while the scanning line of the same length passes through the particle exposed to high temperature (300 °C) for a long time. Consequently, the diffusion could not play the leading role in ω-phase formation at 300 °C and plays the secondary role manifested at a higher aging temperature (375 °C).

A comparison of the diffusion mobility of Nb atoms in Ti at temperatures of 300 and 375 °C shows that such a significant difference in the development of the redistribution of Nb atoms at not too large a temperature difference is not something unexpected. To compare the diffusion rates of Nb in β-Ti at 300 and 375 °C, the Nb diffusion coefficients in β–Ti were calculated using the Arrhenius Equation D = Do × e[− E/(R × T)], for which Do = 2.91 × 10–8 m2/s and E = 129.9 kJ/mol were taken from [42]. The calculations have brought the following results: DNb = 4.19 × 10–20 and 9.84 × 10–19 m2/s for 300 and 375 °C, respectively. This means that the diffusion rate of Nb at a temperature of 300 °C is more than 20 times less than at a temperature of 375 °C. This fully correlates with the experimentally observed absence of a significant contribution of the diffusion mechanism to the process of formation of the ωiso-phase at 300 °C.

Study of β→ωiso Transformation Thermocyclic Stability

The study of β → ωiso transformation thermocyclic stability was carried out on polygonized and recrystallized structure states of the alloy in order to exclude the influence of crystal lattice defects on this process. The X-ray diffractograms corresponding to quenching from the characteristic temperatures in the 1st, 4th, and 10th cycles in the experiments on thermocyclic stability are shown in Fig. 4a, b. In both P and R structure states, the main phase in the studied temperature range of this alloy is a body-centered cubic (BCC) β-phase. Appearance of the ωiso-phase X-ray diffraction lines is observed after heating to 375 °C during all the studied cycles. Further heating up to 550 °C led to the ωiso-phase disappearance. Such a behavior of ωiso-phase correlates well with the β → ω → β transformation peak in the temperature dependence of square of resonant oscillation frequency fr2 upon heating in a torsion pendulum experiment [34]. There was no evidence of any other phase formation.

Fig. 4
figure 4

X-ray diffractograms (a, b) in the polygonized (a) and recrystallized (b) states of Ti-22Nb-6Zr during thermal cycling (at RT after quenching)

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For an integral assessment of the stability of β-phase composition upon heating after water-quenching from characteristic temperatures, the β-phase lattice parameter aβ and the half-height width Bhkl of {110}β and {211}β X-ray line profiles were measured at RT (Fig. 5). Figure 5a, b show that the β-phase lattice parameter aβ does not change after quenching from all the characteristic temperatures. This confirms that the observed diffusional element redistribution in the composition of β-phase in Fig. 3 and Table 1 has a local nano-scale nature and does not affect the whole volume of β-phase body during the ω-phase formation. The X-ray line profiles have normal symmetry without a gravity center shift, which confirms the absence of solution inhomogeneity. The Bhkl of β-phase does not change, except for certain cases of a slight systematic increase in the B211 values after quenching from 375 °C due to the ωiso-phase formation. This increase does not exceed the error limits (Fig. 5c, d). The ωiso-phase lattice parameters a, c, c/a and unit cell volume (Ω) stay unchanged at RT after each heating–cooling cycle (Fig. 6). The calculated c/a of ratio 0.613 ± 0.004 coincides with the previously obtained values for isothermal and athermal ω-phases measured for the Ti–22Nb–6Zr alloy in [31, 39].

Fig. 5
figure 5

Lattice parameters aβ (c, d) and half-height width Bhkl of β-phase X-ray lines (e, f) in the polygonized (a, c, e) and recrystallized (b, d, f) states of Ti–22Nb–6Zr during thermal cycling (at RT after quenching)

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Fig. 6
figure 6

Lattice parameters of ωiso-phase in polygonized (a, c) and recrystallized (b, d) states of Ti–22Nb–6Zr SMA during thermal cycling (measured at RT after quenching from 375 °C)

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It can finally be asserted that the observed formation of ωiso-phase upon heating occurs by the shear mechanism accompanied by the diffusional redistribution of elements only at higher temperatures, and this process is stable and reproducible up to at least ten thermal cycles; the nature of stress fields which accompany the ω-phase formation requires further detailed investigation.

Conclusion

  1. 1.

    The absence of diffusional redistribution of elements across the ωiso/β interfaces and in areas surrounding the ωiso-phase particles was revealed in Ti–22Nb–6Zr SMA at lower aging temperature of 300 °C. This process was observed only at higher temperature of 375 °C. These results indicate that the leading mechanism of the isothermal ωiso-phase formation is a crystal lattice shear, while the diffusional mechanism plays a secondary role which appears only at higher aging temperatures. Its effect is local and does not affect the composition of a main β-phase body in the studied aging conditions. It could take a part in the stress relaxation mechanisms inherent in isothermal shear transformations.

  2. 2.

    The β → ωiso transformation features, β- and ω-phases structure parameters during thermal cycling of Ti–22Nb–6Zr SMA are stable and reproducible up to at least 10 thermal cycles. The ωiso-phase and β-phase lattice parameters, β-phase X-ray line width and the amount of the precipitated phase are similar within the error limits after 1st, 4th, and 10th cycles of the ωiso-phase precipitation–dissolution in both polygonized and recrystallized states.