Introduction

Group IVB transition metals such as Ti and Zr display three phases at room temperature, depending on the amount of pressure. These metals possess a hexagonal close-packed (hcp) structure (α-phase) at ambient pressure. The α-phase structure transforms into a simple hexagonal structure (ω-phase) under high pressure; this pressure-induced α-to-ω transformation was first observed by Jamieson [1]. The α-to-ω phase transition pressure for Ti at ambient temperature has been reported to be approximately 2.0–9.0 GPa [2–6]. Under extremely high pressure, the ω-Ti further transforms into another phases [7–10]. A number of mechanisms on the α-to-ω transformation have been previously proposed. Silcock was the first to propose the orientation relationships between the α-phase matrix and isothermal ω-phase precipitates on the basis of X-ray observations of Ti–V, Ti–Mo, and Ti–Cr alloys [11]. Since the α-to-ω transformation exhibits hysteresis, the high-pressure ω-phase is partially retained under ambient condition after the application of hydrostatic pressure [1, 2, 12–14]. By employing this feature, the transformation mechanisms in pure Ti and/or Zr have been also proposed by Rabinkin et al. [12], Usikov et al. [13], Song et al. [15], and Trinkle et al. [16]. Such pressure-induced α-to-ω transformation is known as diffusionless martensitic transformation.

The retention of the ω-phase was also observed after deformation through shock loading [17, 18] and high-pressure torsion (HPT) [19–21]. The HPT process has a unique feature which can obtain a 100 vol% bulk ω-phase [22, 23]. In addition, the ω-phase obtained after the HPT process has a strong texture [22, 23]. This fact enables the determination of the properties of high-pressure ω-phase alone, such as elastic constants [24], slip systems [22], and orientation relationships [23]. However, the structural factor (e.g., grain size and dislocation density) which enables to obtain 100 vol% ω-phase state is still unknown. Since an HPT process is a severe plastic deformation process under a high pseudo hydrostatic pressure, it can be expected that densely introduced lattice defects such as dislocations and grain boundaries pin the ω-to-α reverse transformation. Once the ω-phase stabilization mechanism in the HPT-processed pure Ti is clarified, a new strategy for controlling a microstructure of Group IVB metals utilizing a high-pressure phase will be possible. In this study, we systematically investigated the ω-to-α reverse transformation kinetics in the HPT-processed pure Ti to determine activation energy, and investigated its corresponding microstructure. Finally, the transformation mechanism in the HPT-processed sample is discussed.

Experimental procedures

In this study, two kinds of pure Ti (99.9 %) samples were used, hereafter referred to as samples A and B, with their chemical compositions summarized in Table 1. First, the Ti disks—with diameters of 20 (sample A) and 10 (sample B) mm and a thickness of 0.85 mm—were annealed at 1073 K for 3.6 ks in a vacuum, while using sponge Ti as an oxygen getter to homogenize their microstructures. The disks were then placed individually between two anvils with a depression of 0.25 mm in depth, after which a torsional strain was applied under high pressure. A compressive pressure, P, of 5 and 1.5 GPa was used, and the number of revolutions, N, was 5 and 10. The rotating speed was fixed at 0.2 rpm, and the HPT process was performed at room temperature. Both samples A and B showed an almost identical X-ray diffraction (XRD) profile after the HPT process under the P at 5 GPa, indicating that the effect of the compositional difference between samples A and B on the stabilization behavior of the ω-phase is negligibly small.

Table 1 Chemical compositions of the samples (mass%); balance is Ti
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The shear strain, γ, introduced by the HPT process was calculated using the expression γ = 2πrN/d, where r is the distance from the disk’s center and d is the sample thickness. It should be noted that a γ introduced into a sample has r dependence. The temperature increment during the HPT process for the Ti specimen with the diameter of 10 mm was approximately 30 °C, suggesting that the effect of the heat generated was negligibly small.

An X-ray diffraction (XRD, Rigaku Ultima IV) experiment was conducted using Cu-Kα radiation to investigate the phase composition of the samples. The beam size of the incident X-ray in this measurement is about 10 × 10 mm2.

By employing the benefit of the high penetration depth of neutrons, the radial dependence of the amount of ω-phase formed by the HPT process was investigated by the neutron diffraction (ND) technique. The size of incident neutron beam was 2 mm in width and 15 mm in height. The ND experiment was carried out using an HPT sample (sample A, P = 5 GPa, N = 5). The detailed procedure of an ND experiment is fully described in previous literature [22].

In order to observe the reverse transformation of the ω-phase directly, and to compare the microstructure of the ω-phase and the reverse transformed α-phase with previously reported results, the microstructures of the as-HPT and annealed HPT samples were observed by transmission electron microscopy (TEM, Hitachi H-800) at an accelerating voltage of 200 kV. The samples for TEM observation were prepared by twin-jet electrolytic thinning.

The ω-to-α reverse phase transformation kinetics were investigated by the temperature, T, and time, t, dependences of electrical resistivity, ρ(T) and ρ(t), respectively. The ρ was measured by a four-terminal method using ULVAC ZEM-1, which is generally used to measure the thermoelectric properties of material, in an He atmosphere. The ρ(T) was measured in the T range of 273–573 K with various heating rates, ϕ (1.0 × 10−3 to 2.7 × 10−1 K/s). The ρ(t) was measured at a constant T of 373, 383, and 393 K.

The ω-to-α reverse phase transformation kinetics were also investigated using differential scanning calorimetry (DSC) measured using various ϕ (5.0 × 10−2 to 1.7 K/s) in an Ar atmosphere.

Results and discussion

Figure 1 shows the XRD profiles of pure Ti (sample A) before (non-deformed) and after the HPT process of N = 5 under the P of 1.5 and 5 GPa. In the non-deformed and P = 1.5 GPa samples, only the diffraction peaks of α-phase were observed. On the other hand, the diffraction peaks of ω-phase were mainly observed in the P = 5 GPa sample. These results indicate that, by changing the P during the HPT process, the phase obtained after the HPT process can be easily controlled; the HPT process under a P of 1.5 and 5 GPa gives a deformed α- and ω-phase structures, respectively. In the P = 5 GPa sample in Fig. 1, however, small peaks of α-phase were still observed.

Fig. 1
figure 1

XRD profiles of sample A before and after the HPT process of N = 5 under the compressive pressures of 1.5 and 5 GPa

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In order to investigate the distribution of high-pressure ω-phase after the HPT process, an ND experiment was performed. The ND patterns of pure Ti after the HPT process (P = 5 GPa, N = 5) measured at r = 0 and 4 mm are shown in Fig. 2. At r = 4 mm, the diffraction peaks of α-phase could not be observed, whereas that was clearly observed at r = 0 mm. We should note that the width of neutron beam used in this study is 2 mm and that the ND profile measured at r = 4 mm contains the information of the region between r = 3 and 5 mm. Therefore, it can be concluded that single ω-phase samples can be obtained at a region with r > 3 mm. Since the XRD profiles measured in this study contain the information of the center region of the sample, the small α-phase peak was observed in the XRD experiment (Fig. 1).

Fig. 2
figure 2

ND profiles of the HPT-processed pure Ti (sample A, P = 5 GPa, N = 5) measured at the center of the sample (r = 0 mm) and 4 mm away from the center (r = 4 mm)

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In accordance with the results of the ND experiment, the samples for ρ measurement (length of 14 mm, width of 1 mm, and thickness of 0.4 mm) were cut out from the 100 vol% ω-phase region of HPT-processed sample using a wire electrical discharge machine as shown in Fig. 3a. The ρ(T) curves of the HPT-processed pure Ti (sample A, P = 5 GPa, N = 10) measured with various ϕ are shown in Fig. 3b. The ρ(T) curves of non-deformed and deformed α-phase (HPT P = 1.5 GPa, N = 10) are also shown in the figure. The ρ value of the sample after the HPT process under 5 GPa (single ω-phase), ρ(T)ω, showed 0.95 μΩ m at 350 K, which is a higher value than that of non-deformed (0.55 μΩ m) and deformed α-phase (0.62 μΩ m). The slight increase in ρ of the deformed α-phase is owing to the introduction of a large number of dislocations and grain boundaries (grain refinement). At a certain T (e.g., 370 K at the ϕ of 2.7 × 10−1 K/s), the ρ of the HPT-processed sample decreased significantly, and the ρ(T) curve overlapped with that of α-phase, ρ(T)α, which means that a ω-to-α reverse phase transformation occurred. The reverse transformation was also confirmed by an XRD measurement. Figure 4 shows the XRD profiles of the as-HPT (sample A, P = 5 GPa. N = 5) and the HPT samples annealed at a temperature just below and above the phase transformation temperature measured in ρ(T) measurement for 3.6 × 103 s. As can be clearly seen, in accordance with the ρ(T) measurement, the ω-to-α reverse phase transformation took place between the annealing temperatures of 373 and 423 K. The reverse transformation temperature, T ω−α, increased with increasing ϕ (Fig. 3b). Here, the T ω−α value was defined following three different rules: (#1) the T where ρ(Τ) is 1 % deviated from a ρ(T) of ω-phase (the start temperature of reverse transformation, T Sω−α ); (#2) the T where ρ(T) is 1 % deviated from a ρ(T) of α-phase (the finish temperature of reverse transformation, T Fω−α ); and (#3) the T where ρ = [ρ(T)α + ρ(T)ω]/2 (the intermediate temperature of reverse transformation, T Mω−α ). Using these T ω−α values, the activation energy for a ω-to-α reverse phase transformation, E ω−α, was estimated from the slope of the Kissinger plot, E Kω−α (Fig. 5) [25]. The estimated E values from each T ω−α definition showed an almost identical value; 156 (T Sω−α ), 160 (T Mω−α ), and 157 kJ/mol (T Fω−α ), respectively.

Fig. 3
figure 3

a Sample geometry for electrical resistivity measurement. The hatched region in the center of the disk shows the α + ω two-phase region (r < 3 mm). b Temperature dependence of electrical resistivity, ρ(T), in the HPT-processed Ti under 5 GPa (sample A, N = 10) measured using various heating rates, ϕ, and that in the non-deformed and deformed α-phases (sample A, P = 1.5 GPa, N = 10)

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Fig. 4
figure 4

XRD profiles of the as-HPT (sample A, P = 5 GPa, N = 5) and annealed HPT samples at 373 and 423 K for 3.6 × 103 s

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Fig. 5
figure 5

The Kissinger plots obtained from the temperature dependence of electrical resistivity (Fig. 3b) for the determination of the activation energy for the ω-to-α reverse phase transformation, E Kω−α

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The E ω−α was also estimated from the ρ(t) at constant T. Figure 6a shows the ρ(t) curves of the HPT-processed sample (sample A, P = 5 GPa, N = 10) at a holding T of 383 K. The initial increase in the ρ value is a result of the rapid heating of the sample from room temperature to the holding T. The time required to complete the ω-to-α reverse transformation, t ω−α, was derived from this ρ(t) curve. Here, the start and finish of the transformation was defined as the time where the ρ(t) value is deviated by 1 % from the linear fit of initial and saturated part of ρ(t) curve. As shown in Fig. 6b, the estimated E ω−α from the Arrhenius T dependence of t ω−α, E Aω−α , showed a consistent value with E Kω−α (E Aω−α  = 144 kJ/mol).

Fig. 6
figure 6

a Electrical resistivity of the HPT-processed sample (sample A, P = 5 GPa, N = 10) plotted against time, ρ(t), measured at the holding temperature of 383 K. b The holding temperature dependence of the time required to complete the ω-to-α reverse phase transformation, t ω−α (Arrhenius plot)

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The ω-to-α reverse phase transformation kinetics can also be investigated through the DSC experiment. The samples for DSC measurement were also cut out from the 100 vol% ω-phase region in the sample as shown in Fig. 7a. The typical heat flow curves, Q(T), of the HPT-processed sample (sample A, P = 5 GPa, N = 10) measured with ϕ of 5.0 × 10−2 and 1.7 K/s are shown in Fig. 7b. The exothermic peak was clearly observed in every ϕ. The exothermic peak temperature, T p, which is defined as dQ(T)/dT = 0, increased with increasing ϕ as was observed in ρ(T) (Fig. 3b). When comparing with similar ϕ, T p (ϕ = 5.0 × 10−2 K/s) and T ω−α (ϕ = 6.7 × 10−2 K/s) values showed consistent value. The E Qω−α was estimated using T p values in the same manner as the ρ(T) measurement (Fig. 5). The derived E from Q(T) analysis, E Qω−α , was 158 kJ/mol. A similar result has been reported in shock-loaded pure Zr; the sample loaded to 8 and 10.5 GPa showed E ω−α of 101 and 167 kJ/mol, respectively.

Fig. 7
figure 7

a Sample geometry for DSC measurement. b Typical heat flow curves obtained from the DSC measurement, Q(T), of HPT samples (sample A, P = 5 GPa, N = 10) measured at a heating rate, ϕ, of 5.0 × 10−2 (upper portion) and 1.7 K/s (lower portion). c Dependence of the transformation temperature, T p, on the ϕ (Kissinger plot)

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Figure 8b shows the bright-field (BF) TEM image of the as-HPT sample observed at r = 3.2 mm. The selected area diffraction (SAD) pattern measured using the entire area of the BF image showed that the as-HPT sample mainly consists of ω-phase (Fig. 8c). It can be seen that a large number of dislocations are introduced to the equiaxed ω-phase grains. The size of the ω-phase grains was around 200 nm. After annealing at 423 K for 3.6 × 103 s (Fig. 8d), recrystallization partially occurred and a bimodal structure with coarse recrystallized grains and fine grains was observed. The corresponding SAD pattern indicates that the ω-phase was partially reverse transformed to α-phase (Fig. 8e). Furthermore, it can be seen that the reverse transformed α-phase showed a spotty SAD pattern, which indicates that the α-phase grains possess a low dislocation density structure, while the ω-phase kept a ring-like pattern. From these BF images and SAD patterns, it can be concluded that the reverse transformed α-phase has coarse fully recrystallized α-phase grains, while the surrounding ω-phase matrix maintains a fine-grained structure with a high dislocation density. This microstructure indicates that new α-phase grains were nucleated from a deformed matrix and grown during annealing, which is a characteristic of the diffusion-controlled process. Therefore, the diffusionless martensitic ω-to-α transformation was prohibited and the new transformation mechanism, controlled by atomic diffusion, occurred in the HPT-processed pure Ti.

Fig. 8
figure 8

a Sample geometry for TEM observations. TEM micrographs and SAD patterns of b, c the as-HPT sample (sample B, P = 5 GPa, N = 5, r = 3.2 mm) and d, e the HPT sample annealed at 423 K for 3.6 × 103 s

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Recently, Low et al. have reported the reverse transformation behavior of shock-loaded pure Zr which has an α + ω two-phase structure [26]. In our results, the microstructures differed. The as-shocked sample had the fine α laths in the ω-phase matrix, which indicates that the ω-to-α reverse martensitic transformation occurred during the reduction of applied load. A similar result is also reported in shock-loaded pure Ti [27]. Upon annealing, the coarsening of the pre-existing α laths and nucleation of new α laths were observed. These results indicate that, in the case of a shock-loaded sample, the ω-to-α reverse transformation is still governed by the diffusionless martensitic transformation. In the HPT-processed samples, however, a lath martensite structure, which is evidence of an occurrence of diffusionless martensitic transformation, could not be observed during the ω-to-α reverse transformation (Fig. 8).

The difference between HPT-processed and shock-loaded samples also appeared in the orientation relationship (OR) between the α- and ω-phases. In the shock-loaded Ti and Zr, (0001)α || (10-11)ω and [10] α || [11-2-3]ω, the orientation relationship was maintained [15, 26]. In the HPT-processed Ti, however, the OR reported by Silcock, namely {0001}α || {11-20}ω and 〈11-20〉 α || 〈0001〉 ω, was maintained during the ω-to-α reverse transformation [23]. It is noteworthy that the Silcock relation was observed in the isothermal α-to-ω phase transformation.

The E for the self-diffusion of Ti in α- (E diffα) is 123–169 kJ/mol [28–32]. Owing to the experimental difficulty, E diff, in the ω-phase has not yet been reported. The E ω− α values estimated in this study showed a consistent value with E diff, which means, as also suggested by the microstructure (Fig. 8), that the ω-to-α reverse transformation process is governed by the diffusion. There are two possible reasons why the ω-to-α diffusionless transformation changed to a diffusion-controlled transformation after the HPT process.

One reason is the extremely high dislocation density. An HPT process, which is one of the severe plastic deformation processes, can introduce intense strain into a sample, and as a result high-density dislocation is introduced to the sample. As the maximum shear strain introduced to the sample used in this study was an extremely high value of 1.26 × 103 (N = 10, r = 10 mm), it can be easily expected that a large number of dislocations are introduced to the sample. The TEM micrograph and SAD pattern of the as-HPT sample (Fig. 8a, b) indicated that the microstructure of the sample possesses high dislocation density structure. The effect of dislocation on the martensitic transformation has been investigated in the Ti–Ni shape memory alloy [33]. In the Ti–Ni shape memory alloy, two types of martensitic transformations can be seen: the M-phase with a monoclinic structure and the R-phase with a rhombohedral structure. One of the differences between these phases is the amount of transformation strain; the former has a relatively large transformation strain of nearly 11 % [34], whereas the latter has a small transformation strain of 1 % [35]. Miyazaki et al. found that the formation of the M-phase is mechanically suppressed by the stress field formed by dislocations, while the R-phase, with a small transformation strain, is not much affected. In case of Ti, the α-to-ω phase transformation shows a relatively high transformation strain of 5–10 % [11, 16], suggesting that the existence of dislocations has notable effects on the transformation.

The other reason for the change to a diffusion-controlled mechanism is the effect of grain size on martensitic transformation. The effect of grain size on martensitic transformation is well documented in Fe–Cr–Ni [36], Fe–Ni–C [37], and Fe–Mn [38] systems. In case of the Fe–Mn system, when the grain size of the austenite matrix becomes below 30 μm, a volume fraction of a thermal ε martensite decreases significantly, and ε martensite cannot be formed in the ultrafine austenite grain with a grain size below 1 μm. Since the HPT process gives the ultrafine ω-phase grain of around 200 nm (see Fig. 8b), the martensitic transformation could be suppressed in the HPT-processed pure Ti.

Conclusions

In this work, the reverse transformation kinetics of the high-pressure ω-phase formed by the HPT process were investigated through both electrical resistivity and calorimetric measurements. The obtained results can be summarized as follows:

  • By changing the compressive pressure during an HPT process, the obtained phase of pure Ti after the HPT process can be easily controlled: when an applied compressive pressure is 1.5 and 5 GPa, deformed α- and ω-phase samples are obtained, respectively.

  • Through the neutron diffraction technique, it was revealed that the 100 vol% ω-phase sample could be obtained in the region which has a 3 mm or longer distance from the center of an HPT-processed (P = 5 GPa, N = 5) disk. This result enables an investigation of the properties of the high-pressure ω-phase alone.

  • The ω-to-α transformation was observed by XRD, electrical resistivity, and calorimetric measurements. The electrical resistivity of a 100 vol% ω-phase sample showed a value of 0.95 μΩ m at 350 K, which is much higher than that of α-phase (0.55–0.62 μΩ m). Upon annealing of the ω-phase sample, the ω-to-α reverse transformation was clearly observed as a decrease in electrical resistivity and an exothermic peak in the calorimetric experiment. After the annealing at just above exothermic peak temperature, the diffraction peaks of reverse transformed α-phase were measured in the XRD measurement. The activation energies for reverse transformation, estimated from the Kissinger and Arrhenius plots performed using the results of electrical resistivity and calorimetric experiments, showed the value in the range of 144–160 kJ/mol, which is a consistent with the activation energy for the self-diffusion of Ti.

  • After the ω-to-α reverse transformation, the coarse recrystallized α-phase grains with low dislocation density were observed instead of α laths after the ω-to-α reverse transformation, which is a different microstructure to those seen in the samples deformed by other techniques such as shock loading. These results clearly indicate that the mechanism of ω-to-α reverse transformation changes from being martensitic to a diffusion-controlled phase transformation.