Self-Accommodation and Deformation Microstructure of Martensite in Ti₃₀Ni₅₀Zr₂₀ Alloy

Abstract

In a thermoelastic martensitic transformation, there is a “self-accommodation” in which the microstructure itself relieves strain induced by the transformation. In this study, the crystal structure and self-accommodation microstructure of martensite in Ti₃₀Ni₅₀Zr₂₀ alloy were investigated using X-ray diffraction, scanning electron microscopy with electron backscatter diffraction, and transmission electron microscopy. In addition, the deformation microstructure was investigated by observing the samples after tensile tests. The crystal structure of the martensite in the Ti₃₀Ni₅₀Zr₂₀ alloy was determined to be the B19′ monoclinic structure. In this alloy, plate- and polygonal-like variants with a width of a few microns were observed, and pairs of habit-plane variants (HPVs) forming {011}_B19′ twins were observed at the interface. The self-accommodation has a mosaic-like morphology because of the combination of these pairs of HPVs. The (001)_B19′ compound twins were formed as internal defects. These twins are considered to be lattice-invariant shear (LIS) of martensite in this alloy. No plateau region was observed in the tensile test. In the deformed specimen, the self-accommodation was collapsed by the movement of the HPV interface and the introduction of (100)_B19′ compound twins was observed as an internal defect. This defect is considered to be not LIS but a deformation twin. The lack of a plateau region in the stress–displacement curve was attributed to these deformed microstructures.

1. Introduction

Thermoelastic martensitic transformation is a phase transformation observed in nonferrous alloys, and this is associated with shape memory and superelastic properties.¹⁾ Shape-memory alloys have a mechanism known as “self-accommodation” in which the microstructure itself relieves strain induced by martensitic transformation through a combination of crystallographically equivalent habit-plane variants (HPVs), which is closely related to shape-memory properties. Ti–Ni alloys are widely used as shape-memory alloys in the industrial and medical fields because they exhibit excellent shape-memory properties.²⁾ The self-accommodation structure of the Ti–Ni alloy with B19′ monoclinic martensite has a V-shaped variant as the minimum unit, and the HPV interface is a {111}_B19′ Type I twin. Inside the variant, ⟨011⟩_B19′ Type II twins are introduced as lattice-invariant shear (LIS), and three of these V-shaped variants have been reported to combine to form HPV clusters with an ideal hexagonal shape.^3–5) Ti–Ni–Pd alloys partially substituted with Pd, which is a member of the same periodic group as Ni, form B19 orthorhombic martensite, and four types of HPVs with {111}_B19 Type I twins introduced as LIS are known to form three types of interfaces: {011}_B19 compound twins, {111}_B19 Type I twins, and ⟨211⟩_B19 Type II twins.^6,7) Ti–Ni–Hf alloys substituted with Hf, which is a member of the same group as Ti, have been reported to have martensitic transformation points above 373 K.^8,9) The morphology of the self-accommodation structure is a pair of plate-like HPVs with {011}_B19′ Type I twins or {021}_B33 compound twins as interfaces, and the internal defects have been found to be (001)_B19′ compound twins or (010)_B33 stacking faults.¹⁰⁾

Ti–Ni–Zr alloys are composed of Ti–Ni alloys in which Ti is substituted with Zr of the same family. Shape-memory properties and an elevation of the transformation temperature with increasing Zr content have been reported for Ti–Ni–Zr alloys,¹¹⁾ and these alloys are expected to find applications as high-temperature shape-memory alloys. The crystal structure is the same as that of Ti–Ni alloys and Ti–Ni–Hf alloys (Hf content as high as 25 at%) with a monoclinic B19′ structure for compositions with a Zr content as high as 20 at%.¹¹⁾ As microstructural characteristics, plate-like variants with (100)_B19′ compound twins introduced as internal defects have been observed.¹²⁾ However, self-accommodation in Ti–Ni–Zr alloys—that is, twinning at the HPV interface and HPV combinations—has not been investigated. In Ti–Ni–Zr and Ti–Ni–Hf alloys, the H-phase^13–17) is precipitated by an aging treatment. However, Ti₃₀Ni₅₀Zr₂₀ alloy have been reported to not exhibit any H-phase even after an aging treatment.¹⁸⁾ Therefore, Ti₃₀Ni₅₀Zr₂₀ alloy is considered appropriate for investigating the microstructural characteristics of Ti–Ni–Zr alloys that exhibit the B19′ structure. In addition, the microstructure of Ti–Ni alloys has been reported to change geometrically with strain.^19–21) Furthermore, a preferential variant is generally formed for the tensile direction. That is, strain-induced reorientation and morphological changes of the variants occur in both Ti–Ni–Zr alloys and Ti–Ni alloys. However, microstructural changes that result from the application of strain to self-accommodation have not been well investigated. Therefore, it is important to investigate crystallographic features such as the HPV interface and changes of the LIS in Ti–Ni–Zr alloys subjected to deformation.

In the present study, we investigate the self-accommodation and deformation microstructure of martensite in Ti₃₀Ni₅₀Zr₂₀ alloy using X-ray diffraction (XRD) analysis, scanning electron microscopy and electron–backscatter diffraction (SEM–EBSD), and transmission electron microscopy (TEM).

2. Materials and Methods

The Ti₃₀Ni₅₀Zr₂₀ alloy was prepared by arc melting 99.97% Ti, 99.97 mass% Ni, and 99.7 mass% Zr under an Ar atmosphere. The Ti₃₀Ni₅₀Zr₂₀ alloy specimens were annealed under an Ar atmosphere at 1273 K for 86.4 ks. The samples with a prescribed shape were subsequently encapsulated in quartz ampoules under an Ar atmosphere and solution-treated at 1173 K for 3.6 ks, followed by quenching in ice water by breaking the ampoule. Tensile tests were performed using a DEBEN CT500N. A dog-bone-shaped specimen with a gauge section of 0.7 mm × 0.8 mm × 0.8 mm were fabricated by electrical-discharge machining. The uniaxial tensile test was carried out at a deformation rate of 0.2 mm/min. Differential scanning calorimetry (DSC) measurements were performed using a NETZSCH DSC-3500 Sirius at a heating and cooling rate of 0.17 K s⁻¹. XRD analyses using Cu Kα radiation were performed to investigate the crystal structures of the alloy. Structural analyses and lattice-parameter refinement were performed by the Pawley method²²⁾ using Rigaku software PDXL 2.4. The specimen for EBSD analysis was embedded in resin and mirror-polished using silica. SEM–EBSD observations were performed using a HITACHI High-Tech SU5000 with a working distance of 8 mm and an acceleration voltage of 20 kV. In the orientation analysis, a variant map and a pole figure (PE) were made after terminating points with confidence index threshold of 0.1. TEM samples were prepared by focused-ion-beam (FIB) machining with a HITACHI High-Tech NB5000 instrument or by the twin-jet method in an electrolyte solution composed of 20% H₂SO₄ and 80% CH₃OH by volume. TEM observations were performed using a JEM2100 PLUS electron microscope equipped with a CMOS camera (EM-24830FLASH) and operated at an acceleration voltage of 200 kV.

3. Results

DSC measurements were performed to determine the martensitic transformation temperature. Figure 1 shows the DSC cooling and heating curves of Ti₃₀Ni₅₀Zr₂₀ alloy. From the exothermic peak during cooling and the endothermic peak during heating, the martensitic transformation start (M_s) temperature and finish (M_f) temperature and the reverse transformation start (A_s) temperature and finish (A_f) temperature of this alloy were found to be M_f = 336.0 K, M_s = 383.8 K, A_s = 425.0 K, and A_f = 458.8 K, respectively, using the tangent method. From the results of DSC measurements, we estimated that this alloy is in the martensitic phase at room temperature.

Fig. 1

DSC cooling and heating curves of water-quenched Ti₃₀Ni₅₀Zr₂₀ alloy.

Figure 2 shows the XRD pattern of the Ti₃₀Ni₅₀Zr₂₀ alloy at room temperature. The crystal structure of this alloy is a monoclinic B19′ structure (space group: P2₁/m), and the Pawley method was used to refine the lattice parameters, which were found to be a = 0.3074 nm, b = 0.4086 nm, c = 0.4916 nm, and β = 103.64°; in addition, the reliability was R_wp = 1.89% and S = 1.94. These results are in good agreement with the data for Ti_0.64Zr_0.36Ni alloy reported in a previous study.²³⁾ On the basis of the results of DSC measurements, this alloy clearly forms B19′ monoclinic martensite at room temperature.

Fig. 2

XRD pattern of the Ti₃₀Ni₅₀Zr₂₀ alloy at room temperature (λ = 0.15418 nm).

SEM–EBSD measurements were performed to investigate the crystal orientation of the martensite variant. Figure 3(a) shows the inverse pole figure (IPF) map of the B19′ martensite. The martensite variant has a polygonal- and plate-like morphology with a width of 1–2 µm. Table 1 shows a table of lattice correspondences based on previous studies^24,25) of alloy transforming from the B2 matrix to the B19′ martensite. The B19′ martensite has 12 different corresponding variants (CVs); however, the resolution of the EBSD is insufficient to distinguish between CV1 and CV1′. Therefore, the analysis was performed assuming six types of CVs. Figure 3(b) shows a variant map and the area fraction of each CV based on the lattice correspondence shown in Table 1. The results show that CV1(1′)–CV2(2′), CV3(3′)–CV4(4′), and CV5(5′)–CV6(6′) have approximately the same area ratio. In addition, as shown in Fig. 3(c), a PF of the {011} plane of the B19′ structure was used for trace analysis. In Fig. 3(b) and (c), the CV1(1′)–CV2(2′) interface shown in i and the CV3(3′)–CV4(4′) interface shown in ii were found to be {011}_B19′ twins. On the basis of the lattice correspondence shown in Table 1, {011}_B19′ is identical to {100}_B2. The point indicated by the arrow in Fig. 3(c) is the {100} plane of the B2 matrix, showing that a four-variant cluster is formed around this plane.

Fig. 3

(a) Inverse pole figure map of the B19′ martensite. (b) Lattice correspondence variant map and area ratio. (c) Pole figure taken for the {011} plane of the B19′ structure.

Table 1 Lattice correspondence between the B2 parent phase and the B19′ martensite.

To investigate the microstructure in detail, we conducted detailed TEM observations. Figure 4(a) and (c) show the bright-field images, and (b) and (d) show the selected-area electron diffraction patterns (SADPs) obtained from B and D in (a) and (c), respectively. Figure 4(a) and (b) show that the interface of CV is (011)_B19′, in agreement with the SEM–EBSD results. From Fig. 4(c) and (d), fine (001)_B19′ compound twins were formed as internal defects. These twins are frequently observed as LIS in Ti–Ni–Hf alloys and Zr-based alloys with {100}_B2 as the habit plane^10,26) and are considered to be formed with CV1–CV1′ mirror symmetry at the basal plane on the basis of the lattice correspondence.

Fig. 4

(a), (c) Bright-field images of water-quenched Ti₃₀Ni₅₀Zr₂₀ alloy. (b), (d) Selected-area electron diffraction patterns corresponding to region B in (a) and D in (c), respectively.

Tensile tests were conducted to introduce strain into the martensite of this alloy. The stress–displacement curve of the test is shown in Fig. 5. The displacement is crosshead displacement of the tensile test machine. The specimen fractured at approximately 0.49 mm displacement, as indicated by the cross mark, and the maximum stress was approximately 1100 MPa. The stress increased linearly with increasing displacement to ∼0.17 mm; however, the slope became more gradual thereafter. These behaviors are considered reasonable because they are in good agreement with previous studies²⁷⁾ in which compression tests were performed on Ti–Ni–Zr alloys. In the stress–strain curve of shape-memory alloys, a plateau region is typically observed,^28,29) where martensite variants are considered to reorient; however, the stress–displacement curve of the Ti₃₀Ni₅₀Zr₂₀ alloy investigated in the present study did not show a plateau. The reasons for this lack of a plateau are discussed below. Samples subjected to tensile testing and in which strain was introduced are henceforth referred to as “deformed specimens”.

Fig. 5

Stress–displacement curve of the Ti₃₀Ni₅₀Zr₂₀ alloy.

Figure 6 shows the results of SEM–EBSD measurements on the deformed specimens. IPF map is shown in Fig. 6(a) and variant map distinguished by CVs and area fraction is shown in Fig. 6(b). Comparing the results with those of the solution-treated sample shown in Fig. 3 reveals that, in addition to the straight interfaces indicated by the white arrows in Fig. 6(a), there are also interfaces that are curved, such as those indicated by the red double arrows in Fig. 6(a). The variant map shown in Fig. 6(b) indicates that both of these interfaces are CV5(5′)–CV6(6′) and CV3(3′)–CV4(4′) boundaries and are HPV interfaces. Trace analysis based on the PE of the {011}_B19′ plane shown in Fig. 6(c) indicates that the HPV interface is the {011}_B19′ plane, as was also observed for the solution-treated sample; it also shows that a cluster of four HPVs is formed around {100}_B2. TEM observations were performed to investigate the microstructure of the curved HPV interface in greater detail.

Fig. 6

(a) Inverse pole figure map of Ti₃₀Ni₅₀Zr₂₀ alloy after the tensile test. (b) Lattice correspondence variant map and area ratio. (c) Pole figure taken by {011} plane of the B19′ structure.

The bright-field image in Fig. 7(a) shows a fine twin contrast, and the electron diffraction pattern obtained from B in (a), presented in (b), shows the formation of (100)_B19′ compound twins. Although (100)_B19′ compound twins have been observed in solution-treated Ti–Ni–Zr alloys,¹²⁾ in the Ti₃₀Ni₅₀Zr₂₀ alloy, they were only observed in the deformed specimen. In addition, we observed some contrasts that appeared to be (001)_B19′ compound twins. Therefore, one of two types of internal defects, (001) or (100) compound twins, was observed in the deformed specimen.

Fig. 7

(a) Bright-field image of the Ti₃₀Ni₅₀Zr₂₀ alloy after the tensile test. (b) Selected-area electron diffraction pattern corresponding to region B in (a).

4. Discussion

We here discuss the self-accommodation of a solution-treated Ti₃₀Ni₅₀Zr₂₀ alloy. In this alloy, the crystal structure is the same B19′ structure observed in Ti–Ni alloys. Variants with mirror symmetry at {011}_B19′ were observed, and we found that (001)_B19′ compound twins were introduced as internal defects in these variants. The {011}_B19′ plane observed as a variant interface in this alloy is {001}_B2 based on the lattice correspondence and is considered to be near a habit plane. That is, the plate- or polygonal-like variant pairs forming {011}_B19′ twins (i.e., CV1(1′)–2(2′), 3(3′)–4(4′), and 5(5′)–6(6′)) are HPV pairs. Therefore, the (001)_B19′ compound twin introduced into the HPV is formed by CVs (i.e., CV1–1′) with mirror symmetry at the basal plane and can be considered to be the LIS in this alloy. The introduction of (100)_B19′ compound twins was also observed in the deformed specimens. The (001) and (100)_B19′ compound twins will be discussed in the next paragraph. The self-accommodation in which the HPV interface is {011}_B19′//{100}_B2 planes and (001)_B19′ compound twins introduced as LIS have been observed in Zr-based alloys showing orthorhombic martensite with the B33 structure, as well as in Ti–Ni–Hf alloys showing the B19′ monoclinic martensite with a larger β-angle than Ti–Ni alloys, and are assumed to form via a similar microstructure formation mechanism.^10,26,30) Although the B33 structure is orthorhombic, its lattice is similar to that of the B19′ structure. Specifically, when the β-angle of the monoclinic B19′ structure increases, the angle between the (001)_B19′ and $(20\bar{1})_{\text{B}19'}$ planes becomes 90° and can be treated as an orthorhombic B33 structure.¹⁸⁾ Therefore, even if the same B19′ structure is formed, as the β-angle increases, the HPV interface becomes not {111}_B19′ of the Ti–Ni alloy³⁾ but {011}_B19′//{100}_B2, and the LIS is considered to change to (001)_B19′ compound twins instead of ⟨011⟩_B19′ Type II twins. This consideration is supported by the observation that the habit plane becomes {021}_B33//{100}_B2 in the self-accommodation of alloys with B33 orthorhombic martensite. In martensite with the B33 orthorhombic structure in Zr–Co–Pd alloys and Ti–Ni–Hf alloys, the internal defects have been assumed to not be defects or (010)_B33 stacking faults.^10,30) Assuming that the β-angle of the B19′ structure increases and changes to the B33 structure, the (010)_B33//(001)_B19′ orientation relationship indicates that the LIS of this alloy is also similar to the self-accommodation of B33 orthorhombic martensite. Also, in pairs of HPVs that form another interface (i.e., CV1(1′)–3(3′) and CV2(2′)–4(4′)), the interface is parallel to {110}_B2, forming a diagonal boundary (Fig. 3). These variants have a different habit plane. Thus, the interface forming {110}_B2 observed in this alloy is considered to be formed by HPV collision, as in the Ti–Ni–Hf alloy.¹⁰⁾ The self-accommodation of martensite in this alloy can therefore be considered a combination of plate- and polygonal-like variants (i.e., a mosaic-like microstructure) with a minimum unit of HPV pairs whose habit plane is the {011}_B19′//{100}_B2 plane, and LIS-introduced (001)_B19′ compound twins.

Here, we discuss the effect of strain on the microstructure of Ti₃₀Ni₅₀Zr₂₀ alloy. In general, as a microstructural change when strain is introduced in shape memory alloys and superelastic alloys, detwinning and reorientation occur in the plateau region after elastic deformation, forming a preferential variant in the tensile direction. However, no obvious plateau region was observed in the stress–displacement curve shown in Fig. 5 for the Ti₃₀Ni₅₀Zr₂₀ alloy. In the deformed specimens in which strain was introduced via tensile test, the EBSD analysis shown in Fig. 6(b) reveals differences in the volume fraction of HPV. Specifically, the HPVs with straight interfaces (CV5(5′)–CV6(6′)) indicated by a white arrow had approximately the same volume, whereas the HPVs with curved interfaces (CV3(3′)–CV4(4′)) indicated by the red double arrow had a different volume fraction. These results indicate that the mosaic-like microstructure observed in the solution-treated sample was collapsed by the movement of the HPV interface as a result of the introduction of strain. Furthermore, the movement of HPV interface should depend on the tensile direction. It is very useful to identify the tensile direction for the development of prior variants of martensite. This is now under study. The TEM observation results also show the introduction of a fine (100)_B19′ compound twin.

We here discuss the difference between the (001)_B19′ compound twins observed in the solution-treated samples and the (100)_B19′ compound twins observed in the deformed specimens. On the basis of the lattice parameters obtained from the XRD analysis, the twin shear s was calculated to be 0.485 for both materials.³¹⁾ Thus, the two types of twins were expected to have the same easiness of introduction into the internal of the variant. However, in the present study, no (100)_B19′ compound twinning was observed unless strain was applied. As mentioned in the preceding paragraph, the (001)_B19′ compound twins were considered to have been introduced as LIS and are attributed to the shear-shuffling of martensitic transformation. The shear during the transformation from the B2 structure to the B19′ structure is expected to be $[\bar{1}00]$, and this shear forms (001)_B19′ compound twins with mirror symmetry of CV1 and CV1′ at the basal plane. Therefore, even if the amount of s is the same, (001)_B19′ compound twins, not the (100)_B19′ compound twins, are expected to be introduced as LIS. Therefore, the (100)_B19′ compound twin observed in the deformed specimens was considered to be a deformation twin formed by the introduction of strain. The (100)_B19′ compound twins observed in a previous study¹²⁾ were also observed in the solution-treated sample. The results suggest that these compound twins are deformation twins formed by elastic interactions between martensite, not twins introduced as LIS in Ti–Ni–Zr alloys.³²⁾ In addition, because s is the same, the (001)_B19′ compound twins might also be introduced as deformation twins. The curved HPV interface observed in the EBSD analysis is attributed to the introduction of these deformation twins near the interface. In summary, the HPV interface moves and deformation twins are introduced as a deformation microstructure when the displacement is applied to the Ti₃₀Ni₅₀Zr₂₀ alloy. The lack of an observed stress plateau is speculated to be caused by these deformation structures, and this alloy is expected to not be able to relax large strains like other shape-memory alloys whose stress–strain curves exhibit plateau regions.

5. Conclusion

We investigated the self-accommodation and deformation microstructure of the martensite of Ti₃₀Ni₅₀Zr₂₀ alloy using XRD analysis, SEM–EBSD analysis, and TEM observations. The results are summarized as follows.

The transformation temperatures of the Ti₃₀Ni₅₀Zr₂₀ alloy were M_f = 336.0 K, M_s = 383.8 K, A_s = 425.0 K, and A_f = 458.8 K.

The martensite of the Ti₃₀Ni₅₀Zr₂₀ alloy has a B19′ monoclinic structure at room temperature, and the lattice parameters are a = 0.3074 nm, b = 0.4086 nm, c = 0.4916 nm, and β = 103.64°.

The habit plane was found to be near {011}_B19′//{100}_B2. In addition, the polygonal- and plate-like HPV interface with a width of 1–2 µm formed {011}_B19′ Type I twins; (001)_B19′ compound twins were introduced as internal defects.

The mosaic-like self-accommodation was collapsed under applied strain, and the movement of the HPV interface and the introduction of (100)_B19′ deformation twins were observed. Some curved HPV interfaces were also observed.

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP20H02427.

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