2018 Volume 59 Issue 10 Pages 1567-1573
The antiphase boundary (APB)-like structure of B33 martensite in a Zr–Co–Pd alloy was investigated by means of conventional transmission electron microscopy and high-angle annular dark-field scanning transmission electron microscopy. The APB-like structure had atomic shifts along both the c-axis on the (010)B33 basal plane and the b-axis on the (001)B33 plane. The displacement vector of the APB-like structure could be expressed as R = ⟨0, 1/4, 1/2⟩B33. The formation mechanism of the APB-like structure was also elucidated.
The shape memory effect and superelasticity are caused by a thermoelastic martensitic transformation. Near-equiatomic Ti–Ni alloys undergo thermoelastic martensitic transformation from B2 to B19′ structures near room temperature.1) Near-equiatomic Ti–Pd alloys are candidates for high-temperature shape memory materials because their thermoelastic martensitic transformation temperature is approximately 800 K.2) We have so far analyzed the antiphase boundary (APB)-like contrast of martensite in Ti–Ni and Ti–Pd shape memory alloys.3,4) We characterized those APB-like structures as a kind of stacking fault, with an APB-like morphology induced by the martensitic transformation. Such structures were also observed in Ti–Pd–Fe martensite with a long-period stacking order structure,5) as well as in martensite consisting of simple 2H structures.3,4) Further, Inamura et al. discovered an APB-like contrast in α′′ (orthorhombic)-martensite in a Ti–Nb–Al alloy in which athermal ω-phase was dispersed in the parent bcc phase.6) We also analyzed the APB-like contrast of B19′ martensite via an R-phase transformation in a Ti–Ni–Fe alloy.7) These results suggest that the atomic displacement of APB-like structures is influenced by not only martensitic transformation itself but also atomic arrangement of preexistence phase prior to martensitic transformation. However, all alloys with APB-like structures described above are Ti-based alloys, and their martensitic transformations are caused by the shear and shuffling process, corresponding to atomic movement along the $[01\bar{1}]_{\text{B2}}$ and $[0\bar{1}1]_{\text{B2}}$ directions alternately on the {011}B2 plane of the B2 parent phase.8)
We expect that APB-like structures should exist not only in Ti-based alloys but also in other alloys with the shear and shuffling process, regardless of specific directions and planes, because this structure is induced by the local heterogeneity of atomic movements during the martensitic transformation. Therefore, we focus on a Zr–Co–Pd alloy with high elongation resulting from transformation-induced plasticity associated with deformation-induced martensite.9) This Zr–Co–Pd alloy undergoes a thermally induced martensitic transformation from the B2 to B33 structure as a result of substituting Pd for Co. The lattice correspondence between the B2 parent phase and the B33 martensite is illustrated in Fig. 1. The dotted and solid lines in Fig. 1(a) indicate the B2 and B33 structures, respectively. The orientation relationship between the B2 parent phase and the B33 martensite was determined to be (011)B2 // (010)B33, $(01\bar{1})_{\text{B2}}$ // (001)B33, and [100]B2 // [100]B33.9–11) Shear and shuffle during martensitic transformation to form from the B2 to B33 structures are successive atomic shifts along two opposite directions by the +1/2[100]B2 and −1/2[100]B2 on pairs of {011}B2 planes as indicated in Fig. 1(b), which is quite different from that in Ti-based alloys.11,12) Although the APB-like contrasts in the B33 structure has been reported in Zr–Cu–Al–Co alloy,13) their detailed characterizations such as displacement vector have not been performed.
(a) Lattice correspondence between the B2 parent phase and the B33 martensite. Dotted and solid lines indicate B2 and B33 structures, respectively. (b) Shear and shuffle during martensitic transformation to form the B33 structure, which indicates successive atomic shifts along two opposite directions by +1/2[100]B2 and −1/2[100]B2 on pairs of {011}B2 planes.
The aim of the present study is to clarify the crystallography and morphology of the APB-like structure of B33 martensite in a Zr–Co–Pd alloy by conventional transmission electron microscopy (CTEM) and high-angle annular dark-filed scanning transmission electron microscopy (HAADF-STEM). The formation mechanism of such an APB-like structure is also discussed on the basis of these observations.
A Zr–30.0 at% Co–20.0 at% Pd alloy was prepared from 99.7% Zr, 99.9% Co, and 99.9% Pd (mass%) by arc melting in an argon atmosphere. The ingot was solution-treated in an argon atmosphere at 1173 K for 3.6 ks and then quenched in ice water. The transformation temperature to the martensite (Ms) of the Zr–30.0 at% Co–20 at% Pd alloy, measured by differential thermal analysis, was about 518 K, indicating that this alloy consisted of full martensite with a B33 structure at room temperature. For the TEM studies, disks with diameters of 3 mm were spark-cut from the solution-treated specimens and ground to thicknesses of 80 µm. The samples were then dimpled with a GATAN Model 656 dimple grinder and Ar-ion milled with a GATAN Model 691 PIPS system. TEM observations were carried out with a JEM-2000FX microscope with an accelerating voltage of 200 kV. HAADF-STEM observations were performed using a JEM-ARM200F microscope (Cs-corrected 200 kV STEM; JEOL). The beam diameter of the electron probe was 0.1 nm and the current was approximately 20 pA. For obtaining the HAADF-STEM images, the annular detector was set to collect electrons scattered at angles between 90 and 170 mrad. The following lattice parameters were used for the analysis of the B33 martensite: aB33 = 0.333 nm, bB33 = 1.030 nm, and cB33 = 0.441 nm.14)
Figures 2(a) and (b) show a typical bright-field image and the electron diffraction pattern taken from area B in (a) for a Zr–Co–Pd alloy, respectively. Martensitic variants with a plate-like morphology are observed in Fig. 2(a). The electron diffraction pattern shown in Fig. 2(b) consists of two sets of reflections, which are in mirror symmetry with respect to the (021)B33 plane, from the [100]B33 direction of the B33 structure. The trace of boundaries in region B is parallel to the (021)B33 plane. This fact indicates that the two sets of reflections show a (021)B33 twin pattern and that the platelet is a (021)B33 twin. Most variant boundaries show (021)B33 twinning. These observations are consistent with the results in our previous report.9) Note that many line contrasts are observed within the martensitic platelets, as indicated by the arrows in Fig. 2(a). In order to analyze these contrasts, CTEM observations are carried out from the [001]B33 direction, which is the edge-on condition for the (010)B33 basal plane of the B33 structure derived from (011)B2 plane, that is, the shuffling plane on martensitic transformation, as shown in Fig. 1.
(a) Bright-field image for the Zr–30.0 at% Co–20.0 at% Pd alloy. The martensitic variants with plate-like morphology are present. (b) Electron diffraction pattern taken from area B in (a). The pattern consists of two sets of reflections, showing a (021)B33 twin pattern, and the platelet is a (021)B33 twin.
Figures 3(a) and (b) show the bright-field image and the corresponding electron diffraction pattern of the [001]B33 direction of the B33 structure, respectively. Some APB-like structures with thin linear contrasts along the (010)B33 basal plane and wider contrasts along the (100)B33 plane are observed in the martensitic plates, as indicated by the single and double arrows in Fig. 3(a), respectively. Figures 3(c), (d), and (e) show the dark-field images taken by using 020B33, 040B33, and 200B33 reflections, respectively. These contrasts are observed when using the 020B33 reflection, whereas no contrast is observed when using the 040B33 and 200B33 reflections. These morphologies are similar to those of the APB-like contrasts in the Ti-based alloys previously reported,3–7) although the atomic displacements are quite different in the present and the Ti-based alloy, as mentioned above. Furthermore, thin linear contrasts are present along the (010)B33 shuffling plane, indicating that such contrasts are related to the martensitic transformation.
(a) Bright-field image and (b) corresponding electron diffraction pattern of [001]B33 direction of the B33 structure. Some APB-like structures with thin linear contrasts along the (010)B33 basal plane and wider contrasts along the (100)B33 plane are observed in the martensitic plates. (c), (d) and (e) Dark-field images taken by using 020B33, 040B33, and 200B33 reflections, respectively. APB-like contrasts are observed when using 020B33 reflections, whereas no contrast is observed when using the 040B33 and 200B33 reflections.
In order to observe the variation in contrast of the APB-like structure, CTEM observations are carried out from the [101]B33 and [100]B33 directions, which are parallel to the (010)B33 basal plane of the B33 structure. Figures 4(a) and (b) show the bright-field image and corresponding electron diffraction pattern taken at the same area as that shown in Fig. 3, respectively. The specimen was tilted about 36 degrees around the b*-axis from the [001]B33 to the [101]B33 zone axes. Some APB-like structures with thin linear contrasts along the (010)B33 basal plane and wider contrasts, as indicated by the single and double arrows in Fig. 4(a), respectively, are observed in the martensitic plates, similar to the results shown in Fig. 3(a). Figures 4(c) and (d) show the dark-field images taken using the 020B33 and 040B33 reflections, respectively. These APB-like contrasts are observed when using the 020B33 reflection, whereas no contrast is observed when using the 040B33 reflection, consistent with the results shown in Figs. 3(c) and (d), indicating that APB-like contrast has a specific atomic displacement. Figures 5(a) and (b) show the bright-field image and the corresponding electron diffraction pattern taken at the different area from Fig. 3 of the [100]B33 direction of the B33 structure, respectively. Thin linear contrasts are observed along the (010)B33 basal plane, as shown in the dark-field image taken by using the 020B33 reflection of Fig. 5(c), indicating that thin linear contrasts are present on the (010)B33 basal plane, as is apparent from the contrasts along the [001]B33 direction in Fig. 3(c) and the [101]B33 direction in Fig. 4(c). On the other hand, no contrast is observed when using the 040B33 and 002B33 reflections shown in Figs. 5(d) and (e), respectively. Here, the 002B33 reflection is used because the 001B33 reflection is forbidden according to the extinction rule for the B33 structure.15)
(a) Bright-field image and (b) corresponding electron diffraction pattern taken at the same area in Fig. 3, respectively, from the [101]B33 direction obtained by tilting the specimen about 36 degrees around the b*-axis from the [001]B33 zone axis of the B33 structure. (c) and (d) Dark-field images taken by using 020B33 and 040B33 reflections, respectively. APB-like contrasts are observed when using 020B33 reflection, whereas no contrast is observed when using 040B33 reflection.
(a) Bright-field image and (b) corresponding electron diffraction pattern taken at the different area from Fig. 3 of [100]B33 direction of the B33 structure. (c), (d) and (e) Dark-field images taken by using 020B33, 040B33, and 002B33 reflections, respectively. APB-like contrasts are observed when using 020B33 reflections, whereas no contrast is observed when using 040B33 and 002B33 reflections.
Based on these observations, we discuss the displacement vector R = ⟨Rx, Ry, Rz⟩ of the APB-like structure in the present Zr–Co–Pd alloy. APB-like contrasts are observed using g = 020B33, whereas no APB-like contrasts are observed using g = 040B33, implying that atomic displacement along the b-axis of APB-like contrast, that is, Ry, is 1/4 on the basis of the relationship between the phase angle and R.16) As depicted in Fig. 3(c), APB-like contrasts are observed at neither g = 200B33 nor 400B33, although the micrograph using g = 400B33 is not included here, indicating that the atomic displacement along the a-axis of the APB-like contrast, that is, Rx, is 0 or 1/2. Furthermore, Rz is 0 or 1/2 because no APB-like contrasts are observed using g = 002B33, as seen in Fig. 5(c). From the relationship of g·R in the present APB-like contrasts described above, the atomic displacement of the APB-like structure can be expressed as R = ⟨0 or 1/2, 1/4, 0 or 1/2⟩.
HAADF-STEM analysis using Z contrast was performed along the [001]B33 direction of the B33 structure to determine the positions of the atomic columns at the interface in the APB-like contrasts. The atomic columns of Zr and Co and/or Pd in the B33 structure can be easily distinguished along the [001]B33 direction, which is also the edge-on condition for the (010)B33 shuffling plane described above. Figure 6(a) shows the HAADF-STEM image of the APB-like structure taken along the [001]B33 direction of the B33 structure. Figure 6(b) shows the image intensity profile taken along the white line A–B in Fig. 6(a). The binary phase diagram for Co and Pd shows that these metals form a complete solid-solution system. Because the amount of substitution of Pd for Co is limited to 20 at% in the present alloy, the Pd atoms are considered to be present at Co sites. Therefore, because of the nature of Z-contrast, the higher-intensity profile shows Zr (Z = 40) columns, whereas the lower-intensity profile shows Co (Z = 27) and/or Pd (Z = 46) columns. The bright and dim spots in Fig. 6(a), therefore, correspond to the Zr and Co(Pd) atomic columns, respectively. The Fourier filter-processed image around the APB-like interface of Fig. 6(a) is presented in Fig. 6(d), and the atomic arrangements in Fig. 6(d) are schematically illustrated in Fig. 6(e). The open and solid circles indicate the Zr and Co(Pd) atomic columns, respectively. The atomic arrangements of the white-framed area in Fig. 6(d) correspond to a unit cell of the B33 structure. Undoubtedly, the presence of the atomic shift R along the b-axis is confirmed across one extra (010)B33 plane, shown by the arrows in Figs. 6(d) and (e). This provides clear evidence at the atomic level of an APB-like structure on the (010)B33 basal plane in B33 martensite. Concerning the atomic species of the APB-like structure on the (010)B33 basal plane, the intensities of each Co and/or Pd columns in Fig. 6(c) are scattered as compared to those of Zr columns, as shown in the image intensity profiles taken along the white line C–D in Fig. 6(a). Therefore, Co and Pd columns are not ordered along the [001]B33 direction. Furthermore, Zr and Co and/or Pd sites based on these HAADF-STEM observations are also consistent with those expected geometrically by martensitic transformation from B2 parent phase as described below.
(a) A HAADF-STEM image of the APB-like structure along the [001]B33 zone axis. (b) and (c) Image intensity profiles taken along the white lines A–B and C–D in (a), respectively. (d) Fourier filter-processed HAADF-STEM image around the APB-like interface. (e) Schematic illustration of the atomic arrangements in (d). The open and solid circles indicate the Zr and Co(Pd) atom columns, respectively.
We discuss the R of the APB-like structure. There is no atomic displacement along the a-axis component, but that along the b-axis is 1/4, as seen in Fig. 6(d). In order to determine the atomic displacement along the c-axis, HAADF-STEM observations are carried out along the [100]B33 direction; the results reveal the displacement along the c-axis on the b–c plane. Figure 7(a) shows the HAADF-STEM image of the APB-like structure along the [100]B33 zone axis. Figure 7(b) shows the image intensity profile taken along the white line X–Y in Fig. 7(a). The bright and dim spots in Fig. 7(a) correspond to the Zr and Co(Pd) atomic columns, respectively, because of the nature of the Z contrast, as found in Fig. 6(a). The Fourier filter-processed image around the APB-like interface of Fig. 7(a) is presented in Fig. 7(c), and the atomic arrangement in Fig. 7(c) is schematically illustrated in Fig. 7(d). The open and solid circles indicate the Zr and Co(Pd) atomic columns, respectively. The atomic arrangements of the white-framed area in Fig. 7(c) correspond to a unit cell of the B33 structure. We can see the atomic shift R along both the c-axis on the (010)B33 basal plane and the b-axis on the (001)B33 plane, as depicted in Figs. 7(c) and (d). The atomic displacement along the b-axis is 1/4, similar to the result shown in Fig. 6. It is also obvious that the atomic displacement along the c-axis is 1/2, as indicated by the R value in Fig. 7(d). Based on these atomic displacements and g·R analysis, the R value of the APB-like structure on the B33 martensite in the present Zr–Co–Pd alloy can be expressed as R = ⟨0, 1/4, 1/2⟩B33.
(a) A HAADF-STEM image of the APB-like structure along the [100]B33 zone axis. (b) Image intensity profile taken along the white line X–Y in (a). (c) Fourier filter-processed HAADF-STEM image around the APB-like interface. (d) Schematic illustration of the atomic arrangements in (c). The open and solid circles indicate the Zr and Co(Pd) atom columns, respectively.
As described in the introduction, the B33 structure is formed by shearing pairs of {011}B2 planes along two opposite directions successively by +1/2[100]B2 and −1/2[100]B2. The displacement of the b-axis of the B33 structure stemming from the atomic shuffling upon martensitic transformation is 1/4 because the (011)B2 plane corresponds to the (040)B33 plane, as seen in Fig. 1. Similarly, based on the atomic shuffling upon the martensitic transformation, there is no displacement of the a-axis of the B33 structure, but that along the c-axis is 1/2. Consequently, R = ⟨0, 1/4, 1/2⟩B33 of the APB-like structure on the B33 structure is equal to the displacement because of the atomic shuffling upon martensitic transformation, as the B33 structure should be maintained across the APB-like interfaces.
Furthermore, the interface structure of the APB-like structure on a non-basal plane is discussed. Figure 8(a) and (b) show the HAADF-STEM and a Fourier filter-processed images along the [001]B33 zone axis of another APB-like structure in different area from Fig. 6, respectively. We can clearly see atomic shifts on the (010)B33, as indicated by the single arrows in Fig. 8(b). Atomic shifts on a non-basal plane can be also seen in the white-framed area in Fig. 8(b). Compared with the APB-like structure on only the (010)B33 basal plane in Fig. 6, these APB-like structure on the non-basal plane has diffuse contrasts, as shown in Fig. 8(b). This supports the wider APB-like contrasts along the (100)B33 plane by the CTEM observations shown in Fig. 3.
(a) A HAADF-STEM and (b) a Fourier filter-processed image of the APB-like structure on a non-basal plane in different area from Fig. 6 along the [001]B33 zone axis.
We now discuss the mechanism of formation of the APB-like structure on the basis of our observations. It is well known that the displacement vector of the APB interface induced by the order-disorder transformation in the B2 structure is 1/2(111)B2,17) although there is no evidence for APB in the B2 phase of the Zr–Co–Pd alloy. If the APB formed in the B2 parent phase is inherited to the B33 phase after martensitic transformation in the present alloy, the atomic arrangements of the Zr and Co(Pd) columns on the (010)B33, (001)B33, and/or (100)B33 planes should be replaced. However, there is no irregularity of the atomic arrangements on those planes, as judged from the intensity profiles and the atomic positions shown in Figs. 6 and 7. Therefore, we conclude that the APB-like structure in the B33 martensite of the present Zr–Co–Pd alloy is not inherited from the APB in the B2 parent phase. Furthermore, the APB-like structure is independent of the displacement stemming from the pre-martensitic transformation18) because the Zr–Co–Pd alloy directly undergoes martensitic transformation from B2 to B33 without any pre-martensitic transformation.9,14) The APB-like structure is therefore directly related to the martensitic transformation mechanism. In the case of martensitic transformation from B2 to B33, the shear and shuffling process is an atomic shift along two opposite directions successively by +1/2[100]B2 and −1/2[100]B2 on pairs of {011}B2 planes shown in Fig. 1(b). The change in the shear direction on one (010)B33 basal plane in the B33 structure, i.e., the shear in the same direction accidentally on three (010)B33 basal planes indicated by the bold arrows in Fig. 9, produces an APB-like boundary. However, it is difficult to explain the atomic displacement on the non-basal plane in terms of just the difference in the shear direction, as seen in Fig. 9. Therefore, the presence of these interfaces is possibly related to the growth of martensite, as well as to the APB-like contrasts in the Ti-based alloy. Figure 10 is a schematic illustration of the mechanism underlying the formation of the APB-like structure. The hatched large and small circles in Fig. 10(a) denote the Zr and Co(Pd) atomic columns, respectively, in the B2 parent phase. Martensitic domains nucleate at various sites within a variant during the transformation, as seen in Fig. 10(b). Finally, the APB-like structure develops through accidental impingement of such domains, as shown in Fig. 10(c). This can lead to displacement on the non-basal plane. Furthermore, accidental impingement of such domains during martensitic transformation should provide the kink-like structure on both the (010)B33 and (100)B33 planes, as seen in Fig. 10(c). This schematic illustration seems to be consistent with an image of APB-like structure on the non-basal plane of Fig. 8(b). However, the APB-like structure would consist of two-dimensional interfaces in a three-dimensional crystal; that is, the boundary would be curved in the projected direction by location, resulting in the diffuse and wider contrasts. Therefore, more detail investigation containing accurate STEM image acquisition, image simulations for STEM, and boundaries energy simulation should be performed to determine the structural model of such three-dimensional defect including the atomic displacement of kink-like structure on the non-basal plane exactly. Furthermore, as shown in Figs. 6(d) and 7(a), the APB-like structure on the (010)B33 basal plane seems to be a slight modulation along ⟨010⟩B33 direction, indicating a little difference from the ideal model. One of this reason could be explained by the stress relief originated from accidental impingement of such martensitic domains. This should be also related to the diffuse contrasts on the non-basal plane. Consequently, it is concluded that the APB-like structure is induced by the difference in the shear direction during martensitic transformation and/or impingement of martensitic domains that nucleate at various sites. This study proves that the APB-like structure is observed in the B33 martensite plate of Zr-based alloys with the shear and shuffling process, as opposed to the case of Ti-based alloys. It is obvious that the APB-like structure on the B33 structure is induced by the martensitic transformation. Consequently, the APB-like structure should exist in the martensitic variant of other alloys with the ordered parent phase.
Schematic illustration of shear and shuffle during martensitic transformation to form the APB-like structure, which indicates the shear in the same direction accidentally on three (010)B33 basal plane, producing an APB-like boundary.
Schematic illustration of the mechanism underlying the formation of the APB-like structure, showing atomic arrangements (a) of B2 parent phase, (b) during the martensitic transformation, and (c) of B33 martensite. The APB-like structure develops through accidental impingement of domains.
The APB-like structure of B33 martensite in a Zr–Co–Pd alloy is investigated by means of CTEM and HAADF-STEM observations. The APB-like structure shows the atomic shifts along both the c-axis on the (010)B33 basal plane and the b-axis on the (001)B33 plane. The displacement vector of the APB-like structure can be expressed as R = ⟨0, 1/4, 1/2⟩B33. It is concluded that the APB-like structure is induced by the difference in the shear direction during martensitic transformation and/or impingement of the martensitic domains nucleated at various sites. These results support that APB-like structure should exist in the martensitic variant of not only Ti-based shape memory alloys but also other alloys with the ordered parent phase.
This work was supported by JSPS KAKENHI Grant Number 26420725.
