2020 Volume 61 Issue 11 Pages 2107-2114
To quantitatively understand the thin foil effect in in situ observations of the B2 to B19′ transformation in Ti–Ni alloy, the microstructure of the B19′ martensite in thin foil and bulk specimens was compared. The transformation temperatures decreased with decreasing specimen thickness. There were large habit plane variants more than several tens of micrometers in size in the area of the specimen less than 10 µm thick. The critical thicknesses for reproducing the transformation behavior in the bulk material was about 20 µm based on the self-accommodation morphology and 4 µm based on the twin width ratio of the ⟨011⟩ type II twin.
Although more than 50 years have passed since the discovery of Ti–Ni alloy,1) research is continuing into its fundamental properties and applications due to its excellent superelasticity and shape memory effect.2–5) These properties are associated with thermoelastic martensitic transformation from the high-temperature cubic phase (B2) to low-temperature phases with trigonal, orthorhombic (B19), and/or monoclinic (B19′) structures, depending on the chemical composition and production history.2,3)
Many researchers have reported on in situ studies of the thermoelastic martensitic transformation using various microscopy techniques and have contributed to understanding the transformation.6–24) In particular, in situ scanning electron microscopy (SEM) allows extensive high-resolution observations,18–22) and thus combines the advantages of optical microscopy and transmission electron microscopy (TEM). The thin foil effect occurs in in situ TEM observations of the thermoelastic martensitic transformation in Ti–Ni alloys, especially from the B2 to B19′ phases. In TEM specimens, the B19′ martensite nucleates in the thicker areas and propagates to the thinner areas and no transformation occurs in the thinnest area of the electropolished hole.6,14,23) Therefore, in situ TEM observations may provide useful information about the transformation behavior in micrometer- and nanometer-sized shape memory alloy films used in microelectromechanical and nanoelectromechanical system devices. However, the discussion of the thin foil effect in in situ TEM observations of martensitic transformation is limited to the change in transformation temperatures in most articles.6,14,23–26) The crystallography and morphology in thin foils have not been analyzed based on the phenomenological theory of martensite crystallography (PTMC). To fully understand the thin foil effect in in situ observations, it is necessary to discuss not only the transformation temperatures but also the differences in martensite microstructures between thin foil and bulk specimens.
In the present study, we focus on two typical microstructural features. The first feature is the self-accommodation morphology of the B19′ martensite. We have analyzed the self-accommodation morphologies experimentally and theoretically,27–29) and the dynamical observations of their formation process with in situ SEM from B2 to B19′ in Ti–Ni alloys.20) There were three minimum unit pairs comprising two V-shaped habit plane variants (HPVs) connected with a $\{ \bar{1}\bar{1}1\} _{\text{B}19'}$ type I variant accommodation twin around each of the ⟨111⟩B2 traces, which indicates that there were a total of 12 pairs in the entire crystal. We call this V-shaped HPV cluster (HPVC) “2HPVC”. Around each {111}B2 pole, three self-accommodation morphologies based on the V-shaped minimum unit developed that had triangular, rhombic, and hexangular shapes consisting of three HPVs (3HPVC), four HPVs (4HPVC), and six HPVs (6HPVC), respectively. The 6HPVC morphology has a unique shape called a dual semi-regular hexagon. Details related to this shape can be found in the appendix (Figs. A1 and A2) of the present report. 3HPVC has six combinations, 4HPVC has three combinations, and 6HPVC has only one combination around a given {111}B2 pole; therefore, in the whole crystal, there are totals of 24, 12, and 4 combinations, respectively. 6HPVC is an ideal self-accommodation morphology because the transformation strain is reduced equally by each of the 6 HPVs with an equal volume fraction. In in situ SEM observations, 6HPVC appeared homogeneously in the grain interior during the initial stage of the transformation. The formation of 6HPVC was triggered by nucleation of 2HPVC and produced a strain gradient, along which 2HPVC and 3HPVC appeared. These results indicate that the formation of 6HPVC has the lowest energy barrier among the HPVCs and is important for characterizing the B2 to B19′ transformation behavior in the Ti–Ni bulk specimen. The second morphological feature is the twin width ratio of the ⟨011⟩ type II twin as a lattice invariant deformation (LID) of the transformation. The theoretically predicted ratio30,31) agrees well with the experimentally observed ratio.30,32,33)
In the present study, we compare the microstructures in B19′ martensite in thin foil and bulk specimens of Ti–Ni alloy based on the self-accommodation morphology and the twin width ratio of ⟨011⟩ type II twin as a LID of the transformation. The results provide a quantitative understanding of not only the thin foil effect in in situ TEM observations but also the microstructure difference between thin film and bulk materials which is vital to understand the shape memory properties of thin films.34)
A set of disks prepared from a cold-drawn Ti–50.8 at% Ni alloy rod (diameter, 3 mm) was used in all the observations. Disks with 1, 0.5 and 0.2 mm in thickness were cut from the rod and used for differential scanning calorimetry (DSC), SEM and TEM, respectively. Solution treatment was performed at 1173 K for 3.6 ks, and then the disks were quenched into ice water. A calorimeter (DSC-60, Shimadzu) was used to perform DSC measurements at a cooling and heating rate of 0.17 K/s. The martensite start (Ms) and finish (Mf) temperatures were 236 and 221 K, respectively, and the austenite start (As) and finish (Af) temperatures were 254 and 269 K, respectively. Electropolishing in H2SO4/CH3OH (1:4 v/v) was performed on the disks for in situ SEM and TEM observations above the Ms. The disks for SEM observations of the reverse transformation relief27) were electropolished in HNO3/CH3OH (1:3 v/v) below Mf.
Field emission-scanning electron microscopy (FE-SEM; Ultra55, Carl Zeiss) with a Peltier stage (ULTRA Coolstage, Deben) at a working temperature range of about 220–320 K was used for the in situ SEM observations. In situ TEM observations were performed with a transmission electron microscope (JEM-2010, JEOL) at 200 kV using a side-entry double-tilt liquid nitrogen specimen holder (Model 636, GATAN). The thickness at the observation area in the TEM specimen was estimated by electron energy-loss spectroscopy (EELS).35) In addition, the thickness of the TEM specimen for in situ SEM observations was measured directly by focused ion beam milling (NB5000, Hitachi).
The twin width ratio was evaluated as follows. The noise reduction and the segmentation of specific HPVs from HPVCs in the SEM and TEM images were conducted using Avizo (Thermo Fisher Scientific) and Photoshop (Adobe) software, respectively. The major and minor twins in each HPV in SEM images were binarized using IMAGE J software (NIH). The area fraction of each of the twins was measured from the binarized image, and then the twin width ratio was determined.
Figure 1(a) shows a low-magnification SEM-backscattered electron (BSE) image of the reverse transformation relief at room temperature after the specimen was electropolished to a flat surface in the fully martensitic state below Mf. Each of the B2 grains is clearly visible due to the channeling contrast. The average grain size is about 30 µm in diameter, as determined by electron backscattered diffraction (EBSD). There are nonmetallic inclusions with the darkest contrast that are less than 5 µm in diameter in the matrix. EBSD confirms that the surface normal of each grain is nearly parallel to ⟨111⟩B2 because the ⟨111⟩B2 recrystallization fiber texture develops in solution-treated rod specimens.36) Therefore, there are many 6HPVCs20,27–29) with the dual semi-regular hexagon shape with characteristic three pointed star shape in Fig. 1(a). Figure 1(b) shows the enlarged SEM-secondary electron (SE) image of the 6HPVC marked B in Fig. 1(a). Previous studies have shown that 6HPVC consists of three V-shaped minimum units consisting of HPVs 4′(+)/2′(−), 2′(+)/6′(−), and 6′(+)/4′(−) around [111]B2.20,27–29) The traces of the K1 planes of the characteristic twins, the ⟨011⟩ type II LID twin and $\{ \bar{1}\bar{1}1\} $ type I variant accommodation twin are the same as those in previous reports27–29,33,36) and supplementary figure (Fig. A2). Apparently, the three-pointed star morphology in Fig. 1(a) corresponds to the traces of the K1 planes of the $\{ \bar{1}\bar{1}1\} $ type I twins, which are derived from {110}B2. These results and the previous in situ observations show that the appearance of 6HPVC is a characteristic microstructural feature of the B2 to B19′ transformation in the bulk material.
(a) Low-magnification SEM-BSE image of reverse transformation relief at room temperature. (b) Enlarged SEM-SE electron image of the 6HPVC labeled B in (a).
Figures 2(a) and (b) show TEM-bright field (BF) images around the electropolished hole of the TEM specimen before and after in situ cooling. The foil normal of the B2 parent phase is nearly parallel to [111]B2 as indicated by inset in (a). The specimen thicknesses measured by EELS at points 1, 2 and 3 are 45, 70 and 120 nm, respectively, with a general accuracy of ±20%.35) Although most of the area around the hole is transformed to B19′ martensite upon cooling at about 110 K, untransformed areas are observed (marked by black and white single arrows in Fig. 2(b)). Similar transformation behavior was reported previously as a thin foil effect.6,14,23) The V-shaped and triangular self-accommodation-like configurations of small HPVs are visible in the upper left corner of the center grain marked by white double arrow in Fig. 2(b), whereas there are large HPVs in the thinner part around the edge of hole. Figure 2(c) shows an enlarged TEM-BF image taken from rectangular area C in Fig. 2(b). 6′(+) and 6′(−) HPVs consisting of ⟨011⟩ type II twins are identified from the corresponding electron diffraction patterns (lower left and upper right insets in Fig. 2(c)).27–29) The twin width ratio of 6′(+) and 6′(−) HPVs is estimated to be 8.08 and 5.25, respectively, as discussed later. These are considerably larger than the theoretically calculated ratio of 2.69 based on the PTMC.30,31) Therefore, TEM in situ cooling experiments are unsuitable for analyzing the B19′ martensite morphology, even though the crystallography of the LID is the same as that in the bulk material.
TEM-bright field images (a) before and (b) after in situ cooling observations. (c) Enlarged TEM-bright field image and corresponding selected area electron diffraction patterns taken from area C enclosed by the rectangle in (b).
To clarify the difference in microstructural features between thinner and thicker areas, in situ SEM observations were performed on the TEM specimen. Before reproduction of the results of in situ SEM observation, we demonstrate the thickness of the same specimen used for the observation, which was directly measured with focused ion beam milling after the observation as seen in Fig. 3(a). The thickness gradually increases with increasing distance from the edge of hole (Fig. 3(b)). For instance, the thickness is about 30 µm in the area 500 µm away from the hole. The thicknesses at the edge of hole and the region about 10 µm from the edge are 85 and 750 nm, respectively (enlarged figure inset in Fig. 3(b)). Although these values are larger than those measured by EELS of the specimen in Fig. 2, the transparency to the 200 kV electron beam was confirmed around the edge of the hole. SEM-SE images before and after cooling to 220 K are presented in Fig. 3(c) and (d), respectively. The transformation occurs over most of the specimen, although there are untransformed areas in some places. Figures 3(e)–(i) show enlarged SEM-SE images taken from areas E–I in Fig. 3(d). There are no surface reliefs around the hole marked by white single arrow in Fig. 3(e). It is difficult to determine whether there is a thin foil effect around the hole because the maximum cooling temperature of the in situ stage is 220 K, which is only 16 and 1 K below the Ms and Mf temperatures of the specimen, respectively. However, it is confirmed that the transformation is suppressed around the hole. There are large HPVs over several tens of micrometers in size in the area within about 300 µm from the hole to the left-hand side border of area G (Figs. 3(d)–(f)), which is attributed to the small three-dimensional restriction in the region less than 10 µm in thickness. When the thickness of the specimen exceeds 10 µm, the size of the HPVs becomes smaller and the morphology changes to one with less incompatibility, as seen in the previous studies in bulk materials27–29) (Figs. 3(g)–(i)). Further enlarged images of the framed areas in Figs. 3(e)–(i) are reproduced at the bottom of each of the images to estimate the twin width ratio and confirm the self-accommodation morphology. The notation for the HPVs is referred from previous reports,20,27–29) since the surface normal of each grain is nearly parallel to ⟨111⟩B2 as described above. V-shaped 2HPVC morphologies are observed even in the area less than 1 µm in thickness (Fig. 3(e)). As the specimen thickness increases, 3HPVC becomes visible in addition to 2HPVC (single arrows in Figs. 3(f) and (g)). When the thickness is greater than about 20 µm, 6HPVC appears (double arrows in Figs. 3(h) and (i)). From the viewpoint of self-accommodation morphology characterized with 6HPVC, the same transformation behavior in the bulk material is reproduced in the region more than 20 µm in thickness in the polycrystalline Ti–Ni alloy with the average grain size of about 30 µm. One can easily imagine that the self-accommodation microstructure is affected not only by the specimen thickness, but also by the grain size of the parent phase. Waitz reported that the herring-bone microstructure consisting of (001)B19′ compound twin autocatalytically appears as the self-accommodation morphology in nanocrystalline Ti–Ni alloys.37) It is necessary to study the effect of both grain size and specimen thickness for the deeper understanding of the martensite microstructure in thin foil.
(a) SEM-SE image after focused ion beam milling in TEM disk specimen. (b) Specimen thickness versus distance from the edge of the hole. SEM-SE images. (c) before and (d) after in situ cooling observations. (e)–(i) Enlarged SEM-SE images taken from areas E–I indicated by dashed rectangles in (d). Further enlarged images taken from areas enclosed by rectangles along the bottom.
To confirm the microstructure stability in the thin foil specimen electropolished in the martensitic state below Mf, the reverse transformation relief around the hole in the TEM specimen was observed (Fig. 4(a)). There are typical 2HPVC, 3HPVC, and 6HPVC (Fig. 4(b)), even around the edge of the hole, and their size is comparable to those in Figs. 1, 3(h) and (i). Thus, the martensite morphology is maintained its characteristic aspects with less incompatibility in bulk materials if the specimen is prepared under appropriate polishing conditions. This is apparent that 6HPVC was observed in Ti–50.3 at% Ni alloy (Ms = 284 K, Mf = 273 K, As = 304 K and Af = 314 K) electropolished below Mf by TEM.16,27)
(a) Low-magnification SEM-SE image of reverse transformation relief around the hole in the TEM disk at room temperature. (b) Enlarged SEM-SE electron image of the 6HPVC labeled B in (a).
Subsequently, we examine the twin width ratio in ⟨011⟩ type II twins. The theoretical value is 2.69,30,31) which was confirmed experimentally in several studies.30,32,33) The estimated values from all the micrographs in the present paper are summarized in Fig. 5. The average experimental values of the six HPVs in Fig. 1(b) and 4(b) are 2.42 and 3.04, respectively, which are plotted as those for the bulk material in Fig. 5. Both values are within ±15% of the theoretical value of 2.69 which is indicated by the broken line. In the in situ TEM observation, five HPVs including two HPVs in Fig. 2(c) consisting of ⟨011⟩ type II twins were selected from the regions between points 2 and 3 in Fig. 2(a). As already described, the specimen thicknesses at points 2 and 3 are 70 and 120 nm, respectively, the thickness is assumed to be 100 nm for convenience. The estimated values were scattered from 5.02 to 8.08 and those average is 6.12. Total ten HPVs from 2, 3, 4 and 6HPVCs including those in the enlarged images in Figs. 3(e)–(i) were randomly selected from the areas E to I in Fig. 3(d). The specimen thickness presumed the thickness of center point in each area from Fig. 3(b). In the thinner area E below about 1 µm in thickness, the average value is 5.28 and is fairly large, and in agreement with the value obtained from the specimen for in situ TEM observation as described above. That is, the width of the minor twin plates is quite narrow as seen in the enlarged image in Fig. 3(e), although the origin of this phenomenon is not clear at present. On the other hand, the experimental average values in the areas F to I are less than ±20% of the theoretical value when the thickness of the specimen exceeds 4 µm. Based on the twin width ratio in ⟨011⟩ type II twin, the same transformation behavior in the bulk material is reproduced in the region more than 4 µm in thickness.
Twin width ratio versus specimen thickness estimated from all the micrographs in the present paper. The broken line indicates the theoretical twin width ratio.
Finally, we discuss the critical thickness at which the thin foil effect disappears. The critical thickness value was estimated to be 20 µm judging from in the self-accommodation morphology and 4 µm judging from in the twin width ratio. In the thinner area less than about 1 µm in thickness, the twin width ratio was larger and there are huge HPVs over several tens of micrometers in size. The huge HPVs was continuously observed up to the region less than 10 µm in thickness, although the average values of twin width ratio are within - 20% of the theoretical value as shown in Fig. 5. When the thickness exceeded about 20 µm, 6HPVC which is typical self-accommodation morphology in the bulk material appeared. The theoretical twin width ratio is related to the theoretical habit plane predicted from the PTMC, the experimental value agrees well with the theoretical value in the initial stage of transformation, namely, the invariant plane strain condition at habit plane. It is likely that the twin width ratio changes with the progress of transformation. In fact, relatively large scatters have been reported from 1.03 to 5.57 in the experimental values in the fully martensitic state at room temperature observed by TEM, although their average is close to the theoretical value.32,33) Therefore, the twin width ratio should not be a factor in determining the existence of the thin foil effect. Consequently, we conclude that the critical thickness at which martensitic transformation occurs without being influenced by the thin foil effect is 20 µm in the polycrystalline Ti–Ni alloy with the average grain size of about 30 µm.
To understand the thin foil effect quantitatively in in situ observations of the B2 to B19′ transformation in Ti–Ni alloy, the microstructure of B19′ martensite were characterized as a function of specimen thickness. The following conclusions were obtained.
This work was partly supported by JSPS KAKENHI Grant Numbers JP18K18955, 18H01728 and JP19H00829, and the Japan Science and Technology Agency (JST) (Grant Number: 20100113) under Industry-Academia Collaborative R&D Program “Heterogeneous Structure Control: Towards Innovative Development of Metallic Structural Materials”. The authors thank Dr. T. Yamamuro of Kumamoto University for his skillful focused ion beam operation.
Figure A1 shows schematic illustrations of regular, semi-regular and dual semi-regular hexagons which are drawn in red, blue and pink lines, respectively. These shapes frequently appear as Petrie polygon of the regular polyhedron.38,39) Any semi-regular and dual semi-regular hexagons are illustrated from the same regular hexagon. Accordingly, we indicate two examples of those shapes in Figs. A1(a) and (b). It is apparent that the length of the side and the size of the interior angle are all equal in the regular hexagon. There are both circumscribed and inscribed circles. The semi-regular hexagon is obtained by alternately cutting a set of small and large isosceles triangles painted in gray from each of vertices in the regular hexagon. In this case, the base of each isosceles triangle is perpendicular to the diagonal lines of the regular hexagon and its extension line drawn in blue should intersect at the same point on the circumscribed circle of the original regular hexagon. Therefore, six intersections corresponds to the vertices of semi-regular hexagon. The semi-regular hexagon has the sides with two distinct lengths while maintaining the all 6 interior angles of 120 degrees. The regularity is reduced to half in comparison with a regular hexagon. In addition, this shape shares only the same circumscribed circle of the original regular hexagon. The dual semi-regular hexagon appears when the middle points of six sides in the semi-regular hexagon are linked. The lengths of the sides are equal, but there are now two interior angles. The sum of the two adjacent interior angles is 240 degrees inevitably the same as that in the regular hexagon. Small and large interior angles of the dual semi-regular hexagon in Fig. A1(a) are 100 and 140 degrees. Those in Fig. A1(b) are 75.6 and 164.4 degrees. The latter corresponds to the 6HPVC of B19′ martensite as discussed later in Fig. A2. Another characteristic of this shape is that there is only an inscribed circle, but no circumscribed circle.
Figure A2(a) illustrates traces of the habit plane for six HPVs around the [111]B2 trace. The habit plane index used is theoretical one of {0.88888 0.40443 0.21523}B2 predicted from the PTMC.30,31) The two interior angles are calculated to be 75.6 and 164.4 degrees as shown in Fig. A2(a). Figure A2(b) is SEM-SE image of the reverse transformation relief of 6HPVC which is macroscopic ideal self-accommodation morphology for B19′ martensite around one of the ⟨111⟩B2 traces as reported previously.27–29) The surface normal of the B2 grain was determined to be almost parallel to ⟨111⟩B2 by EBSD. The small and large interior angles measured in Fig. A2(b) are about 74 to 80 and 162 to 164 degrees, respectively, which are fairly good agreement with the calculated values in Fig. A1(b) and A2(a). These figures clearly deomstrate that 6HPVC has unique shape of the dual semi-regular hexagon.
Schematic illustrations of regular, semi-regular and dual semi-regular hexagons drawn in red, blue and pink lines, respectively. Small and large interior angles of the dual semi-regular hexagon are 100 and 140 degrees in (a), and 75.6 and 164.4 degrees in (b).
(a) Traces of the habit plane drawn in pink lines for six HPVs around the [111]B2 trace. The K1 plane traces of $\{ \bar{1}\bar{1}1\} _{\text{B}19'}$ type I variant accommodation twin between two HPVs and ⟨011⟩B19′ type II LID twin in each of HPVs are indicated by solid and dotted lines, respectively, and the dashed line represents the interface between the N′(+) and N′(−) HPVs. (b) SEM-SE image of the reverse transformation relief of 6HPVC.
