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A sharp drop in hysteresis is observed for shape memory alloys satisfying the compatibility condition between austenite and martensite, i.e. λ 2 = 1, where λ 2 is the middle eigenvalue of the transformation strain matrix. The present work investigates the evolution of microstructure by transmission electron microscopy as the composition of the Ti 50 Ni 50− x Pd x system is systemically tuned to achieve the condition λ 2 = 1. Changes in morphology, twinning density and twinning modes are reported along with twinless martensite and exact austenite–martensite interfaces. Keywords Shape memory alloys (SMA) Transmission electron microscopy (TEM) Martensitic phase transformation Hysteresis Twinning Reducing the hysteresis is an important improvement for the design of many shape memory devices. A small hysteresis is particularly important for applications such as actuators, sensors and other cycling parts. It would also improve the resistance of shape memory alloys (SMAs) to fracture since the dissipated work measured by the hysteresis goes mainly into the creation of defects that subsequently become the sites of crack initiation [1] . Until recently, the development of low-hysteresis alloys was largely based on trial and error. The latest developments of the general non-linear theory of martensite (GNLTM) [2–4] support the dependence of the hysteresis with λ 2 , an indicator of the compatibility between the austenite and martensite phases [4] . The experimental confirmation came with the work of Cui et al. [1] , who investigated the lattice parameters and the thermal hysteresis of composition-spread Ti–Ni–Cu and Ti–Ni–Pd thin-films using a high throughput, combinatorial approach. They observed in all cases a sharp drop of the hysteresis for alloys when the middle eigenvalue λ 2 of their transformation stretch tensor approaches 1. James and Zhang [4] found the same correlation for bulk alloys of Ti–Ni–Au, Ti–Ni–Pt and Ti–Ni–Pd. The drop in hysteresis is symmetric on both sides of λ 2 = 1 with an apparent singularity when λ 2 = 1. These combined results point towards a universal behavior of hysteresis as a function of λ 2 . In this paper, we investigate the evolution of microstructures by transmission electron microscopy (TEM) as the composition in the Ti 50 Ni 50− x Pd x system is systemically tuned to approach the condition λ 2 = 1. Alloys were prepared from pure elements (99.98 mass% Ti, 99.995 mass% Ni, 99.95 mass% Pd) by arc melting in an argon atmosphere. Slabs 1 mm or less in thickness were cut from the ingot by electrical discharge machining and subsequently homogenized at 1100 °C during 20 ks followed by quenching in room-temperature water. Lattice parameters of both martensite and austenite were measured on a Scintag X-ray diffractometer on polycrystalline slabs previously chemically etched using an electrolyte of 85% CH 3 COOH and 15% HClO 4 . Transformation temperatures and hysteresis were measured by differential scanning calorimetry on a TA Instruments Q1000 with 100 μm thick slabs, previously etched by the same method. For the TEM study, disks 3 mm in diameter were spark-cut or slurry drilled from the slabs, mechanically polished to 200 μm thickness and finally electropolished to perforation in a Tenupol 3 operated at 12 V, 0.1 A, −20 °C with an electrolyte of 80% CH 3 OH and 20% H 2 SO 4 . Conventional Transmission Electron Microscopy (CTEM) observations were carried out in a Phillips CM20 microscope operated at 200 kV using a side-entry type double-tilt specimen holder with angular ranges of ±45°. High Resolution Electron Microscopy (HREM) observations were carried out in a FEG Phillips CM30 microscope operated at 300 kV using a side-entry type double-tilt specimen holder. The Ti 50 Ni 50− x Pd x system undergoes a martensitic transformation on cooling from a cubic (B2) to an orthorhombic (B19) lattice for compositions above x = 7 [6,7] . This transformation gives rise to six variants of martensite, denoted 1, 2, 3, 4, 5 and 6. Each of the possible transformations can be described by its own transformation strain matrix, U 1 – U 6 , with U 1 shown as an example in Eq. (1) : (1) U 1 = β 0 0 0 α - γ 2 α + γ 2 0 α + γ 2 α - γ 2 β = a a 0 α = b 2 a 0 γ = c 2 a 0 Lattice parameters of austenite ( a 0 ) and martensite ( a , b , c ) are listed in Table 1 for the different compositions studied, along with λ 2 , the middle eigenvalue of any one of the six transformation strain matrices, θ c , defined as the average of the four characteristic transformation temperatures, and H , the thermal hysteresis. Variants are associated in pairs to form twins. The pairs 1–2, 3–4 and 5–6 have a compound twin connection, while all other pairs (e.g. 1–3) have type I/type II twin connections. Table 2 shows the twin parameters for three selected alloys calculated with the GNLTM. K 1 is the twinning plane and η 1 the shear direction. There are three twinning modes, {1 1 1} type I, 〈2 1 1〉 type II and {0 1 1} compound. Only the values of the irrational planes and directions depend on the composition. It has been shown that, in the frame of the GNLTM [4,5] , type I/II twins cannot participate in the austenite–martensite interface when λ 2 < 1 and conversely compound twin cannot participate when λ 2 > 1. For this reason, the twin ratio λ , defined such that λ /(1 – λ ) is the volume fraction of the smaller variant participating in the austenite–martensite interface, only has meaning when these conditions are satisfied. The closer λ 2 is to 1, the smaller the twin ratio λ . Figure 1 (a)–(c) shows the evolution of morphology of the B19 martensite as the content of Pd is decreased towards the compatibility condition. The alloy with the highest Pd content, Ti 50 Ni 25 Pd 25 , has a λ 2 of 1.0070, the largest value in the series studied. Its morphology ( Fig. 1 (a)) is one commonly found in SMAs with parallel lamellae of martensite internally twinned. The internal twins extend diagonally across the width of the martensite plates with rather regular spacing. Twins from alternate plates share the same orientation dependence to each other throughout the sample. The selected-area diffraction (SAD) patterns in Figure 1 (d) and (e) were taken from internally twinned plates A and B ( Fig. 1 (a)) in two different orientations, the beam edge-on with the twinning plane. Each pattern consists of two sets of reflections which are in mirror symmetry with respect to the (1 1 1) plane. The same {1 1 1} type I twin is found throughout the sample and is considered to be the lattice invariant shear (LIS), which means that martensite is sheared along this mode to accommodate a habit plane with austenite during the phase transformation. The same morphology and LIS twinning have been reported for higher Pd content [8,9] . As the content of Pd decreases, so does λ 2 . Ti 50 Ni 30 Pd 20 ( λ 2 = 1.0050) shows some significant changes in microstructure compared to higher Pd alloys. The lamellar morphology is retained, but many plates now exhibit a lower twin ratio or even no twinning. Figure 2 (a) is a bright-field micrograph taken inside a martensite plate of this alloy with an average twin ratio of 0.09, meaning that one variant is now more than 10 times larger than the other one. The smaller variant appears as thin parallel lines in the bright-field image and its width does not exceed 20 nm, as shown in the high-resolution picture in Figure 2 (c). As expected, both variants are still related along a {1 1 1} type I twin relationship, as shown by the diffraction pattern and the FFT from the high-resolution image in Figure 2 (b) and (d), respectively. In some plates of the x = 20 sample, no twinning could be detected in image or diffraction mode. However, fine parallel line contrasts were repeatedly observed at certain orientations, as shown in Figures 1(b) and 3 . The same type of line contrasts were also observed in all the samples with a lower Pd content, which all have a λ 2 very close to 1. In order to characterize these defects, selected-area electron diffraction was carried in a direction where two sets of reflections could be seen. Figure 3 (a) and (b) illustrates a case study for Ti 50 Ni 30 Pd 20 where one set of reflections was found to belong to a [1 2 1] B19 martensite zone axis and the other to a [1 3 1] B2 zone axis. This enables us to conclude that the observed line contrasts are lines of retained austenite. To further confirm this result, we used the crystallographic relationship between martensite and austenite calculated with the GNLTM to simulate the B2/B19 interface. Figure 3 (c) is the corresponding simulated diffraction pattern that nicely reproduces the experimental one. Our model was also tested with other diffraction patterns in different samples, in a different zone axis. Finally, we discovered with trace analysis of the retained austenite lines that their directions are consistent with the traces of the predicted habit plane, namely (7 −5 5) in the B2 basis (see Fig. 3 (a)) or (7 0 10) in the B19 basis. The calculation is made by considering a single variant of martensite forming an interface with the austenite. The presence of lines of retained austenite oriented along the habit plane for a sample close to λ 2 = 1 can be explained by the fact that the austenite–martensite transition layer energy must be very small due to their compatibility. The observed austenite regions are remnants of an incomplete transformation. It is also possible that a small-scale fluctuation in composition resulted in a region with λ 2 closer to 1, or that the observed λ 2 was sufficiently close to 1 that a single interface transformation, accompanied by a delocalized elastic field, is preferred over a twinned austenite–martensite interface. Ti 50 Ni 39 Pd 11 has the lowest hysteresis from the series and a λ 2 of 1.0001, meaning that virtually no lattice invariant shear is required for an undistorted plane (habit plane) to exist during transformation. This compatibility between a single variant of martensite and the austenite matrix allows for twinless transformation that minimizes the overall energy of interfaces, leading to lower hysteresis. Figure 1 (c) shows an example of large twinless martensite plates commonly observed in Ti 50 Ni 39 Pd 11 . The absence of internal twins was also reported for Ti 79 Ta 21 [10] , Ti 49.5 Ni 40.5 Cu 10 [11,12] and Ti 50 Ni 30 Cu 20 [14] , which also have a λ 2 close to 1. In contrast with higher Pd content alloys showing a typical lamellar morphology, plates in Ti 50 Ni 39 Pd 11 come in different shapes and sizes. Self-accommodation of the plates is believed to play an important role in the final morphology of the microstructure. Figure 4 (a) shows a typical triangular self-accommodation pattern between three variants. Two variants were found to be twin-related along a {1 1 1} type I twin interface, as shown in the diffraction pattern 4 (b) taken in a [−2 1 1] orientation. Although the observed morphology resembles the accommodating structures already described by Saburi et al. [13,15] , the available crystallographic data are not sufficient to fully confirm their three-dimensional self-accommodating model of martensite [13] . The three predicted twinning modes ( Table 2 ) were observed in Ti 50 Ni 39 Pd 11 . The twin microstructure is, however, clearly different from the LIS type of twinning observed with a higher Pd content. The twins in Ti 50 Ni 39 Pd 11 are introduced as a result of self-accommodation and/or sporadic nucleation. The interface between plates was often found to be a type I/II twin ( Fig. 4 (a)), whereas compound twins appeared as a single or a small group of parallel twins near nucleation sites (precipitates, defects). Figure 4 (b) shows several parallel compound twins observed in the [1 0 0] zone axis that have nucleated at an interface between two plates and Figure 1 (c) shows a single compound twin inside a twinless plate. The same microstructure and specific features mentioned for Ti 50 Ni 39 Pd 11 have been observed in Ti 50 Ni 41 Pd 9 . This shows that, with λ 2 = 0.9988, the compatibility between the two phases is still fulfilled and affects the microstructure. We did not investigate any alloys with a lower content of Pd since the crystallography of martensite becomes monoclinic. There is, however, evidence [4] that monoclinic systems also experience a drop in hysteresis around λ 2 = 1. Changes in the microstructure should also be expected. It is now known that SMAs alloys experience a drop in hysteresis when approaching the compatibility condition λ 2 = 1. The present study shows that this effect is accompanied by important changes in the microstructure. As λ 2 approaches 1, the microstructure evolves from a lamellar morphology of fully twinned martensite plates to a self-accommodated morphology of twinless martensite plates. Along the way, the mode of twinning changes from a unique and well-defined {1 1 1} type I LIS to a more chaotic combination of the three types of twins arising from self-accommodation or sporadic nucleation. The authors thank MULTIMAT “Multi-scale modeling and characterization for phase transformations in advanced materials”, a Marie Curie Research Training Network (MRTN-CT-2004-505226), for supporting this work. References [1] J. Cui Y.S. Chu O.O. Famodu Y. Furuya J. Hattrick-Simpers R.D. James A. Ludwig S. Thienhaus M. Wuttig Z. Zhang I. Takeuchi Nat. Mater. 5 2006 286 290 [2] J.M. Ball R.D. James Philos. Trans. R. Soc. Lond. Ser. A 338 1992 389 [3] J.M. Ball R.D. James Arch. Ration. Mech. Anal. 13 2005 100 [4] Z. Zhang, S. Müller, R. D. James, private communication. [5] K.F. Hane T.W. Shield J. Elast. 59 2000 267 318 [6] V.P. Sivokha A.S. Savvinov Voronin V.N. Khachin Phys. Met. Metall. 56 1983 112 116 [7] Y.C. Lo S.K. Wu Scr. Metall. Mater. 27 1992 1097 1102 [8] P.G. Lindquist, PhD Thesis, University of Illinois at Urbana-Champaign, 1988. [9] M. Nishida T. Hara Y. Morizono A. Ikeya H. Kijima A. Chiba Acta Mater. 45 1997 4847 4853 [10] K.A. Bywater J.W. Christian Philos. Mag. 25–26 1972 1249 1273 [11] T. Tadaki C.M. Wayman Metallography 15 1982 247 258 [12] T. Saburi T. Komatsu S. Nenno Y. Watanabe J. Less-Common Met. 118 1986 217 226 [13] T. Saburi Y. Watanabe S. Nenno ISIJ Int. 29 1989 405 411 [14] W.J. Moberly J.L. Proft T.W. Duerig R. Sinclair Mater. Sci. Forum 56–58 1990 605 610 [15] K. Otsuka X. Ren Prog. Mater Sci. 50 2005 511 678

Transmission electron microscopy investigation of microstructures in low-hysteresis alloys with special lattice parameters